Research activity information

• Nov. 2012 ACM, Gordon Bell Prize

  ISHIYAMA Tomoaki, NITADORI Keigo, MAKINO Junichiro


• 2003 IEEE Gordon Bell 賞（福重俊幸、小久保英一郎、台坂博と共同受賞）


• 2002 第14回中小企業新技術・新製品賞(技術・製品部門、浜松メトリクス(株)と共同受賞)


• 2002 情報処理学会論文賞(朴泰祐、須佐元、梅村雅之、福重俊幸、宇川彰と共同受賞)


• 2001 IEEE Gordon Bell 賞（福重俊幸と共同受賞）


• 2000 IEEE Gordon Bell 賞（福重俊幸、古賀正基と共同受賞）


• 1999 ゴードン・ベル賞(Gordon Bell Prize)


• 1998 日本天文学会 林忠四郎賞


• 1996 ゴードン・ベル賞(Gordon Bell Prize)


• 1995 ゴードン・ベル賞(Gordon Bell Prize)

• Self-consistent N-body simulation of planetesimal-driven migration. I. The trajectories of single planets in the uniform background

  Tenri Jinno, Takayuki R Saitoh, Yoko Funato, Junichiro Makino

  Abstract Recent exoplanet observations have revealed a diversity of exoplanetary systems, which suggests the ubiquity of radial planetary migration. One powerful known mechanism of planetary migration is planetesimal-driven migration (PDM), which can let planets undergo significant migration through gravitational scattering with planetesimals. In this series of papers, we present the results of our high-resolution, self-consistent N-body simulations of PDM, in which gravitational interactions among planetesimals, the gas drag, and Type I migration are all taken into account. In this first paper (Paper I), we investigate the migration of a single planet through PDM within the framework of the classical standard disk model (the minimum-mass solar nebula model). Paper I aims to improve our understanding of planetary migration through PDM, addressing previously unexplored aspects of both the gravitational interactions among planetesimals and the interactions with disk gas. Our results show that even small protoplanets can actively migrate through PDM. Such active migration can act as a rapid radial diffusion mechanism for protoplanets and significantly influence the early stages of planetary formation (i.e., during the runaway growth phase). Moreover, a fair fraction of planets migrate outward. This outward migration may offer a potential solution for the “planet migration problem” caused by Type I migration and gives a natural mechanism for outward migration assumed in many recent scenarios for the formation of outer planets.

  Oxford University Press (OUP), Nov. 2024, Publications of the Astronomical Society of Japan

  [Refereed]

  Scientific journal


• An Independent Hybrid Imaging of Sgr A* from the Data in EHT 2017 Observations

  Makoto Miyoshi, Yoshiaki Kato, Junichiro Makino

  Abstract We propose that the ring structure found by the Event Horizon Telescope Collaboration (EHTC) as the black hole shadow of Sgr A* is an artifact by the bumpy PSF (Point Spread Function) of the EHT2017. The imaging using sparse u-v data requires detailed scrutiny of the PSF. The estimated shadow diameter ($\mathrm{48.7\pm 7~\mu \rm as}$) is equal to the spacing between the main beam and the first sidelobe of the PSF ($\mathrm{49.09~\mu \rm as}$), which immediately suggests a potential problem in the deconvolution of the PSF. We show that the ring image can be derived from non-ring simulated datasets (noise only; point source) with a narrow Field-of-View (FOV) and an assumed self-calibration suggesting the EHT2017’s u-v coverage is insufficient for reliable imaging. The EHTC analysis, based on calibrations with assumptions about the source’s size and properties, selected the final image by prioritizing appearance rate of the similar structure from a large imaging parameter space over data consistency. Our independent analysis with the conventional hybrid mapping reveals an elongated east-west structure, consistent with previous observations. We believe it to be more reliable than the EHTC image, due to half the residuals in normalized visibility amplitude. The eastern half is brighter, possibly due to a Doppler boost from the rapid rotating disk. We hypothesize our image shows a portion of the accretion disk about 2 to a few RS away from the black hole, rotating with nearly $\mathrm{60~\%}$ of the speed of light viewed from an angle of 40 − 45○.

  Oxford University Press (OUP), May 2024, Monthly Notices of the Royal Astronomical Society

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Fast and accurate short read alignment with hybrid hash-tree data structure

  Junichiro Makino, Toshikazu Ebisuzaki, Ryutaro Himeno, Yoshihide Hayashizaki

  Feb. 2024


• The Jet and Resolved Features of the Central Supermassive Black Hole of M87 Observed with EHT in 2017—Comparison with the GMVA 86 GHz Results

  Makoto Miyoshi, Yoshiaki Kato, Junichiro Makino, Masato Tsuboi

  Abstract M87 is the best target for studying black hole accretion and jet formation. Reanalysis of the Event Horizon Telescope (EHT) public data at 230 GHz shows a core–knots structure at the center and jet features. We here compare this with the new results of GMVA at 86 GHz showing a spatially resolved central core. There are similarities and differences between the two. At 86 GHz, “two bright regions” are seen on the ring in the core. The “core–knot–west knot” triple structure in the 230 GHz image shows apparent appearance of two peaks similar to the “two bright regions” when convolved with the GMVA beam. This similarity suggests that both frequencies reveal the same objects in the core area. Protrusions are observed on both the south and north sides of the core at both frequencies, becoming prominent and winglike at 230 GHz. The 86 GHz image shows a triple ridge jet structure, while the 230 GHz image shows only a bright central ridge with two roots. Both frequencies show a shade between the core and the central ridge. To detect the faint features from the EHT2017 data, we found that the use of all baseline data is essential. Using all baseline data, including the ultrashort data, revealed the jet and faint structures. Without the ultrashort baselines, these structures were not detectable. The lack of detection of any faint structures other than the ring in the M87 data by the EHTC is presumably due to the exclusion of ultrashort baselines from their analysis.

  American Astronomical Society, Feb. 2024, The Astrophysical Journal Letters, 963(1) (1), L18 - L18

  Scientific journal


• Surrogate Modeling for Computationally Expensive Simulations of Supernovae in High-Resolution Galaxy Simulations

  Keiya Hirashima, Kana Moriwaki, Michiko S Fujii, Yutaka Hirai, Takayuki R Saitoh, Junichiro Makino

  Nov. 2023, NeurIPS 2023 AI4Science Workshop, English

  [Refereed]

  International conference proceedings


• N-body simulation of planetary formation through pebble accretion in a radially structured protoplanetary disk

  Tenri Jinno, Takayuki R Saitoh, Yota Ishigaki, Junichiro Makino

  Abstract In the conventional theory of planet formation, it is assumed that protoplanetary disks are axisymmetric and have a smooth radial profile. However, recent radio observations of protoplanetary disks have revealed that many of them have complex radial structures. In this study, we perform a series of N-body simulations to investigate how planets are formed in protoplanetary disks with radial structures. For this purpose, we consider the effect of continuous pebble accretion onto the discontinuity boundary within the terrestrial planet-forming region (∼0.6 au). We find that protoplanets grow efficiently at the discontinuity boundary, reaching the Earth mass within ∼104 yr. We confirm that giant collisions of protoplanets occur universally in our model. Moreover, we find that multiple planet-sized bodies form at regular intervals in the vicinity of the discontinuity boundary. These results indicate the possibility of the formation of solar system-like planetary systems in radially structured protoplanetary disks.

  Oxford University Press (OUP), Sep. 2023, Publications of the Astronomical Society of Japan, 75(5) (5), 951 - 969

  Scientific journal


• 3D-Spatiotemporal Forecasting the Expansion of Supernova Shells Using Deep Learning toward High-Resolution Galaxy Simulations

  Keiya Hirashima, Kana Moriwaki, Michiko S. Fujii, Yutaka Hirai, Takayuki R. Saitoh, Junichiro Makino

  Jan. 2023, Monthly Notices of the Royal Astronomical Society, English

  Scientific journal


• Origin of highly r-process-enhanced stars in a cosmological zoom-in simulation of a Milky Way-like galaxy

  Yutaka Hirai, Timothy C Beers, Masashi Chiba, Wako Aoki, Derek Shank, Takayuki R Saitoh, Takashi Okamoto, Junichiro Makino

  Nov. 2022, Monthly Notices of the Royal Astronomical Society

  [Refereed]

  Scientific journal


• The Jet and Resolved Features of the Central Supermassive Black Hole of M87 Observed with the Event Horizon Telescope (EHT)

  Makoto Miyoshi, Yoshiaki Kato, Junichiro Makino

  Jul. 2022, The Astrophysical Journal

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Predicting the Expansion of Supernova Shells for High-Resolution Galaxy Simulations Using Deep Learning

  K. Hirashima, K. Moriwaki, M. S. Fujii, Y. Hirai, T. Saitoh, J. Makino

  Abstract Small integration timesteps for a small fraction of the particles become a bottleneck for future galaxy simulations with a higher resolution, especially for massively parallel computing. As we increase the resolution, we must resolve physics on a smaller timescale while the total integration time is fixed as the universe age. The small timesteps for a small fraction of the particles worsen the scalability. More specifically, the regions affected by supernovae (SN) have the smallest timestep in the whole galaxy. Using a Hamiltonian splitting method, we calculate the SN regions with small timesteps using a few thousand CPU cores but integrate the entire galaxy using a shared timestep. For this approach, we need to pick up particles in regions, which will be affected by SN (the target particles) by the next global step (the integration timestep for the entire galaxy) in advance. In this work, we developed the deep learning model to predict the region where the shell due to a supernova explosion expands during one global step. In addition, we identify the target particles using image processing of the density distribution predicted by our deep learning model. Our algorithm could identify the target particles better than the method based on the analytical solution. This particle selection method using deep learning and the Hamiltonian splitting method will improve the performance of galaxy simulations with extremely high resolution.

  IOP Publishing, Mar. 2022, Journal of Physics: Conference Series, 2207(1) (1), 012050 - 012050

  Scientific journal


• Particle–particle particle–tree code for planetary system formation with individual cut-off method: GPLUM

  Yota Ishigaki, Junko Kominami, Junichiro Makino, Masaki Fujimoto, Masaki Iwasawa

  Abstract In a standard theory of the formation of the planets in our Solar System, terrestrial planets and cores of gas giants are formed through accretion of kilometer-sized objects (planetesimals) in a protoplanetary disk. Gravitational N-body simulations of a disk system made up of numerous planetesimals are the most direct way to study the accretion process. However, the use of N-body simulations has been limited to idealized models (e.g., perfect accretion) and/or narrow spatial ranges in the radial direction, due to the limited number of simulation runs and particles available. We have developed new N-body simulation code equipped with a particle–particle particle–tree (P3T) scheme for studying the planetary system formation process: GPLUM. For each particle, GPLUM uses the fourth-order Hermite scheme to calculate gravitational interactions with particles within cut-off radii and the Barnes–Hut tree scheme for particles outside the cut-off radii. In existing implementations, P3T schemes use the same cut-off radius for all particles, making a simulation become slower when the mass range of the planetesimal population becomes wider. We have solved this problem by allowing each particle to have an appropriate cut-off radius depending on its mass, its distance from the central star, and the local velocity dispersion of planetesimals. In addition to achieving a significant speed-up, we have also improved the scalability of the code to reach a good strong-scaling performance up to 1024 cores in the case of N = 106.

  Oxford University Press ({OUP}), Jun. 2021, Publications of the Astronomical Society of Japan, 73(3) (3), 660 - 676, English

  Scientific journal


• petar: a high-performance N-body code for modelling massive collisional stellar systems

  Long Wang, Masaki Iwasawa, Keigo Nitadori, Junichiro Makino

  ABSTRACT The numerical simulations of massive collisional stellar systems, such as globular clusters (GCs), are very time consuming. Until now, only a few realistic million-body simulations of GCs with a small fraction of binaries ($5{ { \ \rm per\ cent } }$) have been performed by using the nbody6++gpu code. Such models took half a year computational time on a Graphic Processing Unit (GPU)-based supercomputer. In this work, we develop a new N-body code, petar, by combining the methods of Barnes–Hut tree, Hermite integrator and slow-down algorithmic regularization. The code can accurately handle an arbitrary fraction of multiple systems (e.g. binaries and triples) while keeping a high performance by using the hybrid parallelization methods with mpi, openmp, simd instructions and GPU. A few benchmarks indicate that petar and nbody6++gpu have a very good agreement on the long-term evolution of the global structure, binary orbits and escapers. On a highly configured GPU desktop computer, the performance of a million-body simulation with all stars in binaries by using petar is 11 times faster than that of nbody6++gpu. Moreover, on the Cray XC50 supercomputer, petar well scales when number of cores increase. The 10 million-body problem, which covers the region of ultracompact dwarfs and nuclear star clusters, becomes possible to be solved.

  Oxford University Press ({OUP}), Sep. 2020, Monthly Notices of the Royal Astronomical Society, 497(1) (1), 536 - 555, English

  Scientific journal


• Predicting the Expansion of Supernova Shells Using Deep Learning toward Highly Resolved Galaxy Simulations

  Keiya Hirashima, Kana Moriwaki, Michiko Fujii, Yutaka Hirai, Takayuki Saitoh, Junichiro Makino

  Abstract The load imbalance and communication overhead of parallel computing are crucial bottlenecks for galaxy simulations. A successful way to improve the scalability of astronomical simulations is a Hamiltonian splitting method, which needs to identify such regions integrated with smaller timesteps than the global timestep for integrating the entire galaxy. In the case of galaxy simulations, the regions inside supernova (SN) shells require the smallest steps. We developed the deep learning model to forecast the region affected by the SN shell’s expansion during one global step. In addition, we identified the particles with small timesteps using image processing. We can identify target particles using our method with a higher identification rate (88 % to 98 % on average) and lower “non-target”-to-“target” fraction (6.4 to 5.5 on average) compared to the analytic approach with the Sedov-Taylor solution. Our method using Hamiltonian splitting and deep learning will improve the performance of extremely high-resolution galaxy simulations.

  Cambridge University Press (CUP), Jun. 2020, Proceedings of the International Astronomical Union, 16(S362) (S362), 209 - 214

  Scientific journal


• Are long-term N-body simulations reliable?

  Junichiro Makino

  ABSTRACT N-body integrations are used to model a wide range of astrophysical dynamics, but they suffer from errors which make their orbits diverge exponentially in time from the correct orbits. Over long time-scales, their reliability needs to be established. We address this reliability by running a three-body planetary system over about 200 e-folding times. Using nearby initial conditions, we can construct statistics of the long-term phase-space structure and compare to rough estimates of resonant widths of the system. We compared statistics for a wide range of numerical methods, including a Runge–Kutta method, Wisdom–Holman method, symplectic corrector methods, and a method by Laskar and Robutel. ‘Improving’ an integrator did not increase the phase-space accuracy, but simply increasing the number of initial conditions did. In fact, the statistics of a higher order symplectic corrector method were inconsistent with the other methods in one test.

  Apr. 2020, Monthly Notices of the Royal Astronomical Society, English

  [Refereed]

  Scientific journal


• INO: Interplanetary network of optical lattice clocks

  Toshikazu Ebisuzaki, Hidetoshi Katori, Jun’ichiro Makino, Atsushi Noda, Hisaaki Shinkai, Toru Tamagawa

  The new technique of measuring frequency by optical lattice clocks now approaches to the relative precision of [Formula: see text]. We propose to place such precise clocks in space and to use Doppler tracking method for detecting low-frequency gravitational wave below 1[Formula: see text]Hz. Our idea is to locate three spacecrafts at one A.U. distance (say at L1, L4 and L5 of the Sun–Earth orbit), and apply the Doppler tracking method by communicating “the time” each other. Applying the current available technologies, we obtain the sensitivity for gravitational wave with third- or fourth-order improvement ([Formula: see text] or [Formula: see text] level in [Formula: see text]–[Formula: see text][Formula: see text]Hz) than that of Cassini spacecraft in 2001. This sensitivity enables us to observe black hole (BH) mergers of their mass greater than [Formula: see text] in the cosmological scale. Based on the hierarchical growth model of BHs in galaxies, we estimate the event rate of detection will be 20–50 a year. We nickname “INO” (Interplanetary Network of Optical Lattice Clocks) for this system, named after Tadataka Ino (1745–1818), a Japanese astronomer, cartographer, and geodesist.

  World Scientific Pub Co Pte Lt, Mar. 2020, International Journal of Modern Physics D, 29(04) (04), 1940002 - 1940002, English

  [Refereed]

  Scientific journal


• Extreme-scale particle-based simulations on advanced HPC platforms

  M. Iwasawa, D. Namekata, K. Nomura, M. Tsubouchi, J. Makino

  Springer Science and Business Media {LLC}, Feb. 2020, CCF Transactions on High Performance Computing, 2(2) (2), 183 - 195

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• A slow-down time-transformed symplectic integrator for solving the few-body problem

  Junichiro Makino

  Abstract An accurate and efficient method dealing with the few-body dynamics is important for simulating collisional N-body systems like star clusters and to follow the formation and evolution of compact binaries. We describe such a method which combines the time-transformed explicit symplectic integrator (Preto & Tremaine 1999; Mikkola & Tanikawa 1999) and the slow-down method (Mikkola & Aarseth 1996). The former conserves the Hamiltonian and the angular momentum for a long-term evolution, while the latter significantly reduces the computational cost for a weakly perturbed binary. In this work, the Hamilton equations of this algorithm are analyzed in detail. We mathematically and numerically show that it can correctly reproduce the secular evolution like the orbit averaged method and also well conserve the angular momentum. For a weakly perturbed binary, the method is possible to provide a few order of magnitude faster performance than the classical algorithm. A publicly available code written in the c++ language, sdar, is available on https://github.com/lwang- astro/SDARGitHub. It can be used either as a standalone tool or a library to be plugged in other N-body codes. The high precision of the floating point to 62 digits is also supported.

  Feb. 2020, Monthly Notices of the Royal Astronomical Society, English

  [Refereed]

  Scientific journal


• Accelerated FDPS: Algorithms to use accelerators with FDPS

  Junichiro Makino

  Abstract We describe algorithms implemented in FDPS (Framework for Developing Particle Simulators) to make efficient use of accelerator hardware such as GPGPUs (general-purpose computing on graphics processing units). We have developed FDPS to make it possible for researchers to develop their own high-performance parallel particle-based simulation programs without spending large amounts of time on parallelization and performance tuning. FDPS provides a high-performance implementation of parallel algorithms for particle-based simulations in a “generic” form, so that researchers can define their own particle data structure and interparticle interaction functions. FDPS compiled with user-supplied data types and interaction functions provides all the necessary functions for parallelization, and researchers can thus write their programs as though they are writing simple non-parallel code. It has previously been possible to use accelerators with FDPS by writing an interaction function that uses the accelerator. However, the efficiency was limited by the latency and bandwidth of communication between the CPU and the accelerator, and also by the mismatch between the available degree of parallelism of the interaction function and that of the hardware parallelism. We have modified the interface of the user-provided interaction functions so that accelerators are more efficiently used. We also implemented new techniques which reduce the amount of work on the CPU side and the amount of communication between CPU and accelerators. We have measured the performance of N-body simulations on a system with an NVIDIA Volta GPGPU using FDPS and the achieved performance is around 27% of the theoretical peak limit. We have constructed a detailed performance model, and found that the current implementation can achieve good performance on systems with much smaller memory and communication bandwidth. Thus, our implementation will be applicable to future generations of accelerator system.

  Feb. 2020, Publications of the Astronomical Society of Japan, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Implementation and Performance of Barnes-Hut N-body algorithm on Extreme-scale Heterogeneous Many-core Architectures

  Masaki Iwasawa, Daisuke Namekata, Ryo Sakamoto, Takashi Nakamura, Yasuyuki Kimura, Keigo Nitadori, Long Wang, Miyuki Tsubouchi, Jun Makino, Zhao Liu, Haohuan Fu, Guangwen Yang

  In this paper, we report the implementation and measured performance of our extreme-scale global simulation code on Sunway TaihuLight and two PEZY-SC2 systems: Shoubu System B and Gyoukou. The numerical algorithm is the parallel Barnes-Hut tree algorithm, which has been used in many large-scale astrophysical particle-based simulations. Our implementation is based on our FDPS framework. However, the extremely large numbers of cores of the systems used (10M on TaihuLight and 16M on Gyoukou) and their relatively poor memory and network bandwidth pose new challenges. We describe the new algorithms introduced to achieve high efficiency on machines with low memory bandwidth. The measured performance is 47.9, 10.6 PF, and 1.01PF on TaihuLight, Gyoukou and Shoubu System B (efficiency 40\%, 23.5\% and 35.5\%). The current code is developed for the simulation of planetary rings, but most of the new algorithms are useful for other simulations, and are now available in the FDPS framework.

  SAGE PUBLICATIONS LTD, Jul. 2019, INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS, 34(6) (6), 615 - 628, English

  [Refereed]

  Scientific journal


• INO: Interplanetary network of optical lattice clocks

  Junichiro Makino

  The new technique of measuring frequency by optical lattice clocks now approaches to the relative precision of [Formula: see text]. We propose to place such precise clocks in space and to use Doppler tracking method for detecting low-frequency gravitational wave below 1[Formula: see text]Hz. Our idea is to locate three spacecrafts at one A.U. distance (say at L1, L4 and L5 of the Sun–Earth orbit), and apply the Doppler tracking method by communicating “the time” each other. Applying the current available technologies, we obtain the sensitivity for gravitational wave with third- or fourth-order improvement ([Formula: see text] or [Formula: see text] level in [Formula: see text]–[Formula: see text][Formula: see text]Hz) than that of Cassini spacecraft in 2001. This sensitivity enables us to observe black hole (BH) mergers of their mass greater than [Formula: see text] in the cosmological scale. Based on the hierarchical growth model of BHs in galaxies, we estimate the event rate of detection will be 20–50 a year. We nickname “INO” (Interplanetary Network of Optical Lattice Clocks) for this system, named after Tadataka Ino (1745–1818), a Japanese astronomer, cartographer, and geodesist.

  Feb. 2019, International Journal of Modern Physics D, English

  [Refereed]

  Scientific journal


• Hermite integrator for high-order mesh-free schemes

  Yamamoto, Satoko, Makino, Junichiro

  2019, Publications of the Astronomical Society of Japan, English

  [Refereed]

  Scientific journal


• Terrestrial magma ocean origin of the Moon

  Hosono, Natsuki, Karato, Shun-ichiro, Makino, Junichiro, Saitoh, Takayuki R.

  Springer Science and Business Media {LLC}, 2019, Nature Geoscience, 12(6) (6), 418, English

  [Refereed]

  Scientific journal


• Real-time simulation of a cat-scale artificial cerebellum on PEZY-SC processors

  Yamazaki, Tadashi, Igarashi, Jun, Makino, Junichiro, Ebisuzaki, Toshikazu

  2019, International Journal of High Performance Computing Applications, English

  [Refereed]

  Scientific journal


• Global simulation of planetary rings on sunway TaihuLight

  Masaki Iwasawa, Long Wang, Keigo Nitadori, Daisuke Namekata, Takayuki Muranushi, Miyuki Tsubouchi, Junichiro Makino, Zhao Liu, Haohuan Fu, Guangwen Yang

  In this paper, we report the implementation and measured performance of a global simulation of planetary rings on Sunway TaihuLight. The basic algorithm is the Barnes-Hut tree, but we have made a number of changes to achieve good performance for extremely large simulations on machines with an extremely large number of cores. The measured performance is around 35% of the theoretical peak. The main limitation comes from the performance of the interaction calculation kernel itself, which is currently around 50%.

  Springer Verlag, 2018, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 10860, 483 - 495, English

  [Refereed]

  International conference proceedings


• Automatic Generation of High-Order Finite-Difference Code with Temporal Blocking For Extreme-Scale Many-Core Systems

  Tanaka, Hideyuki, Ishihara, Youhei, Sakamoto, Ryo, Nakamura, Takashi, Kimura, Yasuyuki, Nitadori, Keigo, Tsubouchi, Miyuki, Makino, Jun

  2018, PROCEEDINGS OF IEEE/ACM 4TH INTERNATIONAL WORKSHOP ON EXTREME SCALE PROGRAMMING MODELS AND MIDDLEWARE (ESPM2)

  [Refereed]

  Scientific journal


• Fortran interface layer of the framework for developing particle simulator FDPS

  Namekata, Daisuke, Iwasawa, Masaki, Nitadori, Keigo, Tanikawa, Ataru, Muranushi, Takayuki, Wang, Long, Hosono, Natsuki, Nomura, Kentaro, Makino, Junichiro

  Numerical simulations based on particle methods have been widely used in various fields including astrophysics. To date, simulation softwares have been developed by individual researchers or research groups in each field, with a huge amount of time and effort, even though numerical algorithms used are very similar. To improve the situation, we have developed a framework, called

  2018, Publications of the Astronomical Society of Japan, 70(4) (4), 70, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Variable inertia method: A novel numerical method for mantle convection simulation

  Kosuke Takeyama, Takayuki R. Saitoh, Junichiro Makino

  3D numerical simulations have been very useful for the understanding of mantle convection of the earth. In almost all previous simulations of mantle convection, the (extended) Boussinesq approximation has been used. This method is implicit in the sense that buoyancy force and viscosity are balanced, and allows the use of long timesteps that are not limited by the CFL condition. However, the resulting matrix is ill-conditioned, in particular since the viscosity strongly depends on the temperature. It is not well suited to modern large-scale parallel machines. In this paper, we propose an explicit method which can be used to solve the mantle convection problem. If we can reduce the sound speed without changing the characteristics of the flow, we can increase the timestep and thus can use the explicit method. In order to reduce the sound speed, we multiplied the inertia term of the equation of motion by a large and viscosity-dependent coefficient Theoretically, we can expect that this modification would not change the flow as long as the Reynolds number and the Mach number are sufficiently smaller than unity. We call this method the variable inertia method (VIM). We have performed an extensive set of numerical tests of the proposed method for thermal convection, and concluded that it works well. In particular, it can handle differences in viscosity of more than five orders of magnitude. (C) 2016 Elsevier B.V. All rights reserved.

  ELSEVIER SCIENCE BV, 2017, New Astronomy, 50, 82 - 103, English

  [Refereed]

  Scientific journal


• Unconvergence of very-large-scale giant impact simulations

  Hosono, Natsuki, Iwasawa, Masaki, Tanikawa, Ataru, Nitadori, Keigo, Muranushi, Takayuki, Makino, Junichiro

  The giant impact (GI) hypothesis is one of the most important hypotheses both in planetary science and in geoscience, since it is related to the origin of the Moon and also the initial condition of the Earth. A number of numerical simulations have been done using the smoothed particle hydrodynamics (SPH) method. However, GI hypothesis is currently in a crisis. The "canonical" GI scenario failed to explain the identical isotope ratio between the Earth and the Moon. On the other hand, little has been known about the reliability of the result of GI simulations. In this paper, we discuss the effect of the resolution on the results of the GI simulations by varying the number of particles from 3 x 10(3) to 10(8). We found that the results does not converge, but show oscillatory behaviour. We discuss the origin of this oscillatory behaviour.

  OXFORD UNIV PRESS, 2017, Publications of the Astronomical Society of Japan, 69(2) (2), English

  [Refereed]

  Scientific journal


• 連載「FDPS入門(1)」

  牧野 淳一郎

  本稿では、私達が開発・公開している多体シミュレーションプログラム開発フレームワーク「FDPS (Framework for Developping Particle Simulators)」を紹介します。FDPS は、粒子シミュレーションを研究に使っている多くの研究者が、並列化や計算機アーキテクチャ固有のチューニングに多大な時間を費やすことなく、自分の扱いたい問題向けのシミュレーションプログラムを容易に作成できるようになることを目標として開発したフレームワークです。連載第一回の今回は、FDPS の開発の背景、考え方と、実際にどのようなことができるか、という簡単な例を紹介します。

  分子シミュレーション研究会, 2017, アンサンブル, 19(2) (2), 105 - 110, Japanese


• A formulation of consistent particle hydrodynamics in strong form

  Satoko Yamamoto, Junichiro Makino

  In fluid dynamical simulations in astrophysics, large deformations are common and surface tracking is sometimes necessary. The smoothed particle hydrodynamics (SPH) method has been used in many such simulations. Recently, however, it has been shown that SPH cannot handle contact discontinuities or free surfaces accurately. There are several reasons for this problem. The first one is that SPH requires that the density is continuous and differentiable. The second one is that SPH does not have consistency, and thus the accuracy is of the zeroth-order in space. In addition, we cannot express accurate boundary conditions with SPH. In this paper, we propose a novel, high-order scheme for particle-based hydrodynamics of compressible fluid. Our method is based on a kernelweighted high-order fitting polynomial for intensive variables. With this approach, we can construct a scheme which solves all of the three problems described above. For shock capturing, we use a tensor form of von Neumann-Richtmyer artificial viscosity. We have applied our method to many test problems and obtained excellent results. Our method is not conservative, since particles do not have mass or energy, but only their densities. However, because of the Lagrangian nature of our scheme, the violation of the conservation laws turned out to be small. We name this method Consistent Particle Hydrodynamics in Strong Form (CPHSF).

  OXFORD UNIV PRESS, 2017, Publications of the Astronomical Society of Japan, 69(2) (2), English

  [Refereed]

  Scientific journal


• The detection rates of merging binary black holes originating from star clusters and their mass function

  Fujii, Michiko S., Tanikawa, Ataru, Makino, Junichiro

  2017, Publications of the Astronomical Society of Japan, 69(6) (6)

  [Refereed]

  Scientific journal


• The implication of the detection of the gravitational wave and future research direction

  牧野 淳一郎

  岩波書店, May 2016, 科学, 86(5) (5), 456 - 460, Japanese


• Terrestrial magma ocean origin of the Moon: A numerical study of a giant impact incorporating the different equations of state for melts and solids

  Hosono N, Karato SI, Makino J

  2016, AGU Fall Meeting Abstracts


• Formation and Evolution of Massive Black Holes in Star Clusters

  Holger Baumgardt, Junichiro Makino, Simon Portegies Zwart

  2016, Highlights of Astronomy

  [Refereed]

  Scientific journal


• Implementation and evaluation of data-compression algorithms for irregular-grid iterative methods on the PEZY-SC processor

  Yoshifuji, Naoki, Sakamoto, Ryo, Nitadori, Keigo, Makino, Jun

  2016, PROCEEDINGS OF 6TH WORKSHOP ON IRREGULAR APPLICATIONS: ARCHITECTURE AND ALGORITHMS (IA3)

  [Refereed]

  Scientific journal


• GLOBAL HIGH-RESOLUTION N -BODY SIMULATION OF PLANET FORMATION. I. PLANETESIMAL-DRIVEN MIGRATION

  J. D. Kominami, H. Daisaka, J. Makino, M. Fujimoto

  2016, The Astrophysical Journal, 819(1) (1)

  [Refereed]

  Scientific journal


• Automatic Generation of Efficient Codes from Mathematical Descriptions of Stencil Computation

  Muranushi, Takayuki, Nishizawa, Seiya, Tomita, Hirofumi, Nitadori, Keigo, Iwasawa, Masaki, Maruyama, Yutaka, Yashiro, Hisashi, Nakamura, Yoshifumi, Hotta, Hideyuki, Makino, Junichiro, Hosono, Natsuki, Inoue, Hikaru

  2016, FHPC'16: PROCEEDINGS OF THE 5TH INTERNATIONAL WORKSHOP ON FUNCTIONAL HIGH-PERFORMANCE COMPUTING, 17 - 22

  [Refereed]

  Scientific journal


• Simulations of Below-Ground Dynamics of Fungi: 1.184 Pflops Attained by Automated Generation and Autotuning of Temporal Blocking Codes

  Muranushi, Takayuki, Hotta, Hideyuki, Makino, Junichiro, Nishizawa, Seiya, Tomita, Hirofumi, Nitadori, Keigo, Iwasawa, Masaki, Hosono, Natsuki, Maruyama, Yutaka, Inoue, Hikaru, Yashiro, Hisashi, Nakamura, Yoshifumi

  2016, Sc '16: Proceedings of the International Conference For High Performance Computing, Networking, Storage and Analysis, 23 - 33

  [Refereed]

  Scientific journal


• Santa Barbara Cluster Comparison Test with DISPH

  Saitoh, T. R, Makino, J

  2016, The Astrophysical Journal, English

  [Refereed]

  Scientific journal


• A COMPARISON OF SPH ARTIFICIAL VISCOSITIES AND THEIR IMPACT ON THE KEPLERIAN DISK

  Natsuki Hosono, Takayuki R. Saitoh, Junichiro Makino

  2016, The Astrophysical Journal Supplement Series, 224(2) (2)

  [Refereed]

  Scientific journal


• The giant impact simulations with density independent smoothed particle hydrodynamics

  Natsuki Hosono, Takayuki R. Saitoh, Junichiro Makino, Hidenori Genda, Shigeru Ida

  2016, Icarus, 271, 131 - 157

  [Refereed]

  Scientific journal


• SANTA BARBARA CLUSTER COMPARISON TEST WITH DISPH

  Takayuki R. Saitoh, Junichiro Makino

  2016, The Astrophysical Journal, 823(2) (2)

  [Refereed]

  Scientific journal


• Implementation and performance of FDPS: a framework for developing parallel particle simulation codes

  Masaki Iwasawa, Ataru Tanikawa, Natsuki Hosono, Keigo Nitadori, Takayuki Muranushi, Junichiro Makino

  2016, Publications of the Astronomical Society of Japan, 68(4) (4)

  [Refereed]

  Scientific journal


• FDPS: A novel framework for developing high-performance particle simulation codes for distributed-memory systems

  Masaki Iwasawa, Ataru Tanikawa, Natsuki Hosono, Keigo Nitadori, Takayuki Muranushi, Junichiro Makino

  We have developed FDPS (Framework for Developing Particle Simulator), which enables researchers and programmers to develop high-performance particle simulation codes easily. The basic idea of FDPS is to separate the program code for complex parallelization including domain decomposition, redistribution of particles, and exchange of particle information for interaction calculation between nodes, from actual interaction calculation and orbital integration. FDPS pro- vides the former part and the users write the latter. Thus, a user can implement, for example, a high-performance N- body code, only in 120 lines. In this paper, we present the structure and implementation of FDPS, and describe its performance on two sample applications: gravitational N-body simulation and Smoothed Particle Hydrodynamics simulation. Both codes show very good parallel efficiency and scalability on the K computer. FDPS lets the researchers concentrate on the implementation of physics and mathematical schemes, without wasting their time on the development and performance tuning of their codes.

  Association for Computing Machinery, Inc, Nov. 2015, Proceedings of WOLFHPC 2015: 5th International Workshop on Domain-Specific Languages and High-Level Frameworks for High Performance Computing - Held in conjunction with SC 2015: The International Conference for High Performance Computing, Networking, Storage and Analysis, 1, English

  [Refereed]

  International conference proceedings


• A development of an accelerator board dedicated for multi-precision arithmetic operations and its application to Feynman loop integrals

  Motoki, S., Daisaka, H., Nakasato, N., Ishikawa, T., Yuasa, F., Fukushige, T., Kawai, A., Makino, J.

  2015, Journal of Physics: Conference Series

  [Refereed]

  Scientific journal


• Optimal Temporal Blocking for Stencil Computation

  Muranushi, Takayuki, Muranushi, Takayuki, Makino, Junichiro, Makino, Junichiro

  2015, Procedia Computer Science, 51, 1303 - 1312

  [Refereed]

  Scientific journal


• Smoothed particle hydrodynamics with smoothed pseudo-density

  Satoko Yamamoto, Takayuki R. Saitoh, Junichiro Makino

  2015, Publications of the Astronomical Society of Japan, 67(3) (3)

  [Refereed]

  Scientific journal


• Nanoblock unroll: Towards the automatic generation of stencil codes with the optimal performance

  Takayuki Muranushi, Keigo Nitadori, Junichiro Makino

  A number of automatic code generation systems have been proposed for stencil computations on modern parallel com- puters. However, codes they generate are rather inefficient. Typically they achieve < 10% of the peak performance of the platforms. The primary cause for this inefficiency is that the generated codes contain several layers of array indices for array accesses. This layers of indices prevent the com- piler from generating efficient assembly codes. In this paper we propose a new approach for the automatic code genera- tion in which the generated code is "compiler-friendly," in the sense that the compilers can generate highly optimized assembly codes than typical automatically generated codes. We demonstrate the effectiveness of our approach with a simple example of diffusion equation on a small grid. The measured efficiency can reach 85% of the theoretical peak.

  Association for Computing Machinery, Inc, Oct. 2014, WOSC 2014 - Proceedings of the 2014 ACM SIGPLAN Workshop on Stencil Computations, Part of SPLASH 2014, 49 - 55, English

  [Refereed]

  International conference proceedings


• Binary formation in planetesimal disks. II. Planetesimals with a mass spectrum

  KominAmi, Junko D., Makino, Junichiro

  Many massive objects have been found in the outer region of the solar system. How they were formed and evolved has not been well understood, although there have been intensive studies of the accretion process of terrestrial planets. One of the mysteries is the existence of binary planetesimals with near-equal mass components and highly eccentric orbits. These binary planetesimals are quite different from the satellites observed in the asteroid belt region. The ratio of the Hill radius to the physical radius of the planetesimals is much larger for the outer region of the disk, compared to the inner region of the disk. The Hill radius increases with the semimajor axis. Therefore, planetesimals in the outer region can form close and eccentric binaries, while those in the inner region would simply collide. In this paper, we carried out N-body simulations in different regions of the disk and studied whether binaries form in the outer region of the disk. We found that large planetesimals tend to form binaries. A significant fraction of large planetesimals are components of binaries. Planetesimals that become the components of binaries eventually collide with a third body, through three-body encounters. Thus, the existence of binaries can enhance the growth rate of planetesimals in the trans-Neptunian object region.

  OXFORD UNIV PRESS, 2014, Publications of the Astronomical Society of Japan, 66(6) (6), 123 - 1-13, English

  [Refereed]

  Scientific journal


• Flaring up of the compact cloud G2 during the close encounter with Sgr A*

  Takayuki R. Saitoh, Junichiro Makino, Yoshiharu Asaki, Junichi Baba, Shinya Komugi, Makoto Miyoshi, Tohru Nagao, Masaaki Takahashi, Takaaki Takeda, Masato Tsuboi, Ken-ichi Wakamatsu

  A compact gas cloud G2 is predicted to reach the pericenter of its orbit around the supermassive black hole (SMBH) of our Galaxy, Sagittarius A*. This event will give us a rare opportunity to observe the interaction between the SMBH and the gas around it. We report on the result of a fully three-dimensional simulation of the evolution of G2 during the first pericenter passage. The strong tidal force from the SMBH stretches the cloud along its orbit, and strongly compresses it in the vertical direction, resulting in its heating up and flaring up. The bolometric luminosity will reach a maximum of similar to 100 L-circle dot. This flare should be easily observed in the near-IR.

  OXFORD UNIV PRESS, 2014, Publications of the Astronomical Society of Japan, 66(1) (1), English

  [Refereed]

  Scientific journal


• Binary formation in planetesimal disks. II. Planetesimals with a mass spectrum

  Junko D. Kominami, Junichiro Makino

  Many massive objects have been found in the outer region of the solar system. How they were formed and evolved has not been well understood, although there have been intensive studies of the accretion process of terrestrial planets. One of the mysteries is the existence of binary planetesimals with near-equal mass components and highly eccentric orbits. These binary planetesimals are quite different from the satellites observed in the asteroid belt region. The ratio of the Hill radius to the physical radius of the planetesimals is much larger for the outer region of the disk, compared to the inner region of the disk. The Hill radius increases with the semimajor axis. Therefore, planetesimals in the outer region can form close and eccentric binaries, while those in the inner region would simply collide. In this paper, we carried out N-body simulations in different regions of the disk and studied whether binaries form in the outer region of the disk. We found that large planetesimals tend to form binaries. A significant fraction of large planetesimals are components of binaries. Planetesimals that become the components of binaries eventually collide with a third body, through three-body encounters. Thus, the existence of binaries can enhance the growth rate of planetesimals in the trans-Neptunian object region.

  OXFORD UNIV PRESS, 2014, Publications of the Astronomical Society of Japan, 66(6) (6), English

  [Refereed]

  Scientific journal


• A Density-independent Formulation of Smoothed Particle Hydrodynamics

  Saitoh, T. R, Makino, J

  2013, The Astrophysical Journal, English

  [Refereed]

  Scientific journal


• THE COSMOGRID SIMULATION: STATISTICAL PROPERTIES OF SMALL DARK MATTER HALOS

  Tomoaki Ishiyama, Steven Rieder, Junichiro Makino, Simon Portegies Zwart, Derek Groen, Keigo Nitadori, Cees de Laat, Stephen McMillan, Kei Hiraki, Stefan Harfst

  2013, The Astrophysical Journal, 767(2) (2)

  [Refereed]

  Scientific journal


• A DENSITY-INDEPENDENT FORMULATION OF SMOOTHED PARTICLE HYDRODYNAMICS

  Takayuki R. Saitoh, Junichiro Makino

  2013, The Astrophysical Journal, 768(1) (1)

  [Refereed]

  Scientific journal


• Density-Independent Smoothed Particle Hydrodynamics for a Non-Ideal Equation of State

  Hosono, Natsuki, Saitoh, Takayuki R., Makino, Junichiro

  2013, Publications of the Astronomical Society of Japan, 65(5) (5)

  [Refereed]

  Scientific journal


• Few-body modes of binary formation in core collapse

  Tanikawa, Ataru, Heggie, Douglas C., Hut, Piet, Makino, Junichiro

  2013, Astronomy and Computing, 3-4, 35 - 49

  [Refereed]

  Scientific journal


• Evolution of star clusters in a cosmological tidal field

  Steven Rieder, Tomoaki Ishiyama, Paul Langelaan, Junichiro Makino, Stephen L. W. McMillan, Simon Portegies Zwart

  2013, Monthly Notices of the Royal Astronomical Society, 436(4) (4), 3695 - 3706

  [Refereed]

  Scientific journal


• GRAPE-MPs: Implementation of an SIMD for quadruple/hexuple/octuple- precision arithmetic operation on a structured asic and an FPGA

  Naohito Nakasato, Hiroshi Daisaka, Toshiyuki Fukushige, Atsushi Kawai, Junichiro Makino, Tadashi Ishikawa, Fukuko Yuasa

  We describe the design and performance of the GRAPE-MPs, a series of SIMD accelerator boards for quadruple/hexuple/octuple-precision arithmetic operations. Basic design of GRAPE-MPs is that it consists of a number of processing elements (PE) and memory components which handle data with quadruple/hexuple/octuple-precision. A GRAPE-MPs processor is implemented on a structured ASIC chip and an FPGA chip. GRAPE-MP (quadruple-precision) uses a structured ASIC chip from eASIC corp., which has 6 PE and operates with 100MHz clock cycle. The theoretical peak quadruple-precision performance of the single board is 1.2 Gflops and the achieved performance for the Feynman loop integrals is about 0.5 Gflops. GRAPE-MP4/6/8 (quadruple/hexuple/octuple-precision) uses an FPGA chip from Aletra corporation. For example, in the current implementation, MP8 has 10 PE with 70MHz operation clock cycle. We also present the performance results with the multiple GRAPE-MPs boards. The achieved performance of four MP8 boards is about 1.6 Gflops. It is roughly 90 times faster than the performance of a single core of a CPU with comparable precision. We show that our hardware based approach to evaluate the Feynman loop integrals in high precision arithmetic operations is highly effective. © 2012 IEEE.

  2012, Proceedings - IEEE 6th International Symposium on Embedded Multicore SoCs, MCSoC 2012, 75 - 83, English

  International conference proceedings


• The dynamics of long-lived spiral arms

  Fujii, M. S., Baba, J., Saitoh, T. R., Kokubo, E., Makino, J., Wada, K.

  2012, EPJ Web of Conferences

  [Refereed]

  Scientific journal


• The Formation and Evolution of First Dark Matter Microhalos

  Ishiyama, Tomoaki, Makino, Junichiro, Ebisuzaki, Toshikazu

  2012, AIP Conference Proceedings, 1480, 382 - 384

  [Refereed]

  Scientific journal


• GRAPE-8-An Accelerator for Gravitational N-body Simulation with 20.5Gflops/W Performance

  Makino, Junichiro, Daisaka, Hiroshi

  2012, SC14: International Conference for High Performance Computing, Networking, Storage and Analysis

  [Refereed]

  Scientific journal


• Astrophysics with GRAPE

  Junichiro Makino, Takayuki Saitoh

  2012, Progress of Theoretical and Experimental Physics, (1) (1)

  [Refereed]

  Scientific journal


• 4.45 Pflops Astrophysical N-Body Simulation on K computer - The Gravitational Trillion-Body Problem

  Ishiyama, Tomoaki, Nitadori, Keigo, Makino, Junichiro

  2012, SC14: International Conference for High Performance Computing, Networking, Storage and Analysis

  [Refereed]

  Scientific journal


• A natural symmetrization for the plummer potential

  Takayuki R. Saitoh, Junichiro Makino

  2012, New Astronomy, 17(2) (2), 76 - 81

  [Refereed]

  Scientific journal


• ORIGIN OF MULTIPLE NUCLEI IN ULTRALUMINOUS INFRARED GALAXIES

  Hidenori Matsui, Takayuki R. Saitoh, Junichiro Makino, Keiichi Wada, Kohji Tomisaka, Eiichiro Kokubo, Hiroshi Daisaka, Takashi Okamoto, Naoki Yoshida

  2012, The Astrophysical Journal, 746(1) (1)

  [Refereed]

  Scientific journal


• Unexpected formation modes of the first hard binary in core collapse

  Ataru Tanikawa, Piet Hut, Junichiro Makino

  2012, New Astronomy, 17(3) (3), 272 - 280

  [Refereed]

  Scientific journal


• PSDF: Particle Stream Data Format for N-body simulations

  Will M. Farr, Jeff Ames, Piet Hut, Junichiro Makino, Steve McMillan, Takayuki Muranushi, Koichi Nakamura, Keigo Nitadori, Simon Portegies Zwart

  2012, New Astronomy, 17(5) (5), 520 - 523

  [Refereed]

  Scientific journal


• High-performance gravitational N-body simulations on a planet-wide- distributed supercomputer

  Derek Groen, Simon Portegies Zwart, Tomoaki Ishiyama, Jun Makino

  We report on the performance of our cold dark matter cosmological N-body simulation that was carried out concurrently using supercomputers across the globe. We ran simulations on 60-750 cores distributed over a variety of supercomputers in Amsterdam (The Netherlands, Europe), in Tokyo (Japan, Asia), Edinburgh (UK, Europe) and Espoo (Finland, Europe). Regardless of the network latency of 0.32 s and the communication over 30 000 km of optical network cable, we are able to achieve ∼87% of the performance compared to an equal number of cores on a single supercomputer. We argue that using widely distributed supercomputers in order to acquire more compute power is technically feasible and that the largest obstacle is introduced by local scheduling and reservation policies. © 2011 IOP Publishing Ltd.

  Dec. 2011, Computational Science and Discovery, 4(1) (1), English

  [Refereed]

  Scientific journal


• THE DYNAMICS OF SPIRAL ARMS IN PURE STELLAR DISKS

  M. S. Fujii, J. Baba, T. R. Saitoh, J. Makino, E. Kokubo, K. Wada

  2011, The Astrophysical Journal, 730(2) (2)

  [Refereed]

  Scientific journal


• The performance of GRAPE-DR for dense matrix operations

  Makino, Junichiro, Daisaka, Hiroshi, Fukushige, Toshiyuki, Sugawara, Yutaka, Inaba, Mary, Hiraki, Kei

  We describe the implementation and performance of dense matrix multiplication and LU decomposition on the GRAPE-DR SIMD accelerator board. A GRAPE-DR card, with 4 GRAPE-DR chips, has the theoretical peak DP performance of 819 Gflops. Each GRAPE-DR chip has 512 processing elements and operates with 400 MHz clock cycle. each PE can perform one addition and one multiplication in every two clock cycles. The measured performance of matrix multiplication is 730 Gflops for the multiplication of matrices with size 51200 by 2048 and 2048 by 51200. The performance of LU decomposition is 480 Gflops for the problem size of 51200.

  ELSEVIER SCIENCE BV, 2011, Procedia Computer Science, 4, 888 - 897, English

  [Refereed]

  Scientific journal


• Shock-induced star cluster formation in colliding galaxies

  Saitoh, Takayuki R., Saitoh, Takayuki R., Daisaka, Hiroshi, Daisaka, Hiroshi, Kokubo, Eiichiro, Kokubo, Eiichiro, Makino, Junichiro, Makino, Junichiro, Okamoto, Takashi, Okamoto, Takashi, Tomisaka, Kohji, Tomisaka, Kohji, Wada, Keiichi, Wada, Keiichi, Yoshida, Naoki, Yoshida, Naoki

  We studied the formation process of star clusters using high-resolution N-body/smoothed particle hydrodynamics simulations of colliding galaxies. The total number of particles is 1.2 x 10(8) for our high resolution run. The gravitational softening is 5 pc and we allow gas to cool clown to similar to 10 K. During the first encounter of the collision, a giant filament consists of cold and dense gas found between the progenitors by shock compression. A vigorous starburst took place in the filament, resulting in the formation of star clusters. The mass of these star clusters ranges from 10(5-8) M-circle dot. These star clusters formed hierarchically: at first small star clusters formed, and then they merged via gravity, resulting in larger star clusters.

  CAMBRIDGE UNIV PRESS, 2011, Proceedings of the International Astronomical Union, (270) (270), 483 - 486, English

  [Refereed]

  Scientific journal


• GRAPE-MP: An SIMD Accelerator Board for Multi-precision Arithmetic

  Daisaka, Hiroshi, Nakasato, Naohito, Makino, Junichiro, Yuasa, Fukuko, Ishikawa, Tadashi

  We describe the design and performance of the GRAPE-MP board, an SIMD accelerator board for quadruple-precision arithmetic operations. A GRAPE-MP board houses one GRAPE-MP processor chip and an FPGA chip which handles the communication with the host computer. A GRAPE-MP chip has 6 processing elements (PE) and operates with 100MHz clock cycle. Each PE can perform one addition and one multiplication in every clock cycle. The architecture of the GRAPE-MP is similar to that of the GRAPE-DR. It is implemented using the structured ASIC chip from eASIC corp. A GRAPE-MP processor board has the theoretical peak quadruple-precision performance of 1.2 Gflops. As a preliminary result, we present the performance of the GRAPE-MP board for two target applications. The performance of the numerical integration of Feynman loop is 0.53 Gflops. The performance of a N-body simulation with the second order leapfrog schema is 0.505 Gflops for N = 1984, which is more than 10 times faster than the performance of the host computer.

  ELSEVIER SCIENCE BV, 2011, Procedia Computer Science, 4, 878 - 887, English

  [Refereed]

  Scientific journal


• GRAPE Accelerators

  Junichiro Makino

  I'll overview the past, present, and future of the GRAPE project, which started as the effort to design and develop specialized hardware for gravitational N-body problem. The current hardware, GRAPE-DR, has an architecture quite different from previous GRAPEs, in the sense that it is a collection of small, but programmable processors, while previous GRAPEs had hardwired pipelines. discuss pros and cons of these two approaches, comparisons with other accelerators and future directions.

  CAMBRIDGE UNIV PRESS, 2011, Proceedings of the International Astronomical Union, (270) (270), 389 - 396, English

  [Refereed]

  Scientific journal


• ECCENTRIC EVOLUTION OF SUPERMASSIVE BLACK HOLE BINARIES

  Masaki Iwasawa, Sangyong An, Tatsushi Matsubayashi, Yoko Funato, Junichiro Makino

  In recent numerical simulations, it has been found that the eccentricity of supermassive black hole (SMBH)-intermediate black hole (IMBH) binaries grows toward unity through interactions with the stellar background. This increase of eccentricity reduces the merging timescale of the binary through the gravitational radiation to a value well below the Hubble time. It also gives a theoretical explanation of the existence of eccentric binaries such as that in OJ287. In self-consistent N-body simulations, this increase of eccentricity is always observed. On the other hand, the result of the scattering experiment between SMBH binaries and field stars indicated that the eccentricity dose not change significantly. This discrepancy leaves the high eccentricity of the SMBH binaries in N-body simulations unexplained. Here, we present a stellar-dynamical mechanism that drives the increase of the eccentricity of an SMBH binary with a large mass ratio. There are two key processes involved. The first one is the Kozai mechanism under a non-axisymmetric potential, which effectively randomizes the angular momenta of surrounding stars. The other is the selective ejection of stars with prograde orbits. Through these two mechanisms, field stars extract the orbital angular momentum of the SMBH binary. Our proposed mechanism causes the increase in the eccentricity of most of SMBH binaries, resulting in the rapid merger through gravitational wave radiation. Our result has given a definite solution to the "last-parsec problem."

  IOP PUBLISHING LTD, 2011, The Astrophysical Journal, 731(1) (1), English

  [Refereed]

  Scientific journal


• Particle–Particle Particle–Tree: A Direct-Tree Hybrid Scheme for Collisional N -Body Simulations

  Shoichi Oshino, Yoko Funato, Junichiro Makino

  In this paper, we present a new hybrid algorithm for the time integration of collisional N-body systems. In this algorithm, the gravitational force between two particles is divided into short- and long-range terms, using a distance-dependent cutoff function. The long-range interaction is calculated using a tree algorithm, and integrated with a constant-timestep leapfrog integrator. The short-range term is calculated directly and integrated with the high-order Hermite scheme. We can reduce the calculation cost per orbital period from O(N-2) to O(NlogN), without significantly increasing the long-term integration error. The results of our test simulations show that close encounters are integrated accurately. Long-term errors of the total energy show random-walk behaviour, because they are dominated by the error caused by the tree approximation.

  OXFORD UNIV PRESS, 2011, Publications of the Astronomical Society of Japan, 63(4) (4), 881 - 892, English

  [Refereed]

  Scientific journal


• Binary Formation in Planetesimal Disks. I. Equal Mass Planetesimals

  Junko D. Kominami, Junichiro Makino, Hiroshi Daisaka

  2011, Publications of the Astronomical Society of Japan, 63(6) (6), 1331 - 1344

  [Refereed]

  Scientific journal


• GAMMA-RAY SIGNAL FROM EARTH-MASS DARK MATTER MICROHALOS

  Tomoaki Ishiyama, Junichiro Makino, Toshikazu Ebisuzaki

  Earth-mass dark matter microhalos with a size of similar to 100 AU are the first structures formed in the universe, if the dark matter of the universe is made of neutralinos. Here, we report the results of ultra-high-resolution simulations of the formation and evolution of these microhalos. We found that microhalos have the central density cusps of the form rho alpha r(-1.5), much steeper than the cusps of larger dark halos. The central regions of these microhalos survive the encounters with stars except in the very inner region of the galaxy down to the radius of a few hundreds parsecs from the galactic center. The annihilation signals from the nearest microhalos are observed as gamma-ray point sources (radius less than 1(/)), with unusually large proper motions of similar to 0.2 deg yr(-1). Their surface brightnesses are similar to 10% of that of the galactic center. Their signal-to-noise ratios might be better if they are far from the galactic plane. Luminosities of subhalos are determined only by their mass, and they are more than one order of magnitude more luminous than the estimation by Springel et al.: a boost factor can be larger than 1000. Perturbations to the millisecond pulsars by gravitational attractions of nearby Earth-mass microhalos can be detected by the observations of Parkes Pulsar Timing Array.

  IOP PUBLISHING LTD, Nov. 2010, ASTROPHYSICAL JOURNAL LETTERS, 723(2) (2), L195 - L200, English

  [Refereed]

  Scientific journal


• THE ORIGIN OF S-STARS AND A YOUNG STELLAR DISK: DISTRIBUTION OF DEBRIS STARS OF A SINKING STAR CLUSTER

  M. Fujii, M. Iwasawa, Y. Funato, J. Makino

  Within the distance of 1 pc from the Galactic center (GC), more than 100 young massive stars have been found. The massive stars at 0.1-1 pc from the GC are located in one or two disks, while those within 0.1 pc from the GC, S-stars, have an isotropic distribution. How these stars are formed is not well understood, especially for S-stars. Here, we propose that a young star cluster with an intermediate-mass black hole (IMBH) can form both the disks and S-stars. We performed a fully self-consistent N-body simulation of a star cluster near the GC. Stars that escaped from the tidally disrupted star cluster were carried to the GC due to a 1:1 mean motion resonance with the IMBH formed in the cluster. In the final phase of the evolution, the eccentricity of the IMBH becomes very high. In this phase, stars carried by the 1:1 resonance with the IMBH were dropped from the resonance and their orbits are randomized by a chaotic Kozai mechanism. The mass function of these carried stars is extremely top-heavy within 10 ''. The surface density distribution of young massive stars has a slope of -1.5 within 10 '' from the GC. The distribution of stars in the most central region is isotropic. These characteristics agree well with those of stars observed within 10 '' from the GC.

  IOP PUBLISHING LTD, Jun. 2010, ASTROPHYSICAL JOURNAL LETTERS, 716(1) (1), L80 - L84, English

  [Refereed]

  Scientific journal


• Triplets of supermassive black holes: astrophysics, gravitational waves and detection

  Pau Amaro-Seoane, Alberto Sesana, Loren Hoffman, Matthew Benacquista, Christoph Eichhorn, Junichiro Makino, Rainer Spurzem

  2010, Monthly Notices of the Royal Astronomical Society, 402(4) (4), 2308 - 2320

  [Refereed]

  Scientific journal


• THE ORIGIN OF S-STARS AND A YOUNG STELLAR DISK: DISTRIBUTION OF DEBRIS STARS OF A SINKING STAR CLUSTER

  M. Fujii, M. Iwasawa, Y. Funato, J. Makino

  2010, The Astrophysical Journal, 716(1) (1), 80 - 84

  [Refereed]

  Scientific journal


• Star Cluster Migration Near the Galactic Center

  Fujii, Michiko, Iwasawa, Masaki, Funato, Yoko, Makino, Junichiro

  2010, Proceedings of the International Astronomical Union, (267) (267), 329

  [Refereed]

  Scientific journal


• Shock-Induced Starburst and Star Cluster Formation in Colliding Galaxies

  Saitoh, Takayuki R., Daisaka, Hiroshi, Kokubo, Eiichiro, Makino, Junichiro, Okamoto, Takashi, Tomisaka, Kohji, Wada, Keiichi, Yoshida, Naoki

  2010, Galaxy Wars: Stellar Populations and Star Formation in Interacting Galaxies, 423, 185 - +

  [Refereed]

  Scientific journal


• GRAPE-DR: 2-Pflops massively-parallel computer with 512-core, 512-Gflops processor chips for scientific computing

  Makino, Junichiro, Hiraki, Kei, Inaba, Mary

  2010, ACM/IEEE SC07 CONFERENCE, 548 - +

  [Refereed]

  Scientific journal


• GAMMA-RAY SIGNAL FROM EARTH-MASS DARK MATTER MICROHALOS

  Tomoaki Ishiyama, Junichiro Makino, Toshikazu Ebisuzaki

  2010, The Astrophysical Journal, 723(2) (2), 195 - 200

  [Refereed]

  Scientific journal


• FAST: A Fully Asynchronous Split Time-Integrator for a Self-Gravitating Fluid

  Takayuki R. Saitoh, Junichiro Makino

  Astronomical Society of Japan, 2010, Publications of the Astronomical Society of Japan, 62(2) (2), 301--314 - 314, English

  [Refereed]

  Scientific journal


• Simulating the Universe on an Intercontinental Grid

  Simon Portegies Zwart, Derek Groen, Tomoaki Ishiyama, Keigo Nitadori, Junichiro makino, Cees de Laat, Steve McMillan, Kei Hiraki, Stefan Harfst, Paola Grosso

  2010, Computer, 43(8) (8), 63 - 70

  [Refereed]

  Scientific journal


• A NECESSARY CONDITION FOR INDIVIDUAL TIME STEPS IN SPH SIMULATIONS

  Takayuki R. Saitoh, Junichiro Makino

  We show that the smoothed particle hydrodynamics (SPH) method, used with individual time steps in the way described in the literature, cannot handle strong explosion problems correctly. In the individual time-step scheme, particles determine their time steps essentially from a local Courant condition. Thus they cannot respond to a strong shock, if the pre-shock timescale is too long compared to the shock timescale. This problem is not severe in SPH simulations of galaxy formation with a temperature cutoff in the cooling function at 10(4) K, while it is very dangerous for simulations in which the multiphase nature of the interstellar medium under 10(4) K is taken into account. A solution for this problem is to introduce a time-step limiter which reduces the time step of a particle if it is too long compared to the time steps of its neighbor particles. Thus this kind of time-step constraint is essential for the correct treatment of explosions in high-resolution SPH simulations with individual time steps.

  IOP PUBLISHING LTD, Jun. 2009, ASTROPHYSICAL JOURNAL LETTERS, 697(2) (2), L99 - L102, English

  [Refereed]

  Scientific journal


• アクセラレータによる四倍精度演算

  中里 直人, 石川 正, 牧野淳一郎, 湯浅富久子

  2009, 情報処理学会研究会, HPC-121, 39


• A Compiler for High Performance Computing With Many-Core Accelerators

  Nakasato, Naohito, Makino, Jun

  2009, IEEE International Conference on Cluster Computing and Workshops

  [Refereed]

  Scientific journal


• AstroSim: Collaborative Visualization of an Astrophysics Simulation in Second Life

  A. Nakasone, K. Miura, H. Prendinger, P. Hut, S. Holland, J. Makino

  2009, IEEE Computer Graphics and Applications, 29(5) (5)

  [Refereed]

  Scientific journal


• VARIATION OF THE SUBHALO ABUNDANCE IN DARK MATTER HALOS

  Tomoaki Ishiyama, Toshiyuki Fukushige, Junichiro Makino

  2009, The Astrophysical Journal, 696(2) (2), 2115 - 2125

  [Refereed]

  Scientific journal


• TROJAN STARS IN THE GALACTIC CENTER

  M. Fujii, M. Iwasawa, Y. Funato, J. Makino

  2009, The Astrophysical Journal, 695(2) (2)

  [Refereed]

  Scientific journal


• THE ORIGIN OF LARGE PECULIAR MOTIONS OF STAR-FORMING REGIONS AND SPIRAL STRUCTURES OF OUR GALAXY

  Junichi Baba, Yoshiharu Asaki, Junichiro Makino, Makoto Miyoshi, Takayuki R. Saitoh, Keiichi Wada

  2009, The Astrophysical Journal, 706(1) (1), 471 - 481

  [Refereed]

  Scientific journal


• A NECESSARY CONDITION FOR INDIVIDUAL TIME STEPS IN SPH SIMULATIONS

  Takayuki R. Saitoh, Junichiro Makino

  2009, The Astrophysical Journal, 697(2) (2), 99 - 102

  [Refereed]

  Scientific journal


• Toward First-Principle Simulations of Galaxy Formation: II. Shock-Induced Starburst at a Collision Interface during the First Encounter of Interacting Galaxies

  Takayuki R. Saitoh, Hiroshi Daisaka, Eiichiro Kokubo, Junichiro Makino, Takashi Okamoto, Kohji Tomisaka, Keiichi Wada, Naoki Yoshida

  Astronomical Society of Japan, 2009, Publications of the Astronomical Society of Japan, 61(3) (3), 481 - 486, English

  [Refereed]

  Scientific journal


• GreeM: Massively Parallel TreePM Code for Large Cosmological N -body Simulations

  Tomoaki Ishiyama, Toshiyuki Fukushige, Junichiro Makino

  Astronomical Society of Japan, 2009, Publications of the Astronomical Society of Japan, 61(6) (6), 1319 - 1330, English

  [Refereed]

  Scientific journal


• Fully Self-consistent N-body Simulation of Star Cluster in the Galactic Center, Dynamical Evolution of Dense Stellar Systems

  Fujii,M.S., Iwasawa,M., Funato,Y., Makino,J.

  2008


• Simulating N-body systems on the grid using dedicated hardware

  Groen, Derek, Zwart, Simon Portegies, McMillan, Steve, Makino, Jun

  2008, Lecture Notes in Computer Science

  [Refereed]

  Scientific journal


• Sixth- and eighth-order Hermite integrator for N-body simulations

  Keigo Nitadori, Junichiro Makino

  2008, New Astronomy, 13(7) (7), 498 - 507

  [Refereed]

  Scientific journal


• Evolution of Star Clusters near the Galactic Center: Fully Self‐Consistent N ‐Body Simulations

  M. Fujii, M. Iwasawa, Y. Funato, J. Makino

  2008, The Astrophysical Journal, 686(2) (2), 1082 - 1093

  [Refereed]

  Scientific journal


• Do-it-yourself computational astronomy

  Makino, Junichiro

  2008, Japanese Journal of Mathematics, 3(1) (1), 49 - 92

  [Refereed]

  Scientific journal


• Distributed N-body simulation on the grid using dedicated hardware

  Derek Groen, Simon Portegies Zwart, Steve McMillan, Jun Makino

  2008, New Astronomy, 13(5) (5), 348 - 358

  [Refereed]

  Scientific journal


• Toward First-Principle Simulations of Galaxy Formation: I. How Should We Choose Star-Formation Criteria in High-Resolution Simulations of Disk Galaxies?

  Takayuki R. Saitoh, Hiroshi Daisaka, Eiichiro Kokubo, Junichiro Makino, Takashi Okamoto, Kohji Tomisaka, Keiichi Wada, Naoki Yoshida

  Astronomical Society of Japan, 2008, Publications of the Astronomical Society of Japan, 60(4) (4), 667 - 681, English

  [Refereed]

  Scientific journal


• Environmental Effect on the Subhalo Abundance—a Solution to the Missing Dwarf Problem

  Tomoaki Ishiyama, Toshiyuki Fukushige, Junichiro Makino

  Astronomical Society of Japan, 2008, Publications of the Astronomical Society of Japan, 60(4) (4), L13 - L18, English

  [Refereed]

  Scientific journal


• Current status of GRAPE project

  J. Makino

  I'll summarize the current status of GRAPE project. GRAPE-6, completed in 2002, has been used by a number of people, for a wide variety of problems such as planet formation, star cluster dynamics, galactic nuclei, and cosmology. In 2004, we started the development of the next-generation machine, GRAPE-DR. GRAPE-DR has a architecture radically different from that of previous GRAPEs. It does not have hardwired pipeline for gravitational force calculation but a large number of small and simple programmable processors. This change made it possible to apply GRAPE-DR to a wide range of problems to which GRAPE was not efficient, and at the same time it helps us to explore new algorithms for N-body simulations. The GRAPE-DR chip was completed in 2006, and second prototype board was completed in May 2007. We hope to have full production-level board commercially available by the end of year 2007. A single board will offer the theoretical peak speed of 2 Tflops, about 20 times as that of a single PCI card version of GRAPE-6. © 2008 Copyright International Astronomical Union 2008.

  Sep. 2007, Proceedings of the International Astronomical Union, 3(246) (246), 457 - 466, English

  [Refereed]

  Scientific journal


• Test of the accuracy of approximate methods to handle distant binary-single star encounters

  Yoko Funato, D. C. Heggie, P. Hut, Jun Makino

  In the numerical simulations of evolution of star clusters, binary-single star interactions frequently take place. Since the direct integration of them is time consuming, distant interactions between binaries and field stars are often integrated by using some approximations. Traditionally the effect of the error caused by the approximated treatment is regarded as small enough to be ignored. However, if we have a binary-dominated core, the energy drift is large. In this study, we perform numerical experiments to evaluate the effect of neglecting the weak perturbation from distant single particles. We developed an N-body integrator which can manipulate multiple precision floating point numbers. © 2008 Copyright International Astronomical Union 2008.

  Sep. 2007, Proceedings of the International Astronomical Union, 3(246) (246), 469 - 470, English

  [Refereed]

  Scientific journal


• 6th and 8th Order hermite integrator using snap and crackle

  Keigo Nitadori, Masaki Iwasawa, Junichiro Makino

  We present sixth- and eighth-order Hermite integrators for astrophysical N-body simulations, which use the derivatives of accelerations up to second order (snap) and third order (crackle). These schemes do not require previous values for the corrector, and require only one previous value to construct the predictor. Thus, they are fairly easy to be implemented. The additional cost of the calculation of the higher order derivatives is not very high. Even for the eighth-order scheme, the number of floating-point operations for force calculation is only about two times larger than that for traditional fourth-order Hermite scheme. The sixth order scheme is better than the traditional fourth order scheme for most cases. When the required accuracy is very high, the eighth-order one is the best. © 2008 Copyright International Astronomical Union 2008.

  Sep. 2007, Proceedings of the International Astronomical Union, 3(246) (246), 473 - 474, English

  [Refereed]

  Scientific journal


• Gravitational many-body problem

  Makino, J., Makino, J.

  2007, AIP Conference Proceedings

  [Refereed]

  Scientific journal


• Star cluster ecology - VII. The evolution of young dense star clusters containing primordial binaries

  S. F. Portegies Zwart, S. L. W. McMillan, J. Makino

  2007, Monthly Notices of the Royal Astronomical Society, 374(1) (1), 95 - 106

  [Refereed]

  Scientific journal


• Orbital Evolution of an IMBH in the Galactic Nucleus with a Massive Central Black Hole

  Tatsushi Matsubayashi, Junichiro Makino, Toshikazu Ebisuzaki

  2007, The Astrophysical Journal, 656(2) (2), 879 - 896

  [Refereed]

  Scientific journal


• Modeling Dense Stellar Systems

  P. Hut, S. Mineshige, D. C. Heggie, J. Makino

  2007, Progress of Theoretical Physics, 118(2) (2), 187 - 209

  [Refereed]

  Scientific journal


• Formation of Protoplanets from Massive Planetesimals in Binary Systems

  Yusuke Tsukamoto, Junichiro Makino

  2007, The Astrophysical Journal, 669(2) (2), 1316 - 1323

  [Refereed]

  Scientific journal


• Evolution of Collisionally Merged Massive Stars

  Takeru K. Suzuki, Naohito Nakasato, Holger Baumgardt, Akihiko Ibukiyama, Junichiro Makino, Toshi Ebisuzaki

  2007, The Astrophysical Journal, 668(1) (1), 435 - 448

  [Refereed]

  Scientific journal


• The Core Radius of a Star Cluster Containing a Massive Black Hole

  Douglas C. Heggie, Piet Hut, Shin Mineshige, Junichiro Makino, Holger Baumgardt

  Astronomical Society of Japan, 2007, Publications of the Astronomical Society of Japan, 59(3) (3), L11 - L14, English

  [Refereed]

  Scientific journal


• Missing Dwarf Problem in Galaxy Clusters

  Hiroyuki Kase, Junichiro Makino, Yoko Funato

  Astronomical Society of Japan, 2007, Publications of the Astronomical Society of Japan, 59(6) (6), 1071 - 1080, English

  [Refereed]

  Scientific journal


• BRIDGE: A Direct-Tree Hybrid $N$-Body Algorithm for Fully Self-Consistent Simulations of Star Clusters and Their Parent Galaxies

  Michiko Fujii, Masaki Iwasawa, Yoko Funato, Junichiro Makino

  Astronomical Society of Japan, 2007, Publications of the Astronomical Society of Japan, 59(6) (6), 1095 - 1106, English

  [Refereed]

  Scientific journal


• Special-purpose computing for dense stellar systems

  Junichiro Makino

  I'll describe the current status of the GRAPE-DR project. The GRAPE-DR is the next-generation hardware for N-body simulation. Unlike the previous GRAPE hardwares, it is programmable SIMD machine with a large number of simple processors integrated into a single chip. The GRAPE-DR chip consists of 512 simple processors and operates at the clock speed of 500 MHz, delivering the theoretical peak speed of 512/226 Gflops (single/double precision). As of August 2006, the first prototype board with the sample chip successfully passed the test we prepared. The full GRAPE-DR system will consist of 4096 chips, reaching the theoretical peak speed of 2 Pflops. © 2007 International Astronomical Union.

  Aug. 2006, Proceedings of the International Astronomical Union, 2(14) (14), 424 - 425, English

  [Refereed]

  International conference proceedings


• The GRAPE project

  Makino, J

  2006, Computing in Science & Engineering, 8(1) (1)

  [Refereed]

  Scientific journal


• Tidal capture of stars by intermediate-mass black holes

  H. Baumgardt, C. Hopman, S. Portegies Zwart, J. Makino

  2006, Monthly Notices of the Royal Astronomical Society, 372(1) (1), 467 - 478

  [Refereed]

  Scientific journal


• The Ecology of Star Clusters and Intermediate‐Mass Black Holes in the Galactic Bulge

  Simon F. Portegies Zwart, Holger Baumgardt, Stephen L. W. McMillan, Junichiro Makino, Piet Hut, Toshi Ebisuzaki

  2006, The Astrophysical Journal, 641(1) (1), 319 - 326

  [Refereed]

  Scientific journal


• Performance tuning of N-body codes on modern microprocessors: I. Direct integration with a hermite scheme on x86_64 architecture

  Keigo Nitadori, Junichiro Makino, Piet Hut

  2006, New Astronomy, 12(3) (3), 169 - 181

  [Refereed]

  Scientific journal


• High‐Resolution Simulations of a Moon‐forming Impact and Postimpact Evolution

  Keiichi Wada, Eiichiro Kokubo, Junichiro Makino

  2006, The Astrophysical Journal, 638(2) (2), 1180 - 1186

  [Refereed]

  Scientific journal


• Evolution of Massive Black Hole Triples. I. Equal‐Mass Binary‐Single Systems

  Masaki Iwasawa, Yoko Funato, Junichiro Makino

  2006, The Astrophysical Journal, 651(2) (2), 1059 - 1067

  [Refereed]

  Scientific journal


• A time-symmetric block time-step algorithm for N-body simulations

  Junichiro Makino, Piet Hut, Murat Kaplan, Hasan Saygın

  2006, New Astronomy, 12(2) (2), 124 - 133

  [Refereed]

  Scientific journal


• Dynamical Friction on Satellite Galaxies

  Michiko Fujii, Yoko Funato, Junichiro Makino

  Astronomical Society of Japan, 2006, Publications of the Astronomical Society of Japan, 58(4) (4), 743 - 752, English

  [Refereed]

  Scientific journal


• GRAPE-6A: A single-card GRAPE-6 for parallel PC-GRAPE cluster systems

  T Fukushige, J Makino, A Kawai

  In this paper, we describe the design and performance of GRAPE-6A, a special-purpose computer for gravitational many-body simulations. It was designed to be used with a PC cluster, in which each node has one GRAPE-6A. Such a configuration is particularly cost-effective in running parallel tree algorithms. Though the use of parallel tree algorithms was possible with the original GRAPE-6 hardware, it was not very cost-effective since a single GRAPE-6 board was still too fast and too expensive. Therefore, we designed GRAPE-6A as a single PCI card to minimize the reproduction cost and to optimize the computing speed. The peak performance is 130 Gflops for one GRAPE-6A board and 3.1 Tflops for our 24 node cluster. We describe the implementation of the tree, TreePM and individual timestep algorithms on both a single GRAPE-6A system and GRAPE-6A cluster. Using the tree algorithm on our 16-node GRAPE-6A system, we can complete a collisionless simulation with 100 million particles (8000 steps) within 10 days.

  OXFORD UNIV PRESS, Dec. 2005, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 57(6) (6), 1009 - 1021, English

  Scientific journal


• Which globular clusters contain intermediate-mass black holes?

  H Baumgardt, J Makino, P Hut

  It has been assumed that intermediate-mass black holes (IMBHs) in globular clusters can only reside in the most centrally concentrated clusters, with a so-called core-collapsed density profile. While this would be a natural guess, it is in fact wrong. We have followed the evolution of star clusters containing IMBHs with masses between 125 less than or equal to M-BH less than or equal to 1000 M-circle dot through detailed N-body simulations, and we find that a cluster with an IMBH, in projection, appears to have a relatively large "core'' with surface brightness only slightly rising toward the center. This makes it highly unlikely that any of the "core-collapsed'' clusters will harbor an IMBH. On the contrary, the places to look for an IMBH are those clusters that can be fitted well by medium-concentration King models. The velocity dispersion of the visible stars in a globular cluster with an IMBH is nearly constant well inside the apparent core radius. For a cluster of mass M-C containing an IMBH of mass M-BH, the influence of the IMBH becomes significant only at a fraction 2.5M(BH)/M-C of the half-mass radius, deep within the core, where it will affect only a small number of stars. In conclusion, observational detection of an IMBH may be possible, but will be challenging.

  IOP PUBLISHING LTD, Feb. 2005, ASTROPHYSICAL JOURNAL, 620(1) (1), 238 - 243, English

  Scientific journal


• A quantitative analysis of the acidosis of cardiac arrest: a prospective observational study

  Makino, J, Uchino, S, Morimatsu, H, Bellomo, R

  2005, Critical Care, 9(4) (4)

  [Refereed]

  Scientific journal


• GRAPE and Project Milkyway

  2005, Journal of the Korean Astronomical Society


• GRAPE-6A: A Single-Card GRAPE-6 for Parallel PC-GRAPE Cluster Systems

  Toshiyuki Fukushige, Junichiro Makino, Atsushi Kawai

  Astronomical Society of Japan, 2005, Publications of the Astronomical Society of Japan, 57(6) (6), 1009 - 1021, English

  [Refereed]

  Scientific journal


• Formation and evolution of massive black holes in star clusters

  Baumgardt, Holger, Makino, Junichiro, Zwart, Simon Portegies, Engvold, O

  2005, Highlights of Astronomy, Vol 13, 13, 350 - 353

  [Refereed]

  Scientific journal


• Black hole binary mergers

  Makino Junichiro

  2005, Modelling of Stellar Atmospheres, 13, 339 - 342

  [Refereed]

  Scientific journal


• PGPG: An Automatic Generator of Pipeline Design for Programmable GRAPE Systems

  Tsuyoshi Hamada, Toshiyuki Fukushige, Junichiro Makino

  Astronomical Society of Japan, 2005, Publications of the Astronomical Society of Japan, 57(5) (5), 799 - 813, English

  [Refereed]

  Scientific journal


• Formation of omega Centauri by tidal stripping of a dwarf galaxy

  M Ideta, J Makino

  We have investigated whether or not a tidal stripping scenario can reproduce the observed surface brightness profile of omega Centauri using N-body simulations. Assuming that the progenitor of omega Cen is a dwarf elliptical galaxy, we model it with a King model with a core radius the same as that of omega Cen. A dark matter halo of the dwarf is not taken into account. We consider two different models of the Milky Way potential: a singular isothermal sphere and a three-component model. The progenitor dwarf is expressed as an N-body system, which orbits in the fixed Galactic potential. The dwarf lost more than 90% of its mass during the first few pericenter passages. Thereafter, the mass remains practically constant. The final surface density profile is in good agreement with the observational data on omega Cen, if the pericenter distance of the orbit of the progenitor dwarf is around 500 pc. This value is within the error bar of the current proper-motion data on omega Cen and Galactic parameters. Although our simulation is limited to a King-like progenitor dwarf without a dark matter halo, it strongly suggests that the current density profile of omega Cen is nicely reproduced by a tidal stripping scenario, in other words, that omega Cen can plausibly be identified with a stripped dwarf elliptical galaxy.

  UNIV CHICAGO PRESS, Dec. 2004, ASTROPHYSICAL JOURNAL, 616(2) (2), L107 - L110, English

  Scientific journal


• Massive black holes in star clusters. II. Realistic cluster models

  H Baumgardt, J Makino, T Ebisuzaki

  We have followed the evolution of multimass star clusters containing massive central black holes through collisional N-body simulations done on GRAPE6. Each cluster is composed of between 16,384 and 131,072 stars together with a black hole with an initial mass of M-BH = 1000 M-.. We follow the evolution of the clusters under the combined influence of two-body relaxation, stellar mass loss, and tidal disruption of stars by the massive central black hole. We find that the (three-dimensional) mass density profile follows a power-law distribution rho similar to r(-alpha) with slope alpha = 1.55 inside the sphere of influence of the central black hole. This leads to a constant-density profile of bright stars in projection, which makes it highly unlikely that core-collapse clusters contain intermediate-mass black holes (IMBHs). Instead, globular clusters containing massive central black holes can be fitted with standard King profiles. Because of energy generation in the cusp, star clusters with IMBHs expand. The cluster expansion is so strong that clusters that start very concentrated can end up among the least dense clusters. The amount of mass segregation in the core is also smaller compared to postcollapse clusters without IMBHs. Most stellar mass black holes with masses M-BH > 5 M-. are lost from the clusters within a few gigayears through mutual encounters in the cusp around the IMBH. Black holes in star clusters disrupt mainly main-sequence stars and giants and no neutron stars. The disruption rates are too small to form an IMBH out of a M-BH approximate to 50 M-. progenitor black hole even if all material from disrupted stars is accreted onto the black hole, unless star clusters start with central densities significantly higher than what is seen in present-day globular clusters. We also discuss the possible detection mechanisms for IMBHs. Our simulations show that kinematical studies can reveal 1000 M-. IMBHs in the closest clusters. IMBHs in globular clusters are weak X-ray sources, since the tidal disruption rate of stars is low and the star closest to the IMBH is normally another black hole, which prevents other stars from undergoing stable mass transfer. For globular clusters, dynamical evolution can push compact stars near the IMBH to distances small enough that they become detectable sources of gravitational radiation. If 10% of all globular clusters contain IMBHs, extragalactic globular clusters could be one of the major sources of gravitational wave events for LISA.

  UNIV CHICAGO PRESS, Oct. 2004, ASTROPHYSICAL JOURNAL, 613(2) (2), 1143 - 1156, English

  Scientific journal


• Massive black holes in star clusters. I. Equal-mass clusters

  H Baumgardt, J Makino, T Ebisuzaki

  In this paper we report results of collisional N-body simulations of the dynamical evolution of equal-mass star clusters containing a massive central black hole. Each cluster is composed of between 5000 and 180,000 stars together with a central black hole that contains between 0.2% and 10% of the total cluster mass. We find that for large enough black hole masses, the central density follows a power-law distribution with slope rho similar to r(-1.75) inside the radius of influence of the black hole, in agreement with predictions from earlier Fokker-Planck and Monte Carlo models. The tidal disruption rate of stars is within a factor of 2 of that derived in previous studies. It seems impossible to grow an intermediate-mass black hole (IMBH) from an M less than or equal to 100 M-. progenitor in a globular cluster by the tidal disruption of stars, although M = 10(3) M-. IMBHs can double their mass within a Hubble time in dense globular clusters. The same is true for the supermassive black hole at the center of the Milky Way. Black holes in star clusters will feed mainly on stars tightly bound to them, and the repopulation of these stars causes the clusters to expand, reversing core collapse without the need for dynamically active binaries. Close encounters of stars in the central cusp also lead to an increased mass-loss rate in the form of high-velocity stars escaping from the cluster. A companion paper will extend these results to the multimass case.

  UNIV CHICAGO PRESS, Oct. 2004, ASTROPHYSICAL JOURNAL, 613(2) (2), 1133 - 1142, English

  Scientific journal


• A modified Hermite integrator for planetary dynamics

  E Kokubo, J Makino

  We describe a modified time-symmetric Hermite integrator specialized for the long-term integration of planetary orbits. Our time-symmetric integrators have no secular errors in the semi-major axis and the eccentricity for the integration of two-body Kepler problems as usual time-symmetric and symplectic integrators. The usual time-symmetric or symplectic integrators, however, show a secular drift in the argument of pericenter. Our new family of integrators has one free parameter, which we can adjust to reduce the error in the argument of pericenter without breaking the time-symmetry or changing the order of the integrator. We show analytically that the leading term of the error vanishes for a unique value of the parameter, which is independent of the size of the timestep and the eccentricity. It is also possible to eliminate the non-leading, higher-order terms by using a parameter value that depends on both the size of the timestep and the eccentricity. We describe the second- and the fourth-order schemes. An extension to higher order is straightforward.

  OXFORD UNIV PRESS, Oct. 2004, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 56(5) (5), 861 - 868, English

  Scientific journal


• Star cluster ecology - V. Dissection of an open star cluster: spectroscopy

  S Portegies Zwart, P Hut, SLW McMillan, J Makino

  We have modelled in detail the evolution of rich open star clusters such as NGC 2516, NGC 2287, Pleiades, Praesepe, Hyades, NGC 2660 and 3680, using simulations that include stellar dynamics as well as the effects of stellar evolution. The dynamics is modelled via direct N-body integration, while the evolution of single stars and binaries is followed through the use of fitting formulae and recipes. The feedback of stellar and binary evolution on the dynamical evolution of the stellar system is taken into account self-consistently. Our model clusters dissolve in the tidal field of the Galaxy in a time-span of the order of a billion years. The rate of mass loss is rather constant, similar to1 M-. per million years. The binary fraction at first is nearly constant in time, then increases slowly near the end of a cluster's lifetime. For clusters which are more than about 10(8) yr old the fractions of stars in the form of binaries, giants and merger products in the inner few core radii are considerably higher than in the outer regions, beyond the cluster's half-mass radius. When stars with masses greater than or similar to2 M-. escape from the cluster, they tend to do so with velocities higher than average. The stellar merger rate in our models is roughly one per 30 million years. Most mergers are the result of unstable mass transfer in close binaries (similar to70 per cent), but a significant minority are caused by direct encounters between single and binary stars. While most mergers occur within the cluster core, even beyond the half-mass radius stellar mergers occasionally take place. We notice a significant birth rate of X-ray binaries, most containing a white dwarf as the mass acceptor. We also find one high-mass X-ray binary with a neutron-star accretor. If formed and retained, black holes participate in many (higher-order) encounters in the cluster centre, resulting in a large variety of exotic binaries. The persistent triple and higher-order systems formed in our models by dynamical encounters between binaries and single stars are not representative for the multiple systems observed in the Galactic disc. We conclude that the majority of multiples in the disc probably formed when the stars were born, rather than through later dynamical interactions.

  OXFORD UNIV PRESS, Jun. 2004, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 351(2) (2), 473 - 486, English

  Scientific journal


• A fast parallel treecode with GRAPE

  J Makino

  In this paper, we describe an implementation of the Barnes-Hut treecode on a cluster of PCs (Beowulf-class machines) equipped with GRAPE hardware. Our implementation is designed to achieve good performance on clusters of GRAPE with a relatively slow network, such as the standard Gigabit Ethernet. With 12 processors, the speedup over single-processor code reaches around 10. Our code is available on the web.

  OXFORD UNIV PRESS, Jun. 2004, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 56(3) (3), 521 - 531, English

  Scientific journal


• Structure of dark matter halos from hierarchical clustering. III. Shallowing of the inner cusp

  T Fukushige, A Kawai, J Makino

  We investigate the structure of the dark matter halo formed in the cold dark matter scenarios by N-body simulations with a parallel tree code on GRAPE cluster systems. We simulated eight halos with the mass of 4.4 x 10(14) to 1.6 x 10(15) M-circle dot in SCDM and LCDM models using up to 30 million particles. With the resolution of our simulations, the density profile is reliable down to 0.2% of the virial radius. Our results show that the slope of inner cusp within 1% virial radius is shallower than -1.5, and the radius where the shallowing starts exhibits run-to-run variation, which means that the innermost profile is not universal.

  UNIV CHICAGO PRESS, May 2004, ASTROPHYSICAL JOURNAL, 606(2) (2), 625 - 634, English

  Scientific journal


• Formation of massive black holes through runaway collisions in dense young star clusters

  SFP Zwart, H Baumgardt, P Hut, J Makino, SLW McMillan

  A luminous X-ray source is associated with MGG 11-a cluster of young stars similar to200 pc from the centre of the starburst galaxy M 82 (refs 1, 2). The properties of this source are best explained(3,4) by invoking a black hole with a mass of at least 350 solar masses (350M.), which is intermediate between stellar-mass and supermassive black holes. A nearby but somewhat more massive cluster ( MGG 9) shows no evidence of such an intermediate-mass black hole(1,3), raising the issue of just what physical characteristics of the clusters can account for this difference. Here we report numerical simulations of the evolution and motion of stars within the clusters, where stars are allowed to merge with each other. We find that for MGG 11 dynamical friction leads to the massive stars sinking rapidly to the centre of the cluster, where they participate in a runaway collision. This produces a star of 800-3,000 M., which ultimately collapses to a black hole of intermediate mass. No such runaway occurs in the cluster MGG 9, because the larger cluster radius leads to a mass segregation timescale a factor of five longer than for MGG 11.

  NATURE PUBLISHING GROUP, Apr. 2004, NATURE, 428(6984) (6984), 724 - 726, English

  Scientific journal


• Performance analysis of high-accuracy tree code based on the pseudoparticle multipole method

  A Kawai, J Makino, T Ebisuzaki

  In this paper, we describe the performance and accuracy of the (PM2)-M-2 tree code. The (PM2)-M-2 tree code is a high-accuracy tree code based on the pseudoparticle multipole method ((PM2)-M-2). (PM2)-M-2 is a method to express multipole expansion using a small number of pseudoparticles. The potential field of physical particles is approximated by the field generated by the pseudoparticles. The primary advantage of the (PM2)-M-2 tree code is that it can use Gravity Pipe (GRAPE) special-purpose computers efficiently for high-accuracy calculations. Although the tree code has been implemented on GRAPE, it could not handle terms of the multipole expansion higher than dipole, since GRAPE can calculate forces from point mass particles only. Thus, the calculation cost grows quickly when high accuracy is required. In the (PM2)-M-2 tree code, the multipole expansion is expressed by particles, and thus we can evaluate high-order terms on GRAPE. We implemented the (PM2)-M-2 tree code on both MDGRAPE-2 and a conventional workstation and measured the performance. The results show that MDGRAPE-2 accelerates the calculation by a factor between 20 (for low accuracy) and 200 (for high accuracy). Even on general-purpose programmable computers, the (PM2)-M-2 tree code offers the advantage that the mathematical formulae, and therefore the actual program, are much simpler than that of the direct implementation of multipole expansion, although the calculation cost becomes somewhat higher.

  UNIV CHICAGO PRESS, Mar. 2004, ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES, 151(1) (1), 13 - 33, English

  Scientific journal


• The formation of Kuiper-belt binaries through exchange reactions

  Y Funato, J Makino, P Hut, E Kokubo, D Kinoshita

  Recent observations(1-8) have revealed that an unexpectedly high fraction-a few per cent-of the trans-Neptunian objects (TNOs) that inhabit the Kuiper belt are binaries. The components have roughly equal masses, with very eccentric orbits that are wider than a hundred times the radius of the primary. Standard theories of binary asteroid formation tend to produce close binaries with circular orbits, so two models have been proposed(9,10) to explain the unique characteristics of the TNOs. Both models, however, require extreme assumptions regarding the size distribution of the TNOs. Here we report a mechanism that is capable of producing binary TNOs with the observed properties during the early stages of their formation and growth. The only required assumption is that the TNOs were initially formed through gravitational instabilities(11) in the protoplanetary dust disk. The basis of the mechanism is an exchange reaction in which a binary whose primary component is much more massive than the secondary interacts with a third body, whose mass is comparable to that of the primary. The low-mass secondary component is ejected and replaced by the third body in a wide but eccentric orbit.

  NATURE PUBLISHING GROUP, Feb. 2004, NATURE, 427(6974) (6974), 518 - 520, English

  Scientific journal


• Evolution of massive black hole binaries

  J Makino, Y Funato

  We present the results of large-scale N-body simulations of the stellar-dynamical evolution of massive black hole binaries at the center of spherical galaxies. We focus on the dependence of the hardening rate on the relaxation timescale of the parent galaxy. A simple theoretical argument predicts that a binary black hole creates a "loss cone" around it. Once the stars in the loss cone are depleted, the hardening rate is determined by the rate at which field stars diffuse into the loss cone. Therefore, the hardening timescale becomes proportional to the relaxation timescale. Recent N-body simulations, however, have failed to confirm this theory, and various explanations have been proposed. By performing simulations with sufficiently large N (up to 10(6)) for sufficiently long time, we found that the hardening rate does indeed depend on N. Our result is consistent with the simple theoretical prediction that the hardening timescale is proportional to the relaxation timescale. This dependence implies that massive black hole binaries are unlikely to merge within a Hubble time through interaction with field stars and gravitational wave radiation alone.

  UNIV CHICAGO PRESS, Feb. 2004, ASTROPHYSICAL JOURNAL, 602(1) (1), 93 - 102, English

  Scientific journal


• Dynamics of intermediate mass black holes in star clusters

  H Baumgardt, SFP Zwart, SLW McMillan, J Makino, T Ebisuzaki

  We have followed the evolution of multi-mass star clusters containing massive central black holes by N-body simulations on the GRAPE6 Computers of Tokyo University. We find a strong cluster expansion and significant structural changes of the clusters. Clusters with IMBHs have power-law density profiles p similar to r(-alpha) with slopes alpha = 1.55 inside the influence sphere of the central black hole. This leads to a constant density profile of bright stars in projection, which rules out the presence of intermediate mass black holes in core collapse clusters. If the star clusters are surrounded by a tidal field, a central IMBH speeds up the destruction of the cluster until a remnant of a few hundred stars remains, which stays bound to the IMBH for a long time. We also discuss the efficiency of different detection mechanisms for finding IMBHs in star clusters.

  ASTRONOMICAL SOC PACIFIC, 2004, Formation and Evolution of Massive Young Star Clusters, 322, 459 - 467, English

  [Refereed]

  International conference proceedings


• Inner structure of dark matter halos

  T Fukushige, A Kawai, J Makino

  We investigate the structure of the dark matter halo formed in the cold dark matter scenarios by N-body simulations with parallel treecode on GRAPE cluster systems (Fukushige, Kawai, Makino 2003). We simulated 8 halos with the mass of 4.4 x 10(14) M-circle dot to 1.6 x 10(15) M-circle dot in the SCDM and LCDM model using up to 30 million particles. With the resolution of our simulations, the density profile is reliable down to 0.2 percent of the virial radius. Our results show that the slope of inner cusp within 1 percent virial radius is shallower than -1.5, and the radius where the shallowing starts exhibits run-to-run variation, which means the innermost profile is not universal.

  ASTRONOMICAL SOC PACIFIC, 2004, DARK MATTER IN GALAXIES, (220) (220), 99 - 100, English

  [Refereed]

  Scientific journal


• Intermediate mass black holes in star clusters

  H Baumgardt, J Makino

  We have performed N-body simulations of the formation of intermediate mass black holes in young star clusters and the subsequent dynamical evolution of star clusters containing massive black holes. Our simulations show that runaway merging of massive main-sequence stars can produce an intermediate mass black hole in the M82 cluster MGG-11 if the initial concentration of this cluster is larger than a King W-0 = 9 model. This explains the detection of an ultra-luminous X-ray source in this cluster by Matsumoto et al. [Astrophys. J. 547 (2001), L25]. We also find that clusters with intermediate mass black holes evolve to have constant density cores in projection, which makes it unlikely that galactic core collapse globular clusters contain black holes.

  PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE, 2004, PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT, (155) (155), 313 - 314, English

  [Refereed]

  Scientific journal


• Black holes in massive star clusters

  S McMillan, H Baumgardt, SIP Zwart, P Hut, J Makino

  Close encounters and physical collisions between stars in young dense clusters can result in new channels for stellar evolution, and may lead to the formation of very massive stars and black holes via runaway merging. We present some details of this process, using the results of N-body simulations and simple analytical estimates to place limits on the cluster parameters for which it expected to occur. For small clusters, the mass of the runaway is effectively limited by the total number of high-mass stars in the system. For larger clusters, the runaway mass is determined by the fraction of stars that can mass-segregate to the cluster core while still on the main sequence. In typical cases, the result is in the range commonly cited for intermediate-mass black holes. This mechanism may therefore have important implications for the formation of massive black holes and black-hole binaries in dense cluster cores.

  ASTRONOMICAL SOC PACIFIC, 2004, Formation and Evolution of Massive Young Star Clusters, 322, 449 - 457, English

  [Refereed]

  International conference proceedings


• A Fast Parallel Treecode with GRAPE

  MAKINO J

  Astronomical Society of Japan, 2004, PASJ, 56(3) (3), 521 - 531, English


• GRAPE-6: Massively-parallel special-purpose computer for astrophysical particle simulations

  J Makino, T Fukushige, M Koga, K Namura

  In this paper, we describe the architecture and performance of the GRAPE-6 system, a massively-parallel special-purpose computer for astrophysical N-body simulations. GRAPE-6 is the successor of GRAPE-4, which was completed in 1995 and achieved the theoretical peak speed of 1.08 Tflops. As was the case with GRAPE-4, the primary application of GRAPE-6 is simulations of collisional systems, though it can also be used for collisionless systems. The main differences between GRAPE-4 and GRAPE-6 are (a) the processor chip of GRAPE-6 integrates 6 force-calculation pipelines, compared to one pipeline of GRAPE-4 (which needed 3 clock cycles to calculate one interaction), (b) the clock speed is increased from 32 to 90 MHz, and (c) the total number of processor chips is increased from 1728 to 2048. These improvements resulted in a peak speed of 64 Tflops. We also discuss the design of the successor of GRAPE-6.

  OXFORD UNIV PRESS, Dec. 2003, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 55(6) (6), 1163 - 1187, English

  Scientific journal


• Dynamical formation of close binary systems in globular clusters

  D Pooley, WHG Lewin, SF Anderson, H Baumgardt, AV Filippenko, BM Gaensler, L Homer, P Hut, VM Kaspi, J Makino, B Margon, S McMillan, S Portegies Zwart, M van der Klis, F Verbunt

  We know from observations that globular clusters are very efficient catalysts in forming unusual short-period binary systems or their offspring, such as low-mass X-ray binaries (LMXBs; neutron stars accreting matter from low-mass stellar companions), cataclysmic variables ( white dwarfs accreting matter from stellar companions), and millisecond pulsars ( rotating neutron stars with spin periods of a few milliseconds). Although there has been little direct evidence, the overabundance of these objects in globular clusters has been attributed by numerous authors to the high densities in the cores, which leads to an increase in the formation rate of exotic binary systems through close stellar encounters. Many such close binary systems emit X-radiation at low luminosities (L-x less than or similar to 10(34) ergs s(-1)) and are being found in large numbers through observations with the Chandra X-Ray Observatory. Here we present conclusive observational evidence of a link between the number of close binaries observed in X-rays in a globular cluster and the stellar encounter rate of the cluster. We also make an estimate of the total number of LMXBs in globular clusters in our Galaxy.

  IOP PUBLISHING LTD, Jul. 2003, ASTROPHYSICAL JOURNAL, 591(2) (2), L131 - L134, English

  Scientific journal


• Structure of dark matter halos from hierarchical clustering. II. Dependence of cosmological models in cluster-sized halos

  T Fukushige, J Makino

  We investigate the structure of the dark matter halos formed in three different cold dark matter scenarios using N-body simulations of 13 cluster-sized halos. With the resolution of our simulations, the density pro. le is reliable down to similar to1% of the virial radius. In all runs, density cusps proportional to r(-1.5) developed down to the reliable limit. This result was independent of the cosmological models we simulated. We could not reproduce the cusp shallower than r(-1.5), which was obtained in some previous studies.

  UNIV CHICAGO PRESS, May 2003, ASTROPHYSICAL JOURNAL, 588(2) (2), 674 - 679, English

  Scientific journal


• Parameters of core collapse

  H Baumgardt, DC Heggie, P Hut, J Makino

  This paper considers the phenomenon of deep core collapse in collisional stellar systems, with stars of equal mass. The collapse takes place on some multiple, xi(-1), of the central relaxation time, and produces a density profile in which rho proportional to r(-alpha), where alpha is a constant. The parameters alpha and xi have usually been determined from simplified models, such as gas and Fokker-Planck models, often with the simplification of isotropy. Here we determine the parameters directly from N-body simulations carried out using the newly completed GRAPE-6.

  BLACKWELL PUBLISHING LTD, May 2003, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 341(1) (1), 247 - 250, English

  Scientific journal


• MODEST-1: Integrating stellar evolution and stellar dynamics

  P Hut, MM Shara, SJ Aarseth, RS Klessen, JC Lombardi, J Makino, S McMillan, OR Pols, PJ Teuben, RF Webbink

  We summarize the main results from MODEST-1, the first workshop on Modeling DEnse STellar systems. Our goal is to go beyond traditional population synthesis models, by introducing dynamical interactions between single stars, binaries, and multiple systems. The challenge is to define and develop a software framework to enable us to combine in one simulation existing computer codes in stellar evolution, stellar dynamics, and stellar hydrodynamics. With this objective, the workshop brought together experts in these three fields, as well as other interested astrophysicists and computer scientists. We report here our main conclusions, questions and suggestions for further steps toward integrating stellar evolution and stellar (hydro)dynamics. (C) 2002 Elsevier Science B.V. All rights reserved.

  ELSEVIER SCIENCE BV, May 2003, NEW ASTRONOMY, 8(4) (4), 337 - 370, English


• A dynamical model for the globular cluster G1

  H Baumgardt, J Makino, P Hut, S McMillan, S Portegies Zwart

  We present a comparison between the observational data on the kinematical structure of G1 in M31, obtained with the Hubble Space Telescope Wide Field Planetary Camera 2 and Space Telescope Imaging Spectrograph instruments, and the results of dynamical simulations carried out using the special purpose computer GRAPE-6. We have obtained good fits for models starting from single-cluster King model initial conditions and even better fits when starting our simulations with a dynamically constructed merger product of two star clusters. In the latter case, the results from our simulations are in excellent agreement with the observed profiles of luminosity, velocity dispersion, rotation, and ellipticity. We obtain a mass-to-light ratio of M/L = 4.0 +/- 0.4 and a total cluster mass of M = (8 +/- 1) x 10(6) M-.. Given that our dynamical model can fit all available observational data very well, there seems to be no need to invoke the presence of an intermediate-mass black hole in the center of G1.

  IOP PUBLISHING LTD, May 2003, ASTROPHYSICAL JOURNAL, 589(1) (1), L25 - L28, English

  Scientific journal


• Dynamical evolution of star clusters in tidal fields

  H Baumgardt, J Makino

  We report the results of a large set of N-body calculations aimed at studying the evolution of multimass star clusters in external tidal fields. Our clusters start with the same initial mass functions, but varying particle numbers, orbital types and density profiles. Our main focus is to study how the stellar mass function and other cluster parameters change under the combined influence of stellar evolution, two-body relaxation and the external tidal field. We find that the lifetimes of star clusters moving on similar orbits scale as T similar toT(rh)(x), where T-rh is the relaxation time, and the exponent x depends on the initial concentration of the cluster and is around x approximate to 0.75. The scaling law does not change significantly if one goes from circular orbits to eccentric ones. From the results for the lifetimes, we predict that between 53 and 67 per cent of all Galactic globular clusters will be destroyed within the next Hubble time. Low-mass stars are preferentially lost and the depletion is strong enough to turn initially increasing mass functions into mass functions that decrease towards the low-mass end. The details of this depletion are insensitive to the starting condition of the cluster and can be characterized as a function of a single variable, such as, for example, the fraction of time spent until total cluster dissolution. The preferential depletion of low-mass stars from star clusters leads to a decrease of their mass-to-light ratios except for a short period close to final dissolution, when the mass fraction in the form of compact remnants starts to dominate. The fraction of compact remnants increases throughout the evolution. They are more strongly concentrated towards the cluster cores than main-sequence stars and their mass fraction in the centre can reach 95 per cent or more around and after core collapse. For a sample of Galactic globular clusters with well-observed parameters, we find a correlation between the observed slope of the mass function and the lifetimes predicted by us. It seems possible that Galactic globular clusters started with a mass function similar to what one observes for the average mass function of the Galactic disc and bulge.

  BLACKWELL PUBLISHING LTD, Mar. 2003, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 340(1) (1), 227 - 246, English

  Scientific journal


• Performance evaluation and tuning of GRAPE-6 - Towards 40 "real" Tflops

  Junichiro Makino, Eiichiro Kokubo, Toshiyuki Fukushige, Hiroshi Daisaka

  In this paper, we describe the performance characteristics of GRAPE-6, the sixth-generation special-purpose computer for gravitational many-body problems. GRAPE-6 consists of 2048 custom pipeline chips, each of which integrates six pipeline processors specialized for the calculation of gravitational interaction between particles. The GRAPE hardware performs the evaluation of the interaction. The frontend processors perform all other operations, such as the time integration of the orbits of particles, I/O, on-the-fly analysis etc. The theoretical peak speed of GRAPE-6 is 63.4 Tflops. We present the result of benchmark runs, and discuss the performance characteristics. We also present the measured performance for a few real scientific applications. The best performance so far achieved with real applications is 35.3 Tflops. © 2003 ACM.

  2003, Proceedings of the 2003 ACM/IEEE Conference on Supercomputing, SC 2003, English

  [Refereed]

  International conference proceedings


• Collisional dynamics of binary black holes in galactic centres

  R Spurzem, M Hemsendorf, S Sigurdsson, M Benacquista, J Makino

  We follow the sinking of two massive black holes in a spherical stellar system by means of high precision direct N-body simulation. The massive particles become bound under the regime of dynamical friction. Once bound, the binary hardens by superelastic three body encounters with surrounding stars. It is found that the cumulative effect of many of such resonant encounters keeps the black hole binary at a very high eccentricity and helps to bring the black holes close enough together that they can merge by gravitational radiation in a time scale of the order of 10(8) years (avoiding the stalling problem). While most of our study presently uses an idealized system (equal black hole masses, flat galactic core) more simulations are under way which vary black hole mass ratios. We discuss the situation in the recently discovered double black hole nucleus. in NGC6240 (see this conference) in light of our results. Recent models of one of the authors (JM) show, that the presence of a third black hole in a dense nucleus after another merger took place could enhance the eccentricity of a black hole binary even more dramatically. The detectability of gravitational waves via pulsar timing from such extremely eccentric black holes is estimated.

  AMER INST PHYSICS, 2003, ASTROPHYSICS OF GRAVITATIONAL WAVE SOURCES, 686, 235 - 238, English

  [Refereed]

  International conference proceedings


• To circularize or not to circularize? Orbital evolution of satellite galaxies

  Y Hashimoto, Y Funato, J Makino

  We investigate the orbital evolution of satellite galaxies using numerical simulations. It has long been believed that orbits suffer circularization due to dynamical friction from the galactic halo during orbital decay. This circularization was confirmed by numerous simulations in which dynamical friction was added as an external force. However, some of the recent N-body simulations have demonstrated that circularization is much slower than expected from approximate calculations. We find that the dominant reason for this discrepancy is the assumption that the Coulomb logarithm log Lambda is constant, which has been used in practically all recent calculations. Since the size of the satellite is relatively large, an accurate determination of the outer cutoff radius is crucial to obtaining a good estimate for the dynamical friction. An excellent agreement between N-body simulations and approximate calculations is observed when the outer cutoff radius is taken to be the distance of the satellite to the center of the galaxy. When the satellite is at the perigalacticon, the distance to the center is smaller, and therefore log Lambda becomes smaller. As a result, the dynamical friction becomes less effective. We apply our result to the Large Magellanic Cloud (LMC). We find that the expected lifetime of the LMC is twice as long as that which would be predicted with previous calculations. Previous studies predict that the LMC will merge into the Milky Way after 7 Gyr, while we find that the merging will take place 14 Gyr from now. Our result suggests that generally, satellites formed around a galaxy have longer lifetimes than previous estimates.

  UNIV CHICAGO PRESS, Jan. 2003, ASTROPHYSICAL JOURNAL, 582(1) (1), 196 - 201, English

  Scientific journal


• On the central structure of M15

  H Baumgardt, P Hut, J Makino, S McMillan, S Portegies Zwart

  We present a detailed comparison between the latest observational data on the kinematical structure of the core of M15, obtained with the Hubble Space Telescope Space Telescope Imaging Spectrograph and Wide Field Planetary Camera 2 instruments, and the results of dynamical simulations carried out using the special purpose GRAPE-6 computer. The observations imply the presence of a significant amount of dark matter in the cluster core. In our dynamical simulations, neutron stars and/or massive white dwarfs concentrate to the center through mass segregation, resulting in a sharp increase in toward the center. While consistent with the presence of M/L a central black hole, the Hubble Space Telescope data can also be explained by this central concentration of stellar mass compact objects. The latter interpretation is more conservative, since such remnants result naturally from stellar evolution, although runaway merging leading to the formation of a black hole may also occur for some range of initial conditions. We conclude that no central massive object is required to explain the observational data, although we cannot conclusively exclude such an object at the level of. Our findings are similar to500-1000 M-circle dot. Our findings are unchanged when we reduce the assumed neutron star retention fraction in our simulations from 100% to 0%.

  IOP PUBLISHING LTD, Jan. 2003, ASTROPHYSICAL JOURNAL, 582(1) (1), L21 - L24, English

  Scientific journal


• An efficient parallel algorithm for O(N-2) direct summation method and its variations on distributed-memory parallel machines

  J Makino

  We present a novel, highly efficient algorithm to parallelize O(N-2) direct summation method for N-body problems with individual timesteps on distributed-memory parallel machines such as Beowulf clusters. Previously known algorithms, in which all processors have complete copies of the N-body system, has the serious problem that the communication-computation ratio increases as we increase the number of processors, since the communication cost is independent of the number of processors. In the new algorithm, p processors are organized as a rootp x rootp two-dimensional array. Each processor has N/rootp particles, but the data are distributed in such a way that complete system is presented if we look at any row or column consisting of rootp processors. In this algorithm, the communication cost scales as N/rootp, while the calculation cost scales as N-2/p. Thus, we can use a much larger number of processors without losing efficiency compared to what was practical with previously known algorithms. (C) 2002 Elsevier Science B.V. All rights reserved.

  ELSEVIER SCIENCE BV, Oct. 2002, NEW ASTRONOMY, 7(7) (7), 373 - 384, English

  Scientific journal


• Collisional evolution of galaxy clusters and the growth of common halos

  K Takahashi, T Sensui, Y Funato, J Makino

  We investigated the dynamical evolution of clusters of galaxies in virial equilibrium using Fokker-Planck models and self-consistent N-body models. In particular, we focused on the growth of a common halo, which is a cluster-wide halo formed by matter stripped from galaxies, and the development of a central density cusp. The Fokker-Planck models include the effects of two-body gravitational encounters both between galaxies and between galaxies and common halo particles. The effects of tidal mass stripping from the galaxies due to close galaxy-galaxy encounters and accompanying dissipation of the orbital kinetic energies of the galaxies were also taken into account in the Fokker-Planck models. We find that the results of the Fokker-Planck models are in excellent agreement with those of the N-body models regarding the growth of the common halo mass and the evolution of the cluster density profiles. In the central region of the cluster, a shallow density cusp, approximated by rho(r) infinity r(-alpha) (alpha similar to 1), develops. This shallow cusp results from the combined effects of two-body relaxation and tidal stripping. The cusp steepness, alpha, weakly depends on the relative importance of the tidal Stripping. When the effect of stripping is important, the central velocity dispersion decreases as the central density increases and, consequently, a shallow (alpha < 2) cusp is formed. In the limit of no stripping, usual gravothermal core collapse occurs, i.e. the central velocity dispersion increases as the central density increases with a steep (alpha > 2) cusp left. We conclude from our consideration of the origin of the cusp demonstrated here that shallow cusps should develop in real galaxy clusters.

  OXFORD UNIV PRESS, Feb. 2002, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 54(1) (1), 5 - 20, English

  Scientific journal


• A 29.5 Tflops simulation of planetesimals in Uranus-Neptune region on GRAPE-6

  Junichiro Makino, Eiichiro Kokubo, Toshiyuki Fukushige, Hiroshi Daisaka

  As an entry for the 2002 Gordon Bell performance prize, we report the performance achieved on the GRAPE-6 system for a simulation of the early evolution of the protoplanet-planetesimal system of the Uranus-Neptune region. GRAPE-6 is a special-purpose computer for astrophysical N-body calculations. The present configuration has 2048 custom pipeline chips, each containing six pipeline processors for the calculation of gravitational interactions between particles. Its theoretical peak performance is 63.4 Tflops. The actual performance obtained was 29.5 Tflops, for a simulation of the early evolution of outer Solar system with 1.8 million planetesimals and two massive protoplanets.

  Association for Computing Machinery, 2002, Proceedings of the International Conference on Supercomputing, 2002-, English

  International conference proceedings


• An efficient parallel algorithm for 0(N2) direct summation method and its variations on distributed-memory parallel machines

  Junichiro Makino

  We present a novel, highly efficient algorithm to parallelize 0(N 2) direct summation method for N-body problems with individual timesteps on distributed-memory parallel machines such as Beowulf clusters. Previously known algorithms, in which all processors have complete copies of the N-body system, has the serious problem that the communication-computation ratio increases as we increase the number of processors, since the communication cost is independent of the number of processors. In the new algorithm, p processors are organized as a √p X√p two-dimensional array. Each processor has N/√p particles, but the data are distributed in such a way that complete system is presented if we look at any row or column consisting of √p processors. In this algorithm, the communication cost scales as N/√p, while the calculation cost scales as N2 /p. Thus, we can use a much larger number of processors without losing efficiency compared to what was practical with previously known algorithms. © 2002 Elsevier Science B.V. All rights reserved.

  Elsevier, 2002, New Astronomy, 7(7) (7), 373 - 384, English

  [Refereed]

  Scientific journal


• Runaway collisions in star clusters

  SFP Zwart, J Makino, SLW McMillan, P Hut

  We study the occurrence of physical collisions between stars in young and compact star clusters. The calculations are performed on the GRAPE-4 with the starlab software environment which include the dynamical evolution and the nuclear evolution of all stars and binaries. The selection of the initial conditions is based on existing and well observed star clusters, such as R136 in the 30 Doradus region in the Large Magellanic Cloud and the Arches and Quintuplet star clusters in the vicinity of the Galactic center. Collisions between stars occurred rather frequently in our models. At any time a single star dominates the collision history of the system. The collision rate of this runaway merger scales with the initial relaxation time of the cluster and is independent of other cluster parameters, such as the initial mass function or the initial density profile of the cluster. Subsequent encounters result in a steady growth in mass of the coagulating star, until it escapes or explodes in a supernova. The collision rate in these models is about 2.2 x 10(-4) collisions per star per Myr for a cluster with an initial relaxation time of I Myr.

  ASTRONOMICAL SOC PACIFIC, 2002, STELLAR COLLISIONS, MERGERS, AND THEIR CONSEQUENCES, 263, 95 - 109, English

  [Refereed]

  International conference proceedings


• Theory in a Virtual Observatory

  P Teuben, D DeYoung, P Hut, S Levy, J Makino, S McMillan, SP Zwart, S Slavin

  During the last couple of years, observers have started to make plans for a Virtual Observatory, as a federation of existing databases, connected through levels of software that enable rapid searches, correlations, and various forms of data mining. We propose to extend the notion of a Virtual Observatory by adding archives of simulations, together with interactive query and visualization capabilities, as well as ways to simulate observations of simulations in order to compare them with observations. For this purpose, we have already organized two small workshops, earlier in 2001, in Tucson and Aspen. We have also provided concrete examples of theory data, designed to be federated with a Virtual Observatory. These data stem from a project to construct an archive for our large-scale simulations using the GRAPE-6 (a 32-Teraflops special purpose computer for stellar dynamics). We are constructing interfaces by which remote observers can observe these simulations. In addition, these data will enable detailed comparisons between different simulations.

  ASTRONOMICAL SOC PACIFIC, 2002, ASTRONOMICAL DATA ANALYSIS SOFTWARE AND SYSTEMS XI, 281, 7 - 10, English

  [Refereed]

  International conference proceedings


• Heterogeneous multi-computer system: A new paradigm of parallel processing

  T Boku, J Makino, H Susa, M Umemura, T Fukushige, A Ukawa

  HMCS (Heterogeneous Multi-Computer System) is a new parallel processing platform combining massively parallel processors for continuum simulation and particle simulation to realize multi-scale computational physics simulations. We constructed a prototype system of HMCS with a general purpose scientific parallel processor CP-PACS and a gravity calculation parallel processor GRAPE-6 connecting them via commodity-base parallel network. On the prototype of HMCS, a microscopic gravity calculation on GRAPE-6 and a macroscopic radiation hydrodynamics calculation on CP-PACS are performed simultaneously to realize detailed simulation on computational astro-physics. In this paper we report the overall concept, design and implementation of HMCS as well as the result of a novel computational simulation for galaxy formation.

  IEEE COMPUTER SOC, 2002, PAR ELEC 2002: INTERNATIONAL CONFERENCE ON PARALLEL COMPUTING IN ELECTRICAL ENGINEERING, 3 - 8, English

  [Refereed]

  International conference proceedings


• Heterogeneous Multi-Computer System: A New Platform for Multi-Paradigm Scientific Simulation

  T., Boku, J., Makino, H., Susa, M., Umemura, T., Fukushige, A., Ukawa

  Jan. 2002, Proc. of ICS2002, New York, 26-34, English

  [Refereed]

  International conference proceedings


• Hydrodynamics in astrophysics with gravity on Heterogeneous Multi-Computer System

  T., Boku, J., Makino, H., Susa, M., Umemura, T., Fukushige, and, A. Ukawa

  Jan. 2002, IPSJ Transactions on High Performance Computing Systems, 41, 5, Japanese

  [Refereed]

  Scientific journal


• Missing link found? The "runaway" path to supermassive black holes

  T Ebisuzaki, J Makino, TG Tsuru, Y Funato, S Portegies Zwart, P Hut, S McMillan, S Matsushita, H Matsumoto, R Kawabe

  Observations of stellar kinematics, gasdynamics, and masers around galactic nuclei have now firmly established that many galaxies host central supermassive black holes (SMBHs) with masses in the range of similar to 10(6)-10(9) M-.. However, how these SMBHs formed is not well understood. One reason for this situation is the lack of observations of intermediate-mass BHs (IMBHs), which could bridge the gap between stellar mass BHs and SMBHs. Recently, this missing link (i.e., an IMBH) has been found in observations made by ASCA and Chandra of the central region of the starburst galaxy M82. Subsequent observations by Subaru have revealed that this IMBH apparently coincides with a young compact star cluster. Based on these findings, we suggest a new formation scenario for SMBHs. In this scenario, IMBHs first form in young compact star clusters through runaway merging of massive stars. While these IMBHs are forming, the host star clusters sink toward the galactic nucleus through dynamical friction and upon evaporation deposit their IMBHs near the galactic center. The IMBHs then form binaries and eventually merge via gravitational radiation, forming an SMBH.

  IOP PUBLISHING LTD, Nov. 2001, ASTROPHYSICAL JOURNAL, 562(1) (1), L19 - L22, English

  Scientific journal


• GRAPE project: special-purpose computers for many-body simulations

  J Makino

  In this paper, we overview the GRAPE (GRAvity piPE) project to develop and use special-purpose computers for astrophysical many-body simulations. First, we discuss the trends in semiconductor technology and computer architecture, and discuss merits and demerits of special-purpose computers. The main advantage of the special-purpose systems is the possibility to utilize a much higher fraction of available silicon to actually do calculations. Most of the silicon on general-purpose microprocessors are now used for control logics and cache, in other words, to assure the generality. As an example, we describe our GRAPE project. In astrophysical many-body simulations, practically all computer time is spent to evaluate particle-particle interactions. This is because the gravitational interaction between astrophysical bodies is a long-range interaction and we cannot apply a cutoff. The basic idea behind the GRAPE project is let the special-purpose computer perform only the evaluation of the particle-particle interaction. All the rest of the calculation, such as the time integration of the orbits of particles, I/O, and diagnostics are handled by a general-purpose host computer. This partitioning has many important advantages, such as the ease of the development of the hardware, the flexibility of the overall system and long lifetime of the system. The newest machine, GRAPE-6, which will be completed soon, will provide the peak speed exceeding 100 Tflops, for the development cost of less than 5 M dollars. (C) 2001 Elsevier Science B.V. All rights reserved.

  ELSEVIER SCIENCE BV, Sep. 2001, COMPUTER PHYSICS COMMUNICATIONS, 139(1) (1), 45 - 54, English

  Scientific journal


• Structure of dark matter halos from hierarchical clustering

  T Fukushige, J Makino

  We investigate the structure of the dark matter halo formed in the cold dark matter scenario using N-body simulations. We simulated 12 halos with masses of 6.6 x 10(11)-8.0 x 10(14) M-circle dot. In all runs, the halos have density cusps proportional to r(-1.5) developed at their centers, which is consistent with the results of recent high-resolution calculations. The density structure evolves in a self-similar way and is universal in the sense that it is independent of the halo mass and initial random realization of density fluctuation. The density profile is in good agreement with the profile proposed by Moore et al., which has a central slope proportional to r(-1.5) and an outer slope proportional to r(-3). The halo grows through repeated accretion of diffuse smaller halos. We argue that the cusp is understood as a convergence slope for the accretion of tidally disrupted matter.

  UNIV CHICAGO PRESS, Aug. 2001, ASTROPHYSICAL JOURNAL, 557(2) (2), 533 - 545, English

  Scientific journal


• Pseudoparticle multipole method: A simple method to implement a high-accuracy tree code

  A Kawai, J Makino

  In this Letter, we describe the pseudoparticle multipole method ((PM2)-M-2), which is a new method to express multipole expansion by a distribution of pseudoparticles. We can use this distribution of particles to calculate high-order terms in both the Barnes-Hut tree code and the fast multipole method. The primary advantage of (PM2)-M-2 is that it works on GRAPE (GRAvity PipE). GRAPE is special-purpose hardware for the calculation of the gravitational force between particles. Although the tree code has been implemented on GRAPE, we could only handle terms up to a dipole since GRAPE can calculate forces from point-mass particles only. Thus, the calculation cost grows quickly when high accuracy is required. With (PM2)-M-2, the multipole expansion is expressed by particles, and thus GRAPE can calculate high-order terms. Using (PM2)-M-2, we implemented an arbitrary-order tree code on GRAPE-4. The timing result shows that GRAPE-4 accelerates the calculation by a factor of between 10 (for low accuracy) and 100 (for high accuracy). Even on general-purpose programmable computers, our method offers the advantage that the mathematical formulae, and therefore the actual program, are much simpler than that of the direct implementation of multipole expansion, although the calculation cost becomes somewhat higher.

  UNIV CHICAGO PRESS, Apr. 2001, ASTROPHYSICAL JOURNAL, 550(2) (2), L143 - L146, English

  Scientific journal


• Star cluster ecology - IV. Dissection of an open star cluster: photometry

  S Portegies Zwart, SLW McMillan, P Hut, J Makino

  The evolution of star clusters is studied using N-body simulations in which the evolution of single stars and binaries is taken self-consistently into account. Initial conditions are chosen to represent relatively young Galactic open clusters, such as the Pleiades, Praesepe and the Hyades. The calculations include a realistic mass function, primordial binaries and the external potential of the parent Galaxy. Our model clusters are generally significantly flattened by the Galactic tidal field, and dissolve before deep core collapse occurs. The binary fraction decreases initially because of the destruction of soft binaries, but increases later because lower mass single stars escape more easily than the more massive binaries. At late times, the cluster core is quite rich in giants and white dwarfs. There is no evidence for preferential evaporation of old white dwarfs. On the contrary, the white dwarfs formed are likely to remain in the cluster. Stars tend to escape from the cluster through the first and second Lagrange points, in the direction of and away from the Galactic Centre. Mass segregation manifests itself in our models well within an initial relaxation time. As expected, giants and white dwarfs are much more strongly affected by mass segregation than main-sequence stars. Open clusters are dynamically rather inactive. However, the combined effects of stellar mass-loss and evaporation of stars from the cluster potential drive the dissolution of a cluster on a much shorter time-scale than if these effects are neglected. The often-used argument that a star cluster is barely older than its relaxation time and therefore cannot be dynamically evolved is clearly iri error for the majority of star clusters. An observation of a blue straggler in an eccentric orbit around an unevolved star or a blue straggler of more than twice the turn-off mass might indicate past dynamical activity. We find two distinct populations of blue stragglers: those formed above the main-sequence turnoff, and those which appear as,blue stragglers as the cluster's turn-off drops below the mass of the rejuvenated star.

  OXFORD UNIV PRESS, Feb. 2001, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 321(2) (2), 199 - 226, English


• Evolution of clusters of galaxies

  T Sensui, Y Funato, J Makino

  We investigated dynamical evolution of clusters of galaxies using self-consistent N-body simulations. We found that about half of the total mass was stripped from galaxies into the intracluster space in a few crossing times of the cluster. This stripped mass formed a cluster-wide common halo. Growth rate of the common halo depends only weakly on the ratio between the sizes of the cluster and its member galaxies. In the central region of a cluster, the mass density shows the cusp with rho proportional to r(-1 similar to1.5).

  ASTRONOMICAL SOC PACIFIC, 2001, PHYSICS OF GALAXY FORMATION, PROCEEDINGS, 222, 401 - 404, English

  [Refereed]

  International conference proceedings


• Star clusters simulations using GRAPE-5

  T Fukushige, A Kawai, J Makino

  We discuss star clusters simulations using GRAPE(GRAvity PipE)-5. GRAPE-5 is a new version of special-purpose computer for many-body simulation, GRAPE. We present some results of simulations using the GRAPE-5 system.

  ASTRONOMICAL SOC PACIFIC, 2001, DYNAMICS OF STAR CLUSTERS AND THE MILKY WAY, 228, 434 - 436, English

  [Refereed]

  International conference proceedings


• How many young star clusters exist in the Galactic center?

  S Portegies Zwart, J Makino, SLW McMillan, P Hut

  We study the evolution and observability of young compact star clusters within similar to 200 pc of the Galactic center. Calculations are performed using direct N-body integration on the GRAPE-4, including the effects of both stellar and binary evolution and the external influence of the Galaxy. The results of these detailed calculations are used to calibrate a simplified model applicable over a wider range of cluster initial conditions. We find that clusters within 200 pc of the Galactic center dissolve within similar to 70 Myr. However, their projected densities drop below the background density in the direction of the Galactic center within similar to 20 Myr, effectively making these clusters undetectable after that time. Clusters farther from the Galactic center but at the same projected distance are more strongly affected by this selection effect and may go undetected for their entire lifetimes. Based on these findings, we conclude that the region within 200 pc of the Galactic center could easily harbor some 50 clusters with properties similar to those of the Arches or the Quintuplet systems.

  IOP PUBLISHING LTD, Jan. 2001, ASTROPHYSICAL JOURNAL, 546(2) (2), L101 - L104, English

  Scientific journal


• Evolution of a circumterrestrial disk and formation of a single moon

  E Kokubo, S Ida, J Makino

  We investigate the evolution of a circumterrestrial disk of debris generated by a giant impact on Earth and the dynamical characteristics of the moon accreted from the disk by using high-resolution N-body simulation. We find that in most cases the disk evolution results in the formation of a single large moon on a nearly circular orbit close to the equatorial plane of the initial disk just outside the Roche limit, which is consistent with the previous work by S. Ida et al, (1997, Nature 389, 353-357), The efficiency of incorporation of disk material into a moon is 10-55%, which increases with the initial specific angular momentum of the disk. These results hardly depend on the initial condition of the disk as long as the mass of the disk is 2 to 4 times the present lunar mass and most mass of the disk exists inside the Roche limit. The timescale of the disk evolution is determined mainly by the surface density of the disk because mass transfer to the outside of the Roche limit and formation of lunar seeds are regulated by collective behavior of disk particles. The evolution of the disk is summarized as follows: The disk contracts through collisional damping. As the velocity dispersion of disk particles decreases, particle clumps grow inside the Roche limit, The clumps become elongated due to Keplerian shear, which forms spiral arm-like structure. Particles are transfered to the outside of the Roche limit through the gravitational torque exerted by the spiral arms, When a tip of a spiral arm goes beyond the Roche limit, it collapses into a small moonlet, The rapid accretion of these small moonlets forms a lunar seed, The seed exclusively grows by sweeping up particles transfered over the Roche limit. When the moon becomes large enough to gravitationally dominate the disk, it pushes the rest of the inner disk to Earth, The formation timescale of the moon is of the order of 1 month if a particulate disk is assumed and the effect of melting/vaporization is not included. (C) 2000 Academic Press.

  ACADEMIC PRESS INC, Dec. 2000, ICARUS, 148(2) (2), 419 - 436, English

  Scientific journal


• PROGRAPE-1: A programmable, multi-purpose computer for many-body simulations

  T Hamada, T Fukushige, A Kawai, J Makino

  We have developed PROGRAPE-1 (PROgrammable GRAPE-1), a programmable multi-purpose computer for many-body simulations. The main difference between PROGRAPE-1 and "traditional" GRAPE systems is that the former uses FPGA (Field Programmable Gate Array) chips as the processing elements, while the latter relies on a hardwired pipeline processor specialized to gravitational interactions. Since the logic implemented in FPGA chips can be reconfigured, we can use PROGRAPE-1 to calculate not only gravitational interactions, but also other forms of interactions, such as the van der Waals force, hydrodynamical interactions in the SPHr calculation, and so on. PROGRAPE-1 comprises two Altera EPF10K100 FPGA chips, each of which contains nominally 100000 gates. To evaluate the programmability and performance of PROGRAPE-1, we implemented a pipeline for gravitational interactions similar to that of GRAPE-3. One pipeline is fitted into a single FPGA chip, operated at 16 MHz clock. Thus, for gravitational interactions, PROGRAPE-1 provided a speed of 0.96 Gflops-equivalent. PROGRAPE will prove to be useful for a wide-range of particle-based simulations in which the calculation cost of interactions other than gravity is high, such as the evaluation of SPH interactions.

  OXFORD UNIV PRESS, Oct. 2000, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 52(5) (5), 943 - 954, English

  Scientific journal


• GRAPE-5: A special-purpose computer for N-body simulations

  A Kawai, T Fukushige, J Makino, M Taiji

  We have developed a special-purpose computer for gravitational many-body simulations, GRAPE-5. GRAPE-5 accelerates the force calculation which dominates the calculation cost of the simulation. All other calculations, such as the time integration of orbits, are performed on a general-purpose computer (host computer) connected to GRAPE-5. A GRAPE-5 board consists of eight custom pipeline chips (G5 chip) and its peak performance is 38.4 Gflops. GRAPE-5 is the successor of GRAPE-5. The differences between GRAPE-5 and GRAPE-S are: (1) The newly developed G5 chip contains two pipelines operating at 80 MHz, while the GRAPE chip, which was used for GRAPE-S, had one at 20 MHz. The calculation speed of GRAPE-5 is 8-times faster than that of GRAPE-5. (2) The GRAPE-5 board adopted a PCI bus as the interface to the host computer instead of VME of GRAPE-3, resulting in a communication speed one order of magnitude faster. (3) In addition to the pure 1/r potential, the G5 chip can calculate forces with arbitrary cutoff functions, so that it can be applied to the Ewald or (PM)-M-3 methods. (4) The pairwise force calculated on GRAPE-5 is about 10-times more accurate than that on GRAPE-3. On one GRAPE-5 board, one timestep with a direct summation algorithm takes 14 (N/128 k)(2) seconds. With the Barnes-Hut tree algorithm (theta = 0.75), one timestep can be done in 15(N/10(6)) seconds.

  OXFORD UNIV PRESS, Aug. 2000, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 52(4) (4), 659 - 676, English

  Scientific journal


• A 1.349 Tflops simulation of black holes in a galactic center on GRAPE-6

  Junichiro Makino, Toshiyuki Fukushige, Masaki Koga

  As an entry for the 2000 Gordon Bell performance prize, we report the performance achieved on a prototype GRAPE-6 system. GRAPE-6 is a special-purpose computer for astrophysical N-body calculations. The present configuration has 96 custom pipeline processors, each containing six pipeline processors for the calculation of gravitational interactions between particles. Its theoretical peak performance is 2.889 Tflops. The complete GRAPE-6 system will consist of 3072 pipeline chips and will achieve a peak speed of 100 Tflops. The actual performance obtained on the present 96-chip system was 1.349 Tflops, for a simulation of massive black holes embedded in the core of a galaxy with 786,432 stars. For a short benchmark run with 1,400,000 particles, the average speed was 1.640 Tflops.

  Association for Computing Machinery, 2000, Proceedings of the International Conference on Supercomputing, 2000-, English

  International conference proceedings


• GRAPE project: A decade of special-purpose computers for many-body simulations

  J Makino, M Koga, A Kawai, T Fukushige

  In this paper, we briefly overview the past history and future prospect of the GRAPE project to develop and use special-purpose computers for astrophysical many-body simulations. First we show that the "hardware efficiency" of general-purpose computers has been going down exponentially, and will continue to do so for the foreseeable future. Then, we describe the approach of building special-purpose computers as an alternative. With general-purpose design, we can use only a small fraction of available transistors on a chip, since most of the transistors are wasted in the control logic and the datapath between arithmetic units and the storage. With a special-purpose design, one can use virtually all transistors to implement arithmetic units, since little control logic is necessary and the datapath is fixed. This difference results in a huge difference in the price-performance, as is observed in GRAPE series hardwares. Of course, special-purpose computing is not a silver bullet. It has its limitations, we discuss these issues and possible alternatives. We also briefly describe the past of GRAPE project, and the status of GRAPE-B, which will be completed by the year 2001. It will provide the peak speed exceeding 100 Tflops, for the development cost of less than 4 M dollars.

  PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE, 2000, PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT, (138) (138), 622 - 631, English

  [Refereed]

  Scientific journal


• Evolution of clusters of galaxies: Mass stripping from galaxies and growth of common halos

  T Sensui, Y Funato, J Makino

  We investigated the evolution of clusters of galaxies using self-consistent N-body simulations in which each galaxy was modeled by many particles. We carried out simulations for about 20 cases using different initial conditions. In all simulations, clusters were initially in virial equilibrium. We found that more than half of the total mass escaped from individual galaxies within a few crossing times of the cluster, and that a diffuse halo was formed. The growth rate of the common halo depended on the size of individual galaxies only weakly. The stripping of the mass from galaxies was mainly due to the interaction of galaxies, not due to the effect of the tidal field of the cluster potential. The amount of stripped mass was larger for galaxies in the central region than for those in the outer region, since the interactions were more frequent in the central region. As a result, a positive correlation between the distance from the center and the mass of the galaxy developed. The volume-density profile of the common halo is expressed as p proportional to r(-1) in the central region. This mass distribution is consistent with the mass distribution in clusters estimated using X-ray observations.

  OXFORD UNIV PRESS, Dec. 1999, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 51(6) (6), 943 - 954, English

  Scientific journal


• On the cusp around central black holes in luminous elliptical galaxies

  T Nakano, J Makino

  In this Letter, we show that a massive black hole (MBH) that falls into the center of a galaxy on the dynamical timescale leaves a weak cusp (rho proportional to r(-1/2)) around it, which is in good agreement with the recent observations of luminous elliptical galaxies by the Hubble Space Telescope. Such an event is a natural outcome of the merging of two galaxies that have central MBHs, This is the only known mechanism for forming weak cusps in luminous elliptical galaxies, Therefore, the existence of the weak cusps indicates that the central black holes of luminous elliptical galaxies have fallen to the center from outside, most likely during a major merger event.

  UNIV CHICAGO PRESS, Nov. 1999, ASTROPHYSICAL JOURNAL, 525(2) (2), L77 - L80, English

  Scientific journal


• Star cluster ecology - III. Runaway collisions in young compact star clusters

  S Portegies Zwart, J Makino, SLW McMillan, P Hut

  The evolution of young compact star clusters is studied using N-body simulations in which both stellar evolution and physical collisions between stars are taken into account. The initial conditions are chosen to represent R 136, a compact star cluster in the 30 Doradus region of the Large Magellanic Cloud. The present runs do not include the effects of primordial binaries. We find that physical collisions between stars in these models are frequent, and that the evolution of the most mas sive stars and the dynamical evolution of the cluster are closely coupled. In all cases, a single star grows steadily in mass through mergers with other stars, forming a very massive ( greater than or similar to 100M.) star in less than 3-4 Myr. The growth rate of this runaway merger is much larger than estimates based on simple cross-section arguments, mainly because the star is typically found in the core and tends to form binaries with other massive stars there. The runaway is "rejuvenated" by each new collision, and its lifetime is extended considerably as a consequence. Observationally, such a star will appear in the Hertzsprung-Russell diagram as a blue straggler. When the runaway forms a black hole, the binary in which it is found is usually dissociated. We further investigate the sensitivity of the runaway to different formulations of mass loss from high-mass main sequence stars. We find that, while the runaway process is less pronounced in the presence of strong stellar winds, the basic effect persists even in the face of large mass loss.

  EDP SCIENCES S A, Aug. 1999, ASTRONOMY & ASTROPHYSICS, 348(1) (1), 117 - 126, English

  Scientific journal


• The stability of protoplanet systems

  K Yoshinaga, E Kokubo, J Makino

  We investigated the stability of 10 protoplanet systems using three-dimensional N-body simulations. We found that the time scale of instability T depends strongly on the initial random velocities v (eccentricities e and inclinations i) and orbital separations Delta a. For zero initial random velocities, we confirmed the result of Chambers et al. (1996, Icarus 119, 261-268) that Tis proportional to exp(Delta a). For finite random velocities, we found that T depends strongly on the initial random velocities. The relation between T and Delta a is still expressed as log T = b + c Delta a. However, both b and c depend on initial random velocities and the slope, b, becomes smaller for larger v. Even for relatively small initial eccentricities such as e similar to 2r(H)/a, where r(H) is the Hill radius, the time scale can be reduced by a factor of 10 compared with the case of the zero random velocity. Therefore, the time scale of the formation of inner planets might be much shorter than what implied by Chambers et al. (C) 1999 Academic Press.

  ACADEMIC PRESS INC, Jun. 1999, ICARUS, 139(2) (2), 328 - 335, English

  Scientific journal


• High-performance special-purpose computers in science

  T Fukushige, P Hut, J Makino

  IEEE COMPUTER SOC, Mar. 1999, COMPUTING IN SCIENCE & ENGINEERING, 1(2) (2), 12 - +, English

  [Refereed]

  Scientific journal


• Change in mass and energy of galaxies through mutual encounters

  Y Funato, J Makino

  We present the result of a systematic study of the evolution of galaxies through their encounters. We performed a series of numerical experiments of encounters of two galaxies and determined how the change of mass and binding energy depends on galaxy models and collision parameters. Using both numerical experiments and analytic theory, we found that the relation between the relative change of energy delta(E) and that of mass delta(M) of one galaxy per unit time is expressed as delta(E) similar or equal to 1.5 delta(M) if the evolution is solely due to encounters. This result suggests that when galaxies in a cluster evolve mainly through frequent encounters with each other, a relation sigma(4) similar to M develops between the mass M and the velocity dispersion sigma of the galaxies. If we assume that M/L is constant, this relation is equivalent to the Faber-Jackson relation, sigma(4) similar to L, which is observed for elliptical galaxies in a cluster of galaxies. This agreement with observations suggests that the encounters of galaxies play an important role in the evolution of galaxies in clusters.

  UNIV CHICAGO PRESS, Feb. 1999, ASTROPHYSICAL JOURNAL, 511(2) (2), 625 - 638, English

  Scientific journal


• Star cluster ecology: III. Runaway collisions in young compact star clusters

  S. F. Portegies Zwart, J. Makino, S. L.W. McMillan, P. Hut

  The evolution of young compact star clusters is studied using N-body simulations in which both stellar evolution and physical collisions between stars are taken into account. The initial conditions are chosen to represent R 136, a compact star cluster in the 30 Doradus region of the Large Magellanic Cloud. The present runs do not include the effects of primordial binaries. We find that physical collisions between stars in these models are frequent, and that the evolution of the most massive stars and the dynamical evolution of the cluster are closely coupled. In all cases, a single star grows steadily in mass through mergers with other stars, forming a very massive ( ≳ 100M⊙ ) star in less than 3-4 Myr. The growth rate of this runaway merger is much larger than estimates based on simple cross-section arguments, mainly because the star is typically found in the core and tends to form binaries with other massive stars there. The runaway is "rejuvenated" by each new collision, and its lifetime is extended considerably as a consequence. Observationally, such a star will appear in the Hertzsprung-Russell diagram as a blue straggler. When the runaway forms a black hole, the binary in which it is found is usually dissociated. We further investigate the sensitivity of the runaway to different formulations of mass loss from high-mass main sequence stars. We find that, while the runaway process is less pronounced in the presence of strong stellar winds, the basic effect persists even in the face of large mass loss.

  1999, Astronomy and Astrophysics, 348(1) (1), 117 - 126, English

  Scientific journal


• $7.0/Mflops astrophysical N-body simulation with treecode on GRAPE-5

  Atsushi Kawai, Toshiyuki Fukushige, Junichiro Makino

  As an entry for the 1999 Gordon Bell price/performance prize, we report an astrophysical N-body simulation performed with a treecode on GRAPE-5 (Gravity Pipe 5) system, a special-purpose computer for astrophysical N-body simulations. The GRAPE-5 system has 32 pipeline processors specialized for the gravitational force calculation. Other operations, such as tree construction, tree traverse and time integration, are performed on a general purpose workstation. The total cost for the GRAPE-5 system is 40,900 dollars. We performed a cosmological N-body simulation with 2.1 million particles, which sustained a performance of 5.92 Gflops averaged over 8.37 hours. The price per performance obtained is 7.0 dollars per Mflops.

  Institute of Electrical and Electronics Engineers Inc., 1999, ACM/IEEE SC 1999 Conference, SC 1999, 66, English

  [Refereed]

  International conference proceedings


• N-body simulation of dark matter halo formation using grape

  T Fukushige, J Makino

  We performed N-body simulation on special-purpose computer, GRAPE-4, to investigate the structure of dark matter halos. Universal profile proposed by Navarro, Frenk, and White (1996), which has cusp with density profiles rho proportional to r(-1) in density profile, cannot be reproduced in the standard Cold Dark Matter (CDM) picture of hierarchical clustering. Previous claims to the contrary were based on simulations with relatively few particles, and substantial softening. We present simulations with particle numbers an order of magnitude higher (N = 786, 400), and essentially no softening, and show that typical central density profiles are clearly steeper than rho proportional to r(-1).

  SPRINGER, 1999, NUMERICAL ASTROPHYSICS, 240, 29 - 32, English

  [Refereed]

  International conference proceedings


• On the origin of density cusps in elliptical galaxies

  T Nakano, J Makino

  We investigated the dynamical reaction of the central region of galaxies to a falling massive black hole by N-body simulations. As the initial galaxy model, we used an isothermal King model and placed a massive black hole at around the half-mass radius of the galaxy. We found that the central core of the galaxy is destroyed by the heating due to the black hole and that a very weak density cusp (rho proportional to r(-alpha), with alpha similar to 0.5) is formed around the black hole. This result is consistent with recent observations of large elliptical galaxies with the Hubble Space Telescope. The velocity of the stars becomes tangentially anisotropic in the inner region, while in the outer region the stars have radially anisotropic velocity dispersion. The radius of the weak cusp region is larger for a larger black hole mass. Our result naturally explains the formation of the weak cusp found in the previous simulations of galaxy merging and implies that the weak cusp observed in large elliptical galaxies may be formed by the heating process by sinking black holes during merging events.

  UNIV CHICAGO PRESS, Jan. 1999, ASTROPHYSICAL JOURNAL, 510(1) (1), 155 - 166, English

  Scientific journal


• Computational physics - Astrophysics on the GRAPE family of special-purpose computers

  P Hut, J Makino

  The GRAPE-4 the world's fastest computer in 1995-1997, has produced some major scientific results through a wide diversity of large-scale simulations in astrophysics. I Applications have included planetary formation, the evolution of star clusters and galactic nuclei, and the formation of galaxies and clusters of galaxies.

  AMER ASSOC ADVANCEMENT SCIENCE, Jan. 1999, SCIENCE, 283(5401) (5401), 501 - 505, English


• On the dissolution of evolving star clusters

  Simon F. Portegies Zwart, Piet Hut, Junichiro Makino, Stephen L. W. McMillan

  Using direct N-body simulations which include both the evolution of single stars and the tidal field of the parent galaxy, we study the dynamical evolution of globular clusters and rich open clusters. We compare our results with other N-body simulations and Fokker-Planck calculations. Our simulations, performed on the GRAPE-4, employ up to 32,768 stars. The results are not in agreement with Fokker-Planck models, in the sense that the lifetimes of stellar systems derived using the latter are an order of magnitude smaller than those obtained in our simulations. For our standard run, Fokker-Plank calculations obtained a lifetime of 0.28 Gyr, while our equivalent N-body calculations find ∼ 4 Gyr. The principal reason for the discrepancy is that a basic assumption of the Fokker-Plank approach is not valid for typical cluster parameters. The stellar evolution timescale is comparable to the dynamical timescale, and therefore the assumption of dynamical equilibrium leads to an overestimate of the dynamical effects of mass loss. Our results suggest that the region in parameter space for which Fokker-Planck studies of globular cluster evolution, including the effects of both stellar evolution and the galactic tidal field, are valid is limited. The discrepancy is largest for clusters with short lifetimes.

  Sep. 1998, Astronomy and Astrophysics, 337(2) (2), 363 - 371, English

  Scientific journal


• On the dissolution of evolving star clusters

  S Portegies Zwart, P Hut, J Makino, SLW McMillan

  Using direct N-body simulations which include both the evolution of single stars and the tidal field of the parent galaxy, we study the dynamical evolution of globular clusters and rich open clusters. We compare our results with other N-body simulations and Fokker-Planck calculations. Our simulations, performed on the GRAPE-4, employ up to 32.768 stars. The results are not in agreement with Fokker-Planck models, in the sense that the lifetimes of stellar systems derived using the latter are an order of magnitude smaller than those obtained in our simulations. For our standard run, Fokker-Plank calculations obtained a lifetime of 0.28 Gyr, while our equivalent N-body calculations find similar to 4 Gyr. The principal reason for the discrepancy is that a basic assumption of the Fokker-Plank approach is not valid for typical cluster parameters. The stellar evolution timescale is comparable to the dynamical timescale, and therefore the assumption of dynamical equilibrium leads to an overestimate of the dynamical effects of mass loss. Our results suggest that the region in parameter space for which Fokker-Planck studies of globular cluster evolution, including the effects of both stellar evolution and the galactic tidal field, are valid is limited. The discrepancy is largest for clusters with short lifetimes.

  EDP SCIENCES S A, Sep. 1998, ASTRONOMY & ASTROPHYSICS, 337(2) (2), 363 - 371, English

  Scientific journal


• On the mass distribution of planetesimals in the early runaway stage

  J Makino, T Fukushige, Y Funato, E Kokubo

  We derived the stationary distribution of the mass of planetesimals from the coagulation equation under the assumption of energy equipartition. In the three-dimensional case, we found that the stationary solution is expressed as n(m)proportional to m(-8 /3), where n is the surface number density and m is the mass of the planetesimals. This solution is in excellent agreement with the result of direct N-body simulations and the numerical integration of the coagulation equation, for the range of mass which contains most of the total mass of the planetesimals (10(22)-10(25) g). In the two-dimensional case, the stationary solution exists but cannot be realized in a finite time. This difference is the direct consequence of the fact that runaway growth takes place in three dimensions, but not in two dimensions. (C) 1998 Elsevier Science B.V. All rights reserved.

  ELSEVIER SCIENCE BV, Aug. 1998, NEW ASTRONOMY, 3(7) (7), 411 - 417, English

  Scientific journal


• On a time-symmetric Hermite integrator for planetary N-body simulation

  E Kokubo, K Yoshinaga, J Makino

  We describe a P(EC)(n) Hermite scheme for planetary N-body simulation. The fourth-order implicit Hermite scheme is a time-symmetric integrator that has no secular energy error for the integration of periodic orbits with time-symmetric time-steps. In general N-body problems, however, this advantage is of little practical significance, since it is difficult to achieve time-symmetry with individual variable time-steps. However, we can easily enjoy the benefit of the time-symmetric Hermite integrator in planetary N-body systems, where all bodies spend most of the time on nearly circular orbits. These orbits are integrated with almost constant time-steps even if we adopt the individual time-step scheme. The P(EC)(n) Hermite scheme and almost constant time-steps reduce the integration error greatly. For example, the energy error of the P(EC)(2) Hermite scheme is two orders of magnitude smaller than that of the standard PEC Hermite scheme in the case of an N = 100, m = 10(25) g planetesimal system with the rms eccentricity [e(2)](1/2) less than or similar to 0.03.

  BLACKWELL SCIENCE LTD, Jul. 1998, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 297(4) (4), 1067 - 1072, English

  Scientific journal


• Performance and accuracy of a GRAPE-3 system for collisionless N-body simulations

  E Athanassoula, A Bosma, JC Lambert, J Makino

  The performance and accuracy of a GRAPE-3 system for collisionless N-body simulations is discussed. After an initial description of the hardware configurations available to us at Marseille, and the usefulness of on-line analysis, we concentrate on the actual performance and accuracy of direct summation and of tree code software. For the former we discuss the sources of round-off errors. The standard Barnes-Hut tree code cannot be used as such on a GRAPE-3 system. Instead particles are divided into blocks and the tree traversal is performed for the whole block, instead of for each particle in the block separately. The forces are then calculated by direct summation over the whole interaction list. The performance of the tree code depends on the number of particles in the block, the optimum number depending on the speed of the front end and the number of boards. We find that the code scales as O(N) and explain this behaviour. The time per step decreases as the tolerance increases, but the dependence is much weaker than for the standard tree code. Finally, we find that, contrary to what is expected for the standard version, the speed of our tree code increases with the clustering of the configuration. We discuss the effect of the front end and compare the performance of direct summation and of tree code on GRAPE-3 with that of other software on general purpose computers. The accuracy of both direct summation and the tree code is discussed as a function of number of particles and softening. For this we consider the accuracy of the force calculation as well as the energy conservation during a simulation. Because of the increased role of the direct summation in the force calculation, our tree code is much more accurate than the standard one. Finally, we follow the evolution of an isolated barred galaxy using different hardware and software in order to assess the reliability and reproducibility of our results. We find excellent agreement between the pattern speed of the bar in direct summation simulations run on the high-precision GRAPE-4 machines and that in direct summation simulations run on our GRAPE-3 system. The agreement with the tree code is also very good provided the tolerance values are smaller than about 1.0. We conclude that GRAPE-3 systems are well suited for collisionless simulations and in particular for those of galaxies. This is due to their good accuracy and their high speed, which allows the use of a large number of particles.

  BLACKWELL SCIENCE LTD, Feb. 1998, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 293(4) (4), 369 - 380, English

  Scientific journal


• On the mass distribution of planetesimals in the early runaway stage

  Junichiro Makino, Toshiyuki Fukushige, Yoko Funato, Eiichiro Kokubo

  We derived the stationary distribution of the mass of planetesimals from the coagulation equation under the assumption of energy equipartition. In the three-dimensional case, we found that the stationary solution is expressed as n(m)∞m-8/3, where n is the surface number density and m is the mass of the planetesimals. This solution is in excellent agreement with the result of direct N-body simulations and the numerical integration of the coagulation equation, for the range of mass which contains most of the total mass of the planetesimals (1022-1025 g). In the two-dimensional case, the stationary solution exists but cannot be realized in a finite time. This difference is the direct consequence of the fact that runaway growth takes place in three dimensions, but not in two dimensions. © 1998 Elsevier Science B.V. All rights reserved.

  Elsevier, 1998, New Astronomy, 3(7) (7), 411 - 417, English

  [Refereed]

  Scientific journal


• On the origin of density cusp in galactic nuclei with central black hole

  T Nakano, T Fukushige, J Makino

  SPRINGER, 1998, CENTRAL REGIONS OF THE GALAXY AND GALAXIES, 487 - 488, English

  [Refereed]

  International conference proceedings


• The PCI interface for GRAPE systems: PCI-HIB

  A Kawai, T Fukushige, M Taiji, J Makino, D Sugimoto

  We developed a PCI interface for GRAPE systems. GRAPE (GRAvity piPE) is a special-purpose computer for gravitational N-body simulations. A GRAPE system consists of GRAPE processor boards and a host computer. GRAPE processors perform the calculation of gravitational forces between particles. The host computer performs the remaining calculations. The newest of the GRAPE machines, GRAPE-4, has achieved a peak performance of 1.08 Tflop. The GRAPE-4 system uses TURBOChannel for the interface to the host, which limits the selection of the host computer. The TURBOChannel bus is not supported by any of recent workstations. We have developed a new host interface board which adopts the PCI bus instead of the TURBOChannel. PCI is an I/O bus standard developed by Intel. It has a fairly high peak transfer speed, and is available on a wide range of computers, from PCs to supercomputers. Thus, the new interface allows us to connect GRAPE-4 to a wide variety of host computers. In test runs with a Barnes-Hut treecode, we found that the performance of the new system with the PCI interface is 40% better than that of the original system.

  OXFORD UNIV PRESS, Oct. 1997, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 49(5) (5), 607 - 618, English

  Scientific journal


• Gravothermal expansion in N-body systems

  H Endoh, T Fukushige, J Makino

  We investigated whether gravothermal expansion occurs in N-body systems. As the most idealized case, we studied the evolution of an N-body system in a spherical adiabatic wall which is initially in thermal equilibrium. Such a system is thermodynamically unstable if the central density is more than 709 times higher than the density just inside the wall. We performed simulation of a 2048-body system with and without artificial perturbations. We found that gravothermal expansion took place as well as gravothermal contraction. Whether gravothermal expansion occurs or not is determined by the perturbation or statistical fluctuation on the temperature structure in the initial model. The results were compared with that of a self-gravitating gas system.

  OXFORD UNIV PRESS, Jun. 1997, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 49(3) (3), 345 - 352, English

  Scientific journal


• Merger rate of equal-mass spherical galaxies

  J Makino, P Hut

  We present cross sections and reaction rates for merging to occur during encounters of equal-mass spherical galaxies. As an application, we determine the rate of galaxy merging in clusters of galaxies. We present results for two types of Plummer models (a full and a truncated one), two King models, and the Hernquist model. Cross sections are determined on the basis of a large number (similar to 500) of simulations of galaxy encounters, using the 10 Gigaflops GRAPE-3A special purpose computer. We characterize the overall merger rate of galaxies in a galaxy cluster by a single number, derived from our cross sections by an integration over galaxy encounter velocities in the limit of a constant density in velocity space. For small clusters, where the cluster velocity dispersion may not significantly exceed the internal velocity dispersion of the individual galaxies, this constant-density approximation may not be valid. For those cases, we present separate results, based on integrations of our cross sections over Maxwellian velocity distributions. Finally, tidal effects from the cluster potential, as well as from neighboring galaxies, may prevent a barely bound galaxy pair from spiraling in after their first encounter. We give a quantitative estimate of the resulting reduction in the actual merger rate that is due to these tidal interactions.

  UNIV CHICAGO PRESS, May 1997, ASTROPHYSICAL JOURNAL, 481(1) (1), 83 - 94, English

  Scientific journal


• Grape-4: A massively parallel special-purpose computer for collisional N-body simulations

  J Makino, M Taiji, T Ebisuzaki, D Sugimoto

  In this paper, we describe the architecture and performance of the GRAPE-4 system, a massively parallel special-purpose computer for N-body simulation of gravitational collisional systems. The calculation cost of N-body simulation of collisional self-gravitating system is O(N-3). Thus, even with present-day supercomputers, the number of particles one can handle is still around 10,000. In N-body simulations, almost all computing time is spent calculating the force between particles, since the number of interactions is proportional to the square of the number of particles. Computational cost of the rest of the simulation, such as the time integration and the reduction of the result, is generally proportional to the number of particles. The calculation of the force between particles call be greatly accelerated by means of a dedicated special-purpose hardware. We have developed a series of hardware systems, the GRAPE (GRAvity PipE) systems, which perform the force calculation. They are used with a general-purpose host computer which performs the rest of the calculation. The GRAPE-4 system is our newest hardware, completed in 1995 summer. Its peak speed is 1.08 TFLOPS. This speed is achieved by running 1692 pipeline large-scale integrated circuits (LSIs), each providing 640 MFLOPS, in parallel.

  UNIV CHICAGO PRESS, May 1997, ASTROPHYSICAL JOURNAL, 480(1) (1), 432 - 446, English

  Scientific journal


• Evolution of compact groups of galaxies .1. Merging rates

  E Athanassoula, J Makino, A Bosma

  We discuss the merging rates in compact groups of five identical elliptical galaxies. All groups have the same mass and binding energy. We consider both cases with individual haloes and cases where the halo is common to all galaxies and enveloping the whole group. In the latter situation the merging rate is lower if the halo is more massive. The mass of individual haloes has little influence on the merging rates, due to the fact that all galaxies in our simulations have the same mass, and so the mure extended ones have a smaller velocity dispersion. Groups with individual haloes merge faster than groups with common haloes if the configuration is centrally concentrated. Like a King distribution of index Psi = 10. On the other hand, for less concentrated configurations the merging is initially faster for individual halo cases than for common halo cases, and slower after part of the group has merged. In cases with a common halo, centrally concentrated configurations merge faster for high halo-to-total mass ratios and more slowly for low halo-to-total mass ratios. Groups with a virial ratio initially less than 1 merge faster than groups in virial equilibrium, while groups that have initially cylindrical rotation merge more slowly than groups starting with no rotation. In order to test how long a virialized group can survive before merging, we follow the evolution of a group with a high halo-to-total mass ratio and a density distribution with very little central concentration. We find that the first merging occurred only after a large number of crossing times. A reasonable calibration of our computer units shows that this time should be larger than a Hubble time. Therefore our simulations suggest that, at least for appropriate initial conditions, the longevity of compact groups is not necessarily a problem, thus presenting an alternative explanation of why we observe so many compact groups despite the fact that their lifetimes seem short.

  BLACKWELL SCIENCE LTD, Apr. 1997, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 286(4) (4), 825 - 838, English

  [Refereed]

  Scientific journal


• On the origin of cusps in dark matter halos

  T Fukushige, J Makino

  Observed cusps with density profiles p proportional to r(-1) or shallower in the central regions of galaxies cannot be reproduced in the standard cold dark matter picture of hierarchical clustering. Previous claims to the contrary were based on simulations with relatively few particles and substantial softening. We present simulations with particle numbers 1 order of magnitude higher and essentially no softening, and we show that typical central density profiles are clearly steeper than p proportional to r(-1). The observed shallower profiles may have formed through the smoothing effect of the spiral-in of central black holes in previous merger phases. In addition, we confirm the presence of a temperature inversion in the inner 5 kpc of massive galactic halos and illustrate its formation as a natural result of the merging of unequal progenitors.

  UNIV CHICAGO PRESS, Mar. 1997, ASTROPHYSICAL JOURNAL, 477(1) (1), L9 - L12, English

  Scientific journal


• Merging of galaxies with central black holes .2. Evolution of the black hole binary and the structure of the core

  J Makino

  We investigated the evolution of the black hole binary formed by the merging of two galaxies, each containing a central massive black hole. Our main goal here is to determine if the black hole binary can merge through the hardening by dynamical friction and the gravitational wave radiation. We performed N-body simulations of the merging of two galaxies with a wide range of the total number of particles to investigate the effect of the number of particles on the evolution of the black hole binary, We found that the evolution timescale was independent of the number of particles in the galaxy N until the semimajor axis reached a critical value. After the semimajor axis became smaller than this critical value, the evolution timescale was longer for larger numbers of particles. Qualitatively, this behavior is understood naturally as the result of the ''loss cone'' effect. However, the dependence of the timescale on N is noticeably weaker than the theoretical prediction. In addition, the critical semimajor axis is smaller than the theoretical prediction. The timescale of evolution through gravitational radiation at this critical semimajor axis is longer than the Hubble time. We discuss the reason of this discrepancy and the implication of the present result on the structure of the elliptical galaxies and QSO activities.

  UNIV CHICAGO PRESS, Mar. 1997, ASTROPHYSICAL JOURNAL, 478(1) (1), 58 - 65, English

  Scientific journal


• Time symmetrization meta-algorithms

  P Hut, Y Funato, E Kokubo, J Makino, S McMillan

  We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for constant time steps, and ensures time symmetry even in the case of varying time steps. The second meta-algorithm can be applied to any self-starting integration scheme to create time symmetry, both for constant and for variable time steps, even if the original scheme was not time-symmetric. Our meta-algorithms are most effective for Hamiltonian systems or systems with periodic solutions. If the system is not Hamiltonian (for example, if some dissipative force exists), our methods are still useful so long as the dissipation is small.

  ASTRONOMICAL SOC PACIFIC, 1997, 12TH KINGSTON MEETING : COMPUTATIONAL ASTROPHYSICS, 123, 26 - 31, English

  [Refereed]

  International conference proceedings


• Productivity of Research Groups : Relation between citation Analysis and Reputation within Research Community

  牧野 淳一郎, 藤垣 裕子, 今井 良行

  科学・技術と社会の会 ; 1992-, 1997, 年報科学・技術・社会, 6, 85 - 100, Japanese


• Postcollapse evolution of globular clusters

  J Makino

  A number of globular clusters appear to have undergone core collapse, in the sense that their predicted collapse times are much shorter than their current ages. Simulations with gas models and the Fokker-Planck approximation have shown that the central density of a globular cluster after the collapse undergoes nonlinear oscillation with a large amplitude (gravothermal oscillation). However, the question whether such an oscillation actually takes place in real N-body systems has remained unsolved because an N-body simulation with a sufficiently high resolution would have required computing resources of the order of several GFLOPS-yr. In the present paper, we report the results of such a simulation performed on a dedicated special-purpose computer, GRAPE-4. We have simulated the evolution of isolated point-mass systems with up to 32,768 particles. The largest number of particles reported previously is 10,000. We confirm that gravothermal oscillation takes place in an N-body system. The expansion phase shows all the signatures that are considered to be evidence of the gravothermal nature of the oscillation. At the maximum expansion, the core radius is similar to 1% of the half-mass radius for the run with 32,768 particles. The maximum core size, r(c), depends on N as [r(c)] proportional to N--1/3.

  UNIV CHICAGO PRESS, Nov. 1996, ASTROPHYSICAL JOURNAL, 471(2) (2), 796 - 803, English


• Time-symmetrized Kustaanheimo-Stiefel regularization

  Y Funato, P Hut, S McMillan, J Makino

  In this paper we describe a new algorithm for the long-term numerical integration of the two-body problem, in which two particles interact under a Newtonian gravitational potential. Although analytical solutions exist in the unperturbed and weakly perturbed cases, numerical integration is necessary in situations where the perturbation is relatively strong. Kustaanheimo-Stiefel (KS) regularization is widely used to remove the singularity in the equations of motion, making it possible to integrate orbits having very high eccentricity. However, even with KS regularization, long-term integration is difficult, simply because the required accuracy is usually very high. We present a new time-integration algorithm which has no secular error in either the binding energy or the eccentricity, while allowing variable stepsize. The basic approach is to take a time-symmetric algorithm, then apply an implicit criterion for the stepsize to ensure strict time reversibility. We describe the algorithm in detail and present the results of numerical tests involving long-term integration of binaries and hierarchical triples. In all cases studied, we found no systematic error in either the energy or the angular momentum. We also found that its calculation cost does not become higher than those of existing algorithms. By contrast, the stabilization technique, which has been widely used in the field of collisional stellar dynamics, conserves energy very well but does not conserve angular momentum. (C) 1996 American Astronomical Society.

  AMER INST PHYSICS, Oct. 1996, ASTRONOMICAL JOURNAL, 112(4) (4), 1697 - 1708, English

  Scientific journal


• GRAPE: A Special-Purpose Computer System for Astrophysical Many-Body Simulations

  TAIJI Makoto, MAKINO Junichiro

  In this paper we describe special-purpose computers for astrophysical N-body simulations , GRAPE (GRAvity PipE) . GRAPE is a hardware accelerator to calculate gravitational forces on particles . We have developed a massively-parallel machine, GRAPE-4 . GRAPE-4 has 1,692 special-purpose pipeline LSI of 640 megaflops . Its peak performance reaches 1.08 Tflops and its sustained performance is 0.5 Tflops with 4 x 10^5 particles. The special-purpose computers , especially GRAPE , will become important tools in computational sciences.

  プラズマ・核融合学会, Sep. 1996, Journal of plasma and fusion research, 72(9) (9), 920 - 925, Japanese


• A highly parallelized special-purpose computer for many-body simulations with an arbitrary central force: MD-GRAPE

  T Fukushige, M Taiji, J Makino, T Ebisuzaki, D Sugimoto

  We have developed a parallel, pipelined special-purpose computer for N-body simulations, MD-GRAPE (for ''GRAvity PipE''). In gravitational N-body simulations, almost all computing time is spent on the calculation of interactions between particles. GRAPE is specialized hardware to calculate these interactions. It is used with a general-purpose front-end computer that performs all calculations other than the force calculation. MO-GRAPE is the first parallel GRAPE that can calculate an arbitrary central force. A force different from a pure 1/r potential is necessary for N-body simulations with periodic boundary conditions using the Ewald or particle-particle/particle-mesh (P(3)M) method. MO-GRAPE accelerates the calculation of particle-particle force for these algorithms. An MO-GRAPE board has four MD chips and its peak performance is 4.2 GFLOPS. On an MO-GRAPE board, a cosmological N-body simulation takes 600(N/10(6))(3/2) s per step for the Ewald method, where N is the number of particles, and would take 240(N/10(6)) s per step for the P(3)M method, in a uniform distribution of particles.

  UNIV CHICAGO PRESS, Sep. 1996, ASTROPHYSICAL JOURNAL, 468(1) (1), 51 - 61, English

  Scientific journal


• Merging of galaxies with central black holes .1. Hierarchical mergings of equal-mass galaxies

  J Makino, T Ebisuzaki

  We have investigated the merging of galaxies with central, massive black holes. We performed simulations of hierarchical mergings, in which the merger remnant of one simulation is used as the progenitor for the next simulation. Our main results are the following: First, the central part of the merger has a very shallow density cusp (p proportional to r(-alpha), with alpha less than or similar to 1). This result is in good agreement with recent Hubble Space Telescope results that suggest most large elliptical galaxies have shallow density cusps. This shallow cusp yields an almost constant surface density. The radius of this shallow cusp (core) roughly doubles at each merger event. This expansion of the core is supported by the energy production from the black hole binary. As a result, the ratio between the core radius and the half-mass radius remains roughly constant. This result is, again, in good agreement with the observed positive correlation between the core radius and effective radius of elliptical galaxies. In previous simulations of galactic mergers, the role of the central black holes was neglected. In these simulations, the half-mass radius increased but the core radius did not, in clear disagreement with observations. Our results imply that the existence of central black holes naturally explains the structure and size of the cores of bright elliptical galaxies, though other explanations (e.g., anisotropy) are not ruled out.

  UNIV CHICAGO PRESS, Jul. 1996, ASTROPHYSICAL JOURNAL, 465(2) (2), 527 - 533, English

  Scientific journal


• N-body simulation of galaxy formation on GRAPE-4 special-purpose computer

  Toshiyuki Fukushige, Junichiro Makino

  We report on resent N-body simulations of galaxy formation performed on the GRAPE-4 (Gravity Pipe 4) system, a special-purpose computer for astrophysical N-body simulations. We review the astrophysical motivation, the algorithm, the actual performance, and the price per performance. The performance obtained is 332 Gflops aver aged over 185 hours for a simulation of a galaxy formation with 786,400 particles. The price per performance obtained is 4,600 dollars per Gflops. The configuration used for the simulation onsists of 1,269 pipeline processors and has a peak speed of 663 Gflops.

  Association for Computing Machinery, 1996, Proceedings of the International Conference on Supercomputing, 1996-, English

  International conference proceedings


• GRAPE-4: A teraflops machine for N-body simulations

  M Taiji, J Makino, T Fukushige, T Ebisuzaki, D Sugimoto

  We have developed a massively parallel special-purpose computer system for N-body simulations, GRAPE-4 (GRAvity-PipE 4). The GRAPE-4 system is designed for high-accuracy simulations of dense stellar systems. The GRAPE-4 calculates gravitational forces, their derivatives in time and potential energies. It has a hardware for prediction of positions and velocities, which is used for the individual timestep scheme. Using multi-chip module technology, we integrated 1692 chips of 640 megaflops performance. The peak speed of GRAPE-4 is 1.08 teraflops.

  KLUWER ACADEMIC PUBL, 1996, DYNAMICAL EVOLUTION OF STAR CLUSTERS - CONFRONTATION OF THEORY AND OBSERVATIONS, (174) (174), 141 - 150, English

  [Refereed]

  Scientific journal


• Evolution of galaxies through their interaction

  Y Funato, J Makino

  KLUWER ACADEMIC PUBL, 1996, NEW LIGHT ON GALAXY EVOLUTION, (171) (171), 378 - 378, English

  [Refereed]

  Scientific journal


• Exponential growth of distance between nearby rays due to multiple gravitational lensing

  T Fukushige, J Makino

  We have investigated multiple gravitational lensing by numerical ''ray tracing'' simulations. We have found that the distance between rays grows exponentially, on average, until. it reaches the projected mean separation of lensing objects (similar to RN-1/2, where R is the system size and N is the number of scattering object). This nature may affect observations of high redshift objects or the anisotropy of the cosmic background radiation.

  KLUWER ACADEMIC PUBL, 1996, ASTROPHYSICAL APPLICATIONS OF GRAVITATIONAL LENSING, (173) (173), 93 - 94, English

  [Refereed]

  Scientific journal


• Time-symmetrized Kustaanheimo-Stiefel regularization

  Y Funato, J Makino, P Hut, S McMillan

  In this paper, we show a new algorithm to integrate the orbits of binaries. Our new algorithm has the good properties of both symmetrized timesteps and KS regularization: (1) no secular error in either energy or angular momentum; (2) a constant number of timesteps per orbit for a binary with arbitrary eccentricity (Funato et al., 1995).

  KLUWER ACADEMIC PUBL, 1996, DYNAMICAL EVOLUTION OF STAR CLUSTERS - CONFRONTATION OF THEORY AND OBSERVATIONS, (174) (174), 367 - 368, English

  [Refereed]

  Scientific journal


• Effect of multiple gravitational lensing on the anisotropy of the cosmic background radiation

  T Fukushige, J Makino, T Ebisuzaki

  We investigated smoothing of the cosmic background radiation (CBR) by multiple gravitational lensing. The CBR is gravitationally scattered by galaxies, clusters of galaxies, and superclusters during the travel from the last scattering surface. Although the effect ofthe gravitational lensing was thought to be unimportant, we found that the multiple gravitational lensing by clusters of galaxies or by superclusters can reduced by a large factor. This result is explained by the fact that the distance between two light rays grows exponentially though multiple gravitational lensing. If such structures were formed at z = 2 - 5 and contain a large fraction of the mass of the universe (Omega(s) > 0.5), then multiple gravitational lensing can reduce the temperature anisotropy of the CBR by 40-60%, approximately up to a degree scale.

  KLUWER ACADEMIC PUBL, 1996, ASTROPHYSICAL APPLICATIONS OF GRAVITATIONAL LENSING, (173) (173), 95 - 96, English

  [Refereed]

  Scientific journal


• BUILDING A BETTER LEAPFROG

  P HUT, J MAKINO, S MCMILLAN

  In stellar dynamical computer simulations, as well as other types of simulations using particles, time step size is often held constant in order to guarantee a high degree of energy conservation. In many applications, allowing the time step size to change in time can offer a great saving in computational cost, but variable-size time steps usually imply a substantial degradation in energy conservation. We present a ''meta-algorithm'' for choosing time steps in such a way as to guarantee time symmetry in any integration scheme, thus allowing vastly improved energy conservation for orbital calculations with variable time steps. We apply the algorithm to the familiar leapfrog scheme, and generalize to higher order integration schemes, showing how the stability properties of the fixed-step leapfrog scheme can be extended to higher order, variable-step integrators such as the Hermite method. We illustrate the remarkable properties of these time-symmetric integrators for the case of a highly eccentric elliptical Kepler orbit and discuss applications to more complex problems.

  UNIV CHICAGO PRESS, Apr. 1995, ASTROPHYSICAL JOURNAL, 443(2) (2), L93 - L96, English

  Scientific journal


• GRAPE project for a dedicated tera-flops computer

  Daiichiro Sugimoto, Junichiro Makino, Makoto Taiji, Toshikazu Ebisuzaki

  We are constructing a one tera-flops machine dedicated to astronomical many-body problems. It consists of parallelized GRAPE machines connected to a host workstation. The GRAPE machines only calculate forces between particles in the system by pipeline architecture. We designed and fabricated LSI chips for it, and about 2000 chips are being connected in parallel. The machine will be in operation by summer of 1995. General concept and features of the machine, mode of parallelization, and their merits are discussed in addition to scientific objectives of the project.

  Institute of Electrical and Electronics Engineers Inc., 1995, Proceedings - 1st Aizu International Symposium on Parallel Algorithms/Architecture Synthesis, AISPAS 1995, 38 - 44, English

  International conference proceedings


• GRAPE-4 - A SPECIAL-PURPOSE COMPUTER FOR GRAVITATIONAL N-BODY PROBLEMS

  J MAKINO, M TAIJI, T EBISUZAKI, D SUGIMOTO

  SIAM, 1995, PROCEEDINGS OF THE SEVENTH SIAM CONFERENCE ON PARALLEL PROCESSING FOR SCIENTIFIC COMPUTING, 343 - 348, English

  [Refereed]

  International conference proceedings


• Astrophysical N-body simulations on GRAPE-4 special-purpose computer

  J Makino, M Taiji

  We report on resent astrophysical N-body simulations performed on the GRAPE-4 (GRAvity PipE 4) system, a special-purpose computer for astrophysical W-body simulations. We first review the astrophysical motivation, the algorithm, tile structure of the GRAPE system, and the actual performance. The GRAPE-4 system consists of 1692 pipeline processors. The peak speed of one pipeline processor is 523 Mflops and that of the total system is 884 Gflops. The performance obtained is 529 Gflops fbr the simulation of two massive black holes in the core of a galaxy with 700,000 stars. Copyright 1995 by the Association for Computing Machinery, Inc. (ACM).

  ASSOC COMPUTING MACHINERY, 1995, SUPERCOMPUTING '95, PROCEEDINGS, VOLS 1 AND 2, 1776 - 1785, English

  [Refereed]

  International conference proceedings


• SMOOTHING OF THE ANISOTROPY OF THE COSMIC BACKGROUND-RADIATION BY MULTIPLE GRAVITATIONAL SCATTERING

  T FUKUSHIGE, J MAKINO, O NISHIMURA, T EBISUZAKI

  We investigated the smoothing of the anisotropy of the cosmic background radiation (CBR) through multiple gravitational scattering. The CBR is gravitationally scattered by galaxies, clusters of galaxies, and superclusters during its travel from the last scattering surface. Although this effect was thought to be unimportant, we found that gravitational scattering by superclusters can reduce the anisotropy of the CBR appreciably We took into account the fact that the distance between nearby photons increases exponentially through multiple scattering. The angle between the directions of two photons increases due to passage by a scattering object. The change in the relative angle is due to the tidal force, which is proportional to the distance between two photons. As a result, the increase in the relative angle is proportional to the distance between photons. This mechanism leads to an exponential growth of the distance. The exponential growth stops when the distance reaches the mean projected separation between the scattering objects. This exponential growth has been neglected in previous studies. We found that multiple gravitational scattering by superclusters can reduce the observed temperature anisotropy of the CBR by 40-60% from the intrinsic one at a scale of a few degrees, provided that the superclusters were formed at z similar or equal to 2-4.

  ASTRONOMICAL SOC JAPAN, 1995, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 47(5) (5), 493 - 508, English

  Scientific journal


• SMOOTHING OF THE ANISOTROPY OF THE COSMIC BACKGROUND-RADIATION BY MULTIPLE GRAVITATIONAL SCATTERING

  T FUKUSHIGE, J MAKINO, O NISHIMURA, T EBISUZAKI

  We investigated the smoothing of the anisotropy of the cosmic background radiation (CBR) through multiple gravitational scattering. The CBR is gravitationally scattered by galaxies, clusters of galaxies, and superclusters during its travel from the last scattering surface. Although this effect was thought to be unimportant, we found that gravitational scattering by superclusters can reduce the anisotropy of the CBR appreciably We took into account the fact that the distance between nearby photons increases exponentially through multiple scattering. The angle between the directions of two photons increases due to passage by a scattering object. The change in the relative angle is due to the tidal force, which is proportional to the distance between two photons. As a result, the increase in the relative angle is proportional to the distance between photons. This mechanism leads to an exponential growth of the distance. The exponential growth stops when the distance reaches the mean projected separation between the scattering objects. This exponential growth has been neglected in previous studies. We found that multiple gravitational scattering by superclusters can reduce the observed temperature anisotropy of the CBR by 40-60% from the intrinsic one at a scale of a few degrees, provided that the superclusters were formed at z similar or equal to 2-4.

  ASTRONOMICAL SOC JAPAN, 1995, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 47(5) (5), 493 - 508, English

  Scientific journal


• THE EFFECT OF GRAVITATIONAL SCATTERING ON THE ANISOTROPY OF THE COSMIC BACKGROUND-RADIATION

  T FUKUSHIGE, J MAKINO, T EBISUZAKI

  The homogeneity of the cosmic microwave background radiation (CBR) is one of the most severe constraints for theories of structure formation in the universe. We investigated the effect of the gravitational scattering (lensing) of galaxies, clusters of galaxies, and superclusters on the anisotropy of the CBR by numerical simulations. Although this effect was thought to be unimportant, we found that the gravitational scatterings by superclusters can significantly reduce the anisotropy of the CBR. We took into account the exponential growth of the distance between two rays due to multiple scatterings. The bending angle of each ray grows through a random walk process. On the other hand, the difference between two rays grows exponentially while it is small. This exponential growth is caused by coherent scatterings that the two rays suffer and was neglected in the previous studies. The gravitational scattering by superclusters reduces the observed temperature anisotropy of the CBR at the present time by similar to 40%-60% from that at the recombination time for an angular scale up to a few degrees if the supercluster were formed at z = 2-4.

  UNIV CHICAGO PRESS, Dec. 1994, ASTROPHYSICAL JOURNAL, 436(2) (2), L107 - L110, English

  Scientific journal


• APPLICATION OF A HIGH-PERFORMANCE, SPECIAL-PURPOSE COMPUTER, GRAPE-2A, TO MOLECULAR-DYNAMICS

  J HIGO, S ENDO, K NAGAYAMA, T ITO, T FUKUSHIGE, T EBISUZAKI, D SUGIMOTO, H MIYAGAWA, K KITAMURA, J MAKINO

  The special-purpose computer GRAPE-2A accelerates the calculation of pairwise interactions in many-body systems. This computer is a back-end processor connected to a host computer through a Versa Module Europe (VME) bus. GRAPE-2A receives coordinates and other physical data for particles from the host and then calculates the pairwise interactions. The host then integrates an equation of motion by using these interactions. We did molecular dynamics simulations for two systems of liquid water: System 1 (1000 molecules), and System 2 (1728 molecules). The time spent for one step of molecular dynamics was 3.9 s (System 1), and 10.2 s (System 2). The larger the molecular system, the higher the performance. The speed of GRAPE-2A did not depend on the formula describing the pairwise interaction. The cost performance was about 20 times better than that of the fastest workstations available today, and GRAPE-2A cost only $22,000. (C) 1994 by John Wiley and Sons, Inc.

  JOHN WILEY & SONS INC, Dec. 1994, JOURNAL OF COMPUTATIONAL CHEMISTRY, 15(12) (12), 1372 - 1376, English

  Scientific journal


• EXPONENTIAL-GROWTH OF DISTANCE BETWEEN NEARBY RAYS DUE TO MULTIPLE GRAVITATIONAL SCATTERINGS

  T FUKUSHIGE, J MAKINO

  We give an estimate of the relative error in the angular measurement of observations for high-redshift objects induced by gravitational scatterings (lensing). Gunn concluded in 1967 that the gravitational scatterings by galaxies induce a relative error of a few percent in observations for objects at z = 1. This estimate has been considered as a fundamental limitation of accuracy of the angular measurements in observational cosmology. In multiple gravitational scatterings, the bending angle of a single ray grows through the random work process. Gunn assumed that the difference of nearby rays also grows through the random walk process. However, the distance between nearby photons grows exponentially because the two rays suffer coherent scatterings by the same scattering object. This exponential growth continues as long as the scattering is coherent. In the case of scattering by individual galaxies, the exponential growth continues until the angular distance reaches 1' or so. The relative error of the angular measurements under 1' due to the exponential growth is similar to 30% at z = 1 and exceeds 100% at z = 3, when the density parameter of galaxies is 0.2. The effects of clusters of galaxies or superclusters are more difficult to estimate accurately but might be significant. In the case of superclusters, the angular measurements up to a few degrees could be affected.

  UNIV CHICAGO PRESS, Dec. 1994, ASTROPHYSICAL JOURNAL, 436(2) (2), L111 - L114, English

  Scientific journal


• ATTENUATION OF LUMINOSITY OF DISTANT GALAXIES BY MULTIPLE GRAVITATIONAL LENSING

  Y FUNATO, J MAKINO, T EBISUZAKI

  We investigated the change of luminosity of distant galaxies due to multiple gravitational lensing. We obtained the luminosity change by calculating the orbits of photons in a model universe in which lensing objects are uniformly distributed. We found that luminosities of galaxies are, in most cases, attenuated by multiple gravitational lensing. There are a few galaxies whose luminosity is amplified through multiple lensing. The number of attenuated galaxies is much larger than that of amplified galaxies. We also found that the median value of attenuation ratio of the distant galaxies is well approximated by (1 + z)-1.3(OMEGA(l))1/2, where OMEGA(l), is the density parameter of lensing objects. This result shows that the gravitational lensing introduces an ''attenuation bias'' into the luminosity function of distant galaxies and quasars.

  UNIV CHICAGO PRESS, Mar. 1994, ASTROPHYSICAL JOURNAL, 424(1) (1), L17 - L20, English

  Scientific journal


• HARP chip : a 600 Mflops application-specific LSI for astrophysical N-body simulations

  Makoto Taiji, Junichiro Makino, Eiichiro Kokubo, Toshikazu Ebisuzaki, Daiichiro Sugimoto

  We have developed an application-specific LSI, the HARP (Hermite AcceleratoR Pipe) chip, which will be used in GRAPE-4, a massively-parallel special-purpose computer for astrophysical N-body simulations. The HARP chip calculates the gravitational interaction between particles. It consists of 15 floating point arithmetic units and one unit for function evaluation. The HARP chip performs about 20 floating point operations per clock cycle and works at 30 MHz in the worst case. Therefore, the performance of the HARP chip exceeds 600 Mflops. It is made using 1.0 μm CMOS cell-based ASIC (LSI Logic, LCB007). The die size is 14.6 mm × 14.6 mm and the total gate count is 95,000. The power consumption is 5W at operating voltage of 5V. We have examined successful operations of the sample chip up to 50 MHz. GRAPE-4 will consist of about 2000 HARP chips using multi-chip modules. The peak speed of GRAPE-4 will exceed 1 Tflops even in the worst case, and will reach around 1.8 Tflops in the typical case.

  Publ by IEEE, 1994, Proceedings of the Hawaii International Conference on System Sciences, 1, 302 - 311, English

  International conference proceedings


• HARP-1: a special-purpose computer for N-body simulation with the hermite integrator

  Eiichiro Kokubo, Junichiro Makino, Makoto Taiji

  We have designed and built HARP (Hermite Accelerato R Pipeline)-1, a special-purpose computer for solving astronomical N-body problems with high accuracy using the Hermite integrator. The Hermite integrator uses analytically calculated time derivatives of the acceleration, in addition to the acceleration, to integrate orbits of particles. HARP-1 has a 24-stage pipeline to perform the calculation of the acceleration and its time derivative, which is the most expensive part of the Hermite scheme. The pipeline calculates one gravitational interaction at every three clock cycles. Thus, the acceleration and its time derivative of a particle are calculated in 3N + 24 clock cycles, where N is the number of particles. The peek speed of HARP-1 is 160Mflops.

  Publ by IEEE, 1994, Proceedings of the Hawaii International Conference on System Sciences, 1, 292 - 301, English

  International conference proceedings


• GRAPE-4: a teraflops massively parallel special-purpose computer system for astrophysical N-body simulations

  Makoto Taiji, Junichiro Makino, Toshikazu Ebisuzaki, Daiichiro Sugimoto

  We are developing a massively parallel special-purpose computer system for astrophysical N-body simulations, GRAPE-4 (GRAvity-PipE 4). The GRAPE-4 system is designed to simulate dynamics of classical particles which interact each other gravitationally by using predictor-corrector methods. We have developed two application-specific LSIs, the HARP-(Hermite AcceleratoR Pipe) chip and the PROMETHEUS chip for the GRAPE-4 system. The HARP chip calculates gravitational forces and its performance exceeds 600 megaflops. The PROMETHEUS chip calculates predictors for the time-integration. Using multi-chip module technology, we can integrate 1920 HARP chips into a single system. The GRAPE-4 system consists of 4 clusters, which are connected to a single host workstation. The peak speed of GRAPE-4 will exceed 1 teraflops even in the worst case, and will reach around 1.8 teraflops in the typical case.

  Publ by IEEE, 1994, Proceedings of the International Conference on Parallel Processing, 280 - 287, English

  International conference proceedings


• DREAM-1A: special-purpose computer for computational fluid dynamics

  Yousuke Ohno, Junichiro Makino, Izumi Hachisu, Toshikazu Ebisuzaki, Daiichiro Sugimoto

  We have developed a special-purpose computer for computational fluid dynamics, DREAM-1A. DREAM-1A has a peak speed of 80 Mflops and a memory size of 1.6 Gbyte. DREAM-1A consists of four units connected in a one-dimensional bidirectional ring network. One unit of DREAM-1A has one vector processing unit (VPU) and one hard-disk unit. The physical variables are stored in hard disk, instead of RAM. The peak speed of a VPU is 20 Mflops. The capacity and the data-transfer rate of the hard-disk unit are 400 Mbyte and 1 Mbyte/s. We implemented one- and two-dimensional fluid dynamics codes on one unit of DREAM-1A. The sustained computing speed of this unit was 6.4 Mflops for 1-D and 3.6 Mflops for 2-D. In 1-D calculation, all variables are stored in small RAM in VPU, while in 2-D calculation, data are stored in hard disk. Thus the speed of 6.4 Mflops represent the raw performance of VPU, while the slow down to 3.6 Mflops of the 2-D simulations represent the performance of the total system. The speed of data transfer between processor units is 40 Mbyte/s. We are implementing 2-D and 3-D fluid dynamics codes on the parallel DREAM system. DREAM-1A will have a sustained computing speed of 14 Mflops and will be able to perform a (256)3 3-D fluid calculation in 3-8 days.

  Publ by IEEE, 1994, Proceedings of the Hawaii International Conference on System Sciences, 1, 282 - 291, English

  International conference proceedings


• GRAPE-4 - A ONE-TFLOPS SPECIAL-PURPOSE COMPUTER FOR ASTROPHYSICAL N-BODY PROBLEM

  J MAKINO, M TAIJI, T EBISUZAKI, D SUGIMOTO

  I E E E, COMPUTER SOC PRESS, 1994, SUPERCOMPUTING '94, PROCEEDINGS, 429 - 438, English

  [Refereed]

  International conference proceedings


• WINE-1 - A SPECIAL PURPOSE COMPUTER FOR PARTICLE DYNAMICS SIMULATION BASED ON THE EWALD METHOD

  T FUKUSHIGE, J MAKINO, T ITO, SK OKUMURA, T EBISUZAKI, D SUGIMOTO

  ELSEVIER SCIENCE PUBL B V, 1994, ADVANCED MATERIALS '93, III - A & B, 16(A & B) (A & B), 153 - 156, English

  [Refereed]

  International conference proceedings


• GRAPE - SPECIAL PURPOSE COMPUTER FOR SIMULATIONS OF MANY-BODY SYSTEMS

  T EBISUZAKI, E KOKUBO, T FUKUSHIGE, M TAIJI, J MAKINO, D SUGIMOTO, T ITO

  ELSEVIER SCIENCE PUBL B V, 1994, ADVANCED MATERIALS '93, III - A & B, 16(A & B) (A & B), 149 - 152, English

  [Refereed]

  International conference proceedings


• A special‐purpose computer for molecular dynamics: GRAPE‐2A

  Tomoyoshi Ito, Toshiyuki Fukushige, Junichiro Makino, Toshikazu Ebisuzaki, Sachiko K. Okumura, Daiichiro Sugimoto, Hiroo Miyagawa, Kunihiro Kitamura

  Molecular dynamics simulations have been extensively used in research of proteins. Since these simulations are quite computer intensive, their acceleration is of main interest of the research. In molecular dynamics simulations, almost all computing time is consumed in calculating the forces between particles, e.g., Coulomb and van der Waals forces. We have designed and built GRAPE‐2A (GRAvity PipE 2A), a special‐purpose computer for use in simulations of classical many‐body systems. GRAPE‐2A calculates forces exerted on a particle from the other particles. GRAPE‐2A can calculate force of an arbitrary functional form of a central force. The host computer, which is connected to GRAPE‐2A through the VME bus, performs other calculations such as time integration. The peak speed of GRAPE‐2A is 180 Mflops. We can also stimulate systems with periodic boundary conditions by the Ewald method, using GRAPE‐2A and another special‐purpose computer, WINE (Wave space INtegrator for the Ewald method). © 1994 Wiley‐Liss, Inc. Copyright © 1994 Wiley‐Liss, Inc.

  1994, Proteins: Structure, Function, and Bioinformatics, 20(2) (2), 139 - 148, English

  Scientific journal


• Triple Black Holes in the core of galaxies

  1994, The astrophysical Journal, 436, 607


• SCATTERING OF PLANETESIMALS BY A PROTOPLANET - SLOWING-DOWN OF RUNAWAY GROWTH

  S IDA, J MAKINO

  ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS, Nov. 1993, ICARUS, 106(1) (1), 210 - 227, English

  Scientific journal


• DREAM - 1A : Special - Purpose Computer for Computational Fluid Dynamics

  Ohno Yousuke, Makino Junichiro, Hachisu Izumi, Ebisuzaki Toshikazu, Sugimoto Daiichiro

  We have developed a special-purpose computer for computational fluid dynamics, DREAM-1A. In computational fluid dynamics, the size of the memory limits the size of the calculation. A DREAM system realizes cheap large memory by using hard disk as the main memory. DREAM-1A has a memory size of 1.6 Gbyte and sustained calculating speed of 14 Mflops, and its cost is about one million yen. The hard disk has two difficulties. The transfer rate is lower than that of a silicon memory, and the access time is also much longer. We improve the transfer rate by parallelization. In addition, the amount of the data transfer is reduced by adding a small fast memory made by silicon chips. This small memory also increase the block size of transfer, thereby reducing the overhead due to the access time.

  Information Processing Society of Japan (IPSJ), Aug. 1993, IPSJ SIG Notes, 1993(72) (72), 41 - 48, Japanese


• THE ORIGIN OF ANISOTROPIC VELOCITY DISPERSION OF PARTICLES IN A DISC POTENTIAL

  S IDA, E KOKUBO, J MAKINO

  The velocity dispersion of particles in a disc potential is anisotropic. N-body simulations and observations show that the ratio between the radial component of the dispersion, sigma(R), and the vertical one, sigma(z), is sigma(z)/sigma(R) congruent-to 0.6 for stars in a galactic disc in the solar neighbourhood, and sigma(z)/sigma(R) = 0.5 for planetesimals in a Kepler potential. These ratios are smaller than the 'isotropic' ratio, sigma(z)/sigma(R) = 1. The velocity dispersion evolves through gravitational scattering between particles. To explain the anisotropic ratio, we performed analytical calculations using the two-body approximation which is similar to that of Lacey, although we calculate the logarithmic term In LAMBDA in the two-body approximation more exactly, since we found that the equilibrium ratio of sigma(z)/sigma(R) depends sensitively on the choice of In LAMBDA. We determined the effective ln LAMBDA for each component of velocity distribution, while Lacey simply took ln LAMBDA as a constant. The numerical results of orbital integrations show that our treatment is correct, whereas Lacey's overestimated dsigma(z)2/dt and underestimated dsigma(R)2/dt considerably, so that he overestimated the equilibrium ratio of sigma(z)/sigma(R). We find that the ratio sigma(z)/sigma(R) approaches a value that is determined mainly by kappa/OMEGA (where kappa and OMEGA are the epicyclic frequency and the angular velocity of a local circular orbit). The equilibrium ratios are predicted to be about 0.5 for the Kepler potential (kappa/OMEGA = 1) and about 0.6 for the galactic potential in the solar neighbourhood (kappa/OMEGA congruent-to 1.4). Therefore the analytical calculation here explains well the ratios sigma(z)/sigma(R) found by N-body simulations and observations.

  BLACKWELL SCIENCE LTD, Aug. 1993, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 263(4) (4), 875 - 889, English

  Scientific journal


• A special purpose computer for particle dynamics simulation based on Ewald method: WINE-1

  Toshiyuki Fukushige, Junichiro Makino, Tomoyoshi Ito, Sachiko K. Okumura, Toshikazu Ebisuzaki, Daiichiro Sugimoto

  The authors have designed and built WINE-1, a special-purpose computer based on the Ewald method. The Ewald method is used to calculate long-range interparticle interactions such as the Coulomb interaction, or the gravitational interaction. It is connected to a host computer via a VME bus, WINE-1 is one board, 38 cm by 40 cm, on which 31 LSI chips and 46 IC chips are wire-wrapped. The peak speed of WINE-1 is equivalent to 480 MFLOPS. Interactions in the real space are calculated using the GRAPE system, another special-purpose computer for the direct calculation of interparticle force. Using the GRAPE-2A/WINE-1 system, for example, one can perform a molecular dynamics simulation for 10000 atoms, or a cosmological N-body simulation for 80000 bodies within a week.

  IEEE Computer Society, 1993, Proceedings of the Annual Hawaii International Conference on System Sciences, 1, 124 - 133, English

  International conference proceedings


• HIGHLY PARALLELIZED SPECIAL-PURPOSE COMPUTER, GRAPE-3

  SK OKUMURA, J MAKINO, T EBISUZAKI, T FUKUSHIGE, T ITO, D SUGIMOTO, E HASHIMOTO, K TOMIDA, N MIYAKAWA

  We have developed a highly parallelized special-purpose computer, GRAPE (GRAvity PipE)-3, for gravitational many-body simulations. Its peak computing speed is equivalent to 15 Gflops. The GRAPE-3 system comprises two identical boards connected to a host computer (workstation) through the VME bus. Each board has 24 custom LSI chips (GRAPE chips) which calculate gravitational forces in parallel. The calculation of the gravitational forces is easily parallelized, since the forces on different particles can be calculated independently. One GRAPE chip running at a 10 MHz clock has a computing speed equivalent to 0.3 Gflops; the GRAPE-3 system with 48 GRAPE chips thus achieves a peak speed of 15 Gflops. The sustained speed of the GRAPE-3 system reached 10 Gflops-equivalent.

  ASTRONOMICAL SOC JAPAN, 1993, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 45(3) (3), 329 - 338, English

  [Refereed]

  Scientific journal


• DREAM-1 - SPECIAL-PURPOSE COMPUTER FOR COMPUTATIONAL FLUID-DYNAMICS

  Y OHNO, J MAKINO, HACHISU, I, M UENO, T EBISUZAKI, D SUGIMOTO, SK OKUMURA, Y CHIKADA

  Based on the concept of DREAM (Disk REsource Array Machine), we have developed a special-purpose computer for computational fluid dynamics, i.e., the first model of DREAM, DREAM-1. In computer simulations of fluid dynamics, the number of grid points determines both the resolution and accuracy. On conventional computers, the number of grid points is limited by the size of the main memory. The essence of the DREAM concept is to use magnetic disk units as the main memory instead of silicon chips. Thus, we are able to use a main memory that is 100-times larger than that of silicon chips for the same cost. DREAM solves two difficulties of using magnetic disk units as the main memory. First, the data-transfer speed of a disk unit is slower than that of the silicon memory chips. We solve this difficulty by accessing many disk units in parallel and using a small cache. Second is the long access time of the disk unit. In finite-difference calculations, we access the data only in long vectors. The access time therefore becomes negligible. DREAM-1 has one vector processing unit (VPU) and one hard-disk unit. The peak speed of VPU is 12 Mflops. The capacity and the data-transfer rate of the hard-disk unit are 400 Mbyte and 2 Mbyte s-1, respectively. We implemented one- and two-dimensional fluid dynamics codes on DREAM-1. The sustained computing speed was 4 Mflops for 1-D and 2.7 Mflops for 2-D. The speed of 4 Mflops is the naked VPU speed while the slow down to 2.7 Mflops of the 2-D simulations is due mainly to the overhead of disk access. We plan to increase the peak speed of the VPU to 20 Mflops and to build 4 units. These units are connected in a one-dimensional ring network. This parallel DREAM system will have a peak speed of 80 Mflops and will be able to perform a (300)3 3-D fluid calculation in 4-12 d. We also discuss the potential ability of DREAM: for example, the DREAM system can solve an I/O neck of such observational instruments as a CCD-camera or a VLBI.

  ASTRONOMICAL SOC JAPAN, 1993, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 45(3) (3), 377 - 392, English

  [Refereed]

  Scientific journal


• GRAPE - SPECIAL-PURPOSE COMPUTER FOR SIMULATIONS OF MANY-BODY SYSTEMS

  T EBISUZAKI, T ITO, T FUKUSHIGE, J MAKINO, SK OKUMURA, D SUGIMOTO, E HASHIMOTO, K TOMIDA, N MIYAKAWA

  ELSEVIER SCIENCE PUBL B V, 1993, COMPUTER AIDED INNOVATION OF NEW MATERIALS II, PTS 1 AND 2, 1171 - 1176, English

  [Refereed]

  International conference proceedings


• N体問題専用計算機:GRAPE 2A

  1993, 45,339


• N体シミュレーションにおける離散化誤差と力の誤差について

  1993, 402,85


• HARP:N体問題専用計算機

  1993, 45,349


• THE GRAPE SOFTWARE SYSTEM

  J MAKINO, Y FUNATO

  We describe the software system used for GRAPE processors, special-purpose computers for gravitational N-body simulations. In gravitational N-body simulations, almost all of the calculation time is spent to calculate the gravitational force between particles. The GRAPE hardware calculates the gravitational force between particles using hardwired pipelines with a speed in the range of 100 Mflops to 10 Gflops, depending on the model. All GRAPE hardware systems axe connected to general-purpose workstations, on which the user program runs. In order to use the GRAPE hardware, a user program calls several library subroutines that actually control GRAPE. In this paper, we present an overview of the user interface of GRAPE software libraries and describe how they work. We also describe how the GRAPE system is used with sophisticated algorithms, such as the tree algorithm or the individual time step algorithm.

  ASTRONOMICAL SOC JAPAN, 1993, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 45(3) (3), 279 - 288, English

  Scientific journal


• DISCRETENESS NOISE VERSUS FORCE ERRORS IN N-BODY SIMULATIONS

  L HERNQUIST, P HUT, J MAKINO

  A low accuracy in the force calculation per time step of a few percent for each particle pair is sufficient for collisionless N-body simulations. Higher accuracy is made meaningless by the dominant discreteness noise in the form of two-body relaxation, which can be reduced only by increasing the number of particles. Since an N-body simulation is a Monte Carlo procedure in which each particle-particle force is essentially random, i.e., carries an error of approximately 1000%, the only requirement is a systematic averaging-out of these intrinsic errors. We illustrate these assertions with two specific examples in which individual pairwise forces are deliberately allowed to carry significant errors: tree-codes on supercomputers and algorithms on special-purpose machines with low-precision hardware.

  UNIV CHICAGO PRESS, Jan. 1993, ASTROPHYSICAL JOURNAL, 402(2) (2), L85 - L88, English

  Scientific journal


• GRAPE PROJECT - AN OVERVIEW

  T EBISUZAKI, J MAKINO, T FUKUSHIGE, M TAIJI, D SUGIMOTO, T ITO, SK OKUMURA

  We axe developing a series of special-purpose computers, GRAPE (GRAvity PipE), for the simulation of N-body systems, such as proto-planetary systems, globular clusters, galaxies, and clusters of galaxies. In simulations of N-body systems, almost all computing time is consumed in calculating the gravitational force between particles. GRAPE calculates the forces at high speed using hard-wired pipelines. The host computer, which is connected to GRAPE, sends the positions of particles to GRAPE. Then, GRAPE calculates the force exerted on a particle and sends this value back to the host computer. Using the force calculated by GRAPE, the host computer then integrates the orbits of the particles. We have already developed six different machines (GRAPE-1, GRAPE-1A, GRAPE-2, GRAPE-2A, GRAPE-3, and GRAPE-3A), which are divided into low- and high-accuracy types. Those machines with odd numbers (GRAPE-1, GRAPE-1A, GRAPE-3, and GRAPE-3A) are among the low-accuracy type. They were designed for simulations of collisionless systems, such as galaxies, in which only the mean potential plays an important role. Simulations of such systems do not require high accuracy in the force calculation. GRAPE-1 and GRAPE-1A are machines made by wire-wrapping. GRAPE-3 is a highly parallel system with 48 full-custom LSI chips (GRAPE chip). Each LSI chip has one GRAPE pipeline. The sustained speed of GRAPE-3 is 10 Gflops for a 200,000 particle simulation. The machines with even numbers (GRAPE-2 and GRAPE-2A) are among the high-accuracy type. They were designed for collisional systems, such as globular clusters and proto-planetary systems, in which close encounters play an important role. In simulations of such collisional systems, we must calculate the force accurately. GRAPE-2 was the first machine of the high-accuracy type. GRAPE-2A was designed for applications involving molecular-dynamics simulations, as well as gravitational N-body simulations. GRAPE-2A can calculate the forces of an arbitrary functional form using interpolation tables. The computational speed of GRAPE-2A is 180 Mflops. We are now developing a highly parallel machine, GRAPE-4, in which many GRAPE pipelines (about 1,600) will work in parallel.

  ASTRONOMICAL SOC JAPAN, 1993, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 45(3) (3), 269 - 278, English

  Scientific journal


• A SPECIAL-PURPOSE COMPUTER FOR N-BODY SIMULATIONS - GRAPE-2A

  T ITO, J MAKINO, T FUKUSHIGE, T EBISUZAKI, SK OKUMURA, D SUGIMOTO

  We have developed GRAPE-2A, which is a back-end processor used to accelerate simulations of gravitational N-body systems, such as stellar clusters, a proto planetary system, and the structure formation of the universe. GRAPE-2A calculates the forces exerted on one particle from all other particles. The host computer, which is connected to GRAPE-2A through a VME bus, performs other calculations, such as time integration. In the simulation of gravitational N-body systems, almost all of the computing time is consumed in calculating the forces between particles. GRAPE-2A performs this force calculation with a speed that is much faster than that of a general-purpose computer. GRAPE-2A can be used for cosmological N-body simulations with periodic boundary conditions using the Ewald method, and for molecular-dynamics simulations of proteins and crystals. The computational speed of GRAPE-2A is 180 Mflops.

  ASTRONOMICAL SOC JAPAN, 1993, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 45(3) (3), 339 - 347, English

  Scientific journal


• HARP - A SPECIAL-PURPOSE COMPUTER FOR N-BODY PROBLEM

  J MAKINO, E KOKUBO, M TAIJI

  We present the concept of HARP (Hermite AcceleratoR Pipeline), a special-purpose computer for solving N-body problem using the Hermite integrator. A Hermite integrator uses analytically calculated derivatives of the acceleration, in addition to the acceleration, to integrate the orbit of a particle. lt has a better stability and allows a longer time step than does an Adams-Bashforth-Moulton type predictor-corrector scheme of the same error order. HARP is a specialized computer for this type of Hermite scheme. Its structure is quite similar to GRAPE; the only difference is that it calculates the time derivative of the acceleration, in addition to the acceleration. We are now developing HARP-1, the first prototype machine with a peak speed of 240 Mflops. The massively parallel GRAPE-4 will be based on this HARP architecture. Its speed will be about 1 Tflops.

  ASTRONOMICAL SOC JAPAN, 1993, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 45(3) (3), 349 - 360, English

  Scientific journal


• WINE-1 - SPECIAL-PURPOSE COMPUTER FOR N-BODY SIMULATIONS WITH A PERIODIC BOUNDARY-CONDITION

  T FUKUSHIGE, J MAKINO, T ITO, SK OKUMURA, T EBISUZAKI, D SUGIMOTO

  We have developed WINE-1 (Wave space INtegrator for Ewald method), a special-purpose computer for N-body simulations with a periodic boundary condition. In N-body simulations with a periodic boundary condition such as cosmological N-body simulations, we use the Ewald method to calculate the gravitational interaction. With the Ewald method, we can calculate the interaction more accurately than a calculation with other methods, such as the PM method, the P3M method, or the tree algorithm. In the Ewald method, the total force exerted on a particle is divided into contributions from real space and wave-number space so that the infinite sum can converge exponentially in both spaces. WINE is a special-purpose computer used to calculate the interaction in wave-number space. WINE is connected to a host computer via the VME bus. We have developed the first machine, WINE-1. It is made of one board having a size of 38 cm by 40 cm, on which 31 LSI chips and 46 IC chips are wire-wrapped. The peak speed of WINE-1 is equivalent to 480 Mflops. The summation in real space is calculated using a GRAPE system, another special-purpose computer for the direct calculation of the interparticle force. For example, we can perform a cosmological N-body simulation for N = 80,000 (500 steps) within a week if we use GRAPE-2A for the summation in real space and WINE-1 for that in wave-number space.

  ASTRONOMICAL SOC JAPAN, 1993, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 45(3) (3), 361 - 375, English

  Scientific journal


• Evolution of Cluster of Galaxies

  1993, Publications of the Astronomical Society of Japan, 45,289


• THE EVOLUTION OF MASSIVE BLACK-HOLE BINARIES IN MERGING GALAXIES .1. EVOLUTION OF A BINARY IN A SPHERICAL GALAXY

  J MAKINO, T FUKUSHIGE, SK OKUMURA, T EBISUZAKI

  We investigated the evolution of a binary massive black hole formed by the merging of galaxies containing central black holes. When two galaxies merge, their central black holes sink towards the center of the merger, due to dynamical friction, and form a binary system. This black-hole binary becomes harder due to dynamical friction from field stars. At the same time, field stars gain kinetic energy and the core of the galaxy expands. When the periastron distance between the black holes has become sufficiently small, the emission of gravitational waves would cause the black holes to merge. We studied the timescale of the merging and the amount of the energy deposited into the core by means of a direct N-body simulation with 16384+2 particles. We found that the black-hole binary tends to have a large eccentricity (greater than or similar to 0.9). This is because the evolution is driven by dynamical friction from the field stars. This dynamical friction is strongest at the apocenter, since its strength is inversely proportional to the third power of the velocity. The binding energy of the binary per unit mass becomes approximately 10 times as large as the kinetic energy of the field particles in the crossing timescale of the core. For a typical elliptical galaxy with an internal velocity dispersion of 300 km s-1, the velocity of the binary at the periastron would easily reach 3000 km s-1, for which the timescale of the merging by the radiation of the gravitational wave is less than or similar to 10(9) yr. Most black-hole binaries which are formed by the merging of ellipticals would merge within a time much shorter than the Hubble time.

  ASTRONOMICAL SOC JAPAN, 1993, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 45(3) (3), 303 - 310, English

  Scientific journal


• SMOOTHED PARTICLE HYDRODYNAMICS WITH GRAPE-1A

  M UMEMURA, T FUKUSHIGE, J MAKINO, T EBISUZAKI, D SUGIMOTO, EL TURNER, A LOEB

  We describe the implementation of a smoothed particle hydrodynamics (SPH) scheme using GRAPE-1A, a special-purpose processor used for gravitational N-body simulations. The GRAPE-1A calculates the gravitational force exerted on a particle from all other particles in a system, while simultaneously making a list of the nearest neighbors of the particle. If a host computer, which is connected to GRAPE-1A, uses this neighbor list in order to calculate hydrodynamical variables, the computational cost of SPH can be greatly reduced. It is found that GRAPE-1A accelerates SPH calculations by direct summation by about two orders of magnitudes for a ten thousand-particle simulation. The effective speed is 80 Mflops, which is about 30% of the peak speed of GRAPE-1A. Also, in order to investigate the accuracy of GRAPE-SPH, some test simulations were executed. We found that the force and position errors are smaller than those due to representing a fluid by a finite number of particles. The total energy and momentum were conserved within 0.2-0.4% and 2-5 x 10(-5), respectively, in simulations with several thousand particles. We conclude that GRAPE-SPH is quite effective and sufficiently accurate for self-gravitating hydrodynamics.

  ASTRONOMICAL SOC JAPAN, 1993, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 45(3) (3), 311 - 320, English

  Scientific journal


• THE GRAPE SOFTWARE SYSTEM

  J MAKINO, Y FUNATO

  We describe the software system used for GRAPE processors, special-purpose computers for gravitational N-body simulations. In gravitational N-body simulations, almost all of the calculation time is spent to calculate the gravitational force between particles. The GRAPE hardware calculates the gravitational force between particles using hardwired pipelines with a speed in the range of 100 Mflops to 10 Gflops, depending on the model. All GRAPE hardware systems axe connected to general-purpose workstations, on which the user program runs. In order to use the GRAPE hardware, a user program calls several library subroutines that actually control GRAPE. In this paper, we present an overview of the user interface of GRAPE software libraries and describe how they work. We also describe how the GRAPE system is used with sophisticated algorithms, such as the tree algorithm or the individual time step algorithm.

  ASTRONOMICAL SOC JAPAN, 1993, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 45(3) (3), 279 - 288, English

  Scientific journal


• THE EVOLUTION OF MASSIVE BLACK-HOLE BINARIES IN MERGING GALAXIES .1. EVOLUTION OF A BINARY IN A SPHERICAL GALAXY

  J MAKINO, T FUKUSHIGE, SK OKUMURA, T EBISUZAKI

  We investigated the evolution of a binary massive black hole formed by the merging of galaxies containing central black holes. When two galaxies merge, their central black holes sink towards the center of the merger, due to dynamical friction, and form a binary system. This black-hole binary becomes harder due to dynamical friction from field stars. At the same time, field stars gain kinetic energy and the core of the galaxy expands. When the periastron distance between the black holes has become sufficiently small, the emission of gravitational waves would cause the black holes to merge. We studied the timescale of the merging and the amount of the energy deposited into the core by means of a direct N-body simulation with 16384+2 particles. We found that the black-hole binary tends to have a large eccentricity (greater than or similar to 0.9). This is because the evolution is driven by dynamical friction from the field stars. This dynamical friction is strongest at the apocenter, since its strength is inversely proportional to the third power of the velocity. The binding energy of the binary per unit mass becomes approximately 10 times as large as the kinetic energy of the field particles in the crossing timescale of the core. For a typical elliptical galaxy with an internal velocity dispersion of 300 km s-1, the velocity of the binary at the periastron would easily reach 3000 km s-1, for which the timescale of the merging by the radiation of the gravitational wave is less than or similar to 10(9) yr. Most black-hole binaries which are formed by the merging of ellipticals would merge within a time much shorter than the Hubble time.

  ASTRONOMICAL SOC JAPAN, 1993, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 45(3) (3), 303 - 310, English

  Scientific journal


• HARP - A SPECIAL-PURPOSE COMPUTER FOR N-BODY PROBLEM

  J MAKINO, E KOKUBO, M TAIJI

  We present the concept of HARP (Hermite AcceleratoR Pipeline), a special-purpose computer for solving N-body problem using the Hermite integrator. A Hermite integrator uses analytically calculated derivatives of the acceleration, in addition to the acceleration, to integrate the orbit of a particle. lt has a better stability and allows a longer time step than does an Adams-Bashforth-Moulton type predictor-corrector scheme of the same error order. HARP is a specialized computer for this type of Hermite scheme. Its structure is quite similar to GRAPE; the only difference is that it calculates the time derivative of the acceleration, in addition to the acceleration. We are now developing HARP-1, the first prototype machine with a peak speed of 240 Mflops. The massively parallel GRAPE-4 will be based on this HARP architecture. Its speed will be about 1 Tflops.

  ASTRONOMICAL SOC JAPAN, 1993, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 45(3) (3), 349 - 360, English

  Scientific journal


• EVOLUTION OF CLUSTERS OF GALAXIES

  Y FUNATO, J MAKINO, T EBISUZAKI

  We have investigated the evolution of clusters of galaxies using direct N-body simulations in which each galaxy is modeled by many particles. We found that the positive correlation between the masses and the distances of galaxies from the center of a cluster develops as the result of perturbations due to close encounters with other galaxies and the tidal field of the potential of the parent cluster. In the inner region of the cluster, the number density of galaxies is higher than that in the outer region, and the tidal field of the cluster is stronger compared to the outer region. Therefore, the masses of the galaxies in the inner region decrease more rapidly than do those in the outer region. The effect of mass segregation is not sufficiently strong to cancel out this tendency. We also found that the galaxies evolve so as to satisfy the Faber-Jackson relation. This implies that the Faber-Jackson relation is a result of the evolution of galaxies driven by interactions with other galaxies and the tidal field of the parent cluster. The coefficient of the L-sigma relation changes as the cluster evolves. Therefore, the Faber-Jackson relation might not be a good standard candle to determine the distance to galaxies. Particles which escape from galaxies form a background halo, which is somewhat less centrally condensed than the distribution of the remaining galaxies. Both of heavier and lighter galaxies sink towards the center of the cluster, since they lose kinetic energy through inelastic collisions and the dynamical friction from halo particles. The density profile of a cluster including both galaxies and halo particles does not significantly change for more than 8 two-body relaxation times in the one-mass component model. This is caused by decreases in the masses of the galaxies, which slow down the speed of the two-body relaxation.

  ASTRONOMICAL SOC JAPAN, 1993, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 45(3) (3), 289 - 302, English

  Scientific journal


• GRAVITATIONAL-WAVE BURST PRODUCED BY MERGING OF CENTRAL BLACK-HOLES OF GALAXIES

  T FUKUSHIGE, T EBISUZAKI, J MAKINO

  When galaxies merge, the central black holes rapidly sink toward the center of the system and make a binary. We found that this black hole binary merges within less than or similar 10(9) yr. This merging of black holes produces an intense burst of the gravitational wave. We investigated the nature of these gravitational wave bursts and found that the dimnensionless amplitude at the Earth is as high as 10(-15) if black holes with masses of 10(8) M . merge at the distance of 2 Gpc. The mean time between bursts is about 2 yr if the elliptical galaxies are the merger remnants of galaxies having central black holes. In previous studies, the time scale of the merging of a black hole binary was estimated to be much longer than a Hubble time (approximately 10(10) yr). In those studies, the orbit of the binary was assumed to be circular. We found, however, that dynamical friction makes the orbit highly eccentric. The lifetime of a binary with a highly eccentric orbit is much shorter than that of a binary with a circular orbit, because the emission of the gravitational wave is much stronger for shorter periastron distance.

  UNIV CHICAGO PRESS, Sep. 1992, ASTROPHYSICAL JOURNAL, 396(2) (2), L61 - L63, English

  [Refereed]

  Scientific journal


• N-BODY SIMULATION OF GRAVITATIONAL INTERACTION BETWEEN PLANETESIMALS AND A PROTOPLANET .2. DYNAMIC FRICTION

  S IDA, J MAKINO

  ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS, Jul. 1992, ICARUS, 98(1) (1), 28 - 37, English

  [Refereed]

  Scientific journal


• N-BODY SIMULATION OF GRAVITATIONAL INTERACTION BETWEEN PLANETESIMALS AND A PROTOPLANET .1. VELOCITY DISTRIBUTION OF PLANETESIMALS

  S IDA, JI MAKINO

  ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS, Mar. 1992, ICARUS, 96(1) (1), 107 - 120, English

  Scientific journal


• VIOLENT RELAXATION IS NOT A RELAXATION PROCESS

  Y FUNATO, J MAKINO, T EBISUZAKI

  We investigated how a gravitational collisionless system approaches to equilibrium through so-called violent relaxation. A system which is far from dynamical equilibrium approaches to dynamical equilibrium through the dissipation of energy from the coherent motion of particles to random motion by wave-particle interaction and phase mixing. Particles change their energies by the wave-particle interaction with the coherent motion of particles. We performed direct N-body simulations of collisionless systems and found (a) that the direction of the evolution through the wave-particle interaction is different from that due to the entropy maximum, and (b) that wave-particle coupling disappears within a few crossing times. Thus, violent relaxation does not lead the system to a thermally relaxed state. In other words, it is not a relaxation process. Evolution through the wave-particle interaction does not lead to thermal equilibrium, since it tries to establish an equipartition between the bulk motion and that of individual particles. As a result, all of the particles are heated, regardless of their initial energies. The wave, itself, decays quickly, since it loses energy through this wave-particle interaction, itself Within a few crossing times, the wave becomes sufficiently small that the wave-particle interaction has a negligible effect on to the energy of the particles. At this stage, however, the system is still not in an dynamical equilibrium. We found that even in this stage the central density shows an oscillating behavior with an amplitude larger than 10%. This oscillation can continue for approximately 10 crossing times or longer. This long lifetime is explained by the fact that it decays only through phase mixing. This phase mixing is slow in the core, since particles have very similar orbital periods there.

  ASTRONOMICAL SOC JAPAN, 1992, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 44(6) (6), 613 - 621, English

  [Refereed]

  Scientific journal


• 微惑星と原始惑星の相互作用のN体計算.I微惑星の速度分布

  1992, 96


• 重力多体問題のためのアーマド・コーエン型エルミート積分公式について

  1992, 44


• ON A HERMITE INTEGRATOR WITH AHMAD-COHEN SCHEME FOR GRAVITATIONAL MANY-BODY PROBLEMS

  J MAKINO, SJ AARSETH

  We describe the implementation of the Ahmad-Cohen scheme based on a fourth-order Hermite integrator. With the fourth-order Hermite scheme, we calculate the force and the time derivative of the force analytically, and construct a third-order interpolation polynomial using two points in time. Compared with the standard scheme (Aarseth 1985) which is widely used, it allows a longer stepsize for the same accuracy, and the program is much simpler. In the case of the Ahmad-Cohen scheme, which uses different stepsizes for the forces from neighboring particles and that from distant particles, the difference in the programming complexity is even larger, since the Hermite scheme does not require corrections of the higher order divided differences for the forces from distant particles. On scalar computers the Hermite schemes are marginally faster than the standard scheme for the same level of accuracy, both with and without the Ahmad-Cohen scheme. On vector machines or special-purpose hardware, such as GRAPE, the Hermite scheme would be significantly faster since the number of scalar operation is much smaller. The gain in computing speed using the Ahmad-Cohen scheme is (N/3.8)1/4 for both the standard and Hermite schemes, where N is the total number of particles. However. this gain can be significantly smaller on vector or parallel machines.

  ASTRONOMICAL SOC JAPAN, 1992, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 44(2) (2), 141 - 151, English

  Scientific journal


• ON A HERMITE INTEGRATOR WITH AHMAD-COHEN SCHEME FOR GRAVITATIONAL MANY-BODY PROBLEMS

  J MAKINO, SJ AARSETH

  We describe the implementation of the Ahmad-Cohen scheme based on a fourth-order Hermite integrator. With the fourth-order Hermite scheme, we calculate the force and the time derivative of the force analytically, and construct a third-order interpolation polynomial using two points in time. Compared with the standard scheme (Aarseth 1985) which is widely used, it allows a longer stepsize for the same accuracy, and the program is much simpler. In the case of the Ahmad-Cohen scheme, which uses different stepsizes for the forces from neighboring particles and that from distant particles, the difference in the programming complexity is even larger, since the Hermite scheme does not require corrections of the higher order divided differences for the forces from distant particles. On scalar computers the Hermite schemes are marginally faster than the standard scheme for the same level of accuracy, both with and without the Ahmad-Cohen scheme. On vector machines or special-purpose hardware, such as GRAPE, the Hermite scheme would be significantly faster since the number of scalar operation is much smaller. The gain in computing speed using the Ahmad-Cohen scheme is (N/3.8)1/4 for both the standard and Hermite schemes, where N is the total number of particles. However. this gain can be significantly smaller on vector or parallel machines.

  ASTRONOMICAL SOC JAPAN, 1992, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 44(2) (2), 141 - 151, English

  Scientific journal


• RAPID ORBITAL DECAY OF A BLACK-HOLE BINARY IN MERGING GALAXIES

  T FUKUSHIGE, T EBISUZAKI, J MAKINO

  Most elliptical galaxies axe believed to have massive central black holes. When they merge, their central black holes sink toward the core of the merger and form a binary system. We investigated the evolution of such a black hole binary under a uniform distribution of field stars. We found that a black hole binary merges in approximately 10(7) yr. The orbital energy and angular momentum of a black hole binary are transferred to the field stars through dynamical friction. The orbit of the binary becomes highly eccentric, since dynamical friction is most effective at the apocenter with the minimum orbital velocity. The periastron distance decreases exponentially, and eventually the black holes merge when the emission of the gravitational radiation becomes significant. The energy transferred from the binary to the field stars is comparable to the binding energy of the core of the parent galaxy.

  ASTRONOMICAL SOC JAPAN, 1992, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 44(3) (3), 281 - 289, English

  Scientific journal


• ENERGY SEGREGATION THROUGH VIOLENT RELAXATION

  Y FUNATO, J MAKINO, T EBISUZAKI

  We performed numerical N-body simulations of a violent relaxation process using a special-purpose computer, GRAPE-1. We found that violent relaxation enhances segregation in energy space. In violent relaxation, particles with higher energy gain more energy than particles with lower energy. In two-body relaxation, however, particles with higher energy lose energy, and particles with lower energy gain it. Therefore, a self-gravitating system doesn't approach thermal equilibrium through violent relaxation. Violent relaxation changes the energies of particles through a time variation of the mean potential field caused by the coherent motion of particles. The change in the kinetic energy does not depend on the energy of the particle, itself, since coherent motion, which has a much larger energy, heats all particles in order to approach energy equipartition, regardless of their velocities. The magnitude of the change in the mean potential field in the outer region is higher than that in the inner region. Therefore, the gain in the average energy in the outer region is larger than that in the inner region. This difference in the energy gain enhances segregation in energy space, since particles with higher energy receive a greater amount of energy. Therefore, violent relaxation does not lead a self-gravitating system to thermal equilibrium. Our result implies that the energy of each particle in a merger remnant is strongly correlated with its initial energy. Therefore, the radial structures of galaxies, such as the color gradient, are likely to survive violent relaxation.

  ASTRONOMICAL SOC JAPAN, 1992, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 44(3) (3), 291 - 301, English

  Scientific journal


• ON CORE COLLAPSE

  J MAKINO, P HUT

  Star clusters undergo core collapse on a thermal time scale. This results follows from detailed simulations in the form of N-body, Fokker-Planck, and gas sphere models. The shrinking of the core, both in size as well as mass, is often heuristically attributed to the negative heat capacity of gravity, as follows from the virial theorem. However, this argument only describes the overall contraction of the inner parts of a star cluster and does not address the evolution of the core mass. We present a linear stability analysis of the isothermal sphere, for different choices of heat conductivity. For some choices the core mass shrinks significantly, while for others it remains constant or even increases. Different physical systems correspond to these different choices. Gaseous systems such as contracting gas clouds with a heat transport based on radiative transfer show a heat conductivity that decreases in the high-density core. When they are isothermal, they will increase their core mass during contraction. When heat transport takes place mostly through thermal conduction by electrons, as in a moderately degenerate star, the core mass will remain nearly constant. Stellar dynamical systems such as globular star clusters have a heat conductivity which strongly peaks toward the central regions, resulting in a rapid shrinking of the core mass.

  UNIV CHICAGO PRESS, Dec. 1991, ASTROPHYSICAL JOURNAL, 383(1) (1), 181 - 191, English

  [Refereed]

  Scientific journal


• MERGER OF BINARY GLOBULAR-CLUSTERS - CASE OF UNEQUAL MASSES

  J MAKINO, K AKIYAMA, D SUGIMOTO

  Merger process of binary globular clusters is discussed for a pair of unequal-mass components. We calculated the case of mass ratio 1:0.5 by means of an N-body code with 6144 particles in total. We have found the followings. The mass exchange between the components takes place through the Roche-lobe overflow. In the early stages, however, the dynamical evolution is mainly governed by escape of particles from the system. As the particles escape carrying angular momentum with them, the separation between the component cluster shrinks. The time-scale of this shrinkage depends upon the size of the clusters. When a critical separation is reached, the orbital angular momentum is transferred unstably to the spins of the component clusters. This is the process of the synchronization instability which was found in a previous study on binary cluster of equal masses. As a result the component clusters merge into a single cluster. The structures of the mergers are quite similar among different cases except for the central cores which retain their initial central concentrations. In particular, the ellipticity and the rotation curve are quite close each other among models of different initial radii and of different mass ratios.

  KLUWER ACADEMIC PUBL, Nov. 1991, ASTROPHYSICS AND SPACE SCIENCE, 185(1) (1), 63 - 78, English

  [Refereed]

  Scientific journal


• MERGING OF 2 GALAXIES WITH CENTRAL BLACK-HOLES

  T EBISUZAKI, J MAKINO, SK OKUMURA

  OBSERVATIONS of elliptical galaxies show a positive correlation 1,2 between total luminosity and core radius, defined as the radius at which surface luminosity becomes half of the central value. This has been taken as evidence against the idea that ellipticals are the result of galaxy mergers, because in simulated mergers 3-5 the core radius remained almost constant. In those simulations, the galaxies contained no central black holes, but there is a body of evidence to suggest that such black holes are common in ellipticals 6. Here, we present simulations of the merging of identical galaxies with and without central black holes, and find that when black holes are included, the merged galaxy acquires an isothermal core comparable in mass to the sum of the two initial black holes. Furthermore, the ratio of the core radius to the half-mass radius is approximately the same as the ratio of the black hole mass to the total galaxy mass, a result also consistent with observational evidence. These results, which can be understood by means of simple analytical arguments, suggest that most elliptical galaxies contain central black holes with masses comparable to the mass of their cores.

  MACMILLAN MAGAZINES LTD, Nov. 1991, NATURE, 354(6350) (6350), 212 - 214, English

  Scientific journal


• STAR CLUSTER EVOLUTION WITH PRIMORDIAL BINARIES .2. DETAILED ANALYSIS

  S MCMILLAN, P HUT, J MAKINO

  We have followed the evolution of globular cluster models containing significant numbers of primordial binaries (about 100 binaries in a 1100 star model), up to the point at which the primordial fuel is spent. This occurs on a time scale about 30 times longer than the original core collapse time. Because of the large numbers of both single stars and binaries present during the first few core collapse times, strong interactions with individual binaries do not dominate the behavior of the cluster, in contrast with all previous studies. The absence of the corresponding wild fluctuations permits a detailed analysis of the average behavior of various cluster parameters. The ratio of the core radius to the half-mass radius is about 0.1 immediately after core collapse, and drops to about 0.05 by the time most of the binaries have been destroyed. The core mass similarly drops by a factor of 2 during this time. The mass fraction of binaries in the core shows a steady, nearlinear decrease from 0.5 to 0.1 between tau approximately 20 and tau approximately 250, where the time increment d-tau is measured in units of the instantaneous half-mass crossing time. We present the first detailed statistical study of the spatial and temporal variations in the binary population throughout a star cluster. Our detailed migration statistics reflect the opposing trends of mass segregation and recoil from energetic interactions in the core. Since we use a direct integration method, based on Aarseth's NBODY5 code, we have also obtained a wealth of microscopic information concerning individual interactions between single stars, binaries, triples, and occasionally more complex multiple-star systems. We present a study of binary interactions in the context of a real cluster environment, and compare our results with earlier "laboratory" simulations, in which similar interactions were studied in isolation. In addition we have performed studies of the formation and evolution of hierarchical triple systems, and the generation of energy within short-lived, overdense "clumps" of stars, rather than via binary interactions in an otherwise smooth background. These data will be useful for future quantitative modeling of processes connected with the origin and evolution of X-ray binaries and millisecond pulsars in globular clusters.

  UNIV CHICAGO PRESS, May 1991, ASTROPHYSICAL JOURNAL, 372(1) (1), 111 - 124, English

  [Refereed]

  Scientific journal


• A SPECIAL-PURPOSE COMPUTER FOR GRAVITATIONAL MANY-BODY PROBLEMS AND MERGER SIMULATIONS

  SK OKUMURA, T EBISUZAKI, J MAKINO, D SUGIMOTO, T ITO, K KODAIRA

  SPRINGER, 1991, IAU SYMPOSIA, (146) (146), 356 - 356, English

  [Refereed]

  Scientific journal


• SPECIAL PURPOSE COMPUTER FOR N-BODY PROBLEMS

  D SUGIMOTO, T EBISUZAKI, T ITO, J MAKINO

  Backend processors for use in gravitational N-body problems were constructed. They are as cheap as a personal computer, yet their speed is comparable to a supercomputer. As an example we show some results of simulations which were done for the dynamical evolution of galaxies in a compact group.

  KLUWER ACADEMIC PUBL, 1991, IAU SYMPOSIA, (148) (148), 489 - 490, English

  [Refereed]

  Scientific journal


• A SPECIAL-PURPOSE COMPUTER FOR GRAVITATIONAL MANY-BODY SYSTEMS - GRAPE-2

  T ITO, T EBISUZAKI, J MAKINO, D SUGIMOTO

  We have designed and built GRAPE-2 (GRAvity PipE 2), the second experimental machine for gravitational many-body systems. GRAPE-2 is designed to calculate the dynamical evolution of astronomical collisional systems which require an accuracy higher than that provided by GRAPE-1, our first experimental machine. GRAPE-2 has a word length of 32/64 bits and calculates gravitational forces at the speed of 40 Mflops. It has been built on a 43 cm by 32 cm board.

  ASTRONOMICAL SOC JAPAN, 1991, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 43(3) (3), 547 - 555, English

  [Refereed]

  Scientific journal


• A SPECIAL-PURPOSE COMPUTER FOR GRAVITATIONAL MANY-BODY PROBLEMS AND MERGER SIMULATIONS

  SK OKUMURA, T EBISUZAKI, J MAKINO, D SUGIMOTO, T ITO, K KODAIRA

  KLUWER ACADEMIC PUBL, 1991, DYNAMICS OF GALAXIES AND THEIR MOLECULAR CLOUD DISTRIBUTIONS, 146, 356 - 356, English

  [Refereed]

  International conference proceedings


• SPECIAL PURPOSE COMPUTER FOR N-BODY PROBLEMS

  D SUGIMOTO, T EBISUZAKI, T ITO, J MAKINO

  KLUWER ACADEMIC PUBL, 1991, MAGELLANIC CLOUDS, 148, 489 - 490, English

  [Refereed]

  International conference proceedings


• DYNAMIC EVOLUTION OF BINARY CLUSTERS AND COLLIDING GALAXIES

  D SUGIMOTO, T EBISUZAKI, J MAKINO

  Merging of stellar systems is investigated by means of N-body simulations. We discuss the synchronization instability to trigger sudden merging, the origin of the ellipticity in the merger remnants, the distribution of stars in the halo, and the survival of the colour gradient of stars against the violent relaxation of the merging process.

  KLUWER ACADEMIC PUBL, 1991, IAU SYMPOSIA, (148) (148), 217 - 218, English

  [Refereed]

  Scientific journal


• DYNAMIC EVOLUTION OF BINARY CLUSTERS AND COLLIDING GALAXIES

  D SUGIMOTO, T EBISUZAKI, J MAKINO

  KLUWER ACADEMIC PUBL, 1991, MAGELLANIC CLOUDS, 148, 217 - 218, English

  [Refereed]

  International conference proceedings


• DYNAMIC EVOLUTION OF COMPACT-GROUPS OF GALAXIES

  K KODAIRA, S OKUMURA, J MAKINO, T EBISUZAKI, D SUGIMOTO

  KLUWER ACADEMIC PUBL, 1991, PRIMORDIAL NUCLEOSYNTHESIS AND EVOLUTION OF EARLY UNIVERSE, 169, 393 - 401, English

  [Refereed]

  International conference proceedings


• GRAPE-1A - SPECIAL-PURPOSE COMPUTER FOR N-BODY SIMULATION WITH A TREE CODE

  T FUKUSHIGE, T ITO, J MAKINO, T EBISUZAKI, D SUGIMOTO, M UMEMURA

  We have designed and built GRAPE (GRAvity PipE)-1A, a special-purpose computer for N-body simulations using the O(N log N) tree code. GRAPE-1A calculates the gravitational force between particles. A host computer, which is connected to GRAPE-1A, performs all other calculations. GRAPE-1A is different from its predecessor, GRAPE-1, which was designed for the N2 direct summation, regarding three points: a) it can handle particles with different masses, b) the speed of communication between the host computer and GRAPE-1A has been increased, c) and a neighbor list unit has been added. The peak speed of GRAPE-1A is equivalent to 240 Mflops. The effective speed is > 200 Mflops for the direct summation, and around 80 Mflops for the tree algorithm. Using GRAPE-1A and the modified tree algorithm code, one time step takes 2 s for N = 4096 and 20 s for N = 32768. GRAPE-1A can complete either a simulation of interacting galaxies (N = 10(5), 5000 timesteps) or a cosmological simulation (N = 10(6), 500 timesteps) within one week. GRAPE-1A can be also applied to particle-based hydrodynamical simulations such as smoothed-particle hydrodynamics (SPH). The performance of GRAPE-1A is comparable to that of a supercomputer with a peak-speed of 500 Mflops for any type of the direct summation, the modified tree algorithm and SPH.

  ASTRONOMICAL SOC JAPAN, 1991, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 43(6) (6), 841 - 858, English

  [Refereed]

  Scientific journal


• 中心ブラックホールをもつ銀河の合体

  1991, 352


• アーセス型N体時間積分のための最適次数と時間刻み

  1991, 369


• Optimal order and timestep criterion for Aarseth-type N-body integraters

  1991, The Astrophysical Journal, 369


• TREECODE WITH A SPECIAL-PURPOSE PROCESSOR

  J MAKINO

  We describe an implementation of the modified Barnes-Hut tree algorithm for a gravitational N-body calculation on a GRAPE (GRAvity PipE) backend processor. GRAPE is a special-purpose computer for N-body calculations. It receives the positions and masses of particles from a host computer and then calculates the gravitational force at each coordinate specified by the host. To use this GRAPE processor with the hierarchical tree algorithm, the host computer must maintain a list of all nodes that exert force on a particle. If we create this list for each particle of the system at each timestep, the number of floating-point operations on the host and that on GRAPE would become comparable, and the increased speed obtained by using GRAPE would be small. In our modified algorithm, we create a list of nodes for many particles. Thus, the amount of the work required of the host is significantly reduced. This algorithm was originally developed by Barnes in order to vectorize the force calculation on a Cyber 205. With this algorithm, the computing time of the force calculation becomes comparable to that of the tree construction, if the GRAPE backend processor is sufficiently fast. The obtained speed-up factor is 30 to 50 for a RISC-based host computer and GRAPE-1A with a peak speed of 240 Mflops.

  ASTRONOMICAL SOC JAPAN, 1991, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 43(4) (4), 621 - 638, English

  Scientific journal


• DREAM - A SPECIAL-PURPOSE COMPUTER FOR LARGE-SCALE MESH CALCULATIONS

  J MAKINO, T EBISUZAKI, SK OKUMURA

  We present the concept of DREAM (Disk Resource Array Machine), a computer designed for large-scale simulations using finite-difference grids. At present, such simulations are usually performed on vector processors. on which the size of the calculation is limited not by the speed of computation but by the size of the memory. The DREAM system uses an array of magnetic disks as the main memory. instead of silicon solid-state memory chips. Since the price per bit of a magnetic disk is about 1/100 that of a silicon memory, we can construct a machine with a 100-times larger memory for the same cost. The access time of a disk is about 10(5) times longer than that of a silicon memory. In the case of finite-difference calculations using regular grids, however, this access time becomes negligible, since the memory is accessed only in long vectors. Using currently available technology, a DREAM system with 2 Gbytes of disk space and effective speed of 40 Mflops costs around 3 million Japanese yen. A system with a 200 Gbytes disk and a 10 Gflops speed would cost a few hundred million yen. We also discuss the reliability of the hardware and the possibility of applying DREAM to other fields, such as the reduction of large amount of observational data.

  ASTRONOMICAL SOC JAPAN, 1991, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 43(4) (4), 639 - 648, English

  Scientific journal


• KINEMATIC STRUCTURES OF MERGER REMNANTS

  SK OKUMURA, T EBISUZAKI, J MAKINO

  We performed a set of N-body simulations of the merging of two identical spherical galaxies using a special-purpose computer, GRAPE-1. We found that the kinematic properties of the resulting merger remnants are consistent with those of observed elliptical galaxies. The ratios of the maximum rotation velocity (V(max)) to the velocity dispersion (sigma(0)) are smaller than 0.6, even in the case of large impact parameters. This is in good agreement with the lack of elliptical galaxies whose V(max)/sigma(0) exceeds 0.6. Previous N-body calculations have contradicted the observed kinematic studies of elliptical galaxies, because relaxation was numerically enhanced due to the small number of particles (approximately 500). Our simulations with N = 16384 resolve this problem. The central velocity dispersion increased by 10-20% through merging for a wide range of impact parameters. This increase is consistent with the Faber-Jackson relation.

  ASTRONOMICAL SOC JAPAN, 1991, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 43(6) (6), 781 - 793, English

  Scientific journal


• A MODIFIED AARSETH CODE FOR GRAPE AND VECTOR PROCESSORS

  J MAKINO

  We discuss the performance of a hierarchical timestep algorithm, which is Aarseth's individual timestep algorithm for N-body problems modified for use with GRAPE hardware and/or vector processors. In Aarseth's original algorithm, each particle has its own time and timestep. At each integration step, we update only one particle. To obtain the force on that particle, we predict the positions of all other particles at its time. In our GRAPE-2 system this prediction is performed on the general-purpose host computer, while the force calculation is performed on fast special-purpose hardware. Since the calculation cost of the prediction and the force calculation are comparable, the total speed is limited by the speed of the host computer. In the hierarchical timestep algorithm, we update several particles simultaneously. Therefore, we predict the positions of other particles only once for these particles. In order to update several particles, we organize the timesteps of particles in a hierarchy, where timesteps are "quantized" to powers of two. Theoretically, the number of particles that can be updated simultaneously is N(g) congruent-to O(N2/3), where N is the number of particles, if the system can be regarded as being homogeneous. For 50 less-than-or-equal-to N less-than-or-equal-to 1000, experimentally we obtained N(g) approximately 0.5N2/3 for a Plummer model. The efficiency that we obtained on GRAPE-2 system is about 70% for N = 1024.

  ASTRONOMICAL SOC JAPAN, 1991, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 43(6) (6), 859 - 876, English

  Scientific journal


• BOTTLENECKS IN SIMULATIONS OF DENSE STELLAR-SYSTEMS

  J MAKINO, P HUT

  UNIV CHICAGO PRESS, Dec. 1990, ASTROPHYSICAL JOURNAL, 365(1) (1), 208 - 218, English

  [Refereed]

  Scientific journal


• STAR CLUSTER EVOLUTION WITH PRIMORDIAL BINARIES .1. A COMPARATIVE-STUDY

  S MCMILLAN, P HUT, J MAKINO

  UNIV CHICAGO PRESS, Oct. 1990, ASTROPHYSICAL JOURNAL, 362(2) (2), 522 - 537, English

  [Refereed]

  Scientific journal


• A SPECIAL-PURPOSE N-BODY MACHINE GRAPE-1

  T ITO, J MAKINO, T EBISUZAKI, D SUGIMOTO

  ELSEVIER SCIENCE BV, Sep. 1990, COMPUTER PHYSICS COMMUNICATIONS, 60(2) (2), 187 - 194, English

  Scientific journal


• A SPECIAL-PURPOSE COMPUTER FOR GRAVITATIONAL MANY-BODY PROBLEMS

  D SUGIMOTO, Y CHIKADA, J MAKINO, T ITO, T EBISUZAKI, M UMEMURA

  MACMILLAN MAGAZINES LTD, May 1990, NATURE, 345(6270) (6270), 33 - 35, English

  Scientific journal


• GRAPE - A SPECIAL-PURPOSE COMPUTER FOR N-BODY PROBLEMS

  J MAKINO, T ITO, T EBISUZAKI, D SUGIMOTO

  I E E E, COMPUTER SOC PRESS, 1990, PROCEEDINGS OF THE INTERNATIONAL CONF ON APPLICATION SPECIFIC ARRAY PROCESSORS, 180 - 189, English

  [Refereed]

  International conference proceedings


• N体計算専用マシンGRAPE-1の誤差解析

  1990, 42


• N体計算専用マシン GRAPE-1

  1990, 60


• ON THE APPARENT UNIVERSALITY OF THE R1/4 LAW FOR BRIGHTNESS DISTRIBUTION IN GALAXIES

  J MAKINO, K AKIYAMA, D SUGIMOTO

  ASTRONOMICAL SOC JAPAN, 1990, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 42(2) (2), 205 - 215, English

  Scientific journal


• ERROR ANALYSIS OF THE GRAPE-1 SPECIAL-PURPOSE N-BODY MACHINE

  J MAKINO, T ITO, T EBISUZAKI

  We discuss the numerical accuracy of GRAPE-1, a special-purpose computer for astrophysical N-body calculations. The word length is the primary factor that determines the construction cost of such a special-purpose computer. Regarding GRAPE-1, we adopted the minimal word length with which we can obtain physically correct results. We used 16-bit fixed-point numbers for the positions of particles, 48-bit fixed-point numbers for the accumulation of force, and 8-bit floating-point numbers for all other force calculations. The theoretical accuracy of the force calculated by GRAPE-1 is approximately 0.4% for a homogeneous sphere with a softening parameter of the order of the average interparticle distance, independent of the number of particles, except for very small N (such as N less-than or approximately 100). The integration error for a typical particle caused by this round-off error scales as a two-body relaxation effect, and is roughly 10-100 times smaller than the relaxation effect itself. This implies that the numerical accuracy of GRAPE-1 is sufficient for collisionless calculations, since two-body relaxation dominates the numerical error of collisionless N-body calculations. The results of calculations on the GRAPE-1 system support our theoretical estimate.

  ASTRONOMICAL SOC JAPAN, 1990, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 42(5) (5), 717 - 736, English

  Scientific journal


• SYNCHRONIZATION INSTABILITY AND MERGING OF BINARY GLOBULAR-CLUSTERS

  D SUGIMOTO, J MAKINO

  ASTRONOMICAL SOC JAPAN, 1989, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 41(6) (6), 1117 - 1144, English

  Scientific journal


• PERFORMANCE ANALYSIS OF DIRECT N-BODY CALCULATIONS

  J MAKINO, P HUT

  UNIV CHICAGO PRESS, Dec. 1988, ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES, 68(4) (4), 833 - 856, English

  Scientific journal


• MODELING THE EVOLUTION OF GLOBULAR STAR-CLUSTERS

  P HUT, J MAKINO, S MCMILLAN

  MACMILLAN MAGAZINES LTD, Nov. 1988, NATURE, 336(6194) (6194), 31 - 35, English


• Galaxies in the connection machine

  Junichiro Makino, Piet Hut

  Many problems in galactic dynamics require computer speeds orders of magnitude larger than what can be achieved on current single-processor machines. In the near future such speeds are likely to become available through computer architectures based on large-scale, fine-grained parallelism. An example of a highly parallel computer is the Connection Machine, with up to 65,636 processors. We have benchmarked gravitational N-body algorithms on the Connection Machine, and compared those with similar benchmarks which we have obtained on more traditional vector supercomputers. Our conclusions are: (1) The direct summation algorithm, with of order N2 interactions for N particles, can be made to run with high efficiency on either type of computer. As a result, the Connection Machine clearly wins in speed over all supercomuters tested, with the exception of an 8-processor ETA, which shows a comparable performance. (2) A more efficient tree algorithm reduces the growth of the number of interactions from N2 to N log N. However, the greater complexity of this algorithm causes a considerable degradation of efficiency, by a factor which is larger on the Connection Machine than on vector supercomputers. As a result, out tree code runs at comparable speeds on both types of machines, with the notable exception of the 8-processor ETA, which has an extrapolated speed for running our tree code which is higher than any of the other machines we have tested. © 1989 Kluwer Academic Publishers.

  Kluwer Academic Publishers, Mar. 1988, Celestial Mechanics, 45(1-3) (1-3), 141 - 147, English

  [Refereed]

  Scientific journal


• GALAXIES IN THE CONNECTION MACHINE

  Junichiro Makino, Piet Hut

  Many problems in galactic dynamics require computer speeds orders of magnitude larger than what can be achieved on current single-processor machines. In the near future such speeds are likely to become available through computer architectures based on large-scale, fine-grained parallelism. An example of a highly parallel computer is the Connection Machine, with up to 65,636 processors. We have benchmarked gravitational N-body algorithms on the Connection Machine, and compared those with similar benchmarks which we have obtained on more traditional vector supercomputers. Our conclusions are: (1) The direct summation algorithm, with of order N(2) interactions for N particles, can be made to run with high efficiency on either type of computer. As a result, the Connection Machine clearly wins in speed over all supercomputers tested, with the exception of an 8-processor ETA, which shows a comparable performance. (2) A more efficient tree algorithm reduces the growth of the number of interactions from N(2) to N log N. However, the greater complexity of this algorithm causes a considerable degradation of efficiency, by a factor which is larger on the Connection Machine than on vector supercomputers. As a result, our tree code runs at comparable speeds on both types of machines, with the notable exception of the 8-processor ETA, which has an extrapolated speed for running our tree code which is higher than any of the other machines we have tested.

  SPRINGER, Mar. 1988, CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 45(1-3) (1-3), 141 - 147, English

  [Refereed]

  Scientific journal


• 直接N体計算の性能分析

  1988, 68


• EFFECT OF SUPRATHERMAL PARTICLES ON GRAVOTHERMAL OSCILLATION

  J MAKINO, D SUGIMOTO

  ASTRONOMICAL SOC JAPAN, 1987, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 39(4) (4), 589 - 603, English

  Scientific journal


• Simple analytical solution for multiplicative nonlinear stochastic differential equations by a perturbation technique

  Akio Morita, Junichiro Makino

  A simple convergent and analytical solution valid for the whole time range for the stochastic Verhulst equation is obtained by treating the strength of the external Gaussian white noise as a perturbation without using the existing approach where the moments are expressed by means of an integral representation. In the case when the deterministic behavior is coupled weakly with the stochastic one induced by the perturbation, it is found that the analytical result is in good agreement with the numerical one. This perturbation technique is also used for treating a class of multiplicative nonlinear stochastic differential equations, and the moments valid for the whole time range are calculated analytically. The result shows explicitly the behavior of the long-time decay of t-1/2, and it also compares satisfactorily with the numerical one in the limit of weak noise strength. © 1986 The American Physical Society.

  1986, Physical Review A, 34(2) (2), 1595 - 1598, English

  [Refereed]

  Scientific journal


• GRAVOTHERMAL OSCILLATION IN GRAVITATIONAL MANY-BODY SYSTEMS

  J MAKINO, J TANEKUSA, D SUGIMOTO

  ASTRONOMICAL SOC JAPAN, 1986, PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 38(6) (6), 865 - 877, English

  Scientific journal


• 24.確率的Verhulst方程式による人口増加のダイナミクスの再考察(パターン形成,運動と統計,研究会報告)

  牧野 淳一郎

  この論文は国立情報学研究所の電子図書館事業により電子化されました。研究会報告

  物性研究刊行会, 1985, 物性研究, 44(3) (3), 484 - 485, Japanese

• 3.11以後の科学リテラシー(no.146)

  牧野 淳一郎

  東京 : 岩波書店, Mar. 2025, 科学, 95(3) (3), 267 - 269, Japanese


• 3.11以後の科学リテラシー(no.145)

  牧野 淳一郎

  東京 : 岩波書店, Feb. 2025, 科学, 95(2) (2), 181 - 184, Japanese


• 3.11以後の科学リテラシー(no.144)

  牧野 淳一郎

  東京 : 岩波書店, Jan. 2025, 科学, 95(1) (1), 77 - 80, Japanese


• 3.11以後の科学リテラシー(no.143)

  牧野 淳一郎

  東京 : 岩波書店, Dec. 2024, 科学, 94(12) (12), 1115 - 1118, Japanese


• 3.11以後の科学リテラシー(no.142)

  牧野 淳一郎

  東京 : 岩波書店, Nov. 2024, 科学, 94(11) (11), 1018 - 1020, Japanese


• 国立感染症研究所が発表する「新型コロナ流行による超過死亡」解析の誤り

  本堂 毅, 牧野 淳一郎, 御手洗 聡, 森内 浩幸

  東京 : 日本医事新報社, 26 Oct. 2024, 日本医事新報, (5244) (5244), 54 - 57, Japanese


• 3.11以後の科学リテラシー(no.141)

  牧野 淳一郎

  東京 : 岩波書店, Oct. 2024, 科学, 94(10) (10), 908 - 911, Japanese


• 3.11以後の科学リテラシー(no.140)

  牧野 淳一郎

  東京 : 岩波書店, Sep. 2024, 科学, 94(9) (9), 846 - 848, Japanese


• 3.11以後の科学リテラシー(no.139)

  牧野 淳一郎

  東京 : 岩波書店, Aug. 2024, 科学, 94(8) (8), 745 - 747, Japanese


• 3.11以後の科学リテラシー(no.138)

  牧野 淳一郎

  東京 : 岩波書店, Jul. 2024, 科学, 94(7) (7), 604 - 606, Japanese


• 3.11以後の科学リテラシー(no.137)

  牧野 淳一郎

  東京 : 岩波書店, Jun. 2024, 科学, 94(6) (6), 564 - 566, Japanese


• 3.11以後の科学リテラシー(no.136)

  牧野 淳一郎

  東京 : 岩波書店, May 2024, 科学, 94(5) (5), 411 - 413, Japanese


• 3.11以後の科学リテラシー(no.135)

  牧野 淳一郎

  東京 : 岩波書店, Apr. 2024, 科学, 94(4) (4), 355 - 357, Japanese


• 3.11以後の科学リテラシー(no.134)

  牧野 淳一郎

  東京 : 岩波書店, Mar. 2024, 科学, 94(3) (3), 266 - 269, Japanese


• 3.11以後の科学リテラシー(no.133)

  牧野 淳一郎

  東京 : 岩波書店, Feb. 2024, 科学, 94(2) (2), 158 - 160, Japanese


• 3.11以後の科学リテラシー(no.132)

  牧野 淳一郎

  東京 : 岩波書店, Jan. 2024, 科学, 94(1) (1), 86 - 88, Japanese


• 3.11以後の科学リテラシー(no.131)

  牧野 淳一郎

  東京 : 岩波書店, Dec. 2023, 科学, 93(12) (12), 1062 - 1064, Japanese


• 3.11以後の科学リテラシー(no.130)

  牧野 淳一郎

  東京 : 岩波書店, Nov. 2023, 科学, 93(11) (11), 982 - 984, Japanese


• 3.11以後の科学リテラシー(no.129)

  牧野 淳一郎

  東京 : 岩波書店, Oct. 2023, 科学, 93(10) (10), 898 - 900, Japanese


• ポスト・ムーア時代のスパコン(4・最終回)効率的なアーキテクチャ(2)

  牧野 淳一郎

  東京 : 岩波書店, Oct. 2023, 科学, 93(10) (10), 901 - 904, Japanese


• 3.11以後の科学リテラシー(no.128)

  牧野 淳一郎

  東京 : 岩波書店, Sep. 2023, 科学, 93(9) (9), 810 - 812, Japanese


• ポスト・ムーア時代のスパコン(3)効率的なアーキテクチャ(1)

  牧野 淳一郎

  東京 : 岩波書店, Sep. 2023, 科学, 93(9) (9), 813 - 816, Japanese


• 3.11以後の科学リテラシー(no.127)

  牧野 淳一郎

  東京 : 岩波書店, Aug. 2023, 科学, 93(8) (8), 661 - 663, Japanese


• ポスト・ムーア時代のスパコン(2)演算性能の向上は限界に近づいているのか

  牧野 淳一郎

  東京 : 岩波書店, Aug. 2023, 科学, 93(8) (8), 732 - 735, Japanese


• ポスト・ムーア時代のスパコン(1)過去の計算機の性能向上

  牧野 淳一郎

  東京 : 岩波書店, Jul. 2023, 科学, 93(7) (7), 570 - 574, Japanese


• 3.11以後の科学リテラシー(no.126)

  牧野 淳一郎

  東京 : 岩波書店, Jul. 2023, 科学, 93(7) (7), 640 - 642, Japanese


• 3.11以後の科学リテラシー(no.125)

  牧野 淳一郎

  東京 : 岩波書店, Jun. 2023, 科学, 93(6) (6), 555 - 557, Japanese


• 3.11以後の科学リテラシー(no.124)

  牧野 淳一郎

  東京 : 岩波書店, May 2023, 科学, 93(5) (5), 467 - 470, Japanese


• 3.11以後の科学リテラシー(no.123)

  牧野 淳一郎

  東京 : 岩波書店, Apr. 2023, 科学, 93(4) (4), 301 - 303, Japanese


• 3.11以後の科学リテラシー(no.122)

  牧野 淳一郎

  東京 : 岩波書店, Mar. 2023, 科学, 93(3) (3), 275 - 278, Japanese


• 3.11以後の科学リテラシー(no.121)

  牧野 淳一郎

  東京 : 岩波書店, Feb. 2023, 科学, 93(2) (2), 182 - 184, Japanese


• 3.11以後の科学リテラシー(no.120)

  牧野 淳一郎

  東京 : 岩波書店, Jan. 2023, 科学, 93(1) (1), 78 - 81, Japanese


• 3.11以後の科学リテラシー(no.119)

  牧野 淳一郎

  東京 : 岩波書店, Dec. 2022, 科学, 92(12) (12), 1109 - 1112, Japanese


• 3.11以後の科学リテラシー(no.118)

  牧野 淳一郎

  東京 : 岩波書店, Nov. 2022, 科学, 92(11) (11), 1026 - 1029, Japanese


• 3.11以後の科学リテラシー(no.117)

  牧野 淳一郎

  東京 : 岩波書店, Oct. 2022, 科学, 92(10) (10), 941 - 944, Japanese


• 3.11以後の科学リテラシー(no.116)

  牧野 淳一郎

  東京 : 岩波書店, Sep. 2022, 科学, 92(9) (9), 854 - 856, Japanese


• 3.11以後の科学リテラシー(no.115)

  牧野 淳一郎

  東京 : 岩波書店, Aug. 2022, 科学, 92(8) (8), 762 - 765, Japanese


• 3.11以後の科学リテラシー(no.114)

  牧野 淳一郎

  東京 : 岩波書店, Jul. 2022, 科学, 92(7) (7), 666 - 668, Japanese


• 3.11以後の科学リテラシー(no.113)

  牧野 淳一郎

  東京 : 岩波書店, May 2022, 科学, 92(5) (5), 407 - 410, Japanese


• 3.11以後の科学リテラシー(no.112)—特集 原発事故と小児甲状腺がん

  Apr. 2022, 92(4) (4), 336 - 341, Japanese


• 3.11以後の科学リテラシー(no.111)

  Mar. 2022, 92(3) (3), 191 - 195, Japanese


• 3.11以後の科学リテラシー(no.110)

  牧野 淳一郎

  Feb. 2022, 92(2) (2), 159 - 162, Japanese


• 3.11以後の科学リテラシー(no.109)

  牧野 淳一郎

  Jan. 2022, 92(1) (1), 19 - 22, Japanese


• 3.11以後の科学リテラシー(no.108)

  牧野 淳一郎

  Dec. 2021, 91(12) (12), 1127 - 1131, Japanese


• 3.11以後の科学リテラシー(no.107)

  牧野 淳一郎

  岩波書店, Nov. 2021, 科学, 91(11) (11), 1034 - 1038, Japanese


• 3.11以後の科学リテラシー(no.106)

  牧野 淳一郎

  岩波書店, Oct. 2021, 科学, 91(10) (10), 946 - 949, Japanese


• 3.11以後の科学リテラシー(no.105)

  牧野 淳一郎

  岩波書店, Sep. 2021, 科学, 91(9) (9), 861 - 863, Japanese


• 3.11以後の科学リテラシー(no.104)

  牧野 淳一郎

  岩波書店, Aug. 2021, 科学, 91(8) (8), 807 - 811, Japanese


• 3.11以後の科学リテラシー(no.103)

  牧野 淳一郎

  岩波書店, Jul. 2021, 科学, 91(7) (7), 655 - 658, Japanese


• 3.11以後の科学リテラシー(no.102) (特集 被曝影響評価をめぐる問題群)

  牧野 淳一郎

  岩波書店, Jun. 2021, 科学, 91(6) (6), 592 - 594, Japanese


• 3.11以後の科学リテラシー(no.101)

  牧野 淳一郎

  岩波書店, May 2021, 科学, 91(5) (5), 497 - 500, Japanese


• 3.11以後の科学リテラシー(no.100)

  牧野 淳一郎

  岩波書店, Apr. 2021, 科学, 91(4) (4), 365 - 368, Japanese


• 3.11以後の科学リテラシー(no.99)

  牧野 淳一郎

  岩波書店, Mar. 2021, 科学, 91(3) (3), 249 - 252, Japanese


• 3.11以後の科学リテラシー(no.98)

  牧野 淳一郎

  岩波書店, Feb. 2021, 科学, 91(2) (2), 137 - 140, Japanese


• 銀河形成シミュレーションで探るrプロセス元素に富んだ星の動力学的性質

  平居悠, 青木和光, BEERS Timothy C., 千葉柾司, 斎藤貴之, 岡本崇, 牧野淳一郎, 牧野淳一郎

  2021, 日本天文学会年会講演予稿集, 2021


• ASURA-FDPSによる銀河形成シミュレーション:富岳向けチューニングの現状

  斎藤貴之, 行方大輔, 野村昴太郎, 岩澤全規, 平居悠, 岡本崇, 牧野淳一郎

  2021, 日本天文学会年会講演予稿集, 2021


• 深層学習を用いた超新星爆発によるシェル膨張の予測

  平島敬也, 森脇可奈, 藤井通子, 斎藤貴之, 牧野淳一郎

  2021, 日本天文学会年会講演予稿集, 2021


• 3.11以後の科学リテラシー(no.97)

  牧野 淳一郎

  岩波書店, Jan. 2021, 科学, 91(1) (1), 69 - 72, Japanese


• 富岳を使えば銀河形成の過程を忠実に再現できる (スパコン世界一「富岳」の正体(第2回))

  牧野 淳一郎

  中央公論新社, Dec. 2020, 中央公論, 134(12) (12), 155 - 159, Japanese


• 3.11以後の科学リテラシー(no.96)

  牧野 淳一郎

  岩波書店, Dec. 2020, 科学, 90(12) (12), 1094 - 1097, Japanese


• 3.11以後の科学リテラシー(no.95)

  牧野 淳一郎

  岩波書店, Nov. 2020, 科学, 90(11) (11), 974 - 977, Japanese


• 3.11以後の科学リテラシー(no.94) (特集 新型コロナウイルス感染症とコミュニケーション)

  牧野 淳一郎

  岩波書店, Oct. 2020, 科学, 90(10) (10), 923 - 927, Japanese


• 3.11以後の科学リテラシー(no.93)

  牧野 淳一郎

  岩波書店, Sep. 2020, 科学, 90(9) (9), 814 - 817, Japanese


• 3.11以後の科学リテラシー(no.92) (特集 複合災害下の問題群)

  牧野 淳一郎

  岩波書店, Aug. 2020, 科学, 90(8) (8), 696 - 698, Japanese


• 3.11以後の科学リテラシー(no.91)

  牧野 淳一郎

  岩波書店, Jul. 2020, 科学, 90(7) (7), 588 - 591, Japanese


• 3.11以後の科学リテラシー(no.90) (特集 新型コロナウイルス感染症と科学的助言)

  牧野 淳一郎

  岩波書店, Jun. 2020, 科学, 90(6) (6), 520 - 526, Japanese


• 3.11以後の科学リテラシー(no.89)

  牧野 淳一郎

  岩波書店, May 2020, 科学, 90(5) (5), 428 - 432, Japanese


• 3.11以後の科学リテラシー(no.88)

  牧野 淳一郎

  岩波書店, Apr. 2020, 科学, 90(4) (4), 305 - 309, Japanese


• 3.11以後の科学リテラシー(no.87)

  牧野 淳一郎

  岩波書店, Mar. 2020, 科学, 90(3) (3), 224 - 226, Japanese


• From "No Immediate Effect" to "No Relationship to Radiation Exposure" : Dose Evaluation and Science

  牧野 淳一郎

  日本学術協力財団, Mar. 2020, 学術の動向 = Trends in the sciences, 25(3) (3), 60 - 64, Japanese


• 3.11以後の科学リテラシー(no.86)

  牧野 淳一郎

  岩波書店, Feb. 2020, 科学, 90(2) (2), 177 - 179, Japanese


• Introduction to Auto-Generator Tool of Massive Parallel Simulation Code

  野村 昴太郎, 沼田 龍介, 八柳 祐一, 行方 大輔, 岩澤 全規, 牧野 淳一郎

  プラズマ・核融合学会編集委員会, Feb. 2020, プラズマ・核融合学会誌 = Journal of plasma and fusion research, 96(2) (2), 57 - 64, Japanese


• 3.11以後の科学リテラシー(no.85)

  牧野 淳一郎

  岩波書店, Jan. 2020, 科学, 90(1) (1), 73 - 75, Japanese


• 3.11以後の科学リテラシー(no.84)

  牧野 淳一郎

  岩波書店, Dec. 2019, 科学, 89(12) (12), 1087 - 1090, Japanese


• 3.11以後の科学リテラシー(no.83)

  牧野 淳一郎

  岩波書店, Nov. 2019, 科学, 89(11) (11), 962 - 965, Japanese


• 3.11以後の科学リテラシー(no.82)

  牧野 淳一郎

  岩波書店, Oct. 2019, 科学, 89(10) (10), 884 - 886, Japanese


• 3.11以後の科学リテラシー(no.81)

  牧野 淳一郎

  岩波書店, Sep. 2019, 科学, 89(9) (9), 790 - 795, Japanese


• 3.11以後の科学リテラシー(no.80)

  牧野 淳一郎

  岩波書店, Aug. 2019, 科学, 89(8) (8), 687 - 692, Japanese


• 3.11以後の科学リテラシー(no.79)

  牧野 淳一郎

  岩波書店, Jul. 2019, 科学, 89(7) (7), 656 - 659, Japanese


• 3.11以後の科学リテラシー(no.78)

  牧野 淳一郎

  岩波書店, Jun. 2019, 科学, 89(6) (6), 559 - 562, Japanese


• 3.11以後の科学リテラシー(no.77)

  牧野 淳一郎

  岩波書店, May 2019, 科学, 89(5) (5), 431 - 435, Japanese


• 3.11以後の科学リテラシー(no.76)

  牧野 淳一郎

  岩波書店, Apr. 2019, 科学, 89(4) (4), 360 - 364, Japanese


• 3.11以後の科学リテラシー(no.75)

  牧野 淳一郎

  岩波書店, Mar. 2019, 科学, 89(3) (3), 266 - 269, Japanese


• 3.11以後の科学リテラシー(no.74)

  牧野 淳一郎

  岩波書店, Feb. 2019, 科学, 89(2) (2), 171 - 173, Japanese


• 分子雲衝突による一様金属量を持つ星団の形成シミュレーション

  斎藤貴之, 平居悠, 藤井通子, 牧野淳一郎, 馬場淳一

  2019, 日本天文学会年会講演予稿集, 2019


• 3.11以後の科学リテラシー(no.73)

  牧野 淳一郎

  岩波書店, Jan. 2019, 科学, 89(1) (1), 22 - 24, Japanese


• 3.11以後の科学リテラシー(no.72)

  牧野 淳一郎

  岩波書店, Dec. 2018, 科学, 88(12) (12), 1182 - 1184, Japanese


• 3.11以後の科学リテラシー(no.71)

  牧野 淳一郎

  岩波書店, Nov. 2018, 科学, 88(11) (11), 1077 - 1080, Japanese


• 3.11以後の科学リテラシー(no.70)

  牧野 淳一郎

  岩波書店, Oct. 2018, 科学, 88(10) (10), 987 - 991, Japanese


• 3.11以後の科学リテラシー(no.69)

  牧野 淳一郎

  岩波書店, Sep. 2018, 科学, 88(9) (9), 879 - 882, Japanese


• 3.11以後の科学リテラシー(no.68)

  牧野 淳一郎

  岩波書店, Aug. 2018, 科学, 88(8) (8), 826 - 829, Japanese


• 3.11以後の科学リテラシー(no.67)

  牧野 淳一郎

  岩波書店, Jul. 2018, 科学, 88(7) (7), 704 - 707, Japanese


• 3.11以後の科学リテラシー(no.66)

  牧野 淳一郎

  岩波書店, Jun. 2018, 科学, 88(6) (6), 625 - 628, Japanese


• 3.11以後の科学リテラシー(no.65)

  牧野 淳一郎

  岩波書店, May 2018, 科学, 88(5) (5), 475 - 478, Japanese


• 3.11以後の科学リテラシー(no.64)

  牧野 淳一郎

  岩波書店, Apr. 2018, 科学, 88(4) (4), 354 - 358, Japanese


• 3.11以後の科学リテラシー(no.63) (特集 原発事故下の7年)

  牧野 淳一郎

  岩波書店, Mar. 2018, 科学, 88(3) (3), 291 - 293, Japanese


• 3.11以後の科学リテラシー(no.62)

  牧野 淳一郎

  岩波書店, Feb. 2018, 科学, 88(2) (2), 131 - 133, Japanese


• New method of gravitational-wave detection using optical lattice clocks

  Shinkai Hisaaki, Tamagawa Toru, Noda Atsushi, Katori Hidetoshi, Makino Jun'ichiro, Ebisuzaki Toshikazu

  The Physical Society of Japan, 2018, Meeting Abstracts of the Physical Society of Japan, 73(0) (0), 477 - 477, Japanese


• 3.11以後の科学リテラシー(no.61)

  牧野 淳一郎

  岩波書店, Jan. 2018, 科学, 88(1) (1), 38 - 41, Japanese


• 光格子時計による重力波検出 (特集 重力波天文学の曙)

  玉川 徹, 真貝 寿明, 野田 篤司, 香取 秀俊, 牧野 淳一郎, 戎崎 俊一

  岩波書店, Dec. 2017, 科学, 87(12) (12), 1109 - 1113, Japanese


• 3.11以後の科学リテラシー(no.60)

  牧野 淳一郎

  岩波書店, Nov. 2017, 科学, 87(11) (11), 1006 - 1008, Japanese


• 3.11以後の科学リテラシー(no.59)

  牧野 淳一郎

  岩波書店, Oct. 2017, 科学, 87(10) (10), 976 - 978, Japanese


• 3.11以後の科学リテラシー(no.58)

  牧野 淳一郎

  岩波書店, Sep. 2017, 科学, 87(9) (9), 830 - 833, Japanese


• 3.11以後の科学リテラシー(no.57)

  牧野 淳一郎

  岩波書店, Aug. 2017, 科学, 87(8) (8), 709 - 711, Japanese


• 3.11以後の科学リテラシー(no.56) (特集 被曝影響と甲状腺がん)

  牧野 淳一郎

  岩波書店, Jul. 2017, 科学, 87(7) (7), 626 - 630, Japanese


• 3.11以後の科学リテラシー(no.55)

  牧野 淳一郎

  岩波書店, Jun. 2017, 科学, 87(6) (6), 575 - 577, Japanese


• 3.11以後の科学リテラシー(no.54)

  牧野 淳一郎

  岩波書店, May 2017, 科学, 87(5) (5), 443 - 445, Japanese


• 3.11以後の科学リテラシー(no.52)

  牧野 淳一郎

  岩波書店, Mar. 2017, 科学, 87(3) (3), 230 - 233, Japanese


• 3.11以後の科学リテラシー(no.51)

  牧野 淳一郎

  岩波書店, Feb. 2017, 科学, 87(2) (2), 121 - 123, Japanese


• Far UVフィードバックの銀河の形成と進化への影響

  斎藤貴之, 馬場淳一, 平居悠, 牧野淳一郎

  2017, 日本天文学会年会講演予稿集, 2017


• Preface

  Makino Junichiro

  The Japanese Society for Planetary Sciences, 2017, Planetary People - The Japanese Society for Planetary Sciences, 26(3) (3), 81 - 81, Japanese


• 3.11以後の科学リテラシー(no.50)

  牧野 淳一郎

  岩波書店, Jan. 2017, 科学, 87(1) (1), 19 - 23, Japanese


• 3.11以後の科学リテラシー(no.49)

  牧野 淳一郎

  岩波書店, Dec. 2016, 科学, 86(12) (12), 1260 - 1263, Japanese


• 3.11以後の科学リテラシー(no.48) (甲状腺検査データ分析)

  牧野 淳一郎

  岩波書店, Nov. 2016, 科学, 86(11) (11), 1087 - 1089, Japanese


• 3.11以後の科学リテラシー(no.47)

  牧野 淳一郎

  岩波書店, Oct. 2016, 科学, 86(10) (10), 998 - 1000, Japanese


• 3.11以後の科学リテラシー(no.46)

  牧野 淳一郎

  岩波書店, Sep. 2016, 科学, 86(9) (9), 891 - 898, Japanese


• 3.11以後の科学リテラシー(no.45) (特集 甲状腺がん172人の現実)

  牧野 淳一郎

  岩波書店, Aug. 2016, 科学, 86(8) (8), 806 - 809, Japanese


• 3.11以後の科学リテラシー(no.44)

  牧野 淳一郎

  岩波書店, Jul. 2016, 科学, 86(7) (7), 661 - 664, Japanese


• 3.11以後の科学リテラシー(no.43)

  牧野 淳一郎

  岩波書店, Jun. 2016, 科学, 86(6) (6), 622 - 626, Japanese


• 3.11以後の科学リテラシー(no.42)

  牧野 淳一郎

  岩波書店, Apr. 2016, 科学, 86(4) (4), 338 - 341, Japanese


• 3.11以後の科学リテラシー(no.41)

  牧野 淳一郎

  岩波書店, Mar. 2016, 科学, 86(3) (3), 235 - 238, Japanese


• 3.11以後の科学リテラシー(no.40)

  牧野 淳一郎

  岩波書店, Feb. 2016, 科学, 86(2) (2), 138 - 142, Japanese


• 慣性変化法によるマントルの熱対流シミュレーション

  竹山浩介, 斎藤貴之, 牧野淳一郎

  2016, 日本天文学会年会講演予稿集, 2016


• 惑星形成N体計算の大粒子数化に向けて:FDPSを用いたParticle-Particle Particle-Tree法の並列計算

  山川暁久, 牧野淳一郎, 斎藤貴之, 小南淳子, 竹山浩介

  2016, 日本地球惑星科学連合大会予稿集(Web), 2016


• SPH法における,人工粘性とそのスイッチ,微分演算子の離散化に関するテスト

  細野七月, 斎藤貴之, 牧野淳一郎, 牧野淳一郎

  2016, 日本地球惑星科学連合大会予稿集(Web), 2016


• 対談 放射能汚染と被ばくの影響、子どもたちにどう伝える? (特集 東日本大震災と原発事故から5年)

  牧野 淳一郎, 山口 幸夫

  アドバンテージサーバー, 2016, 教育と文化 : 季刊フォーラム, (82) (82), 64 - 75, Japanese


• 3.11以後の科学リテラシー(no.39)

  牧野 淳一郎

  岩波書店, Jan. 2016, 科学, 86(1) (1), 28 - 32, Japanese


• 3.11以後の科学リテラシー(no.38)

  牧野 淳一郎

  岩波書店, Dec. 2015, 科学, 85(12) (12), 1186 - 1190, Japanese


• 3.11以後の科学リテラシー(no.37)

  牧野 淳一郎

  岩波書店, Nov. 2015, 科学, 85(11) (11), 1110 - 1113, Japanese


• 3.11以後の科学リテラシー(no.36)

  牧野 淳一郎

  岩波書店, Oct. 2015, 科学, 85(10) (10), 937 - 941, Japanese


• 3.11以後の科学リテラシー(no.35)

  牧野 淳一郎

  岩波書店, Sep. 2015, 科学, 85(9) (9), 848 - 851, Japanese


• 3.11以後の科学リテラシー(no.34)

  牧野 淳一郎

  岩波書店, Aug. 2015, 科学, 85(8) (8), 793 - 795, Japanese


• 3.11以後の科学リテラシー(no.33)

  牧野 淳一郎

  岩波書店, Jul. 2015, 科学, 85(7) (7), 664 - 666, Japanese


• 3.11以後の科学リテラシー(no.32) (特集 人間の論理・自然の摂理) -- (川内原発決定書の論理)

  牧野 淳一郎

  岩波書店, Jun. 2015, 科学, 85(6) (6), 563 - 567, Japanese


• 3.11以後の科学リテラシー(no.31)

  牧野 淳一郎

  岩波書店, May 2015, 科学, 85(5) (5), 454 - 457, Japanese


• 3.11以後の科学リテラシー(no.30)

  牧野 淳一郎

  岩波書店, Apr. 2015, 科学, 85(4) (4), 374 - 378, Japanese


• 3.11以後の科学リテラシー(no.29)

  牧野 淳一郎

  岩波書店, Mar. 2015, 科学, 85(3) (3), 254 - 258, Japanese


• 3.11以後の科学リテラシー(no.28)

  牧野 淳一郎

  岩波書店, Feb. 2015, 科学, 85(2) (2), 133 - 136, Japanese


• 慣性変化法によるマントルの熱対流シミュレーション

  竹山浩介, 斎藤貴之, 牧野淳一郎

  2015, 日本地球惑星科学連合大会予稿集(Web), 2015


• 3.11以後の科学リテラシー(no.27)

  牧野 淳一郎

  岩波書店, Jan. 2015, 科学, 85(1) (1), 33 - 38, Japanese


• 「林忠四郎の全仕事」, 佐藤文隆編, 京都大学学術出版会, 2014年5月刊行, 全816ページ, 定価15,120円, ISBN:9784876984978

  牧野 淳一郎

  日本惑星科学会, 25 Dec. 2014, 遊・星・人 : 日本惑星科学会誌, 23(4) (4), 400 - 400, Japanese


• 3.11以後の科学リテラシー(no.26)

  牧野 淳一郎

  岩波書店, Dec. 2014, 科学, 84(12) (12), 1204 - 1207, Japanese


• 3.11以後の科学リテラシー(no.25)

  牧野 淳一郎

  岩波書店, Nov. 2014, 科学, 84(11) (11), 1147 - 1151, Japanese


• 3.11以後の科学リテラシー(no.24)

  牧野 淳一郎

  岩波書店, Oct. 2014, 科学, 84(10) (10), 1022 - 1026, Japanese


• GRAPE9-MPX : A development of an accelerator dedicated for arbitrary-precision arithmetic by the FPGA boards

  MOTOKI Shinji, DAISAKA Hiroshi, NAKASATO Naohito, ISHIKAWA Tadashi, YUASA Fukuko, FUKUSHIGE Toshiyuki, KAWAI Atsushi, MAKINO Jun'ichiro

  Higher order corrections in perturbative quantum field theory are required for precise theoretical analysis to investigate the new physics. Feynman loop diagrams which appear in the calculation of the corrections are taken into account, leading to the evaluation of loop integrals. We developed GRAPE9-MPX system consisting of multiple FPGA boards to accelerate parallel computation of loop integrals. In the system, we implemented Processor Elements (PE) to realize quadruple/hexuple-precision arithmetics in FPGA. The theoretical perk speed in the current implementation is about 6.6 Gflops (quadruple-precision) and 3.2 Gflops (hexuple-precision). With the compiler we are developing, the program code is generated automatically with only inserting directives in C/C++ code. We present performance results for the case of Feynman two-loop integrals with quadruple precision and achieve the effective performance of 2.4Gflops for 1 board, 4.7Gflops for 2 boards, and 9.1Gflops for 4 boards, respectively.

  The Institute of Electronics, Information and Communication Engineers, 18 Sep. 2014, IEICE technical report, 114(223) (223), 69 - 74, Japanese


• O5-05 任意の不連続面に対応可能なSPH法の開発(口頭発表セッション5 惑星形成III,口頭発表)

  山本 智子, 斎藤 貴之, 牧野 淳一郎

  日本惑星科学会, 10 Sep. 2014, 日本惑星科学会秋期講演会予稿集, 2014, "O5 - 05", Japanese


• 3.11以後の科学リテラシー(no.23)

  牧野 淳一郎

  岩波書店, Sep. 2014, 科学, 84(9) (9), 914 - 917, Japanese


• 3.11以後の科学リテラシー(no.22)

  牧野 淳一郎

  岩波書店, Aug. 2014, 科学, 84(8) (8), 826 - 832, Japanese


• 3.11以後の科学リテラシー(no.21)

  牧野 淳一郎

  岩波書店, Jul. 2014, 科学, 84(7) (7), 715 - 718, Japanese


• 3.11以後の科学リテラシー(no.20)

  牧野 淳一郎

  岩波書店, Jun. 2014, 科学, 84(6) (6), 608 - 612, Japanese


• 3.11以後の科学リテラシー(no.19)

  牧野 淳一郎

  岩波書店, May 2014, 科学, 84(5) (5), 500 - 503, Japanese


• 3.11以後の科学リテラシー(no.18)

  牧野 淳一郎

  岩波書店, Apr. 2014, 科学, 84(4) (4), 399 - 403, Japanese


• Symposium on Computational Planetary Science

  Hayashi Y, Umeda T, Umemura M, Ogawa M, Kameyama M

  The Japanese Society for Planetary Sciences, Mar. 2014, Planetary People, 23(1) (1), 64 - 69, Japanese


• 3.11以後の科学リテラシー(no.17)

  牧野 淳一郎

  岩波書店, Mar. 2014, 科学, 84(3) (3), 263 - 267, Japanese


• 3.11以後の科学リテラシー(no.16)

  牧野 淳一郎

  岩波書店, Feb. 2014, 科学, 84(2) (2), 141 - 146, Japanese


• 微分可能かつ正値な擬密度を用いたSPH法の開発

  山本智子, 斎藤貴之, 牧野淳一郎

  2014, 日本天文学会年会講演予稿集, 2014


• DISPH法によるサンタバーバラクラスターのエントロピーコア形成

  斎藤貴之, 牧野淳一郎

  2014, 日本天文学会年会講演予稿集, 2014


• 慣性変化法によるマントルの熱対流シミュレーション

  竹山浩介, 斎藤貴之, 牧野淳一郎

  2014, 日本天文学会年会講演予稿集, 2014


• 3.11以後の科学リテラシー(no.15)

  牧野 淳一郎

  岩波書店, Jan. 2014, 科学, 84(1) (1), 109 - 113, Japanese


• 3.11以後の科学リテラシー(no.14)

  牧野 淳一郎

  岩波書店, Dec. 2013, 科学, 83(12) (12), 1340 - 1345, Japanese


• O4-03 Density Independent Smoothed Particle Hydrodynamicsの非理想気体への拡張(口頭発表セッション4(惑星形成),口頭発表)

  細野 七月, 斎藤 貴之, 牧野 淳一郎

  日本惑星科学会, 20 Nov. 2013, 日本惑星科学会秋期講演会予稿集, 2013, "O4 - 03", Japanese


• P1-22 物理量の連続性を仮定しないSPH法の開発(ポスターセッション1,ポスター発表)

  山本 智子, 斎藤 貴之, 牧野 淳一郎

  日本惑星科学会, 20 Nov. 2013, 日本惑星科学会秋期講演会予稿集, 2013, "P1 - 22", Japanese


• P1-21 Density Independent Smoothed Particle Hydrodynamicsによる巨大衝突シミュレーション(ポスターセッション1,ポスター発表)

  細野 七月, 斎藤 貴之, 牧野 淳一郎

  日本惑星科学会, 20 Nov. 2013, 日本惑星科学会秋期講演会予稿集, 2013, "P1 - 21", Japanese


• The use of simulations and predictions : In relation to the accident of Fukushima-Daiichi nuclear power plant

  牧野 淳一郎

  岩波書店, Nov. 2013, 科学, 83(11) (11), 1270 - 1274, Japanese


• 3.11以後の科学リテラシー(no.13)

  牧野 淳一郎

  岩波書店, Oct. 2013, 科学, 83(10) (10), 1092 - 1094, Japanese


• 3.11以後の科学リテラシー(no.12)

  牧野 淳一郎

  岩波書店, Sep. 2013, 科学, 83(9) (9), 967 - 972, Japanese


• 3.11以後の科学リテラシー(no.11)

  牧野 淳一郎

  岩波書店, Aug. 2013, 科学, 83(8) (8), 870 - 875, Japanese


• 大規模SIMD型アクセラレータの検討

  児玉祐悦, 山口佳樹, 中里直人, 牧野淳一郎, 朴泰祐, 佐藤三久

  将来のアクセラレータとして有望な大規模 SIMD 型プロセッサについて、検討を行っている。そのアーキテクチャの基本設計方針や、性能パラメータの検討結果を示すとともに、より詳細な評価を行うために、検討のたたき台としてのアーキテクチャの設計を行った。そのアーキテクチャを紹介するとともに、そのアーキテクチャに基づくサイクルベースシミュレータを作成して、いくつかのベンチマークを用いて性能見積もりを行った。また、今後の評価の方針や検討課題について考察する。

  一般社団法人情報処理学会, 24 Jul. 2013, 研究報告ハイパフォーマンスコンピューティング（HPC）, 2013(38) (38), 1 - 8, Japanese


• 3.11以後の科学リテラシー(no.10)

  牧野 淳一郎

  岩波書店, Jul. 2013, 科学, 83(7) (7), 730 - 734, Japanese


• 3.11以後の科学リテラシー(no.09)

  牧野 淳一郎

  岩波書店, Jun. 2013, 科学, 83(6) (6), 611 - 614, Japanese


• 3.11以後の科学リテラシー(no.08)

  牧野 淳一郎

  岩波書店, May 2013, 科学, 83(5) (5), 493 - 496, Japanese


• 3.11以後の科学リテラシー(no.07)

  牧野 淳一郎

  岩波書店, Apr. 2013, 科学, 83(4) (4), 379 - 386, Japanese


• 3.11以後の科学リテラシー(no.06)

  牧野 淳一郎

  岩波書店, Mar. 2013, 科学, 83(3) (3), 261 - 267, Japanese


• 三地球質量ガス雲G2の近点通過によるフレア現象について

  斎藤貴之, 牧野淳一郎, 朝木義晴, 馬場淳一, 小麦真也, 三好真, 長尾透, 高橋真聡, 武田隆顕, 坪井昌人, 若松謙一

  20 Feb. 2013, 日本天文学会年会講演予稿集, 2013, 70, Japanese


• 3.11以後の科学リテラシー(no.05)

  牧野 淳一郎

  岩波書店, Feb. 2013, 科学, 83(2) (2), 153 - 157, Japanese


• The Origin of Matter and the Universe

  MAKINO Junichiro

  日本計算工学会, 31 Jan. 2013, 計算工学, 18(1) (1), 2897 - 2900, Japanese


• 非理想気体も扱えるDensity Independent Smoothed Particle Hydrodynamicsの開発

  細野七月, 斎藤貴之, 牧野淳一郎, 牧野淳一郎

  2013, 日本天文学会年会講演予稿集, 2013


• 幾何学的体積を用いたSPH法の開発

  山本智子, 斎藤貴之, 牧野淳一郎

  2013, 日本天文学会年会講演予稿集, 2013


• Density Independent Formulation of SPH

  斎藤貴之, 牧野淳一郎

  2013, 日本天文学会年会講演予稿集, 2013


• 3.11以後の科学リテラシー(no.04)

  牧野 淳一郎

  岩波書店, Jan. 2013, 科学, 83(1) (1), 29 - 32, Japanese


• 3.11以後の科学リテラシー(no.03)

  牧野 淳一郎

  岩波書店, Dec. 2012, 科学, 82(12) (12), 1291 - 1294, Japanese


• 3.11以後の科学リテラシー(no.02)

  牧野 淳一郎

  岩波書店, Nov. 2012, 科学, 82(11) (11), 1188 - 1191, Japanese


• 専用計算機GRAPEと計算物理 (特集 GRAPEによる計算物理)

  牧野 淳一郎

  丸善, Oct. 2012, パリティ, 27(10) (10), 4 - 9, Japanese


• 国策プロジェクトとしてのスパコン開発

  牧野 淳一郎

  岩波書店, Sep. 2012, 科学, 82(9) (9), 965 - 972, Japanese


• 座談会 消えた論理の謎 : 原発事故後の言葉の融解 (特集 科学の<限界> : 価値の選択と予測)

  押川 正毅, 影浦 峡, 牧野 淳一郎

  岩波書店, Mar. 2012, 科学, 82(3) (3), 285 - 293, Japanese


• 畑村委員会中間報告に書かれていないこと (2011大震災)

  牧野 淳一郎

  岩波書店, Feb. 2012, 科学, 82(2) (2), 149 - 153, Japanese


• 超高光度赤外線銀河の複数個コアの起源

  松井秀徳, 斎藤貴之, 牧野淳一郎, 和田桂一, 富阪幸治, 小久保英一郎, 台坂博, 岡本崇, 吉田直紀

  2012, 日本天文学会年会講演予稿集, 2012


• 座談会 原発事故後の"日本的対応"をよむ (特集 科学は誰のためのものか--原発事故後の科学と社会)

  押川 正毅, 藤垣 裕子, 牧野 淳一郎

  岩波書店, Sep. 2011, 科学, 81(9) (9), 881 - 886, Japanese


• Lectures for Science Teachers of Junior-high School supported by SPP (2)

  モリ, ヤスヒト, スダ, ジュンイチロウ, マキノ, カズナリ, ハラ, ヒサユキ, Yamakita, Hisae

  10 KJ00007544919 論文

  佐世保 : 国立高等専門学校機構佐世保工業高等専門学校, 11 Jan. 2011, RESEARCH REPORTS OF NATIONAL INSTITUTE OF TECHNOLOGY，SASEBO COLLEGE, 47, 55 - 64, Japanese


• 合体による星団の進化と中間質量ブラックホールの形成

  藤井通子, 藤井通子, 斎藤貴之, 牧野淳一郎, 岩澤全規, ZWART Simon F.Portegies

  2011, 日本天文学会年会講演予稿集, 2011


• 星団の階層的合体による形成・進化

  藤井通子, 藤井通子, 斎藤貴之, 牧野淳一郎, PORTEGIES ZWART Simon

  2011, 日本天文学会年会講演予稿集, 2011


• 渦状腕構造の維持機構

  馬場淳一, 藤井通子, 斎藤貴之, 牧野淳一郎, 和田桂一

  2010, 日本天文学会年会講演予稿集, 2010


• 銀河衝突合体におけるHyper Star Clusters形成と銀河中心への質量供給

  松井秀徳, 斎藤貴之, 小久保英一郎, 富阪幸治, 牧野淳一郎, 和田桂一, 台阪博, 岡本崇, 吉田直紀

  2010, 日本天文学会年会講演予稿集, 2010


• FAST:A Fully Asynchronous Split Time-integrator for Self-Gravitational Fluid

  斎藤貴之, 牧野淳一郎

  2010, 日本天文学会年会講演予稿集, 2010


• 強いショックをSPHで扱うための独立時間刻み法の改良

  斎藤貴之, 牧野淳一郎

  2010, 日本天文学会年会講演予稿集, 2010


• Gravitational N-body simulation and LU decomposition with the multi purpose accelerator GRAPE-DR

  小池邦昭, 藤野健, 福重俊幸, 台坂博, 菅原豊, 稲葉真理, 平木敬, 牧野淳一郎

  15 Oct. 2009, 情報処理学会研究報告(CD-ROM), 2009(3) (3), ROMBUNNO.ARC-184,26, Japanese


• 10aSK-7 Acceleration of the computation of loop integrals with GRAPE-DR

  Yuasa F, Ishikawa T, Makino J, Nakasato N, Hamaguchi N, Koike K

  The Physical Society of Japan (JPS), 18 Aug. 2009, Meeting abstracts of the Physical Society of Japan, 64(2) (2), 4 - 4, Japanese


• Gravitational N-body simulation and LU decomposition with the multi purpose accelerator GRAPE-DR

  小池邦昭, 藤野健, 福重俊幸, 台坂博, 菅原豊, 稲葉真理, 平木敬, 牧野淳一郎

  超並列準汎用計算機 GRAPE-DR は 1 チップに 512 個の演算要素を搭載した SIMD アクセラレータを PC に接続し，これを並列に接続したクラスタシステムである．これは従来の重力多体問題専用計算機 GRAPE の発展形として使用できるように構想されたものであるが，アクセラレータ部分が専用ハードウェアパイプラインではなくプログラム可能な演算器を搭載することでより広い応用が可能であることが大きな特徴である．本論文ではアクセラレータ部で動作する重力相互作用計算と行列積計算ルーチンを実装し，1 ノードでの性能評価をおこなった．現在それぞれのライブラリについて最適化を行っている．現状では重力相互作用計算では 362.6 GFlops (N = 262144)，行列積計算では 635.1GFlops (M = N = 32768，K = 2048) の演算性能となった．これを用いて High Performance LINPACK (HPL) の加速を行い，演算性能値は 284.3 GFlops (N = 34816，NB = 2048) となった．The multi purpose computer GRAPE-DR is a cluster of PCs computer with the custom-mad

  情報処理学会, 28 Jul. 2009, 研究報告計算機アーキテクチャ（ARC）, 2009(26) (26), 1 - 11, Japanese


• Fast Quad-Precision Operations On Many-core Accelerators

  中里 直人, 石川 正, 牧野 淳一郎, 湯浅 富久子

  本論文では，GRAPE-DRやGPU などのメニーコアアクセラレータにおける，四倍精度演算 (DD 演算) の性能評価について報告する．四倍精度相当の演算は倍精度演算器を利用することでエミュレーションすることができる．しかしそのためには DD 演算あたり 20-23 回の倍精度演算が必要であり，DD 演算の演算性能は，倍精度演算性能と比べると 20 分の 1 以下となる．また，通常の CPU では，利用できる論理レジスタが最大で 16 個であるため，DD 演算性能はさらに低下する．一方で，メニーコアアクセラレータをベクトル型演算器と考えると，実効的なレジスタ数が非常に多いため，ループアンローリングが効果的に働くことで，演算レイテンシを完全に隠蔽できる．我々は GRAPE-DR と GPU で DD 演算をおこなうための基本ライブラリとそれを利用するためのコンパイラを開発した．これにより，メニーコアアクセラレータでの DD 演算性能を調べた．結果，通常の CPU での DD 演算性能より 30 - 90 倍の高速

  情報処理学会, 28 Jul. 2009, 研究報告ハイパフォーマンスコンピューティング（HPC）, 2009(39) (39), 1 - 7, Japanese


• スーパーコンピューティングの将来

  牧野淳一郎

  2009


• VLBIによる銀河円盤観測の意義と精度

  三好真, 馬場淳一, 朝木義晴, 牧野淳一郎, 斎藤貴之, 和田桂一

  2009, 日本天文学会年会講演予稿集, 2009


• VLBIによる銀河の非円運動の観測結果

  朝木義晴, 馬場淳一, 牧野淳一郎, 三好真, 斎藤貴之, 和田桂一

  2009, 日本天文学会年会講演予稿集, 2009


• 渦巻き銀河の3次元N体/SPH計算

  馬場淳一, 和田桂一, 斎藤貴之, 牧野淳一郎

  2009, 日本天文学会年会講演予稿集, 2009


• ASURAによる様々な衝突パラメータを用いた渦巻き銀河衝突実験

  松井秀徳, 斎藤貴之, 和田桂一, 富阪幸治, 牧野淳一郎

  2009, 日本天文学会年会講演予稿集, 2009


• ASURAによる銀河シミュレーション

  斎藤貴之, 馬場淳一, 松井秀典, 小久保英一郎, 和田桂一, 牧野淳一郎, 富阪幸治, 台坂博, 吉田直紀, 岡本崇

  2009, 日本天文学会年会講演予稿集, 2009


• 銀河の非円運動-理論と観測

  牧野淳一郎, 馬場淳一, 朝木義晴, 三好真, 斎藤貴之, 和田桂一

  2009, 日本天文学会年会講演予稿集, 2009


• 銀河渦巻構造の維持発生機構の新理論

  和田桂一, 馬場淳一, 斎藤貴之, 牧野淳一郎

  2009, 日本天文学会年会講演予稿集, 2009


• 相互作用銀河における星団形成過程の解明

  斎藤貴之, 小久保英一郎, 和田桂一, 牧野淳一郎, 富阪幸治, 台坂博, 吉田直紀, 岡本崇

  2009, 日本天文学会年会講演予稿集, 2009


• 渦巻銀河における恒星渦状腕の動力学進化

  藤井通子, 藤井通子, 馬場淳一, 小久保英一郎, 斎藤貴之, 牧野淳一郎, 和田桂一, 台坂博

  2009, 日本天文学会年会講演予稿集, 2009


• ASURAによる様々な衝突パラメータを用いた渦巻き銀河衝突実験

  松井秀徳, 斎藤貴之, 小久保英一郎, 和田桂一, 牧野淳一郎, 富阪幸治, 台坂博, 吉田直紀, 岡本崇

  2009, 日本天文学会年会講演予稿集, 2009


• 331 微惑星円盤内での連星形成I等質量微惑星円盤(原始惑星系円盤II,オーラルセッション11)

  台坂 淳子, 牧野 淳一郎, 台坂 博

  日本惑星科学会, 01 Nov. 2008, 日本惑星科学会秋期講演会予稿集, 2008, 92 - 92, Japanese


• Prospects of Numerical Simulations in Astrophysics

  MATSUMOTO Ryoji, MAKINO Junichiro

  日本計算工学会, 31 Jan. 2008, Journal of the Japan Society for Computational Engineering and Science, 13(1) (1), 1746 - 1749, Japanese


• 相互作用銀河の初期遭遇時におけるスターバーストと星団形成

  斎藤貴之, 小久保英一郎, 和田桂一, 牧野淳一郎, 富阪幸治, 岡本崇, 台坂博, 吉田直紀

  2008, 日本天文学会年会講演予稿集, 2008


• High-Performance Small-Scale Simulation of Star Clusters Evolution on Cray XD1

  NITADORI KEIGO, MAKINO JUNICHIRO, ABE GEORGE

  In this paper, we describe the implimentation and performance of N-body simulation code for a star cluster with 64 k stars on a Cray XD1 system with 400 dual-core Opteron processors. There have been many reports on the parallelization of astrophysical N-body simulations. For parallel implementations on more than a few tens of processors, performance was usually measured for very large number of particles. For example, all previous entries for the Gordon-Bell prizes used at least 700k particles. The reason for this preference of large numbers of particles is the parallel efficiency. It is very difficult to achieve high performance on large parallel machines, if the number of particles is small. However, for many scientifically important problems the calculation cost scales as O(N^<3.3>), and it is very important to use large machines for relatively small number of particles. We achieved 2.03 Tflops, or 57.7% of the theoretical peak performance, using a direct O(N^2) calculation with the individual timestep algorithm, on 64k particles. The best efficiency previously reported on similar calculation with 64 K or smaller number of particles is 7.8% (9 Gflops) on Cray T3E-900 with 128 pr

  Information Processing Society of Japan (IPSJ), 15 May 2007, 情報処理学会論文誌コンピューティングシステム（ACS）, 48(8) (8), 54 - 61, Japanese


• Massive Black Holes at the Centers of Globular Clusters?

  牧野 淳一郎

  日本天文学会, 20 Jan. 2007, The Astronomical herald, 100(2) (2), 92 - 99, Japanese


• 2007年度の天の川創成プロジェクト

  斎藤貴之, 小久保英一郎, 和田桂一, 富阪幸治, 牧野淳一郎, 岡本崇, 台坂博, 吉田直紀

  2007, 日本天文学会年会講演予稿集, 2007


• 天の川創成プロジェクト零号機の開発 III コード開発

  斎藤貴之, 台坂博, 出田誠, 小久保英一郎, 和田桂一, 富阪幸治, 牧野淳一郎, 吉田直紀

  2006, 日本天文学会年会講演予稿集, 2006


• 天の川創成プロジェクト IV 壱号機の開発と性能報告

  斎藤貴之, 台坂博, 出田誠, 岡本崇, 小久保英一郎, 和田桂一, 富阪幸治, 牧野淳一郎, 吉田直紀

  2006, 日本天文学会年会講演予稿集, 2006


• AM06-19-011 Origin of the Milkyway

  SAITOH Takayuki, DAISAKA Hiroshi, IDETA Makoto, OKAMOTO Takashi, KOKUBO Eiichiro, WADA Keiichi, TOMISAKA Kohji, MAKINO Junichiro, YOSHIDA Naoki

  In this paper, we introduce Project "Origin of the Milkyway". This project aims at reliable modeling of the formation history of our Galaxy (i.e., the Milkyway), as a typical spiral galaxy, with the mass resolution 2-3 orders of magnitude higher than what has been achieved so far. In order to achieve such state-of-the-art simulations, we construct two beowulf type PC-clusters with GRAPE-6A/7, and we develop a new N-body/SPH code for parallel computing.

  日本流体力学会, 2006, 日本流体力学会年会講演論文集, 2006, 286 - 286, Japanese


• 講座 とんでる力学(12・最終回)剛体の運動(3)グライダーの3次元運動

  牧野 淳一郎

  丸善, Mar. 2005, パリティ, 20(3) (3), 56 - 61, Japanese


• 講座 とんでる力学(11)剛体の運動(2)グライダーの安定性

  牧野 淳一郎

  丸善, Feb. 2005, パリティ, 20(2) (2), 64 - 68, Japanese


• 天の川創成プロジェクト零号機の開発 II

  斎藤貴之, 台坂博, 出田誠, 小久保英一郎, 和田桂一, 富阪幸治, 牧野淳一郎, 吉田直紀

  2005, 日本天文学会年会講演予稿集, 2005


• 天の川実験装置零号機の開発

  台坂博, 斎藤貴之, 小久保英一郎, 和田桂一, 牧野淳一郎, 吉田直紀

  2005, 日本天文学会年会講演予稿集, 2005


• Origin of the Moon -- An essential condition for a large satellite --

  Wada Keiichi, Kokubo Eiichiro, Makino Junichiro

  In order to examine the ``giant impact hypothesis'' for the Moon formation, we run the first grid-based, high-resolution hydrodynamic simulations for impact between proto-Earth and a proto-planet. The spatial resolution for the impact-generated disk is greatly improved from previous particle-based simulations. This allows us to explore internal fine structures of the debris disk and its long-term evolution. We find that in order to form a stable debris disk from which a lunar-sized satellite can be accumulated, the impact must result in a disk of mostly liquid debris, where pressure is not effective, well before the accumulation process starts. If the debris is dominated by vapor gas, strong spiral shocks are generated, thereby the circumterrestrial disk cannot survive more than several days.

  THE JAPANESE SOCIETY FOR PLANETARY SCIENCES, 2005, Abstracts for fall meeting of the Japanese Society for Planetary Science, 2005(0) (0), 91 - 91


• 講座:とんでる力学(第10回)剛体の運動(1)グライダーが飛べるわけ

  牧野 淳一郎

  丸善, Jan. 2005, パリティ, 20(1) (1), 77 - 81, Japanese


• Information Technologies Support Astronomy:Milky Way Project

  WADA Keiichi, KOKUBO Eiichiro, TOMISAKA Kohji, DAISAKA Hiroshi, SAITOH Takayuki, MAKINO Junichiro, YOSHIDA Naoki

  大規模理論天文シミュレーションによる「天の川創成プロジェクト」とその背景にある銀河形成の問題について紹介します。プロジェクトでは、詳細な理論モデル、計算手法と高速の専用並列計算機を組み合わせ、宇宙初期から現在まで、銀河の形成・進化過程を高精度でシミュレーションすることにより、（1） 我々の銀河系＝天の川の3次元構造とその形成過程、および（2）銀河の形態の起源、を初めて明らかにすることを目指しています。第I 期計画では、次世代専用超並列計算機GRAPE-DRと高速ホスト計算機、高速ネットワークを組み合わせた計算能力1ペタフロップスの「天の川数値解析装置」を国立天文台内に構築し、現状の最大規模のシミュレーションの100倍規模のシミュレーションを行います。 これにより銀河形成問題にブレークスルーをもたらすことができるはずです。

  Information Processing Society of Japan (IPSJ), 15 Dec. 2004, IPSJ Magazine, 45(12) (12), 1225 - 1228, Japanese


• 講座:とんでる力学(第9回)人工衛星の打ち上げはなぜ大変?

  牧野 淳一郎

  丸善, Dec. 2004, パリティ, 19(12) (12), 66 - 70, Japanese


• 講座:とんでる力学(第8回)惑星の軌道(5)多体問題は解けない?

  牧野 淳一郎

  丸善, Nov. 2004, パリティ, 19(11) (11), 66 - 70, Japanese


• 講座:とんでる力学(第7回)惑星の軌道(4)2つの惑星

  牧野 淳一郎

  丸善, Oct. 2004, パリティ, 19(10) (10), 59 - 63, Japanese


• 講座 とんでる力学(6)惑星の軌道(3)周転円近似

  牧野 淳一郎

  丸善, Sep. 2004, パリティ, 19(9) (9), 57 - 61, Japanese


• Formation Mechanism of Binaries in the Edgeworth-Kuiper-belt (Current Topics)

  Funato Yoko, Makino Junichiro, Kokubo Eiichiro

  Recent observations have revealed an unexpectedly high binary fraction among the Edgeworth-Kuiper-belt objects (EKBOs). The discovered binaries are characteristic so that theories of binary asteroid formation ever known cannot explain the formation of EKBO binaries. Here we show a mechanism which naturally produces the EKBO-type binaries. Our theory implies that EKBOs were formed through gravitational instabilities of the protoplanetary dust layer.

  The Physical Society of Japan (JPS), 05 Aug. 2004, Butsuri, 59(8) (8), 537 - 540, Japanese


• 講座:とんでる力学(第5回)惑星の軌道(2)本当に楕円軌道?

  牧野 淳一郎

  丸善, Aug. 2004, パリティ, 19(8) (8), 48 - 52, Japanese


• 講座:とんでる力学(4)惑星の軌道(1)楕円軌道

  牧野 淳一郎

  丸善, Jul. 2004, パリティ, 19(7) (7), 61 - 64, Japanese


• 講座 とんでる力学(3)ボールの軌跡(3)"魔球"を実験する

  牧野 淳一郎

  丸善, Jun. 2004, パリティ, 19(6) (6), 57 - 61, Japanese


• 講座:とんでる力学(2)ボールの軌跡(2)空気抵抗

  牧野 淳一郎

  丸善, May 2004, パリティ, 19(5) (5), 53 - 57, Japanese


• 講座 とんでる力学(1)ボールの軌跡(1)自由落下

  牧野 淳一郎

  丸善, Apr. 2004, パリティ, 19(4) (4), 62 - 66, Japanese


• 天の川創成プロジェクト

  和田桂一, 富阪幸治, 小久保英一郎, 台坂博, 斎藤貴之, 牧野淳一郎, 吉田直紀

  2004, 日本天文学会年会講演予稿集, 2004


• Evolution of a Narrow Ring Confined by Shepherding Satellites

  Daisaka Hiroshi, Makino Junichiro

  本研究では、中心星ポテンシャルが歪んでいる事に起因する近点の差動回転のような破壊的効果の影響下で、天王星楕円リングのような楕円リングがどのように形成維持されるのかを議論する。

  THE JAPANESE SOCIETY FOR PLANETARY SCIENCES, 2004, Abstracts for fall meeting of the Japanese Society for Planetary Science, 2004(0) (0), 25 - 25


• Formation Mechanism of Binaries in the Edgeworth-Kuiper-belt

  Funato Yoko, Makino Junichiro, Kokubo Eiichiro

  Recent observations have revealed an unexpectedly high binary fraction among the Edgeworth-Kuiper-belt objects (EKBOs). The discovered binaries are characteristic so that theories of binary asteroid formation ever known cannot explain the formation of EKBO binaries. Here we show a mechanism which naturally produces the EKBO-type binaries. Our theory implies that EKBOs were formed through gravitational instabilities of the protoplanetary dust layer.

  The Physical Society of Japan, 2004, Butsuri, 59(8) (8), 537 - 540, Japanese


• Numerical studies of the Giant Impact Hypotthesis of forming Moon using high-resolution hydrodynamic simulations

  Wada Keiichi, Kokubo Eiichiro, Makino Junichiro

  月形成の「巨大衝突仮説」の拠り所の一つとなっているのが、SPH法を用いた一連の数値実験である。しかし、Cameron, Canupらの数値実験には、多くの点で問題がある。特に有効空間分解能が周地球円盤の半径程度しかないのは致命的である。今回、我々は高精度の３次元Euler-Meshコードを用いて、巨大衝突仮説の再検証を行った。その結果、周地球円盤から形成される月質量は数日で急激に減少するという問題点があることがわかった。

  THE JAPANESE SOCIETY FOR PLANETARY SCIENCES, 2004, Abstracts for fall meeting of the Japanese Society for Planetary Science, 2004(0) (0), 106 - 106


• S604 Large-scale Simulation on Special-purpose Computers : The GRAPE Project

  MAKINO Junichiro

  プラズマ・核融合学会, 2004, プラズマ・核融合学会年会予稿集, (21) (21), 37 - 37, Japanese


• HMCS - G : Grid - enabled Hybrid Computing System for Computational Astrophysics

  BOKU TAISUKE, SATO MITSUHISA, ONUMA KENJI, MAKINO JUNICHIRO, SUSA HAJIME, TAKAHASHI DAISUKE, UMEMURA MASAYUKI

  We have developed a hybrid computing system named HMCS-G which combines general purpose parallel systems and a special purpose machine for gravity calculation on computational grid environment. The prototype is implemented with GRAPE-6 gravity engine and OmniRPC as Grid-RPC with high portability and throughput. Through the preliminary performance evaluation on several network conditions, it is confirmed that the function and capability of HMCS-G can support actual application for multiphysics simulation. With HMCS-G, the utilization ratio of special purpose machines such as GRAPE-6 is also greatly enhanced through access from all over the world.

  Information Processing Society of Japan (IPSJ), 15 Aug. 2003, 情報処理学会論文誌コンピューティングシステム（ACS）, 44(11) (11), 1 - 13, Japanese


• 第3章 コンピュータにより可能になった新たな科学/工学分野 基礎からの計算科学・工学--シミュレーション (特集 動きのはやい技術動向をより効率的に理解するための用語解説 現代コンピュータ技術の基礎)

  菊池 誠, 牧野 淳一郎, 吉田 たけお

  CQ出版社, Aug. 2003, インタ-フェ-ス, 29(8) (8), 60 - 66, Japanese


• チャンドラ衛星によるスターバースト銀河NGC2146の観測研究

  松本浩典, 鶴剛, 松下聡樹, 川辺良平, 小林尚人, 舞原俊憲, 戎崎俊一, 牧野淳一郎, 野本憲一, 梅田秀之

  2003, 日本天文学会年会講演予稿集, 2003, 158, Japanese


• 研究ニュース

  平岡 秀一, 塩谷 光彦, 狩野 直和, 川島 隆幸, 川上 厚志, 牧野 淳一郎, 中村 栄一, 磯部 寛之, 尾中 敬, 岡 良隆, 上野 啓司, 島田 敏宏, 小間 篤, 東山 哲也, 濱口 宏夫, 清水 裕子

  金属イオンを自在に並べる／有機ケイ素化合物におけるケイ素の配位数の制御／小型熱帯魚ゼブラフィッシュの変異体を用いた遺伝子ハンティング／GRAPE-6とゴードン・ベル賞／フラーレンの基礎n学て妬くナノバイオテクノロジー／赤外線衛星観測と衛星冷却望遠鏡／やる気を起こさせる神経メカニズム／有機分子ナノ構造のシリコン基板上への自己組織化形成／植物の受精のしくみを解き明かす／酵母生細胞の時空間分解ラマン分光／マカク細胞の加齢に関する研究

  東京大学大学院理学系研究科・理学部, 17 Sep. 2002, 東京大学理学系研究科・理学部ニュース, 34(1) (1), 4 - 12, Japanese


• Space Radiative Transfer and Hydrodynamics Calculation with Self-gravity on Heterogeneous Multi-Computer System

  BOKU TAISUKE, MAKINO JUNICHIRO, SUSA HAJIME, UMEMURA MASAYUKI, FUKUSHIGE TOSHIYUKI, UKAWA AKIRA

  HMCS (Heterogeneous Multi-Computer System) is a new parallel processing platform combining massively parallel processors for continuum simulation and particle simulation to realize multi-scale computational physics simulations. We constructed a prototype system of HMGS with a general purpose scientific parallel processor OP-PAGS and a gravity calculation parallel processor GRAPE-6 connecting them via commodity-base parallel network. On the prototype of HMCS, a micro-scopic gravity calculation on GRAPE-6 and a macro-scopic radiative-transfer hydrodynamics calculation on GP-PACS are performed simultaneously to realize detailed simulation on computational astrophysics. Both systems are connected via parallel network controlling system named PIO (Parallel I/O System). On each time step, all data of particles are exchanged between two systems hiding communication latency with a special algorithm and buffering effect by PIO. In this paper, we describe the overall concept of HMGS, its application and system implementation, and the performance evaluation of a prototype system.

  Information Processing Society of Japan (IPSJ), 15 Sep. 2002, 情報処理学会論文誌. ハイパフォーマンスコンピューティングシステム, 43(5) (5), 219 - 229, Japanese


• 第3章 シミュレーションの結果は本当に正しいものなのか? 物理シミュレーションの手法と結果の検証 (特集 コンピュータにより可能になった新たな科学/工学分野 基礎からの計算科学・工学--シミュレーション)

  牧野 淳一郎

  CQ出版社, Sep. 2002, インタ-フェ-ス, 28(9) (9), 62 - 71, Japanese


• 専用計算機の将来--GRAPEの挑戦 (特集 計算機科学の新展開--超並列・量子情報・分子計算・計算科学)

  牧野 淳一郎

  サイエンス社, Sep. 2002, Computer today, 19(5) (5), 4 - 10, Japanese


• Formation Process of Supermassive Blackholes : From a Stellar-Dynamical Viewpoint

  MAKINO Junichiro

  Recently, an "intermediate mass" black hole (IMBH) was found in the central region of galaxy M82 through observations made by ASCA, Chandra and SUBARU. This is the first finding of a black hole with the mass more than 100 solar mass but significantly less than 1 million solar mass, and, as such, has completely changed our understanding of the formation process of massive blackholes. We describe our new scenario in which IMBHs serve as the "missing link" between small and massive black holes. IMBHs first form in young compact star clusters through runaway merging of massive stars. While these IMBHs are forming, the host star clusters sink toward the galactic nucleus through dynamical friction, and upon evaporation deposit their IMBHs near the galactic center. The IMBHs then form binaries and eventually merge via gravitational radiation, forming an SMBH.

  The Physical Society of Japan (JPS), 05 May 2002, 日本物理學會誌, 57(5) (5), 330 - 336, Japanese


• Building the Fastest Computer in the World--Do-it-yourself Approach to High Performance Computing

  MAKINO Junichirou

  学術雑誌目次速報データベース由来, Feb. 2002, Japanese scientific monthly, 55(2) (2), 15 - 18, Japanese


• Formation Process of Supermassive Blackholes. From a Stellar-Dynamical Viewpoint.:From a Stellar-Dynamical Viewpoint

  Makino Junichiro

  Recently, an "intermediate mass" black hole (IMBH) was found in the central region of galaxy M82 through observations made by ASCA, Chandra and SUBARU. This is the first finding of a black hole with the mass more than 100 solar mass but significantly less than 1 million solar mass, and, as such, has completely changed our understanding of the formation process of massive blackholes. We describe our new scenario in which IMBHs serve as the "missing link" between small and massive black holes. IMBHs first form in young compact star clusters through runaway merging of massive stars. While these IMBHs are forming, the host star clusters sink toward the galactic nucleus through dynamical friction, and upon evaporation deposit their IMBHs near the galactic center. The IMBHs then form binaries and eventually merge via gravitational radiation, forming an SMBH.

  The Physical Society of Japan, 2002, Butsuri, 57(5) (5), 330 - 336, Japanese


• N-body simulations of Uranian elliptical rings

  Daisaka Hiroshi, Makino Junichiro

  THE JAPANESE SOCIETY FOR PLANETARY SCIENCES, 2002, Abstracts for fall meeting of the Japanese Society for Planetary Science, 2002(0) (0), 31 - 31


• The lives and deaths of star clusters near the Galactic center

  S Portegies Zwart, J Makino, SLW McMillan, P Hut

  We study the evolution and observability of young, compact star clusters near the Galactic center, such as the Arches and Quintuplet systems. The clusters are modeled by integrating the equations of motion of all stars while accounting for the internal evolution of stars and binaries, as well as the effect of the Galactic tidal field. We find that clusters within 150 pc of the Galactic center dissolve within similar to55 Myr, but their projected densities drop below the background density in the direction of the Galactic center within only a few megayears, effectively making these clusters undetectable after that time. Detailed observations of the Arches cluster, taken at face value, suggest that its mass function is unusually flat and that the cluster contains an overabundance of stars more massive than 20 M-circle dot. Our dynamical analysis, however, shows that the observed characteristics of the Arches cluster are consistent with a perfectly normal initial mass function. The observed anomalies are then caused by a combination of observational selection effects and the dynamical evolution of the cluster. We calibrate the current parameters of the Arches cluster using a normal initial mass function and conclude that the cluster is more massive than 40,000 M-circle dot, has a half-mass radius of about 0.35 pc, and is located between 50 and 90 pc from the Galactic center.

  IOP PUBLISHING LTD, Jan. 2002, ASTROPHYSICAL JOURNAL, 565(1) (1), 265 - 279, English


• Heterogeneous Multi - Computer System : A massively parallel processing system combining continuum and particle simulators

  BOKU TAISUKE, MAKINO JUNICHIRO, SUSA HAJIME, UMEMURA MASAYUKI, FUKUSHIGE TOSHIYUKI, UKAWA AKIRA

  HMCS (Heterogeneous Multi-Computer System) is a new parallel processing platform combining massively parallel processors for continuum simulation and particle simulation to realize multi-scale computational physics simulations. We are constructing a prototype system of HMCS with a general purpose scientific parallel processor CP-PACS and a gravity calculation parallel processor GRAPE-6 connecting them via commodity-base parallel network. On the prototype of HMCS, a micro-sopic gravity calculation on GRAPE-6 and a macroscopic radiation hydrodynamic calculation on CP-PACS are performed simultaneously to realize very detailed simulation on computational astrophysics. Both systems are connected via parallel network controlling system named PIO (Parallel I/O System). On each time step, all data of particles are exchanged between two systems hiding communication latency with a special algorithm and buffering effect by PIO. In this paper, we report the overall concept of HMCS, predected performance, implementation and preliminary performance evaluation of the system as well as new physics provided by this system.

  Information Processing Society of Japan (IPSJ), 26 Oct. 2001, IPSJ SIG Notes, 2001(102) (102), 55 - 60, Japanese


• Missing Link Found? --- The ``runaway'' path to supermassive black holes

  Toshikazu Ebisuzaki, Junichiro Makino, Takeshi Go Tsuru, Yoko Funato, Simon Portegies Zwart, Piet Hut, Steve McMillan, Satoki Matsushita, Hironori Matsumoto, Ryohei Kawabe

  Observations of stellar kinematics, gas dynamics and masers around galactic nuclei have now firmly established that many galaxies host central supermassive black holes (SMBHs) with masses in the range $10^6 \sim 10^9$M$_{\odot}$. However, how these SMBHs formed is not well understood. One reason for this situation is the lack of observations of intermediate-mass BHs (IMBHs), which could bridge the gap between stellar-mass BHs and SMBHs. Recently, this missing link (i.e., an IMBH) has been found in observations made by the ASCA and the Chandra of the central region of the starburst galaxy M82 \citep{MT99, PG99, MT01, Ka01}. Subsequent observations by SUBARU have revealed that this IMBH apparently coincides with a young compact star cluster. Based on these findings, we suggest a new formation scenario for SMBHs. In this scenario, IMBHs first form in young compact star clusters through runaway merging of massive stars. While these IMBHs are forming, the host star clusters sink toward the galactic nucleus through dynamical friction, and upon evaporation deposit their IMBHs near the galactic center. The IMBHs then form binaries and eventually merge via gravitational radiation, forming an SMBH.

  ASTRONOMICAL SOC PACIFIC, 14 Jun. 2001, ASTROPHYSICAL SUPERCOMPUTING USING PARTICLE SIMULATIONS, (208) (208), 157 - 166, English


• Mass and Activity of the Off-Center Intermediate Massive BH in M82

  鶴剛, 松本浩典, 松下聡樹, 川辺良平, 臼田知史, 小林尚人, 後藤美和, 原島隆, 岩室史英, 戎崎俊一, 海老塚昇, 牧野淳一郎

  2001, 日本天文学会年会講演予稿集, 2001, 67, Japanese


• 超巨大ブラックホールの作り方

  戎崎俊一, 牧野淳一郎, 鶴剛

  2001, 日本天文学会年会講演予稿集, 2001, 187, Japanese


• 超巨大ブラックホールの形成シナリオとセイファート銀河とスターバースト銀河の関係

  戎崎俊一, 牧野淳一郎, 鶴剛, 川辺良平

  2001, 日本天文学会年会講演予稿集, 2001, 68, Japanese


• 重力多体系の物理と数値計算 : 大自由度系における平衡と緩和(第45回物性若手夏の学校(2000年度)(その2),講義ノート)

  牧野 淳一郎

  この論文は国立情報学研究所の電子図書館事業により電子化されました。サブゼミ

  物性研究刊行会, 2001, 物性研究, 75(4) (4), 618 - 627, Japanese


• 重力多体系の数値計算(<シリーズ>物性研究者のための計算手法入門)

  牧野 淳一郎

  この論文は国立情報学研究所の電子図書館事業により電子化されました。

  物性研究刊行会, 2001, 物性研究, 76(3) (3), 374 - 465, Japanese


• 科学者の活動をどう測るか--科学計量学の視点

  藤垣 裕子, 牧野 淳一郎

  岩波書店, Dec. 2000, 科学, 70(12) (12), 1081 - 1090, Japanese


• 科学の目 GRAPE-5からGRAPE-6へ--世界最高速計算機からみる計算科学

  牧野 淳一郎

  岩波書店, Feb. 2000, 科学, 70(2) (2), 99 - 101, Japanese


• ハミルトン系の数値解法--symplectic or symmetric? (特集 ハミルトン力学系の展開--カオス・可積分系へのアプローチ)

  船渡 陽子, 牧野 淳一郎

  サイエンス社, Aug. 1999, 数理科学, 37(8) (8), 34 - 40, Japanese


• 新任教官紹介

  邑田 仁, 塩谷 光彦, 牧野 淳一郎, 紫藤 貴文, 後藤 敬, 船守 展正

  付属植物園着任にあたって／着任にあたって／着任にあたって／着任のご挨拶／着任にあたって／だんご博士

  東京大学大学院理学系研究科・理学部, Jun. 1999, 東京大学大学院理学系研究科・理学部廣報, 31(1) (1), 7 - 12, Japanese


• GRAPEプロジェクト

  牧野 淳一郎

  サイエンス社, May 1999, Computer today, 16(3) (3), 30 - 35, Japanese


• 現実世界における科学者の役割は

  牧野淳一郎

  1999, 科学, 69(2) (2), 146


• REVIEW: Fast Multipole Method-Applications to Particle Systems

  MAKINO Junichiro, KAWAI Atsushi

  We overview the Fast Multipole Method (FMM) and the Barnes-Hut tree method. These algorithms evaluate mutual gravitational interaction between N particles in O (N) or O (N log N) times, respectively. We present basic algorithms as well as recent developments, such as Anderson's method of using Poisson's formula, the use of FFT, and other optimization techniques. We also summarize the current states of two algorithms. Though FMM with O (N) scaling is theoretically preferred over O (N log N) tree method, comparisons of existing implementations proved otherwize.

  Japan Society of Civil Engineers, 1999, Doboku Gakkai Ronbunshuu A, 2(2) (2), 101 - 109, Japanese


• 研究展望:高速多重極展開法--粒子法への応用を中心として

  牧野 淳一郎, 川井 敦

  土木学会, 1999, 応用力学論文集, (2) (2), 101 - 109, Japanese


• 208 Lunar Accretion from an Impacted-Generated Disk

  Kokubo Eiichiro, Ida Shigeru, Makino Junichiro

  The Japanese Society for Planetary Sciences, 13 Oct. 1998, Abstracts Fall Meeting of the Japanese Society for Planetary Sciences, 1998, 80 - 80, Japanese


• Fast Multipole Method and Tree Method : Fast Algorithms for Many Body Simulations(Numerical Computation)

  Makino Junichiro

  I overview the Fast Multipole Method (FMM) and the Barnes-Hut tree method. These algorithms evaluate mutual gravitational interaction between N particles in O(N) or O(N log N) times, respectively. I present basic algorithms as well as recent developments, such as Anderson's method of using Poisson's formula, the use of FFT, and other optimization techniques. I also summarize the current states of two algorithms. Though FMM with O(N) scaling is theoretically preferred over O(N log N) tree method, comparisons of existing implementations proved otherwise. This result is not surprizing, since the calculation cost of FMM scales as O(Np^2) where p is the order of expansion, while that of the tree method scales as O(N log Np).

  The Japan Society for Industrial and Applied Mathematics, 1998, Bulletin of the Japan Society for Industrial and Applied Mathematics, 8(4) (4), 277 - 287, Japanese


• 等質量球状銀河の合体率

  1997, 481, 83


• 中心ブラックホールをもつ銀河の合体II ブラックホール連星の進化とコアの構造

  1997, 478, 58


• 図のひろがり

  砂川 一郎, 玉垣 庸一, 中村 春木, 牧野 淳一郎, 福重 俊幸, 古川 義純, 鈴木 繁夫, 川野 常夫, 細川 力, 高山 峯夫, 石倉 恆之

  日本図学会, 1997, 図学研究, 31(0) (0), 160 - 165, Japanese


• ダ-クマタ-ハロ-のカスプの起源

  1997, 477, 9


• N体系における動力学的膨張

  1997, 49, 345


• GRAPE-4:N体計算のための起並列専用計算機

  1997, 480, 432


• 専用計算機による宇宙物理

  牧野 淳一郎

  日本流体力学会, 25 Dec. 1996, ながれ : 日本流体力学会誌, 15(6) (6), 475 - 478, Japanese


• 1C2 学際的研究における分野間知識統合の解析 : 環境科学と生物物理学を対象とした論文傾向の経年変化

  藤垣 裕子, 牧野 淳一郎, 内田 斉, 土井 伸一

  研究・イノベーション学会, 31 Oct. 1996, 年次学術大会講演要旨集, 11, 35 - 40, Japanese


• 任意力による多体シュミレーションのための専用計算機MD-GRAPE

  1996, 天体, 468, 51


• 中心ブラックホールをもつ銀河の合体I・等重量銀河の階層的合体

  1996, 天体物理学雑誌, 465, 527


• 時間対称化クスタンハイモ・シュティ-フェル正則化

  1996, 112, 1697


• Hydrodynamics in the space. Astrophysics by special purpose computer.

  牧野 淳一郎

  The Japan Society of Fluid Mechanics, 1996, nagare, 15(6) (6), 475 - 478, Japanese


• Black Hole Binaries and the Formation of the Cores of Elliptical Galaxies

  EBISUZAKI Toshikazu, MAKINO Jun-ichiro

  日本天文学会, Jun. 1995, The Astronomical herald, 88(6) (6), 238 - 243, Japanese


• A special - purpose computer for solving a dense matrix based on the Gaussian elimination algorithm : GENERAL - 1

  SEIKI Yasushi, FUKUSHIGE Toshiyuki, TAIJI Makoto, MAKINO Junichiro, OGAWA Masaaki, EBISUZAKI Toshikazu

  We describe a special-purpose computer for solving a set of linear equations. We usually use Gaussian elimination algorithm to solve a dense matrix. In this method the number of operations to solve the matrix is proportional to a cube of the matrix size. Therefore, we require a large amount of computational power for large-scale problems. However, the calculations are dominated by sum-of-products operations in the forward eliminations. In the paper, we propose a system that consists of a special-purpose computer and a host computer. The special-purpose computer does only sum-of-products operations, and the host computer does all the other operations. We are developing an experimental machine of GENERAL-1 (Gaussian ElimiNation mEthod paRALlel machine). It will have a peak performance of 80Mflops and will solve a matrix of n=1000 in 20 seconds.

  Information Processing Society of Japan (IPSJ), 10 Mar. 1995, IPSJ SIG Notes, 1994(29) (29), 65 - 72, Japanese


• A Special - Purpose Computer for Radiosity Method in Computer Graphics

  NARUMI Tetsu, MAKINO Junichiro, EBISUZAKI Toshikazu, OMURA Koichi

  We have designed a special-purpose computer for radiosity method. In the radiosity method, the most time-consuming part is the ray intersection test. We propose `block ray traverse' which reduces the time for voxel traverse and makes parallel processing of ray intersection test easy. The special-purpose computer accelerates only the ray intersection test. This computer is composed of eight boards, and has 512 processors for the ray intersection test. Host computer, which is connected to the special-purpose computer, does all other operations. If we use twenty sets of this system in parallel, we can calculate radiosity equation within ten seconds.

  Information Processing Society of Japan (IPSJ), 10 Mar. 1995, IPSJ SIG Notes, 1994(29) (29), 57 - 64, Japanese


• GRAPE - 4 : THE TERAFLOPS MACHINE FOR GRAVITATIONAL MANY - BODY SIMULATIONS

  EBISUZAKI Toshikazu, MAKINO Junichiro, TAIJI Makoto, SUGIMOTO Daiichiro

  We are developing GRAPE-4, the teraflops machine for gravitational many-body simulations. Gravitational many-body systems, such as galaxies and globular clusters, consists of a lot of stars, which interact each other trough gravitational force. We developed two custom LSIs, HARP chip and PROMETHEUS chip. HARP chip calculates force and time derivative of force, while PROMETHEUS chip performs predictor calculations of positions and velocities of particles. We use about 2000 HARP chips and about 40 PROMETHEUS chips. In the present paper, we briefly describe the GRAPE-4 project.

  Information Processing Society of Japan (IPSJ), 10 Mar. 1995, IPSJ SIG Notes, 1994(29) (29), 49 - 56, Japanese


• 動散乱による背景放射の等方化

  1995, 日本天文学会誌, 47, 493


• より改良されたリープフロッグ法の構成

  1995, 天体物理学雑誌短報, 443, 93


• A Special Purpose Hardware with Disk Array for Radiosity Method

  Narumi Tetsu, Makino Junichiro, Ebisuzaki Toshikazu, Omura Koichi

  We propose a special purpose hardware for radiosity calculation. In the radiosity method, the most time consuming part is the calculation of the form factor. When we perform the rendering of the same room with different lighting, the same form factors are evaluated each time. We propose the new method in which we store the form factors in a disk array and use them many times. The data transfer speed of a disk array can be made comparable to the speed of main memory unit of present workstations. This system will be able to calculate the radiosity in nearly real time.

  Information Processing Society of Japan (IPSJ), 14 Oct. 1994, IPSJ SIG Notes, 1994(88) (88), 19 - 24, Japanese


• 多重重力散乱による光線間距離の指数間数的成長について(共著)

  1994, 天体物理学雑誌短報, 436, 111


• 多重重力散乱による遠方の銀河の減光(共著)

  1994, 天体物理学雑誌 レターズ, 424, 17


• 高性能専用計算機GRAPE-2Aの分子動力学への応用

  1994, 計算化学会誌, 15(12) (12), 1372


• 銀河核中の3重ブラックホール(共著)

  1994, 天体物理学雑誌, 436, 607


• 宇宙線景幅射の異方性への重力散乱の影響

  1994, 天体物理学雑誌短報, 436, 107


• 多重重力レンズによる遠方の銀河像の変形とその宇宙論的意味について(Nonlinear Dynamics in Chaotic Systems,自己重力多体系における非線形・非平衡現象,研究会報告)

  牧野 淳一郎, 船渡 陽子

  遠方の銀河などの天体の像が、多重重力レンズによってどのように変形し、明るさを変化させるかを数値計算で調べた。z>1では、重力レンズ効果がなかったときに比べて典型的な銀河の明るさは(1+z)^<-1.4√<Ω_s>に比例して暗くなることがわかった。ここで、Ω_sは銀河等のレンズ効果がある比較的コンパクトな天体の密度パラメータである。なお、平均の明るさは変化しない、すなわち、小数の銀河は重力レンズによって非常に明るくなる。

  素粒子論グループ 素粒子研究編集部, 20 Dec. 1993, 素粒子論研究, 88(3) (3), C57 - C58, Japanese


• GRAPE - 4 : A massively - parallel special - purpose computer system for astrophysical many - body simulations

  Taiji Makoto, Makino Junichiro, Kokubo Eiichiro, Ebisuzaki Toshikazu, Sugimoto Daiichiro

  We are developing GRAPE-4, a massively-parallel special-purpose computer for astrophysical N-body simulations. We have developed an application-specific LSI, the HARP (Hermite AcceleratoR Pipe) chip. The HARP chip calculates the gravitational interaction between particles. We invented the "Virtual Multiple Pipeline" architecture for HARP chip, which decrease the input data transfer rate. The HARP chip performs about 20 floating point operations per clock cycle and works at 30 MHz in the worst case. Therefore, the performance of the HARP chip exceeds 600 Mflops. GRAPE-4 will consist of about 2000 HARP chips using multi-chip modules. The sustained performance will exceed 1 Tflops when the number of particles exceeds 2×10^5.

  Information Processing Society of Japan (IPSJ), 19 Aug. 1993, IPSJ SIG Notes, 1993(72) (72), 33 - 40, Japanese


• HARP - 1 : A Special - Purpose Computer for N - body Simulation with the Hermite Integrator

  Kokubo Eiichiro, Makino Junichiro, Taiji Makoto

  We have designed and built HARP (Hermite Accelerator Pipeline)-1, a special-purpose computer for solving astronomical N-body problems with a high accuracy using the Hermite integrator. The Hermite integrator uses analytically calculated time-derivatives of the acceleration, in addition to the acceleration, to integrate orbits of particles. HARP-1 has a 24-stage pipeline to perform the calculation of the acceleration and its time derivative, which is the most expensive part of the Hermite scheme. The pipeline calculates one gravitational interaction at every three clock cycles. Thus, the acceleration and its time derivative of a particle are calculated in 3N+24 clock cycles, where N is the number of particles. The peek speed of HARP-1 is 160Mflops.

  Information Processing Society of Japan (IPSJ), 19 Aug. 1993, IPSJ SIG Notes, 1993(72) (72), 49 - 56, Japanese


• DISCRETENESS NOISE VERSUS FORCE ERRORS IN N-BODY SIMULATIONS (VOL 402, PG L85, 1993)

  L HERNQUIST, P HUT, J MAKINO

  UNIV CHICAGO PRESS, Jul. 1993, ASTROPHYSICAL JOURNAL, 411(1) (1), L53 - L53, English

  Others


• 早野龍五・高橋忠幸, 計算物理-Computer in Physics, 共立出版, 東京, 1992, xii+252p., 2,987円

  牧野 淳一郎

  一般社団法人日本物理学会, 05 Mar. 1993, 日本物理學會誌, 48(3) (3), 221 - 222, Japanese


• 多重重力レンズによる遠方の銀河像の変形とその宇宙論的意味について(基研短期研究会「自己重力多体系における非線形・非平衡現象」報告,研究会報告)

  牧野 淳一郎, 船渡 陽子

  遠方の銀河などの天体の像が、多重重力レンズによってどのように変形し、明るさを変化させるかを数値計算で調べた。z>1では、重力レンズ効果がなかったときに比べて典型的な銀河の明るさは(1+z)^<1.4√(Ω_s)>に比例して暗くなることがわかった。ここで、Ω_sは銀河等のレンズ効果がある比較的コンパクトな天体の密度パラメータである。なお、平均の明るさは変化しない、すなわち、小数の銀河は重力レンズによって非常に明るくなる。

  物性研究刊行会, 1993, 物性研究, 61(2) (2), 151 - 152, Japanese


• 合体銀河における巨大連ブラックホールの進化.I.球形銀河の中の連ブラックホールの進化

  1993, 45,303


• 原始惑星による微惑星の散乱:暴走的成長の減速 (共著)

  1993, イカルス, 106, 210


• 銀河団の進化

  1993, 45,289


• ディスクポテンシャル中を運動する粒子の非等方的速度散乱の起源

  1993, 263,875


• ディスクポテンシャヤル中を回転する格子の速度分散の異子性の起源(共著)

  1993, 王立天文学会月報, 263, 875


• グレーププロジェクト:その全体像

  1993, 45,269


• グレープのソフトウェア体系

  1993, 45,279


• グレープによるならされた粒子を用いた流体力学

  1993, 45,311


• WINE-1:周期境界のN体シミュレーション専用計算機

  1993, 45,377


• 天文・物理学における専用計算機--いかにして手を抜くか

  牧野 淳一郎

  日本天文学会, Apr. 1992, 天文月報, 85(4) (4), p142 - 147, Japanese


• コンピュ-タ-・シミュレ-ションが切り拓く天文学--星から宇宙の果てへ-9-自己重力多体系の進化--球状星団,銀河集団化

  牧野 淳一郎, 伊藤 誠

  日本天文学会, Sep. 1990, 天文月報, 83(9) (9), p256 - 260, Japanese


• A special processor for gravitational many-body problems-GRAPE.

  戎崎俊一, 伊藤智義, 牧野淳一郎, 杉本大一郎

  Aug. 1990, 天文月報, 83(8) (8), 224 - 226, Japanese


• GRAVITATIONAL N-BODY ALGORITHMS - A COMPARISON BETWEEN SUPERCOMPUTERS AND A HIGHLY PARALLEL COMPUTER

  J MAKINO, P HUT

  ELSEVIER SCIENCE BV, Jun. 1989, COMPUTER PHYSICS REPORTS, 9(4) (4), 199 - 246, English

  Book review

• Principles of High-Performance Processor Design For High Performance Computing, Deep Neural Networks and Data Science

  Junichiro Makino

  Single work, Springe, Sep. 2021


• 被曝評価と科学的方法

  牧野, 淳一郎

  岩波書店, 2015, Japanese, ISBN: 9784000296366


• 原発事故と科学的方法

  牧野, 淳一郎

  岩波書店, Oct. 2013, Japanese, ISBN: 9784000296168


• シミュレーション天文学

  富阪, 幸治, 花輪, 知幸, 牧野, 淳一郎

  日本評論社, 2007, Japanese, ISBN: 9784535607347


• とんでる力学

  牧野, 淳一郎, パリティ編集委員会

  丸善, 2005, Japanese, ISBN: 4621076094


• 研究評価・科学論のための科学計量学入門

  丸善, 2004


• 科学計量学の挑戦 : コミュニケーションの自己組織化

  Leydesdorff, L. A., 藤垣, 裕子, 林, 隆之, 富沢, 宏之, 平川, 秀幸, 調, 麻佐志, 牧野, 淳一郎

  玉川大学出版部, 2001, Japanese, ISBN: 4472401517


• パソコン物理実地指導

  牧野, 淳一郎

  共立出版, 1999, Japanese, ISBN: 4320033647


• 専用計算機による科学シミュレーション

  ジョン・ワイリー, 1998


• Scientific Simulations with Special-Purpose Computers The GRAPE Systems

  John Wiley and Sons., 1998


• Dynamical evolution of star clusters - confrontation of theory and observations : proceedings of the 174th Symposium of the International Astronomical Union, held in Tokyo, Japan, August 22-25, 1995

  International Astronomical Union. Symposium, Hut, Piet, 牧野, 淳一郎

  Kluwer Academic Publishers, English, ISBN: 0792340698


• Astrophysical supercomputing using particle simulations : proceedings of the 208th Symposium of the International Astronomical Union, held in Tokyo, Japan, 10-13 July 2001

  International Astronomical Union. Symposium, 牧野, 淳一郎, Hut, Piet

  Astronomical Society of the Pacific, English, ISBN: 1583811397


• New horizons of computational science : proceedings of the international symposium on supercomputing held in Tokyo, Japan, September 1-3, 1997

  戎崎, 俊一, 牧野, 淳一郎

  Kluwer Academic Publishers, English, ISBN: 0792370503


• Scientific simulations with special-purpose computers : The GRAPE Systems

  牧野, 淳一郎, Taiji, Makoto

  Wiley, English, ISBN: 047196946X

• スーパーコンピューター「富岳」と宇宙物理・惑星科学

  牧野淳一郎

  日本天文学会2021年春季年会企画セッションZ3「富岳時代のシミュレーション天文学」, Mar. 2021

  Invited oral presentation


• シミュレーションによる宇宙物理―「京」、「富岳」、さらにその先へ

  牧野淳一郎

  日本物理学会大阪支部 2020年度 公開シンポジウム「AIで切り拓く物理の世界」, Dec. 2020

  [Invited]

  Public discourse


• 東日本大震災後の環境放射線研究と科学コミュニケーションの問題点

  牧野淳一郎

  物理学会シンポジウム, Sep. 2020

  [Invited]

  Invited oral presentation


• A64fx アーキテクチャ向けアプリケーションチューニング-差分法を例に

  牧野淳一郎

  第14回アクセラレーション技術発表討論会「COVID-19と戦うアクセラレーション技術」, Sep. 2020, Japanese

  [Invited]

  Invited oral presentation


• 3.11 以後の科学者コミュニティの情報発信

  物理学会シンポジウム ( ウェブ開催 ) 「個人被ばく線量の物理学的評価についての検討」, Mar. 2020

  [Invited]


• 「富岳」の概要と「富岳」での大規模惑星科学シミュレーション

  シンポジウム最新科学で迫る月と地球の起源, Oct. 2019


• Algorithms to use accelerators effectively with FDPS and performance of applications

  Daisuke Namekata, Masaki Iwasawa, Keigo Nitadori, Kentaro Nomura, Long Wang, Miyuki Tsubouchi, Junichiro Makino

  Japan Geoscience Union Meeting 2019, May 2019, Japanese, Makuhari Messe, Chiba, Domestic conference

  Poster presentation


• Current status of post-K Exploratory Challenge, computational planetary science

  牧野 淳一郎

  Japan Geoscience Union Meeting 2019, May 2019, Japanese, Makuhari Messe, Chiba, Domestic conference

  Oral presentation


• Development of N-body Simulation Code for Planetary System Formation With Particle-Particle Particle-Tree Scheme

  Yota Ishigaki, Junko Kominami, Junichiro Makino, Masaki Fujimoto

  Japan Geoscience Union Meeting 2019, May 2019, Japanese, Makuhari Messe, Chiba, Domestic conference

  Oral presentation


• Global N-body Simulation from Inner Region to Outer Region

  Junko Kominami, Shigeru Ida, Junichiro Makino, Yota Ishigaki, Hiroshi Daisaka, Masaki Fujimoto

  Japan Geoscience Union Meeting 2019, May 2019, Japanese, Makuhari Messe, Chiba, Domestic conference

  Poster presentation


• 粒子法シミュレーションコード開発のためのフレームワーク(FDPS)の開発

  岩澤 全規, 行方 大輔, 坂本 亮, 中村 孝史, 木村 耕行, 似鳥 啓吾, 野村 昴太郎, 坪内 美幸, 牧野 淳一郎

  第167回ハイパフォーマンスコンピューティング研究会, Dec. 2018, Japanese, 沖縄産業支援センター, Domestic conference

  Oral presentation


• Temporal blockingと相性のよいメッシュ陽解法スキームの開発

  石原 陽平, 牧野 淳一郎, 似鳥 啓吾, 行方 大輔, 岩澤 全規, 坪内 美幸

  第32回数値流体力学シンポジウム, Dec. 2018, Japanese, 機械振興会館（東京）, Domestic conference

  Oral presentation


• Formura DSL による temporal blocking の PEZY-SC2 での実装と性能評価

  田中 英行, 石原 陽平, 坂本 亮, 中村 孝史, 木村 耕行, 似鳥 啓吾, 坪内 美幸, 牧野 淳一郎

  第32回数値流体力学シンポジウム, Dec. 2018, Japanese, 機械振興会館（東京）, Domestic conference

  Oral presentation


• Pros and Cons of HPCx benchmarks

  Jun Makino

  The International Conference for High Performance Computing, Networking, Storage, and Analysis (SC18), Nov. 2018, English, Dallas, Texas, International conference

  Oral presentation


• Automatic Generation of High-Order Finite-Difference Code with Temporal Blocking for Extreme-Scale Many-Core Systems

  Hideyuki Tanaka, Youhei Ishihara, Ryo Sakamoto, Takashi Nakamura, Yasuyuki Kimura, Keigo Nitadori, Miyuki Tsubouchi, Jun Makino

  Fourth International IEEE Workshop on Extreme Scale Programming Models and Middleware (ESPM2 2018), Nov. 2018, English, Dallas, Texas, International conference

  Oral presentation


• ポスト「京」萌芽的課題「生命を育む惑星の起源・進化と環境変動の解明」の現況

  牧野 淳一郎

  日本地球惑星科学連合2018年大会, May 2018, Japanese, 幕張メッセ, Domestic conference

  Oral presentation


• Speed-up efficiencies of an SPH code with FDPS on GPUs or PEZY-SCs

  Natsuki Hosono, Masaki Iwasawa, Daisuke Namekata, Ataru Tanikawa, Keigo Nitadori, Takayuki Muranushi, Junichiro Makino

  Japan Geoscience Union Meeting 2018, May 2018, English, Makuhari Messe, Chiba, Domestic conference

  Poster presentation


• Numerical simulations of the giant impact onto the magma ocean

  Natsuki Hosono, Shun-ichiro Karato, Junichiro Makino, Takayuki R. Saitoh

  Japan Geoscience Union Meeting 2018, May 2018, English, Makuhari Messe, Chiba, Domestic conference

  Oral presentation


• High-resolution global N-body simulation of planet formation with fragmentation

  Junko Kominami, Hiroshi Daisaka, Junichiro Makino, Masaki Fujimoto

  Japan Geoscience Union Meeting 2018, May 2018, English, Makuhari Messe, Chiba, Domestic conference

  Poster presentation


• Development of a particle-based parallel code for mantle convection with the variable inertia method

  Takayuki Saitoh, Natsuki Hosono, Kosuke Takeyama, satoko yamamoto, Daisuke Namekata, Junichiro Makino

  Japan Geoscience Union Meeting 2018, May 2018, English, Makuhari Messe, Chiba, Domestic conference

  Oral presentation


• 衝突破壊プロセスを入れたN体計算における原始惑星の動径方向移動

  小南 淳子, 台坂 博, MAKINO JUNICHIRO, 藤本 正樹

  JpGU-AGU Joint Meeting 2017, May 2017, Japanese, 幕張メッセ, International conference

  Oral presentation


• ポスト「京」萌芽的課題「生命を育む惑星の起源・進化と環境変動の解明」の現況

  MAKINO JUNICHIRO

  JpGU-AGU Joint Meeting 2017, May 2017, Japanese, 幕張メッセ, International conference

  Oral presentation


• Terrestrial magma ocean origin of the Moon: A numerical study of a giant impact incorporating the difference of the equations of state for liquids and solids

  細野 七月, 唐戸 俊一郎, MAKINO JUNICHIRO

  JpGU-AGU Joint Meeting 2017, May 2017, English, 幕張メッセ, International conference

  Oral presentation


• FDPSとPEZY-SCデバイスを用いた、SPHコードの開発と巨大衝突への応用計算

  細野 七月, 岩澤 全規, 行方 大輔, 谷川 衝, 似鳥 啓吾, 村主 崇行, MAKINO JUNICHIRO

  JpGU-AGU Joint Meeting 2017, May 2017, Japanese, 幕張メッセ, International conference

  Oral presentation


• 惑星形成N体計算の大粒子数化に向けて：FDPSを用いたParticle-Particle Particle-Tree法の並列計算

  山川 暁久, MAKINO JUNICHIRO, 斎藤 貴之, 小南 淳子, 竹山 浩介

  日本地球惑星科学連合2016年大会, May 2016, Japanese, 幕張メッセ, Domestic conference

  Poster presentation


• 大規模惑星集積並列N体計算：ガス円盤内での微惑星による原始惑星の外側移動

  小南 淳子, 台坂 博, MAKINO JUNICHIRO, 藤本 正樹

  日本地球惑星科学連合2016年大会, May 2016, Japanese, 幕張メッセ, Domestic conference

  Oral presentation


• 高性能構造格子計算言語Formura

  村主 崇行, MAKINO JUNICHIRO

  日本地球惑星科学連合2016年大会, May 2016, Japanese, 幕張メッセ, Domestic conference

  Poster presentation


• 「京」からポスト「京」へ

  MAKINO JUNICHIRO

  日本地球惑星科学連合2016年大会, May 2016, Japanese, 幕張メッセ, Domestic conference

  Oral presentation


• メッシュフリー法における自由表面と接触不連続面への適応

  山本 智子, MAKINO JUNICHIRO

  日本地球惑星科学連合2016年大会, May 2016, Japanese, 幕張メッセ, Domestic conference

  Poster presentation


• SPH法における、人工粘性とそのスイッチ、微分演算子の離散化に関するテスト

  細野 七月, 斎藤 貴之, MAKINO JUNICHIRO

  日本地球惑星科学連合2016年大会, May 2016, Japanese, 幕張メッセ, Domestic conference

  Poster presentation


• FDPS(Framework for Developing Particle simulator)による計算惑星科学

  岩澤 全規, 谷川 衝, 細野 七月, 村主 崇行, MAKINO JUNICHIRO

  日本地球惑星科学連合2016年大会, May 2016, Japanese, 幕張メッセ, Domestic conference

  Oral presentation


• Density Independent Smoothed Particle Hydrodynamicsを用いた衝突・クレータリングの数値計算

  細野 七月, 岩澤 全規, 谷川 衝, 似鳥 啓吾, 村主 崇行, MAKINO JUNICHIRO

  日本地球惑星科学連合2016年大会, May 2016, English, 幕張メッセ, Domestic conference

  Poster presentation


• GRAPE9-MPX : A development of an accelerator dedicated for arbitrary-precision arithmetic by the FPGA boards

  MOTOKI Shinji, DAISAKA Hiroshi, NAKASATO Naohito, ISHIKAWA Tadashi, YUASA Fukuko, FUKUSHIGE Toshiyuki, KAWAI Atsushi, MAKINO Jun'ichiro

  IEICE technical report, Sep. 2014, Japanese, Higher order corrections in perturbative quantum field theory are required for precise theoretical analysis to investigate the new physics. Feynman loop diagrams which appear in the calculation of the corrections are taken into account, leading to the evaluation of loop integrals. We developed GRAPE9-MPX system consisting of multiple FPGA boards to accelerate parallel computation of loop integrals. In the system, we implemented Processor Elements (PE) to realize quadruple/hexuple-precision arithmetics in FPGA. The theoretical perk speed in the current implementation is about 6.6 Gflops (quadruple-precision) and 3.2 Gflops (hexuple-precision). With the compiler we are developing, the program code is generated automatically with only inserting directives in C/C++ code. We present performance results for the case of Feynman two-loop integrals with quadruple precision and achieve the effective performance of 2.4Gflops for 1 board, 4.7Gflops for 2 boards, and 9.1Gflops for 4 boards, respectively.


• O5-05 任意の不連続面に対応可能なSPH法の開発(口頭発表セッション5 惑星形成III,口頭発表)

  山本 智子, 斎藤 貴之, 牧野 淳一郎

  日本惑星科学会秋期講演会予稿集, Sep. 2014, Japanese


• P1-22 物理量の連続性を仮定しないSPH法の開発(ポスターセッション1,ポスター発表)

  山本 智子, 斎藤 貴之, 牧野 淳一郎

  日本惑星科学会秋期講演会予稿集, Nov. 2013, Japanese


• P1-21 Density Independent Smoothed Particle Hydrodynamicsによる巨大衝突シミュレーション(ポスターセッション1,ポスター発表)

  細野 七月, 斎藤 貴之, 牧野 淳一郎

  日本惑星科学会秋期講演会予稿集, Nov. 2013, Japanese


• O4-03 Density Independent Smoothed Particle Hydrodynamicsの非理想気体への拡張(口頭発表セッション4(惑星形成),口頭発表)

  細野 七月, 斎藤 貴之, 牧野 淳一郎

  日本惑星科学会秋期講演会予稿集, Nov. 2013, Japanese


• Personal view on the future HPC architecture

  牧野 淳一郎

  ハイパフォーマンスコンピューティングと計算科学シンポジウム論文集, Jan. 2012, Japanese

• 日本天文学会

• アクセラレータ上で動作する粒子系シミュレータ開発フレームワークの開発

  岩澤 全規, 牧野 淳一郎, 細野 七月

  日本学術振興会, 科学研究費助成事業, 基盤研究(C), 松江工業高等専門学校, 01 Apr. 2021 - 31 Mar. 2024

  粒子法シミュレーションは、密度コントラストの強い系や空隙のある系、物体の破壊や衝突等のシミュレーションに適しており、自然科学や工学の幅広い分野で使われている。しかし、並列粒子法シミュレーションコードの開発は容易ではなく、多くの研究者がコード開発や最適化に多くの時間を割く必要があった。そのため、我々は容易に並列粒子法シミュレーションプログラムを開発するためのフレームワークFDPS(Framework for Developing Particle Simulators)を開発した。しかし、現在のFDPSでGPGPUなどのアクセラレータを使う場合、相互作用計算のみをアクセラレータ上で計算することになる。しかし、星団や銀河など粒子の速度分散が大きい系のシミュレーションでは、相互作用リストを再利用することができないため、相互作用計算をアクセラレータで高速化しても、ホストコンピュータ上で行う木構造や相互作用リストの構築が性能ボトルネックになり、性能向上が難しい。そこで、本研究では木構造や相互作用リスト構築、その他の計算も可能な限りアクセラレータ上で動作させる、アクセラレータ対応FDPSの開発を行う。 当該年度では、アクセラレータ上でFDPSを動作させる際に、既存のユーザーアプリケーションからなるべく変更が少ない形で移行できるかの検討を行った。結果、現在のユーザーが開発したアプリケーションプログラム上の関数に関数識別子を付ける程度の変更でプログラムが動作するように改良できることが分かった。さらにアクセラレータとしてはNvidiaのGPGPUを考えCUDAを用い、フレームワークの実装も行っている。現在は領域分割や粒子交換をCUDAで実装した。


• "Telling Fukushima" : ICT teaching resource development and evaluation

  土井 妙子, 藤岡 達也, 西崎 伸子, 牧野 淳一郎, 田口 真奈, 後藤 忍, 明日香 壽川, 濱岡 豊

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Kanazawa University, 01 Apr. 2020 - 31 Mar. 2023


• 国立研究開発法人新エネルギー・産業技術総合開発機構, 「高効率・高速処理を可能とするAIチップ・次世代コンピューティングの技術開発／【研究開発項目①】革新的AIエッジコンピューティング技術の開発」, 「FPGA IP と可変精度演算コアの融合による超低消費電力エッジヘビーコンピューティング向けSoCの研究開発」, Dec. 2018 - Mar. 2023


• 計算機の中の惑星探査: 計算機の中の惑星リングの実現にむけて

  台坂 博, 大槻 圭史, 岩澤 全規, 牧野 淳一郎, 似鳥 啓吾

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Hitotsubashi University, Apr. 2018 - Mar. 2021

  本研究では、土星リングに代表される惑星リングに関する諸問題(構造形成や起源）の解決を図るために、これまでにない大粒子数を用いた惑星リング全系のN体シミュレーションを可能とする方法を確立し、その手法を用いたシミュレーションを実施し、その有用性を実証することを目的とする。本年度は計算手法を検討し、その結果に基づいた数値計算コードの開発を行った。 検討課題の一つは、重力計算で用いられるツリー法のアルゴリズムの改良である。リングはほぼ２次元的な円盤形状で、かつ、リングの幅が軌道半径に比べて小さいため、通常のデカルト座標を用いた空間分割が不適切、また、リング粒子はケプラー回転に移動するため、デカルト座標を用いた空間分割では粒子はすぐに領域外に移動してしまう。結果、それらに起因するノード間通信が発生する。この問題を解決するために、円筒座標系と粒子と回転座標系を導入し、リング系に適合するようにアルゴリズムを改良した。このアルゴリズムに基づいた重力計算を加速するために、PEZY社が開発したPEZY-SC2向けへの実装を行った。また、ミドルウェア(FDPS)への実装も行い、そららを用いた数値計算コードを開発した。現在、コードの検証作業を行っている。 また、リング全系計算に向けた計算の一環として局所系の計算を行った。土星リングはいろいろな大きさの粒子からなるが、小さい粒子の量はサイズ分布から期待された量より少ないことがカッシーニの観測などにより示唆されている。その理解として粘着力が提案されている。その効果を調べるために局所系のN体シミュレーションを行い、粒子間の衝突速度を調べた。土星メインリングでの粒子間衝突は、大きい粒子の表面にくっついた小さい粒子を再放出するには小さいことなど、観測結果を説明することが出来ることなどを明らかにした。 これらの成果については研究会や学会等で発表を行った。


• ヘテロジニアス・メニーコア計算機による大規模計算科学

  姫野 龍太郎, 牧野 淳一郎, 古市 幹人, 山崎 匡, 石川 正, 黒川 顕

  文部科学省, 次世代領域研究開発, 国立研究開発法人理化学研究所, Nov. 2017 - Mar. 2020


• 太陽系外惑星（第二の地球）の誕生と太陽系内惑星環境変動の解明（生命を育む惑星の起源・進化と惑星環境変動の解明）

  牧野 淳一郎

  文部科学省, 平成29年度科学技術試験研究委託事業, 2017, Principal investigator

  Competitive research funding


• 太陽系外惑星（第二の地球）の誕生と太陽系内惑星環境変動の解明（生命を育む惑星の起源・進化と惑星環境変動の解明）

  牧野 淳一郎

  文部科学省, 科学技術試験研究委託事業, 2016, Principal investigator

  Competitive research funding


• Highly productive software environment based on Ruby for parallel and distributed computing systems

  HIRAKI Kei, SASADA Koichi, SADAKANE Kunihiko, MAKINO Junichiro, IDA Shigeru, INABA Mary

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (S), The University of Tokyo, 01 Apr. 2009 - 31 Mar. 2015

  In this study, we extended a computer language Ruby to increase execution performance to establish a new high-productive computer language HPC Ruby. We successfully developed HPC Ruby static compiler and runtime systems. Based on our evaluation, HPC Ruby showed from 50 % to 90% execution performance in numerical programs compared to C language. In order to show feasibility of the use of Ruby in scientific computation, we developed Ruby based software in earth science, astrophysics, and discrete optimization areas. As for the ultra high-speed distributed computing using 100Gbps internet, we developed 40Gbps single stream TCP system and 100Gbps multi-stream TCP system. We performed very long distance internet experiments using Tokyo, New Orleans (US) and Amsterdam (Europe). Performance results shows we can efficiently utilize more than 90% of available bandwidth in both 40G and 100G environment. This was the world first realization of very long-distance high-speed TCP data-transfer.


• Study of the evolution of planetary system, star clusters and galaxies using a special-purpose computer

  MAKINO Junichiro, FUNATO Yoko, NAKASATO Naohito, WADA Keiichi, YOSHIDA Naoki

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (A), 2009 - 2011

  We developed a new special-purpose computer, GRAPE-8, designed to be used with Particle-Particle Particle Tree method, which is a method to handle both collisionless and collisional systems efficiently. The processor chip of GRAPE-8 achieved the performance per watt of 40 Gflops/W, which is more than 30 times better than those of the latest general-purpose microprocessors. The performance per watt of the total system is around 6Gflops/W, nearly an order of magnitude better than that of usual PC clusters. Thus, we succeeded to reduce the cost of electricity for large-scale astrophysical simulations.


• Formation of Our Galaxy Studied with Super-High Resolution Next-Generation Simulator

  TOMISAKA Kohji, MAKINO Junichiro, WADA Keiichi, KOKUBO Eiichiro, MATSUMOTO Tomoaki, YOSHIDA Naoki

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), National Astronomical Observatory of Japan, 2005 - 2007

  1. We completed (1) a parallelized N-body plus SPH hydro code called ASURA and (2) a PC cluster composed of 16 PC's each connected with a specific hardware for self-gravity (GRAPE). Since these enable us to study the formation process of our Galaxy, we call them Milky Way Simulator (MWS). (1) We perform high resolution simulations with MWS, in which one galaxy is expressed with 10^7 particles, which is much larger than previous similar simulations. From them, we can trace the condensation process of interstellar gas to form stars up to〜10^2cm-3, which coincides with the density of molecular clouds in our Galaxy. (2) A phenomenological parameter, C_, has been assumed, with which the star formation rate per unit volume is assumed as C^_×ρ_/t_, where>_ as and t_ represent, respectively, the local gas density and free-wall timescale of the gas. Our high resolution simulations indicate us that the star formation rate is well expressed with a radiative cooling time of a gas with a density of 10^0cm_<-3>, irrespective of C_. (3) Thus, we obtained a prescription how to manage the star formation in low resolution simulations. (4) We performed simulations of galaxy-galaxy collision. We found that a star formation burst is expected in the early phase of the collision far before making a galaxy merger. 2. We developed an adaptive mesh refinement (AMR) code for self-gravitating magnetohydrodynamical simulation based on the finite-difference scheme. Calculating the fragmentation process in the protostellar phase, we have confirmed that this code gives the consistent result obtained with previous nested grid code. This enables us to extend the subjects. 3. To compare the simulation result with observation, we have developed a radiative transfer code for molecular rotational transitions based on Monte Carlo method. We have applied this to starburst galaxy and star forming molecular cloud.


• Study of the evolution of dense stellar systems by large-scale simulations on special-purpose computers

  MAKINO Junichiro, FUNATO Yoko

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), The University of Tokyo, 2003 - 2005

  The purpose of this study is to clarify the dynamical evolution of dense stellar systems, such as globular clusters, so-called young and compact clusters, and galactic nuclei, by means of direct N-body simulations. The focus of the study is how the massive black holes grow at the center of these systems. Specifically, we placed two goals. (a) To determine the criterion for the occurrence of the merging instability, in which massive stars merge with other massive stars progressively to form supermassive stars, and (b) to identify the observable signature of massive central black holes in globular clusters and other massive star clusters. As for the condition for the merging instability, we found that the condition is that the initial dynamical friction timescale of massive stars is short (less than 3Mys) and that the initial core radius is fairly small. When fitted by a King mode, W0 must be 8 or larger. For the observational signature of the central black hole, previous observational studies looked for a cusp with slope -7/4, predicted from simple single-component model. By means of N-body calculation in which stellar evolution and stellar mass function are taken into account, we found that the central region of a globular cluster with central massive black hole appears as almost flat core.


• 中?大?巨大質量ブラックホールの形成に関する恒星系力学からみた統一的理解の構築

  船渡 陽子, 牧野 淳一郎

  日本学術振興会, 科学研究費助成事業, 特定領域研究, 東京大学, 2003 - 2004

  本研究の目標は,N体計算によりブラックホールを持つ恒星系の力学進化を調べ,恒星系の中にあるブラックホールの成長を明らかにすることである。この数値計算が難しいのは,ブラックホールとそのまわりの恒星の質量比が大きいことと,多くの場合にブラックホールを含む恒星系は衝突系であることによる。 そのようなシミュレイションを現実的な時間で行なうため,今年度はまず,衝突系向き重力多体問題専用機GRAPE6を並列化したシステムを構築した.これには,昨年度の予算で購入した計算機のCPUやマザーボード,ネットーワークを用いた.これにより,ホスト計算機自体の計算速度および並列計算におけるネットワークの速度の両方を速くできるようになった. 本研究では巨大ブラックホールは中〜大質量ブラックホールが高密度恒星系の中で合体しあって形成されるという予想をたて,その予想が正しいかどうか調べている.ブラックホールの合体においては,2体系が衝突合体するのは時間がかかるが,3体系だともっと短時間で合体出来る可能性がある. この可能性を調べるべく,本研究では、3体系の合体の確率,および,恒星系の中にブラックホールが3体以上ある場合の合体の確率を調べる数値計算をすすめた.その結果,ブラックホールが3体ある場合には,2体しかない場合に比べ早く合体できることを確認した.


• Study on Early Evolution of Protostars based on Tree-dimensional Radiative Magnetohydrodynamical Numeroca ; l Simulations

  HANAWA Tomoyuki, TOMISAKA Kohji, MATSUMOTO Tomoaki, INUTSUKA Shu-ichiro, MAKINO Junichiro, NAKAMOTO Taishi

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Chiba University, 2003 - 2004

  This project is aimed to study evolution of protostars associated with disks and companions on the basis of numerical simulation in which self-gravity, magnetic field, and radiative transfer are taken into account. We have constructed PC cluster, developed numerical simulation codes employing AMR(adaptive mesh refinement), and published manuals on numerical schemes and data analysis, in order to maintain the basis for our numerical simulation studies. Main scientific achievements are as follows. 1.We have performed three-dimensional numerical simulations of gravitational collapse of rotating magnetized molecular cloud with the nested grid for the first time. We have found that the total of the magnetic and centrifugal forces converges at a certain value at the epoch of the protostar formation irrespectively of the initial magnetic field and rotation. When the centrifugal force dominates over the centrifugal force, the cloud tends to fragment to form binary. 2.We have derived minimum spatial resolution to solve the thermal evolution of two phase gases. The spatial resolution should be smaller than a third of the typical scale length for the heat transfer. 3.We have shown that the primary tends to accrete more gas than the companion. This denies the conventional idea that gas accretion should increase the mass ratio. 4.We have followed gravitational collapse of primordial gas with three-dimensional numerical simulations. The simulations suggest that frequency of binary formation should be high also in population III stars. 5.We have performed one-dimensional numerical simulations of supernova explosion. They show that the supernova explosions promote formation of the second generation stars within 10 thousands years through compression of the surrounding interstellar gas.


• Quantitative Analysis on Dynamics of Development in Research Themesin Interdisciplinary Fields

  FUJIGAKI Yuko, MAKINO Junichiro, SHIRADE Masashi, HIRAKAWA Hideyuki, TOMIZAWA Hiroyuki, HAYASHI Takayuki

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), The University of Tokyo, 2002 - 2004

  Ron R (Research on Research) is an expanded concept of "Science of Science" that defined by D.S. Price, which means an analysis on research activities. In the field of R on R, it is very important to investigate quantitative and qualitative methodology to analyze the development of interdisciplinary studies. The quantitative method is called Scientometrics. The aim of the present study is to systematization of methodologies of RonR, including Scientometrics. In 2002, investigators shared the new trends in Scientometrics, e.g., trends in International conference, trends in scientific papers in the journal, "Scientometrics", application of scientometrics to evaluation of universities and public research institutes. Base on these information, we discussed how can we systematize the definition, methodologies, and research examples. In 2003, we discussed the table of contents of the textbook which aimed systematization of methodology. We decided to set chapters as database, descriptive statistics, words-analysis, co-words analysis, co-authorship analysis, acknowledgement analysis, contents analysis, and relationships between methods, so that other researchers in Japan can utilize these method using Japanese case data. Furthermore, in 2004, we added the investigation of theories to bridge quantitative and qualitative analysis ; to explain what aspect of real research evaluation is indicated by quantitative data. We also conducted further research applying scientometrics to research evaluation and science and public policy.


• 月の起源-巨大衝突仮説の検証-

  和田 桂一, 小久保 英一郎, 牧野 淳一郎

  日本学術振興会, 科学研究費助成事業, 萌芽研究, 国立天文台, 2002 - 2003

  月がどのように誕生したか、なぜ我々の月は、他の惑星の衛星に比べて極端に大きいのか、は古くからの「謎」であり、多くの仮説が提唱されてきた。その中で、最後に生き残ったシナリオは、原始地球に火星程度の大きさの原始惑星が衝突し、その残骸の周地球円盤から月が形成されたという、「巨大衝突仮説」である。その拠り所の一つが、A.Cameronのグループによって行われてきたSPH法を用いた一連の数値実験であり、最近では、同様の計算手法を用いて、R.Canupらが「巨大衝突仮説」を支持する論文をNatureに掲載した。 一方、我々は、Cameron,Canupらの数値実験は、多くの点で信用できないと考えた。最大の問題は、彼らは低密度領域で精度が悪いSPH法を採用したために、周地球円盤のSPH粒子が高々100個程度しかなく、有効空間分解能が円盤の半径程度しかないという点にある。これでは巨大衝突の際の衝撃波をはじめ物理を正しく扱えていないのは明白である。本研究ではCameronグループの数値計算法とはまったく異なる高精度の3次元Euler-Mesh数値流体コードを用いて、巨大衝突仮説の再検証を行った。周地球円盤領域の格子点数は2000万点を越える。これまで得られた結果からは、原始地球に質量が1/5程度の原始惑星が「かすめるように」衝突することで、月質量の2倍程度の厚い周地球円盤がロッシュ半径内に形成されることが示された。しかし、その円盤の質量、角運動量と、月集積過程のN体実験結果(Kokubo et al. 2001)を用いて予想される月質量は数日のタイムスケールで急激に減少し、このモデルでは現在の月を形成することは困難であることがわかった。これらの結果について、2004年3月22日の日本天文学会春季年会(会場:名古屋大学)の「太陽系」セッションにおいて、和田が「月の起源-本当に巨大衝突で形成されたのか?-」と題する口頭発表を行い、海外専門誌への投稿の準備中である。


• Study on the formation and evolution of galaxies by Large-scale numerical simulations on special-purpose computers.

  MAKINO Junichiro, FUKUSHIGE Toshiyuki, NOMOTO Ken'ichi, SUDO Yasushi, KOKUBO Eiichiro, HABE Asao

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), The University of Tokyo, 2001 - 2002

  1. We have developed a high-efficiency parallel implementation of the Barnes-Hut tree algorithm on parallel GRAPE system. Using this calculation code, it is now feasible to perform simulations of cosmological structure formation in the spatial scale smaller than clusters of galaxies using 〜 10^8 particles. Only one such simulation has been previously reported. 2. By cosmological simulations with more than 30 million particles, we have determined the slope of the central cusp of the dark-matter halo in CDM cosmology with unprecedented accuracy and reliability. The slope is around -1.4. We have not observed any tendency of the slope to approach to ―1. This slope does not depend on the cosmological models. 3. We have found the reason of the discrepancy between N-body simulations and semi-analytic calculations of the orbital evolution of satellite galaxies. The evolution of the satellite galaxies in recent high-accuracy N-body simulations turned out to be significantly slower than the result of approximate calculations using Chandrasekhar's dynamical friction formula. We found that the discrepancy is not due to the dynamical friction formula itself, but due to the common exercise of taking the size of the parent galaxy as the upper limit for the Coulomb logarithm. By taking the theoretical preferred value, namely the distance of the satellite from the center of the parent galaxy, we resolved the discrepancy. In the case of the satellite from internal degree of freedom, we found that the evolution is faster than that for analytic dynamical friction formula.


• Dynamical Evolution of Steller Systems with Steller Evolution Included

  SUGIMOTO Daiichiro, HACHISU Izumi, NOMOTO Kenichi, INAGAKI Shogo, MIYAMA Shoken, MAKINO Junichiro

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), University of the Air, 1997 - 1998

  Evolution of selfgravitating systems such as stellar systems was investigated, where the interactions with evolution of each constituent of the system were taken into account. The subjects included phenomena of wide variety such as formation of planets and globular clusters, evolution of the galactic nuclei, as well as the large-scale structure of the universe. Between these different phenomena, common physical processes and their understandings were sought for. Among many accomplishments, the followings were to be noticed. For the globular clusters the direct many-body calculation of dynamical evolution was combined with calculation of stellar evolution. As a result, 1) evaporation of the stars from the globular cluster is found as much slower than the previous estimate with Fokker-Planck approximation, and 2) the merging instability of the stars was shown to occur in young dense star clusters as observed in the Magellanic Clouds (galaxy). The abundance anomaly of the elements as observed in the red-giant branch of globular cluster is shown as related with tidal interaction between the stars in the cluster. For further progress of this research subject, the first importance should be laid in constructing more reliable models for gravitationally interacting hydrodynamic systems consisting of the elements of the system. Typical example is the model of the tidal interaction between the stars. For the galaxies and the clusters of galaxies it will be important to clarify and include the process of star formation, and to make high accuracy simulations possible where numerical dissipation can be avoided.


• The Study of the evolution of star clusters, galaxies, clusters of galaxies by ultra-fast Special-purpose Computer for many-body problem

  SUGIMOTO Daiichiro, EBISUZAKI Toshikazu, TAIJI Makoto, MAKINO Junichiro

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Specially Promoted Research, The University of Tokyo, 1992 - 1996

  In this year, we continued the simulation of the evolution of globular clusters, galaxies and clusters of galaxies using GRAPE-4. In addition, we developed a new host interface board for GRAPE-4, which allows use to use faster host computers. For this new host interface board we adopted the PCI bus, which is now available on wide variety of computers from personal computers to supercomputers. We bought high-performance workstations with this PCI interface as new host computers, fast and large tape systems to save the data, and enhanced the memory capacity of host computers Main scientific results of this year include (a) The determination of the structure of the central region of the CDM halo, (b) The study of the evolution of the massive black hole binaries in merging galaxies, and (c) the systematic survey of the effect of encounters to the structure of galaxies in the clusters. Here we briefly summarize (a). Previous simulations of the formation of the dark matter halo in galactic scale typically employed only 20,000-30,000 particles. Because of this small number of particles, the structure within 10 kilo parsec was strongly affected by the two-body relaxation effect, which is not present in real galaxies. We performed the simulation using 786,432 particles, and successfully determined the structure down to 1 kilo parsec. The result is that the inner region is almost isothermal with temperature slightly decreasing inward, which is inconsistent with the observed structure of large elliptical galaxies. This result and the simulation of galaxy merger with central black holes strongly suggest the dynamical effect of massive central objects is crucial to explain the observed structure of large ellipticals.


• High Performance N-Body Computing

  HACHISU Izumi, BONNEL Iwan, HEGGIE Douglas C., INAGAKI Shogo, OHNO Yosuke, FUKUSHIGE Toshiyuki, FUNATO Yoko, UENO Munetaka, TAIJI Makoto, MAKINO Junichiro, EBISUZAKI Toshikazu, SUGIMOTO Daiichiro, CLARKE Cathey, EGGLETON Peter P., WHITE Simon D.M., POLS Onno, AARSETH Sverre J.

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Overseas Scientific Survey., University of Tokyo, 1993 - 1993

  We, in Japan side, are making a Tera flops machine for gravitational many body problems. The purpose of this project is to make softwares for our special-purpose Tera flops machines under a cooperation with the UK group. The summary of our 1993 fiscal year project is as follows: 1.Taiji and Hachisu have finished designing a new board for Hermite integrator, which is called HARP-3. A copy of the board will be transferred into Institute of Astronomy, Cambridge University until the end of June, 1994. Aarseth will use the board to develop his Hermite code for our Tera flops machine. 2.Aarseth has stayed at the University of Tokyo from 5th of March to 17th of March, 1994. He succeeded in implementing his Hermite code into our test machine, HARP-2, and proved that the Hermite code is useful to integrate the evolution of collisional N-body systems. 3.Hachisu, Funato, and Inagaki visited the Institute of Astronomy, Cambridge University and discussed with the UK group. We are now developing tools to treat binary evolutions, star captures, and star-star collisions in our N-body code.


• Study on Dynamical Evolution of Dense Stellar Systems with Special Purpose Computers.

  ERIGUCHI Yoshiharu, TEUBEN Peter, HEGGIE Douglas C., VERBUNT Frank, MCMILLAN Stephen, BARNES Joshua, HUT Piet, FUNATO Yoko, OHNO Yosuke, UENO Munetaka, HACHISU Izumi, MAKISHIMA Kazuo, INAGAKI Shogo, MIYAMA Shoken, LARS Hunquist, J.J.MONAGHAN

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for international Scientific Research, Univ. of Tokyo, 1991 - 1993

  Academic Year 1991 Dr. Makino visited University of Edinburgh and developed a Hermite integration code for the simulations with the special purpose computer, GRAPE, in collaboration with Drs. Heggie, McMillan, and Aarseth (Cambridge University). This code is simpler and more suitable to GRAPE than the Aarseth code, which has been widely used in the N-body simulations of collisional gravitational systems. Dr.McMillan visited University of Tokyo and implemented his simulation code for stellar cluster to GRAPE-2A in collaboration with Dr.Inagaki. Dr.Hunquist also visited in University of Tokyo and implemented his SPH code to GRAPE-2A. They confirmed that GRAPE systems are suitable to the use of both two codes. Academic Year 1992 Drs.Makino, Hut, and Hunquist systematically investigated the error in the tree code, which is used in collisionless gravitational systems. They found the tree code offers an accuracy high enough for gravitational N-body simulations. Dr.Hachisu developed a vortex dynamics code of incompressible fluid simulations. He found that GRAPE systems can greatly accelerate the vortex dynamics simulations as well as gravitational N-body simulations. Academic Year 1993 We held a workshop on the dynamical evolution of dense stellar systems and the development of special purpose computers to summarize the results of three-years collaborations in Komaba campus University of Tokyo. We concluded that the direct collision of stars plays an important role in dense stellar systems. Drs.Hachisu, Ueno, and Miyama investigated the various types of computational fluid dynamics codes and concluded that the Gudnov type SPH method is most suitable to the special purpose computers for the simulations of self-gravitational fluid. The conceptual and detailed designs of the special purpose computer for SPH were done in collaboration of University of Tokyo and National Astronomical Observatory. In the academic year 1994, we shall make a test board of SPH machine and start to develop a special purpose LSI for the SPH code.


• Numerical Simulations of Collisions of Galaxies by Special Purpose Computer

  EBISUZAKI T., OKUMURA S. K., MAKINO J., SUGIMOTO D.

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for General Scientific Research (C), College of Arts and Sciences, University of Tokyo, 1990 - 1991

  In 1990, we purchased a workstation(U-300T)made by Sumitomo Electric Industries and connected it with the GRAPE-1, special purpose computer for gravitational N-body simulations. In 1991, we developed the advanced system, GRAPE-3, in which 48 full-custom LSIs works in parallel. We connected GRAPE-3 with U-300T and achieved an effective speed of 10 Gflops. This speed well exceeds that of the most advanced super computers. Using this GRAPE-3 system- we performed many numerical simulations of collisions of galaxies. We found the followings. First, the dynamical properties of elliptical galaxies are well explained in terms of the mergings of galaxies. We found that the results of the previous simulations are not appropriate because of their small number of particles and their biased initial conditions. We also found that the central black holes well explain the positive correlation between core radius and luminosity of elliptical galaxies. Second, the process in the mergings of galaxies are well explained in terms of waveparticle interactions and phase mixing. We concluded that the so called violent relaxation does not exist, since these two processes are quite different from the relaxation process.


• Research on Evolution of Stellar Systems with Highly Parallelized Special-purpose Computer for Gravitational Many-body Problems

  SUGIMOTO Daiichiro, OKAMURA Sachiko, MAKINO Junichiro, EBISUZAKI Toshikazu

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for General Scientific Research (B), University of Tokyo, 1990 - 1991

  In 1990 we constructed GRAPE-1A on a wire-wrapped board. It is a prototype of a special-purpose computer for gravitational many-body problems. In close collaboration with Electronic Imaging and Device Research Laboratory of Fuji XEROX Co., Ltd. we then designed a processor chip on one customized LSI which accommodated all the logics of GRAPE-1A. This LSI is 8x8 mm in size and contains 113, 000 transistors. Using this processor chip we constructed a parallelized machine GRAPE-3 in 1991 : We wired 24 processor chips on a VME board, and connected two boards with the host workstation via appropriately designed interface. The machine was tuned in 1991 to reach the peak performance of 14 Gflops, and the sustained speed of 10 Gflops in solving a gravitational 200, 000body problem. It is faster than the any commercially available supercomputer in 1991 so far as the sustained speed is concerned. Using GRAPE-3 we have done a variety of simulations on evolution of stellar systems, and have found that collision and resultant merging of galaxies play important roles in evolution of galaxies and their clusters. In what follows we summarize the new findings. 1) When two galaxies with central massive black holes collide each other, the black holes suffer from dynamical friction due to the field stars near the apocenter of the orbit. They loose rather their angular momentum than their energy. The eccentricity of the orbit approaches to unity and the black holes may merge quickly. At the same time the field stars aquire energy and become hot. Such picture nicely interprets the relation between the core radius and the total mass of the remnants. 2) During the collision of galaxies the gravitational field changes violently. As a result the stars become throughly mixed in the phase space. On the other hand, in the energy space the mixing proceeds quickly only in the initial phases of their collision and much more slowly afterward. Therefore, it is not appropriate to call such process as the "violent" relaxation. 3) After such process, the stars in the core (or halo) of each galaxy before the collision tend to stay in the core (or halo) of the merger. Therefore, the color gradient observed in giant elliptical galaxies can not testify against the merger hypothesis of their origin. 4) Merging of galaxies proceeds effectively by expelling the angular momentum together with the stars in the halo. Thus, the merging of galaxies may be regarded to be frequent phenomena and may play one of the leading roles in the evolution and history of galaxies and the universe.


• 専用計算機による数値天文学

  Competitive research funding


• Numerical Astrophysics by Special-Purpose Computers

  Competitive research funding