Research activity information

• May 2012 IoP Highlights of 2011

  YAMASAKI Kazuhito, YAJIMA Takahiro, IWAYAMA Takahiro


• Mar. 2011 IoP Select

  YAMASAKI Kazuhito, YAJIMA Takahiro, IWAYAMA Takahiro

• Elementary Catastrophe’s Chaos in One-Dimensional Discrete Systems Based on Nonlinear Connections and Deviation Curvature Statistics

  Kazuhito Yamasaki

  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, Jun. 2024, International Journal of Bifurcation and Chaos, 34(08) (08)

  [Refereed]

  Scientific journal


• Kosambi–Cartan–Chern Analysis of the Nonequilibrium Singular Point in One-Dimensional Elementary Catastrophe

  Kazuhito Yamasaki, Takahiro Yajima

  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, Mar. 2022, International Journal of Bifurcation and Chaos, 32(04) (04)

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Kosambi–Cartan–Chern Stability in the Intermediate Nonequilibrium Region of the Brusselator Model

  Kazuhito Yamasaki, Takahiro Yajima

  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, Feb. 2022, International Journal of Bifurcation and Chaos, 32(02) (02)

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• KCC analysis of a one-dimensional system during catastrophic shifts of the Hill function: Douglas tensor in the non-equilibrium region

  K. Yamasaki, T. Yajima

  Oct. 2020, International Journal of Bifurcation and Chaos, 30(11) (11), 2030032-1 - 2030032-13, English

  [Refereed]

  Scientific journal


• Duality of the Incompatibility Tensor

  K. Yamasaki, T. Hasebe

  Jan. 2020, Materials transactions, 61, 875 - 877, English

  [Refereed]

  Scientific journal


• Geometry of curves with fractional-order tangent vector and Frenet-Serret formulas

  T. Yajima, S.Oiwa, K.Yamasaki

  Jan. 2019, Fractional Calculus and Applied Analysis, 21, 1493 - 1505, English

  [Refereed]


• Non-holonomic geometric structures of rigid body system in Riemann-Cartan space

  YAMASAKI KAZUHITO, YAJIMA TAKAHIRO

  Aug. 2018, Journal of Physics Communications, 2, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• KCC analysis of the normal form of typical bifurcations in one-dimensional dynamical systems: geometrical invariants of saddle-node, transcritical, and pitchfork bifurcations

  YAMASAKI KAZUHITO, T. Yajima

  Sep. 2017, Int. J. Bifurcation and Chaos, 27, 1750145(14pages), English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Feynman’s Proof and Non-Elastic Displacement Fields: Relationship Between Magnetic Field and Defects Field

  YAMASAKI KAZUHITO, NAKAMURA NOZOMU

  Aug. 2016, International Journal of Theoretical Physics, (55) (55), 5186 - 5192, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Jacobi stability for dynamical systems of two-dimensional second-order differential equations and application to overhead crane system

  Takahiro Yajima, Kazuhito Yamasaki

  Apr. 2016, INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 13(4) (4), English

  [Refereed]

  Scientific journal


• Differential geometric structure of non-equilibrium dynamics in competition and predation: Finsler geometry and KCC theory

  YAMASAKI KAZUHITO, YAJIMA TAKAHIRO

  Apr. 2016, Journal of Dynamical Systems and Geometric Theories, (14) (14), 137 - 153, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Fractional Calculus Approach to the Deformation Field near the Fault Zone

  YAMASAKI KAZUHITO, YAJIMA TAKAHIRO

  Dec. 2015, A. J. Earth Science, English

  [Refereed]

  Scientific journal


• Geometry of stress function surfaces for asymmetric continuum

  T. Yajima, K. Yamasaki, H. Nagahama

  Dec. 2013, Acta Geophysica, 61, 1703 - 1721, English

  [Refereed]

  Scientific journal


• Lotka-Volterra system and KCC theory: Differential geometric structure of competitions and predations

  Kazuhito Yamasaki, Takahiro Yajima

  Aug. 2013, NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 14(4) (4), 1845 - 1853, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Symmetry and entropy of acoustic emisiion patterns in a rock-fracture experiment

  YAMASAKI KAZUHITO, K. Nanjo

  Jun. 2012, Theory and Uses of Acoustic Emissions (edited by J. K. Burnett), 149 - 162, English

  [Refereed]

  Research society


• Geometry of surfaces with Caputo fractional derivatives and applications to incompressible two-dimensional flows

  Takahiro Yajima, Kazuhito Yamasaki

  Feb. 2012, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 45(6) (6), English

  [Refereed]

  Scientific journal


• Differential geometric approach to the stress aspect of a fault: Airy stress function surface and curvatures

  Kazuhito Yamasaki, Takahiro Yajima

  Feb. 2012, ACTA GEOPHYSICA, 60(1) (1), 4 - 23, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Symmetry and entropy of one-dimensional legal cellular automata

  K. Yamasaki, K.Z. Nanjo, S. Chiba

  2012, Complex Systems, 20, 351-361, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Application of fractal analysis: Understanding of degree of magma mixing

  SATO EIICHI, Kazuhito Yamasaki

  Nova Science Publishers, 2012, Classification and Application of Fractals: New Research (edited by E. W. Mitchell and S. R. Murray), 217 - 230, English

  [Refereed]

  Research society


• Finsler metric and elastic constants for weak anisotropic media

  Takahiro Yajima, Kazuhito Yamasaki, Hiroyuki Nagahama

  Dec. 2011, NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 12(6) (6), 3177 - 3184, English

  [Refereed]

  Scientific journal


• Differential geometric structures of steam functions: incompressible two-dimensional flow and curvatures

  Yamasaki, K, Yajima, T, Iwayama, T

  Mar. 2011, Jounal of Physics A, 44, 155501(19 pages), English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Symmetry and entropy of biological patterns: Discrete Walsh functions for 2D image analysis

  Kazuhito Yamasaki, Kazuyoshi Z. Nanjo, Satoshi Chiba

  Jan. 2011, BIOSYSTEMS, 103(1) (1), 105 - 112, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Continuum mechanics and differential forms

  K. Yamasaki

  2010, Continuum mechancs, 193-221, English

  [Refereed]

  Scientific journal


• Fractal analysis of the fracture strength of lava dome material based on the grain size distribution of block-and-ash flow deposits at Unzen Volcano, Japan

  Keiko Suzuki-Kamata, Takashi Kusano, Kazuhito Yamasaki

  Oct. 2009, SEDIMENTARY GEOLOGY, 220(3-4) (3-4), 162 - 168, English

  [Refereed]

  Scientific journal


• A quantum particle motion and thermodynamics in faults-defects field: Path integral formulation based on extended deformation gradient tensor

  Kazuhito Yamasaki

  Sep. 2009, ACTA GEOPHYSICA, 57(3) (3), 567 - 582, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• A new mathematical tool for analyzing the fracturing process in rock: Partial symmetropy of microfracturing

  K. Yamasaki, K. Z. Nanjo

  Apr. 2009, PHYSICS OF THE EARTH AND PLANETARY INTERIORS, 173(3-4) (3-4), 297 - 305, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Geometrical minimum units of fracture patterns in two-dimensional space: Lattice and discrete Walsh functions

  Yuta Nishiyama, Kazuyoshi Z. Nanjo, Kazuhito Yamasaki

  Nov. 2008, PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 387(25) (25), 6252 - 6262, English

  [Refereed]

  Scientific journal


• Energy integral in fracture mechanics (J-integral) and Gauss-Bonnet Theorem

  Kazuhito Yamasaki, Hiroyuki Nagahama

  Jun. 2008, ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 88(6) (6), 515 - 520, English

  [Refereed]

  Scientific journal


• Betti numbers of defects field

  YAMASAKI KAZUHITO

  Jun. 2007, Forma, English

  [Refereed]

  Scientific journal


• Tensor analysis of dislocation-stress relations based on the extended deformation gradient

  YAMASAKI Kazuhito

  2005, Acta Geophysica Polonica, 53、1-12, English

  [Refereed]

  Scientific journal


• Species-area curve for land snails on Kikai Island in geological time

  MARUI Yasunari, CHIBA Satoshi, OKUNO Junichi, YAMASAKI Kazuhito

  2003, Paleobiology, 30,222-230, English

  [Refereed]

  Scientific journal


• A deformed medium including a defect field and differential forms

  YAMASAKI KAZUHITO, H. Nagahama

  Jun. 2002, Journal of Physics A: Mathematical and General, 35, 3767 - 3778, English

  [Refereed]

  Scientific journal


• Anisotropic Shape of Islands and Species Richness of Land Snail Fauna of the Ryukyus

  YAMASAKI Kazuhito, CHIBA Satoshi, NAGAHAMA Hiroyuki

  日本熱帯生態学会, 2000, Tropics, 10(1) (1), 93 - 101, English

  [Refereed]


• Hodge duality and continuum theory of defects

  YAMASAKI KAZUHITO

  Jun. 1999, Journal of Physics A: Mathematical and General, English

  [Refereed]

  Scientific journal


• Geometrical effect of island shape on the species richness

  YAMASAKI KAZUHITO

  Jun. 1999, Fractals, English

  [Refereed]

  Scientific journal


• Continuum theory of defects and gravity anomaly

  YAMASAKI KAZUHITO

  Jun. 1999, Acta Geophysica, English

  [Refereed]

  Scientific journal

• 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

  山崎和仁

  日本古生物学会 第174回例会（オンライン）, Jan. 2025

  Oral presentation


• カタストロフ過程中の非平衡安定性

  山崎和仁

  日本物理学会 第 79 回年次大会, Sep. 2024


• 非平衡性の「量」と「質」:地質学的時間スケールの場合

  山崎和仁

  統計数理研究所, 地球科学ワークショップ, Sep. 2022


• 非平衡特異点と分岐： 数理生物学への応用

  山崎和仁, 谷島 尚宏

  2021年度 日本数理生物学会年会, Sep. 2021


• 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

  山崎和仁

  ２０２０年度日本数理生物学会例会, Sep. 2020


• [基調講演] 不適合度条件の双対性

  山崎和仁

  日本金属学会２０２０年秋季講演, Sep. 2020, Japanese

  Keynote oral presentation


• Transition of biodiversity in mobile populations from the point of view of the small world

  新田 宏太, 山崎 和仁

  Annual Meeting of the Society of Evolutionary Studies, Japan, Aug. 2019, Japanese, Tokyo University, Domestic conference

  Oral presentation


• Differential geometry in continuum mechanics of Earth science

  山崎 和仁

  研究集会「特異点論による空間研究」, Jun. 2019, Japanese, JR博多シティ会議室, Domestic conference

  Oral presentation


• Transition of biodiversity in mobile populations and the small world in local subpopulations

  Kota Imaoka, Kazuhito Yamasaki

  Japan Geoscience Union Meeting 2019, May 2019, Japanese, Makuhari Messe, Chiba, Domestic conference

  Oral presentation


• Differential geometrical structure of potential surface for two-dimensional deformation and flow

  Kazuhito Yamasaki

  第85回形の科学シンポジウム, Jun. 2018, Japanese, 東北大学 青葉山東キャンパス, Domestic conference

  Oral presentation


• Topological properties of vertebrate phylogenetic trees: Horton analysis and neutral model of stochastic branching

  Yuichiro Ishii, Kazuhito Yamasaki

  第85回形の科学シンポジウム, Jun. 2018, Japanese, 東北大学 青葉山東キャンパス, Domestic conference

  Oral presentation


• 種間相互作用を伴う古生態系の非平衡安定性解析

  山崎 和仁

  日本古生物学会2018年年会, Jun. 2018, Japanese, 東北大学 青葉山北キャンパス, Domestic conference

  Oral presentation


• 移動個体群の生物多様性変化

  今岡 宏太, 山崎 和仁

  日本古生物学会2018年年会, Jun. 2018, Japanese, 東北大学 青葉山北キャンパス, Domestic conference

  Oral presentation


• 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

  石井 友一朗, YAMASAKI KAZUHITO

  JpGU-AGU Joint Meeting 2017, May 2017, Japanese, 幕張メッセ, International conference

  Oral presentation


• 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

  YAMASAKI KAZUHITO

  日本地質学会第123年学術大会, Sep. 2016, Japanese, 日本大学文理学部キャンパス, Domestic conference

  Oral presentation


• 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

  YAMASAKI KAZUHITO, 中村 望

  日本地質学会第120年学術大会（仙台大会）, Sep. 2013, Japanese, Domestic conference

  Oral presentation


• 岩石の流動変形と境界面の幾何学

  高田 和佳, SATO EIICHI, YAMASAKI KAZUHITO

  日本地質学会第120年学術大会（仙台大会）, Sep. 2013, Japanese, 東北大学, Domestic conference

  Oral presentation


• KCC理論に基づくロトカボルテラ系の非平衡安定性解析

  YAMASAKI KAZUHITO, 谷島 尚宏

  第23回日本数理生物学会, Sep. 2013, Japanese, 静岡大学, Domestic conference

  Oral presentation


• Magma mixing/mingling and viscous fingering: Analogue experiments and geometry of interfaces

  Nodoka Takada, SATO EIICHI, Yamasaki Kazuhito

  IAVCEI 2013 Scientific Assembly, Jul. 2013, English, International conference

  Poster presentation


• Forming mechanism of Taiheizan pyroclastic flow: Block and ash flow generated from eruption column collapse

  SUZUKI KEIKO, Shun Orui, YAMASAKI KAZUHITO

  IAVCEI (International Association of Volcanology and Chemistry of the Earth's Interior), Jul. 2013, English, Kagoshima, Japan, International conference

  Poster presentation


• 古生物学における生物間相互作用の微分幾何学的考察

  YAMASAKI KAZUHITO, 谷島 尚宏

  日本古生物学会2013年年会・総会, Jun. 2013, Japanese, 熊本大学, Domestic conference

  Oral presentation


• 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

  高田 和佳, SATO EIICHI, YAMASAKI KAZUHITO

  日本地球惑星科学連合2013年大会, May 2013, Japanese, 幕張メッセ, Domestic conference

  Oral presentation


• 断層欠陥場と応力関数曲面の曲率,

  YAMASAKI KAZUHITO, 谷島 尚宏, IWAYAMA TAKAHIRO

  日本地質学会，, Sep. 2011, Japanese, 水戸，, Domestic conference

  Oral presentation


• Magma mixing in a conduit with magma pocket

  SATO EIICHI, Kazuhito Yamasaki

  IUGG 2011, Jul. 2011, English, Melbourne, International conference

  Poster presentation


• Okubo-Weissの基準を用いた点渦列の安定性の研究

  IWAYAMA TAKAHIRO, YAMASAKI KAZUHITO, 谷島 尚宏

  第60回理論応用力学講演会, Mar. 2011, Japanese, 日本学術会議, 東京工業大学, Domestic conference

  Oral presentation


• block-and-ash flow タイプの火砕流粒度分布と溶岩破砕強度

  KAMATA Keiko, KUSANO Takashi, YAMASAKI Kazuhito

  日本火山学会秋季大会, Oct. 2005, Japanese, 札幌, Domestic conference

  Oral presentation

• 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

  山崎 和仁

  新学術領域研究(研究領域提案型), Apr. 2019 - Mar. 2021, Principal investigator

  Competitive research funding


• 珪長質マグマ水蒸気爆発の噴火機構と火砕密度流の流動・堆積機構の研究

  鈴木 桂子

  学術研究助成基金助成金／基盤研究(C), Apr. 2016 - Mar. 2019

  Competitive research funding


• 地球連続体の不均質非線形変形機構の理論的研究

  山崎 和仁

  学術研究助成基金助成金／基盤研究(C), Apr. 2013 - Mar. 2016, Principal investigator

  Competitive research funding


• Study of vortex motions for a generalized two-dimensional fluid system using point-vortex model

  IWAYAMA Takahiro, WATANABE Takeshi, YAMASAKI Kazuhito, SUEYOSHI Masakazu, MURAKAMI Shinya

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Kobe University, 01 Apr. 2012 - 31 Mar. 2015

  Linear stability of parallel shear flows and turbulent properties of a generalized two-dimensional fluid system were investigated theoretically and numerically. We derived a sufficient condition for stability of parallel shear flows and solved the so-called Kelvin-Helmholtz instability problem. Furthermore, using an asymptotic analysis of Eddy Damped Quasi-Normal Markovianized equation for a generalized two-dimensional fluid system, we predicted the existence of a universal spectrum in the infrared range and the anomalous form of the eddy viscosity. Those results were verified by direct numerical simulations of the governing equation for a generalized two-dimensional fluid system.


• Stability for flows in a generalized two-dimensional fluid

  IWAYAMA Takahiro, WATANABE Takeshi, YAMASAKI Kazuhito, SUEYOSHI Masakazu, YAJIMA Takahiro, MURAKAMI Shinya

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Kobe University, 2008 - 2010

  Stability of parallel shear flows for a generalized two-dimensional (2D) fluid system, which is a unified form of some geophysical 2D fluid systems, is investigated. First, the conservation of the wave activity is derived. Second, it is shown that the governing equation for the generalized 2D fluid system can be written in the form of non canonical Hamiltonian form. Using them, a necessary condition for a linear stability of parallel shear flows is derived as: "if the transverse derivative of the generalized vorticity for the basic state is positive or negative definite, the flow is stable". Moreover, the Green's function for the generalized 2D fluid system is derived. Using the Green's function, physically realizable systems for the generalized 2D fluid system exist only for \alpha less than or equal 3. Here, \alpha is a real parameter describing the scale separation between the generalized vorticity and the velocity. In addition, the transition of the small scale behavior of the generalized vorticity at alpha=2, a well known property of forced and dissipated turbulence for the generalized 2D fluid, is explained in terms of the Green's function.


• 大陸のテクトニクス：大陸の姿・形を変えた様子を古地磁気学から探る

  乙藤 洋一郎

  科学研究費補助金／基盤研究(B), 2010

  Competitive research funding


• 多様性爆発の生物学的メカニズム

  千葉 聡

  科学研究費補助金／基盤研究(A), 2006 - 2008

  Competitive research funding


• 大陸衝突によるアジア大陸東部域の大陸変形の研究

  乙藤 洋一郎

  科学研究費補助金／基盤研究(B), 2006

  Competitive research funding


• 多様性の揺籠:フロンティア環境における生物進化

  千葉 聡

  科学研究費補助金／基盤研究(B), 2003 - 2005

  Competitive research funding


• アジア大陸東部の大陸変形現象を古地磁気学よりさぐる

  乙藤 洋一郎

  科学研究費補助金／基盤研究(B), 2005

  Competitive research funding