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山崎 和仁大学院理学研究科 惑星学専攻講師
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- This study shows, by means of numerical analysis, that the characteristics of discrete dynamical systems, in which chaos and catastrophe coexist, are closely related to the geometric statistics in Finsler geometry. The two geometric statistics introduced are nonlinear connections information, denoted as [Formula: see text], and the mean deviation curvature, denoted as [Formula: see text]. The quantity [Formula: see text] can be used to determine the occurrence of chaos in terms of nonequilibrium stability. The resulting chaos is characterized by [Formula: see text] in terms of the trajectory’s robustness, which is related to the localization or globalization of chaos. The characteristics of catastrophe-induced chaos are clearly visualized through the contour topography of [Formula: see text], in which an abrupt change is represented by cliff topography (i.e. a line of critical points); initial dependence is reflected in the reversibility of topographic patterns. On overlaying the contour topography with the singularity pattern, it is evident that chaos does not arise around the singular point. Furthermore, the extensive development of cusp and butterfly chaos demands information on the nonlinear connections within the singularity pattern. The asymmetry in swallowtail chaos is less distinguishable in an equilibrated state, but becomes more evident when the system is in a state of nonequilibrium. In many analyses, chaos and catastrophe are examined separately. However, these results demonstrate that when both are present, the two have a complex relationship constrained by the singularity.World Scientific Pub Co Pte Ltd, 2024年06月, International Journal of Bifurcation and Chaos, 34(08) (08)[査読有り]研究論文（学術雑誌）
- This paper analyzes the properties of the nonequilibrium singular point in one-dimensional elementary catastrophe. For this analysis, the Kosambi–Cartan–Chern (KCC) theory is applied to characterize the dynamical system based on differential geometrical quantities. When both the nonlinear connection and deviation curvature are zero, that is, when the geometric stability of the KCC theory is neutral, two bifurcation curves are obtained: one is the known curve with an equilibrium singular point, and the other is a new curve with a nonequilibrium singular point. The two singular points are distinguished based on the vanishing condition of the Berwald connection. Applied to the ecosystem described by the Hill function, the absolute value of the cuspidal curvature of the nonequilibrium singular point is larger than that of the equilibrium singular point. The ecological interpretation of this result is that the range of bistability of the ecosystem in the nonequilibrium state is greater than that in the equilibrium state. The type of singular points in equilibrium and nonequilibrium bifurcation curves are not necessarily the same. For instance, there is a combination in which even if the former has one cusp, the latter may show various types, depending on the parametric space. These results demonstrate that there are cases where simply shifting the system from the equilibrium to nonequilibrium state expands the range of bistability and changes the type of singularity. Although singularity analysis is often performed near the equilibrium point, nonequilibrium analysis, i.e. analysis based on the KCC theory, provides a useful perspective for analyzing singularity theory according to the bifurcation phenomenon.World Scientific Pub Co Pte Ltd, 2022年03月, International Journal of Bifurcation and Chaos, 32(04) (04)[査読有り]研究論文（学術雑誌）
- This study applies the Kosambi–Cartan–Chern (KCC) theory to the Brusselator model to derive differential geometric quantities related to bifurcation phenomena. Based on these geometric quantities, the KCC stability of the Brusselator model is analyzed in linear and nonlinear cases to determine the extent to which nonequilibrium affects bifurcation and stability. The geometric quantities of the Brusselator model have a constant value in the linear case, and are functions of spatial variables with parameter dependence in the nonlinear case. Therefore, the KCC stability of the nonlinear case shows various distribution patterns, depending on the distance from the equilibrium point (EQP), as follows: in the regions near or far enough from the EQP, the distribution of KCC stability is uniform and regular; and in the intermediate nonequilibrium region, the distribution varies and shows complex patterns with parameter dependence. These results indicate that stability in the intermediate nonequilibrium region plays an important role in the dynamic complex patterns in the Brusselator model.World Scientific Pub Co Pte Ltd, 2022年02月, International Journal of Bifurcation and Chaos, 32(02) (02)[査読有り]研究論文（学術雑誌）
- 2020年10月, International Journal of Bifurcation and Chaos, 30(11) (11), 2030032-1 - 2030032-13, 英語[査読有り]研究論文（学術雑誌）
- 2020年01月, Materials transactions, 61, 875 - 877, 英語Duality of the Incompatibility Tensor[査読有り]研究論文（学術雑誌）
- 2019年01月, Fractional Calculus and Applied Analysis, 21, 1493 - 1505, 英語Geometry of curves with fractional-order tangent vector and Frenet-Serret formulas[査読有り]
- 2018年08月, Journal of Physics Communications, 2, 英語Non-holonomic geometric structures of rigid body system in Riemann-Cartan space[査読有り]研究論文（学術雑誌）
- 2017年09月, Int. J. Bifurcation and Chaos, 27, 1750145(14pages), 英語[査読有り]研究論文（学術雑誌）
- 2016年08月, International Journal of Theoretical Physics, (55) (55), 5186 - 5192, 英語Feynman’s Proof and Non-Elastic Displacement Fields: Relationship Between Magnetic Field and Defects Field[査読有り]研究論文（学術雑誌）
- Geometric structures of dynamical systems are investigated based on a differential geometric method (Jacobi stability of KCC-theory). This study focuses on differences of Jacobi stability of two-dimensional second-order differential equation from that of one-dimensional second-order differential equation. One of different properties from a one-dimensional case is the Jacobi unstable condition given by eigenvalues of deviation curvature with different signs. Then, this geometric theory is applied to an overhead crane system as a two-dimensional dynamical system. It is shown a relationship between the Hopf bifurcation of linearized overhead crane and the Jacobi stability. Especially, the Jacobi stable trajectory is found for stable and unstable spirals of the two-dimensional linearized system. In case of the linearized overhead crane system, the Jacobi stable spiral approaches to the equilibrium point faster than the Jacobi unstable spiral. This means that the Jacobi stability is related to the resilience of deviated trajectory in the transient state. Moreover, for the nonlinear overhead crane system, the Jacobi stability for limit cycle changes stable and unstable over time.WORLD SCIENTIFIC PUBL CO PTE LTD, 2016年04月, INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 13(4) (4), 英語[査読有り]研究論文（学術雑誌）
- 2016年04月, Journal of Dynamical Systems and Geometric Theories, (14) (14), 137 - 153, 英語Differential geometric structure of non-equilibrium dynamics in competition and predation: Finsler geometry and KCC theory[査読有り]研究論文（学術雑誌）
- 2015年12月, A. J. Earth Science, 英語Fractional Calculus Approach to the Deformation Field near the Fault Zone[査読有り]研究論文（学術雑誌）
- 2013年12月, Acta Geophysica, 61, 1703 - 1721, 英語Geometry of stress function surfaces for asymmetric continuum[査読有り]研究論文（学術雑誌）
- We consider the differential geometric structure of competitions and predations in the sense of the Lotka-Volterra system based on KCC theory. For this, we visualise the relationship between the Jacobi stability and the linear stability as a single diagram. We find the following. (I) Ecological interactions such as competition and predation can be described by the deviation curvature. In this case, the sign of the deviation curvature depends on the type of interaction, which reflects the equilibrium point type. (II) The geometric quantities in KCC theory can be expressed in terms of the mean and Gaussian curvatures of the potential surface. In this particular case, the deviation curvature can be interpreted as the Willmore energy density of the potential surface. (III) When the equations of the system have nonsymmetric structure for the species (e.g. a predation system), each species also has nonsymmetric geometric structure in the nonequilibrium region, but symmetric structure around the equilibrium point. These findings suggest that KCC theory is useful to establish the geometrisation of ecological interactions. (c) 2012 Elsevier Ltd. All rights reserved.PERGAMON-ELSEVIER SCIENCE LTD, 2013年08月, NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 14(4) (4), 1845 - 1853, 英語[査読有り]研究論文（学術雑誌）
- 2012年06月, Theory and Uses of Acoustic Emissions (edited by J. K. Burnett), 149 - 162, 英語Symmetry and entropy of acoustic emisiion patterns in a rock-fracture experiment[査読有り]研究論文（その他学術会議資料等）
- Geometric structures of surfaces are formulated based on Caputo fractional derivatives. The Gauss frame of a surface with fractional order is introduced. Then, the non-locality of the fractional derivative characterizes the asymmetric second fundamental form. The mean and Gaussian curvatures of the surface are defined in the case of fractional order. Based on the fractional curvatures, incompressible two-dimensional flows are discussed. The stream functions are obtained from a fractional continuity equation. The asymmetric second fundamental form of stream-function surface is related to the path dependence of flux. Moreover, the fractional curvatures are calculated for the stream-function surfaces of uniform and corner flows. The uniform flow with fractional order is characterized by the non-vanishing mean curvature. The non-locality of corner flow is expressed by the mean and Gaussian curvatures with fractional order. In particular, the fractional order within the stream-function of corner flow determines the change of sign of Gaussian curvature. Therefore, the non-local property of incompressible flows can be investigated by the fractional curvatures.IOP PUBLISHING LTD, 2012年02月, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 45(6) (6), 英語[査読有り]研究論文（学術雑誌）
- We considered the two-dimensional stress aspect of a fault from the viewpoint of differential geometry. For this analysis, we concentrated on the curvatures of the Airy stress function surface. We found the following: (i) Because the principal stresses are the principal curvatures of the stress function surface, the first and the second invariant quantities in the elasticity correspond to invariant quantities in differential geometry; specifically, the mean and Gaussian curvatures, respectively; (ii) Coulomb's failure criterion shows that the coefficient of friction is the physical expression of the geometric energy of the stress function surface; (iii) The differential geometric expression of the Goursat formula shows that the fault (dislocation) type (strike-slip or dip-slip) corresponds to the stress function surface type (elliptic or hyperbolic). Finally, we discuss the need to use non-biharmonic stress tensor theory to describe the stress aspect of multi-faults or an earthquake source zone.VERSITA, 2012年02月, ACTA GEOPHYSICA, 60(1) (1), 4 - 23, 英語[査読有り]研究論文（学術雑誌）
- 2012年, Complex Systems, 20, 351-361, 英語Symmetry and entropy of one-dimensional legal cellular automata[査読有り]研究論文（学術雑誌）
- Nova Science Publishers, 2012年, Classification and Application of Fractals: New Research (edited by E. W. Mitchell and S. R. Murray), 217 - 230, 英語Application of fractal analysis: Understanding of degree of magma mixing[査読有り]研究論文（その他学術会議資料等）
- Differential geometric expressions of elastic constants for a seismic ray path are studied based on Finsler geometry. A Finsler function named mth root metric is considered to discuss transverse isotropic media in weak anisotropic case. Finsler parameters in the mth root metric are estimated from phase velocity surfaces. The slight differences from an elliptic wavefront can be expressed by the Finsler parameters. It is found a correlation between the Finsler parameters and the weak anisotropy parameters consisted of elastic constants. Especially, a positivity of weak anisotropy parameter influences on a restriction of Finsler parameter. On the other hand, a geometric condition of Finsler parameter gives a limitation of weak anisotropy parameter. Moreover, the Berwald Gauss curvature of mth root metric induces a relationship between the spreading ray paths and the weak anisotropy parameter. Therefore, the seismic ray paths in weak isotropic media can be expressed by the Finslerian properties of;nth root metric. (C) 2011 Elsevier Ltd. All rights reserved.PERGAMON-ELSEVIER SCIENCE LTD, 2011年12月, NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 12(6) (6), 3177 - 3184, 英語[査読有り]研究論文（学術雑誌）
- 2011年03月, Jounal of Physics A, 44, 155501(19 pages), 英語Differential geometric structures of steam functions: incompressible two-dimensional flow and curvatures[査読有り]研究論文（学術雑誌）
- To quantify symmetry and entropy inherent in the discrete patterns such as spatial self-organization in cell sorting and mussel bed ecosystems, we introduce the discrete Walsh analysis. This analysis enables us to estimate the degree of the complicated symmetry, and to extract the symmetry from the pattern that seems to be asymmetric. The results obtained in this paper are summarized as follows. (I) The geometrical patterns of the cell sorting become systematic with the predominance of the particular symmetry. This implies that not only the entropy but also the particular symmetry can decrease in the biological process. (II) The magnitude of the symmetry is related to the absolute value of the adhesion, and the type of the symmetry is related to the sign of the adhesion. That is, centro-symmetry dominates in the cell sorting pattern caused by large negative adhesion, and double symmetry dominates in the pattern caused by large positive adhesion. (III) Spatial self-organization in mussel bed is accompanied by the decreasing of the centro-symmetry. This implies that the positive "adhesion" between mussel individuals increases with time. (IV) In the biological process, the Curie symmetry breaking occurs at intervals. (C) 2010 Elsevier Ireland Ltd. All rights reserved.ELSEVIER SCI LTD, 2011年01月, BIOSYSTEMS, 103(1) (1), 105 - 112, 英語[査読有り]研究論文（学術雑誌）
- 2010年, Continuum mechancs, 193-221, 英語Continuum mechanics and differential forms[査読有り]研究論文（学術雑誌）
- A fractal theory of rock fragmentation is applied to block-and-ash flow deposits from the Fugendake dome, Unzen Volcano, Kyushu, Japan, in order to analyze the material strength and the energy required for size reduction of the source lava dome. Two fractal dimensions h and D-s, which are mutually interchangeable, represent the relative strength and energy for particles reduced to a given size. They can be theoretically estimated from the power relations of a reference grain size to the cumulative mass and number of fragments smaller than that size. The Unzen-Fugendake block-and-ash flow deposits have been further modified by size sorting and secondary fragmentation that occurred during flowage, so that the h value decreases (or D-s value increases) with increasing distance from the source. Coarse, reversely graded deposits are, however, found to retain the original size population relatively well. The D-s values estimated from deposits of this type are compatible with those previously reported from decompression-fragmentation experiments conducted on the same dome material. The employed fractal approach could thus give insights into the potential mode of dome collapse that generates block-and-ash flows. (C) 2009 Elsevier B. V. All rights reserved.ELSEVIER SCIENCE BV, 2009年10月, SEDIMENTARY GEOLOGY, 220(3-4) (3-4), 162 - 168, 英語[査読有り]研究論文（学術雑誌）
- We consider the effect of the faults-defects (FD) field on the following quantum phenomena: (i) the motion of a particle expressed by the Green function; (ii) thermodynamic phenomena expressed by the partition function. We use the path integral formulation based on the extended deformation gradient (EDG) tensor. This formulation connects the Green function of (i) with the partition function of (ii) to describe the thermodynamics in terms of a quantum particle motion. We obtain the following results: (a) The Lagrangian in the Green function includes the new potential consisting of stress functions that shift the path of the free particle from the shortest distance; (b) The solution of the partition function in one-dimensional space makes it possible to deduce the thermodynamic relations in the FD field. Such results could not be obtained by taking the traditional mechanical and quantum approaches, so the path integral formulation based on the EDG tensor is a useful tool.VERSITA, 2009年09月, ACTA GEOPHYSICA, 57(3) (3), 567 - 582, 英語[査読有り]研究論文（学術雑誌）
- We have shown that the symmetry of fracturing process in a macro-scale can be quantified by using the concept of symmetropy (an entropy-like measure of symmetry). Here we extend this approach to examining the symmetries in a range from small (partial) scales to larger (whole) scales: this approach is called partial symmetropy (PS). To check its applicability, we consider one illustrative example, the temporal change of the spatial patterns of acoustic-emission events in a well-documented rock fracture experiment. Our results are summarized as follows: (i) the PS enables us to distinguish the nucleation phases from the other phases such as the pre-nucleation and the propagation phases: (ii) the variation of the PS shows that the fracturing process is associated with a type of phase transitions from the subcritical state to the critical state: (iii) the scale dependence of the PS reveals the presence of the sandwich structure that consists of order and non-order in the evolution of the fracturing pattern: (iv) within the framework of non-extensive Tsallis entropy we develop the PS concept, and show that the degree of non-extensivity on a large scale increases immediately after the nucleation. The results shown in the present paper are not obtained by taking the traditional fractal approach, nor using only a simply symmetropy. We therefore propose that the PS is a useful tool to providing a strategy for describing qualitatively the phase changes in the observed fracturing process. (C) 2009 Elsevier B.V. All rights reserved.ELSEVIER SCIENCE BV, 2009年04月, PHYSICS OF THE EARTH AND PLANETARY INTERIORS, 173(3-4) (3-4), 297 - 305, 英語[査読有り]研究論文（学術雑誌）
- We present the geometrical minimum units of fracture patterns in two-dimensional space. For this analysis, a new method is developed from the algebraic approach: the concept of lattice (a type of partially ordered set) is applied to the discrete Walsh functions that have been used to measure symmetropy (an object related to symmetry and entropy) of fracture patterns. We concluded that the minimum units of fracture patterns can be expressed as three kinds of lattice. Our model is applied to the temporal change of the spatial pattern of acoustic-emission events in a rock-fracture experiment. As a result, the symmetropy of lattice decreases with the evolution of fracture process. We find that the pre-nucleation process of fracture corresponds to the subcritical states, and the propagation process to the critical states. Moreover, using a particular mathematical structure called sheaf on a lattice, we suggest the algebraic interpretation of fracture process, and provide justification to regard fracturing as an irreversible process. (C) 2008 Elsevier B.V. All Fights reserved.ELSEVIER SCIENCE BV, 2008年11月, PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 387(25) (25), 6252 - 6262, 英語[査読有り]研究論文（学術雑誌）
- The J-integral (a path-independent energy integral) formalism is the standard method of analyzing nonlinear fracture mechanics. It is shown that the energy density of deformation fields in terms of the homotopy operator corresponds to the J-integral for dislocation-disclination fields and gives the force on dislocation-disclination fields as a physical interpretation. The continuum theory of defects gives a natural framework for understanding the topological aspects of the J-integral. This geometric interpretation gives that the J-integral is an alternative expression of the well-known theorem in differential geometry, i.e., the Gauss-Bonnet theorem (with genus = 1). The geometrical expression of the J-integral shows that the Eshelby's energy-momentum (the physical quantity of the material space) is closely related to the Einstein 3-form (the geometric objects of the material space). (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.WILEY-BLACKWELL, 2008年06月, ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 88(6) (6), 515 - 520, 英語[査読有り]研究論文（学術雑誌）
- 2007年06月, Forma, 英語Betti numbers of defects field[査読有り]研究論文（学術雑誌）
- 2005年, Acta Geophysica Polonica, 53、1-12, 英語Tensor analysis of dislocation-stress relations based on the extended deformation gradient[査読有り]研究論文（学術雑誌）
- 2003年, Paleobiology, 30,222-230, 英語Species-area curve for land snails on Kikai Island in geological time[査読有り]研究論文（学術雑誌）
- 2002年06月, Journal of Physics A: Mathematical and General, 35, 3767 - 3778, 英語A deformed medium including a defect field and differential forms[査読有り]研究論文（学術雑誌）
- 日本熱帯生態学会, 2000年, Toropics, 10(1) (1), 93 - 101, 英語Anisotropic shape of islands and species richness of land snail fauna of the Ryukyus[査読有り]
- 1999年06月, Journal of Physics A: Mathematical and General, 英語Hodge duality and continuum theory of defects[査読有り]研究論文（学術雑誌）
- 1999年06月, Fractals, 英語Geometrical effect of island shape on the species richness[査読有り]研究論文（学術雑誌）
- 1999年06月, Acta Geophysica, 英語Continuum theory of defects and gravity anomaly[査読有り]研究論文（学術雑誌）
- 日本古生物学会 第174回例会（オンライン）, 2025年01月過去の地球システムにおける海洋古生物の役割：炭素循環の例口頭発表（一般）
- 日本物理学会 第 79 回年次大会, 2024年09月カタストロフ過程中の非平衡安定性
- 統計数理研究所, 地球科学ワークショップ, 2022年09月非平衡性の「量」と「質」:地質学的時間スケールの場合
- 2021年度 日本数理生物学会年会, 2021年09月非平衡特異点と分岐： 数理生物学への応用
- ２０２０年度日本数理生物学会例会, 2020年09月カタストロフィックシフト中における生態系の安定性:非平衡領域におけるダグラステンソル
- 日本金属学会２０２０年秋季講演, 2020年09月, 日本語[基調講演] 不適合度条件の双対性口頭発表（基調）
- 日本進化学会第20回大会, 2019年08月, 日本語, 東京大学 駒場Iキャンパス, 国内会議拡散個体群の局所的スモールワールド性からみる生物多様性の変化口頭発表（一般）
- 研究集会「特異点論による空間研究」, 2019年06月, 日本語, JR博多シティ会議室, 国内会議地球連続体力学における微分幾何学口頭発表（一般）
- 日本地球惑星科学連合2019年大会, 2019年05月, 日本語, 幕張メッセ, 国内会議地質学的時間スケールでみる生物多様性の変遷：拡散個体群と局所集団のスモールワールド性から考える種分化のメカニズム口頭発表（一般）
- 第85回形の科学シンポジウム, 2018年06月, 日本語, 東北大学 青葉山東キャンパス, 国内会議二次元変形・流動現象におけるポテンシャル曲面の微分幾何学的構造口頭発表（一般）
- 第85回形の科学シンポジウム, 2018年06月, 日本語, 東北大学 青葉山東キャンパス, 国内会議脊椎動物の系統樹の位相的性質：Horton 解析と中立的確率分岐モデルに基づくアプローチ口頭発表（一般）
- 日本古生物学会2018年年会, 2018年06月, 日本語, 東北大学 青葉山北キャンパス, 国内会議種間相互作用を伴う古生態系の非平衡安定性解析口頭発表（一般）
- 日本古生物学会2018年年会, 2018年06月, 日本語, 東北大学 青葉山北キャンパス, 国内会議移動個体群の生物多様性変化口頭発表（一般）
- JpGU-AGU Joint Meeting 2017, 2017年05月, 日本語, 幕張メッセ, 国際会議生物進化と多様性の中立的確率モデル：系統樹の位相的性質からの考察口頭発表（一般）
- 日本地質学会第123年学術大会, 2016年09月, 日本語, 日本大学文理学部キャンパス, 国内会議非整数空間における岩石変形の分数階微分に基づく考察口頭発表（一般）
- 日本地質学会第120年学術大会（仙台大会）, 2013年09月, 日本語, 国内会議断層・欠陥場における変形場と磁場の相互作用：非Riemann幾何学とFeynman証明口頭発表（一般）
- 日本地質学会第120年学術大会（仙台大会）, 2013年09月, 日本語, 東北大学, 国内会議岩石の流動変形と境界面の幾何学口頭発表（一般）
- 第23回日本数理生物学会, 2013年09月, 日本語, 静岡大学, 国内会議KCC理論に基づくロトカボルテラ系の非平衡安定性解析口頭発表（一般）
- IAVCEI 2013 Scientific Assembly, 2013年07月, 英語, 国際会議Magma mixing/mingling and viscous fingering: Analogue experiments and geometry of interfacesポスター発表
- IAVCEI (International Association of Volcanology and Chemistry of the Earth's Interior), 2013年07月, 英語, Kagoshima, Japan, 国際会議Forming mechanism of Taiheizan pyroclastic flow: Block and ash flow generated from eruption column collapseポスター発表
- 日本古生物学会2013年年会・総会, 2013年06月, 日本語, 熊本大学, 国内会議古生物学における生物間相互作用の微分幾何学的考察口頭発表（一般）
- 日本地球惑星科学連合2013年大会, 2013年05月, 日本語, 幕張メッセ, 国内会議マグマ混合過程とビスカスフィリング：アナログモデル実験と境界面の幾何学口頭発表（一般）
- 日本地質学会，, 2011年09月, 日本語, 水戸，, 国内会議断層欠陥場と応力関数曲面の曲率,口頭発表（一般）
- IUGG 2011, 2011年07月, 英語, Melbourne, 国際会議Magma mixing in a conduit with magma pocketポスター発表
- 第60回理論応用力学講演会, 2011年03月, 日本語, 日本学術会議, 東京工業大学, 国内会議Okubo-Weissの基準を用いた点渦列の安定性の研究口頭発表（一般）
- 日本火山学会秋季大会, 2005年10月, 日本語, 札幌, 国内会議block-and-ash flow タイプの火砕流粒度分布と溶岩破砕強度口頭発表（一般）
- 新学術領域研究(研究領域提案型), 2019年04月 - 2021年03月, 研究代表者ミルフィーユ構造のキンク強化理論：砂泥互層褶曲の微分幾何学的考察競争的資金
- 学術研究助成基金助成金／基盤研究(C), 2016年04月 - 2019年03月競争的資金
- 学術研究助成基金助成金／基盤研究(C), 2013年04月 - 2016年03月, 研究代表者競争的資金
- 日本学術振興会, 科学研究費助成事業, 基盤研究(C), 神戸大学, 2012年04月01日 - 2015年03月31日点渦モデルを用いた一般化された２次元流体系における渦運動の研究一般化された2次元流体系の平行流の線形安定性，及び乱流特性に関する研究を行った．平行流の安定性の研究では，安定性の十分条件を導き，この条件を破り最も基本的な流れである渦層の不安定問題（ケルヴィン・ヘルムホルツ不安定問題）を解いた． 乱流特性の研究では，赤外領域に方程式に含まれるパラメターαに依存しない普遍的スペクトルが存在することを完結近似方程式の漸近解析により予測した．さらに，完結近似方程式の漸近解析により，渦粘性は低波数極限でも一般に異常拡散型であり，ナビエ・ストークス系のときに拡散型になることを導いた．これらの結果の正当性は直接数値実験により確認された．
- 日本学術振興会, 科学研究費助成事業, 基盤研究(C), 神戸大学, 2008年 - 2010年一般化された2次元流体における流れの安定性地球流体力学で知られた複数の2次元流体系を統一的に記述できる一般化された2次元流体系において,平行流の安定性の研究を行った.支配方程式から波動活動度保存則を導き,また支配方程式をHamilton形式に書き下した.これらを利用して,平行流の安定の十分条件を導出した.さらに,一般化された2次元流体のGreen関数を導出した.Green関数を用いて,一般化された2次元流体系は,系に含まれるスケール分離パラメターαが3以下の場合が物理的に理にかなった系であること,乱流状態において一般化された渦度の小スケールにおける振る舞いの転移を説明した.
- 科学研究費補助金／基盤研究(B), 2010年競争的資金
- 科学研究費補助金／基盤研究(A), 2006年 - 2008年多様性爆発の生物学的メカニズム競争的資金
- 科学研究費補助金／基盤研究(B), 2006年競争的資金
- 科学研究費補助金／基盤研究(B), 2003年 - 2005年多様性の揺籠:フロンティア環境における生物進化競争的資金
- 科学研究費補助金／基盤研究(B), 2005年競争的資金