| 松江 要（まつえ かなめ） | データ更新日：2024.05.07 |
教授 ／
マス・フォア・インダストリ研究所
リエゾン戦略部門
| 1. | Norio Konno, Kaname Matsue, Etsuo Segawa, A crossover between open quantum random walks to quantum walks, Journal of Statistical Physics, https://doi.org/10.1007/s10955-023-03211-6, 190, 2024.12, [URL], We propose an intermediate walk continuously connecting an open quantum random walk and a quantum walk with parameters M\in \mathbb{N} controlling a decoherence effect; if M=1, the walk coincides with an open quantum random walk, while M=\infty, the walk coincides with a quantum walk. We define a measure which recovers usual probability measures on \mathbb{Z} for M=\infty and M=1 and we observe intermediate behavior through numerical simulations for varied positive values M. In the case for M=2, we analytically show that a typical behavior of quantum walks appears even in a small gap of the parameter from the open quantum random walk. More precisely, we observe both the ballistically moving towards left and right sides and localization of this walker simultaneously. The analysis is based on Kato’s perturbation theory for linear operator. We further analyze this limit theorem in more detail and show that the above three modes are described by Gaussian distributions.. |
| 2. | Kaname Matsue, Rigorous numerics for fast-slow systems, Sugaku Expositions, https://doi.org/10.1090/suga/483, 36, 221-253, 2023.08, [URL], We show a series of results about rigorous numerics for dynamical systems generated by ordinary differential equations called fast-slow systems obtained through the author’s recent research. The contents of the present paper are mainly based on the results of Matsue [Topol. Methods Nonlinear Anal. 50 (2017), pp. 357–486].. |
| 3. | Jean-Philippe Lessard, Kaname Matsue, Akitoshi Takayasu, Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs: Validation and Extraction of Global Nature, Journal of Nonlinear Science, https://doi.org/10.1007/s00332-023-09900-6, 33, 2023.03, [URL], In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations of initial points, referred to as saddletype blow-up solutions, are studied. Combining dynamical systems machinery (e.g., compactifications, timescale desingularizations of vector fields) with tools from computer-assisted proofs (e.g., rigorous integrators, the parameterization method for invariant manifolds), these blow-up solutions are obtained as trajectories on local stable manifolds of hyperbolic saddle equilibria at infinity. With the help of computer-assisted proofs, global trajectories on stable manifolds, inducing blow-up solutions, provide a global picture organized by global-in-time solutions and blow-up solutions simultaneously. Using the proposed methodology, intrinsic features of saddle-type blow-ups are observed: locally smooth dependence of blow-up times on initial points, level set distribution of blow-up times and decomposition of the phase space playing a role as separatrixes among solutions, where the magnitude of initial points near those blow-ups does not matter for asymptotic behavior. Finally, singular behavior of blow-up times on initial points belonging to different family of blow-up solutions is addressed.. |
| 4. | Kaname Matsue, Moshe Matalon, Dynamics of hydrodynamically unstable premixed flames in a gravitational field - Local and global bifurcation structures, Combustion Theory and Modelling, https://doi.org/10.1080/13647830.2023.2165968, 27, 3, 346-374, 2023.01, [URL], The dynamics of hydrodynamically unstable premixed flames are studied using the nonlinear Michelson–Sivashinsky (MS) equation, modified appropriately to incorporate effects due to gravity. The problem depends on two parameters: the Markstein number that characterises the combustible mixture and its diffusion properties, and the gravitational parameter that represents the ratio of buoyancy to inertial forces. A comprehensive portrait of all possible equilibrium solutions are obtained for a wide range of parameters, using a continuation methodology adopted from bifurcation theory. The results heighten the distinction between upward and downward propagation. In the absence of gravity, the nonlinear development always leads to stationary solutions, namely, cellular flames propagating at a constant speed without change in shape. When decreasing the Markstein number, a modest growth in amplitude is observed with the propagation speed reaching an upper bound. For upward propagation, the equilibrium states are also stationary solutions, but their spatial structure depends on the initial conditions leading to their development. The combined Darrieus–Landau and Rayleigh–Taylor instabilities create profiles of invariably larger amplitudes and sharper crests that propagate at an increasingly faster speed when reducing the Markstein number. For downward propagation, the equilibrium states consist in addition to stationary structures time-periodic solutions, namely, pulsating flames propagating at a constant average speed. The stabilising influence of gravity dampens the nonlinear growth and leads to spatiotemporal changes in flame morphology, such as the formation of multicrest stationary profiles or pulsating cell splitting and merging patterns, and an overall reduction in propagation speed. The transition between these states occurs at bifurcation and exchange of stability points, which becomes more prominent when reducing the Markstein number and/or increasing the influence of gravity. In addition to the local bifurcation characterisation the global bifurcation structure of the equation, obtained by tracing the continuation of the bifurcation points themselves unravels qualitative features such as the manifestation of bi-stability and hysteresis, and/or the onset and sustenance of time-periodic solutions. Overall, the results exhibit the rich and complex dynamics that occur when gravity, however small, becomes physically meaningful.. |
| 5. | Kaname Matsue, Kyoko Tomoeda, A mathematical treatment of the bump structure of the particle-laden flows with particle features, Japan Journal of Industrial and Applied Mathematics, https://link.springer.com/article/10.1007/s13160-022-00521-2, 39, 1003-1023, 2022.07, [URL], The particle laden flows on an inclined plane under the effect of the gravity is considered. It is observed from preceding experimental works that the particle-rich ridge is generated near the contact line. The bump structure observed in particle-rich ridge is studied in terms of Lax’s shock waves in the mathematical theory of conservation laws. In the present study, the effect of particles with nontrivial radii on morphology of particle laden flows is explicitly considered, and dependence of radius and concentration of particles on the bump structure is extracted.. |
| 6. | Koki Nitta, Nobito Yamamoto, Kaname Matsue, A numerical verification method to specify homoclinic orbits as application of local Lyapunov functions, Japan Journal of Industrial and Applied Mathematics, https://doi.org/10.1007/s13160-022-00502-5, 39, 467-513, 2022.03, [URL]. |
| 7. | Kazunori Kuwana, Kaname Matsue, Yasuhide Fukumoto, Ritsu Dobashi, Kozo Saito, Fire whirls: A Combustion Science Perspective, Combustion Science and Technology, https://doi.org/10.1080/00102202.2021.2019234, 2022.01, [URL], Fire whirls occur in urban and wildland fires, intensifying the local burning rate and generating long-distance firebrands. A striking feature of fire whirls is their increased flame heights, and this article provides a review of previous efforts to understand how the height of a fire whirl is determined. This paper mainly discusses four factors that influence fire-whirl height: burning rate, strong vorticity, turbulence reduction, and vortex breakdown. It is shown that each influence can be understood based on a simple constant-density mixture- fraction model. In the constant-density approximation, the flame shape can be analyzed in a prescribed flow field. This paper considers a one-celled Burgers vortex, a two-celled Sullivan vortex, and a strong- vorticity flow in which the axial velocity near the axis of rotation is faster than that in the peripheral region.. |
| 8. | Yu Ichida, Kaname Matsue and Takashi Okuda Sakamoto, A refined asymptotic behavior of traveling wave solutions for degenerate nonlinear parabolic equations, JSIAM Letters, 1-4, 2020.10, In this paper, we consider the asymptotic behavior of traveling wave solutions of the degenerate nonlinear parabolic equation: $u_{t}=u^{p}(u_{xx}+u)-¥delta u¥, (¥delta = 0 or 1)$ for $¥xi ¥equiv x - ct ¥to - ¥infty$ with $c>0$. We give a refined one of them, which was not obtain in the preceding work [Ichida-Sakamoto, J. Elliptic and Parabolic Equations, to appear], by an appropriate asymptotic study and properties of the Lambert $W$ function.. |
| 9. | Kaname Matsue, Akitoshi Takayasu, Numerical validation of blow-up solutions with quasi-homogeneous compactifications, Numerische Mathematik, 10.1007/s00211-020-01125-z, 50 pages, 2020.06, [URL]. |
| 10. | Kaname Matsue, Akitoshi Takayasu, Rigorous numerics of blow-up solutions for ODEs with exponential nonlinearity, Journal of Computational and Applied Mathematics, 2020.02, Our concerns here are blow-up solutions for ODEs with exponential nonlinearity from the viewpoint of dynamical systems and their numerical validations. As an example, the finite difference discretization of $u_t = u_{xx} + e^{u^m}$ with the homogeneous Dirichlet boundary condition is considered. Our idea is based on compactification of phase spaces and time-scale desingularization as in previous works. In the present case, treatment of exponential nonlinearity is the main issue. Fortunately, under a kind of exponential homogeneity of vector field, we can treat the problem in the same way as polynomial vector fields. In particular, we can characterize and validate blow-up solutions with their blow-up times for differential equations with such exponential nonlinearity in the similar way to previous works. A series of technical treatments of exponential nonlinearity in blow-up problems is also shown with concrete validation examples.. |
| 11. | 松江 要, Fast-slow系における精度保証付き数値計算, 『数学』（日本数学会編集）, 71, 252-281, 2019.07, Fast-slow系における著者の近年の精度保証付き数値計算に関する研究を、幾何学的特異摂動論や近年の精度保証付き数値計算による力学系の研究の動向も交えて解説する。. |
| 12. | Kaname Matsue, Geometric treatments and a common mechanism in finite-time singularities for autonomous ODEs, Journal of Differential Equations, 10.1016/j.jde.2019.07.022, 267, 12, 7313-7368, 2019.12, [URL], Geometric treatments of blow-up solutions for autonomous ordinary differential equations and their blow-up rates are concerned. Our approach focuses on the type of invariant sets at infinity via compactifications of phase spaces, and dynamics on their center-stable manifolds. In particular, we show that dynamics on center-stable manifolds of invariant sets at infinity with appropriate time-scale desingularizations as well as blowing-up of singularities characterize dynamics of blow-up solutions as well as their rigorous blow-up rates. Similarities for characterizing finite-time extinction and asymptotic behavior of compacton traveling waves to blow-up solutions are also shown.. |
| 13. | Kaname Matsue, Shikhar Mohan, Moshe Matalon, Effect of gravity on hydrodynamically unstable flames, The 12th Asia-Pacific Conference on Combustion, 2019.07, The hydrodynamic instability, due to the large deviation of density between fresh cold mixture and hot combusted products, was discovered by Darrieus and Landau. After seven or eight decades, many aspects of this intrinsic flame instability have been revealed, such as the effects of the flame front curvature and of flow strain rate, its influence on turbulent flames and the self-wrinkling and self-turbulization of expanding flames. In the present study we focus on the composite effects of thermal expansion, differential diffusion, and gravity on flame dynamics, based on a fully nonlinear, hydrodynamic model obtained by a multi-scale analysis that exploits the distinct length scales associated with such problems. The simulations verify the stabilization effect of gravity on planar flames propagating downwards, known from linear stability theory, and show that in the presence of gravity the nonlinear development beyond the stability threshold leads to cusp-like structures of smaller amplitude that propagate at a reduced speed. Finally, we observe that a judicious choice of the Markstein number, controlled by mixture composition and domain size, and of the Froude number creates richer morphological flame structures than in the absence of gravity.. |
| 14. | 松江 要, 微分方程式の爆発解：精度保証付き数値計算と力学系的解釈, 日本シミュレーション学会誌「シミュレーション」, 37, 3, 2018.10, [URL]. |
| 15. | Kaname Matsue, On blow-up solutions of differential equations with Poincare-type compactifications, SIAM Journal on Applied Dynamical Systems, doi:10.1137/17M1124498, 17, 2249-2288, 2018.08, [URL]. |
| 16. | 松江 要, 数学・数理科学的アプローチの可能性 - 予混合火炎のモデル方程式を例に -, 公益社団法人自動車技術会2018年春季大会, 1-6, 2018.05. |
| 17. | Kaname Matsue, Leo Matsuoka, Osamu Ogurisu and Etsuo Segawa, Resonant-tunneling in discrete-time quantum walk, Quantum Studies: Mathematics and Foundations, https://doi.org/10.1007/s40509-017-0151-9, 1-10, 2018.01. |
| 18. | Kaname Matsue, Rigorous numerics for fast-slow systems with one-dimensional slow variable: topological shadowing approach, Topological Methods in Nonlinear Analysis, doi=http://dx.doi.org/10.12775/TMNA.2016.072, 50, 2, 357-468, 2017.12. |
| 19. | Norio Konno, Kaname Matsue, Hideo Mitsuhashi and Iwao Sato, Quaternionic quantum walks of Szegedy type and zeta functions of graphs, Quantum Information & Computation, 17, 1349-1371, 2017.12. |
| 20. | 中嶋 健, 伊藤 万喜子, 梁 暁斌, 松江 要, 原子間力顕微鏡によるナノメカニクスの現状と展望, 表面科学, 38, 10, 520-525, 2017.11. |
| 21. | Kaname Matsue, Osamu Ogurisu and Etsuo Segawa, Quantum Search on Simplicial Complexes, Quantum Studies: Mathematics and Foundations, https://doi.org/10.1007/s40509-017-0144-8, 1-27, 2017.10. |
| 22. | Kaname Matsue and Kyoko Tomoeda, Toward a mathematical analysis for a model of suspension flowing down an inclined plane, Proceedings of EquaDiff 2017 Conference, 349-358, 2017.09. |
| 23. | Kaname Matsue, Osamu Ogurisu and Etsuo Segawa, A note on the spectral mapping theorem of quantum walk models, Interdisciplinary Information Sciences, 23, 105-114, 2017.03. |
| 24. | Kaname Matsue, Tomohiro Hiwaki and Nobito Yamamoto, On the construction of Lyapunov functions with computer assistance, Journal of Computational and Applied Mathematics, 319, 385-412, 2017.02. |
| 25. | Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi and Shin'ichi Oishi, Numerical validation of blow-up solutions for ODEs, Journal of Computational and Applied Mathematics, 314, 10-29, 2017.01. |
| 26. | Yasuaki Hiraoka, Takenobu Nakamura, Akihiko Hirata, Emerson G. Escolar, Kaname Matsue and Yasumasa Nishiura, Hierarchical structures of amorphous solids characterized by persistent homology, Proceedings of the Nathonal Academy of Sciences, 113, 26, 7035-7040, 2016.06. |
| 27. | Kaname Matsue, Osamu Ogurisu and Etsuo Segawa, Quantum walks on simplicial complexes, Quantum Information Processing, 15, 5, 1865-1896, 2016.02. |
| 28. | 松江 要, 内藤 久資, 非一様拡散係数を持つ熱方程式固有値問題の第一固有値の最適化 - 粘性近似問題の大域適切性 -, 京都大学数理解析研究所講究録別冊, B54, 25-48, 2016.01. |
| 29. | Kaname Matsue, Hisashi Naito, Numerical studies of the optimization of the first eigenvalue of the heat diffusion in inhomogeneous media, Japan Journal of Industrial and Applied Mathematics, 32, 2, 489-512, 2015.10. |
| 30. | 松江 要, 内藤 久資, 二値の熱伝導率を持つ領域の第一固有値に対する最適配置, 応用数理, 23, 4, 10-15, 2013.11. |
| 31. | Akihiko Hirata, L.J. Kang, Takeshi Fujita, B. Klumov, Kaname Matsue, Motoko Kotani, A.R. Yavari and Mingwei Chen, Geometric frustration of icosahedron in metallic glasses, Science, 341, 6144, 376-379, 2013.07. |
| 32. | Kaname Matsue, Rigorous numerics for stationary solutions of dissipative PDEs - Existence and local dynamics -, NOLTA, 4, 1, 62-79, 2013.07. |
| 33. | Kaname Matsue, Rigorous verification of bifurcations of differential equations via the Conley index theory, SIAM Journal on Applied Dynamical Systems, 10, 1, 325-359, 2011.07. |
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