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Kaname Matsue Last modified date:2021.10.07

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Academic Degree
Dr. of Science
Country of degree conferring institution (Overseas)
Field of Specialization
Dynamical Systems, Numerical Analysis, Rigorous Numerics, Singular Perturbation Theory, Differential Equations (Blow-up Solutions, Shock Waves), Singularities, Quantum Walks, Topology Optimizations, Combustion
Total Priod of education and research career in the foreign country
Research Interests
  • Nature of premixed laminar, turbulent flames
    keyword : Premixed planar and spherical propagating flames, Darrieus-Landau instability, Michelson-Sivashinsky-type equation, hydrodynamic model, turbulent combustion, gravity effect
  • Various problems inspired by materials science
    keyword : Amorphous structured materials, crystals, minimal surface, discrete geometry, topology optimization, computational homology, structure preserving numerical method
  • Quantum walks : geometric aspects of dynamics
    keyword : quantum walks, simplicial complex, quantum search, spectral analysis
  • Finite-time singularities (blow-up solutions, extinction, quenching, canard) from the viewpoint of singularity theory with rigorous numerics, Shock waves and rigorous numerics
    keyword : blow-up, extinction, quenching, canard, shock waves, rigorous numerics, covering relations, Lyapunov functions, cone conditions
  • Geometric singular perturbation theory and rigorous numerics
    keyword : Fast-slow systems, rigorous numerics, geometric singular perturbation, isolating blocks and cones, covering relations
Academic Activities
1. Akihito Hirata, Kaname Matsue and MingWei Chen, Structural analysis of metallic glasses with computational homology, Springer, 2016.06.
1. 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].
2. 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.
3. 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, 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..
4. 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..
5. 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].
6. Kaname Matsue, Rigorous numerics for fast-slow systems with one-dimensional slow variable: topological shadowing approach, Topological Methods in Nonlinear Analysis, doi=, 50, 2, 357-468, 2017.12.
7. Kaname Matsue, Osamu Ogurisu and Etsuo Segawa, Quantum Search on Simplicial Complexes, Quantum Studies: Mathematics and Foundations,, 1-27, 2017.10.
8. 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.
9. Kaname Matsue, Osamu Ogurisu and Etsuo Segawa, Quantum walks on simplicial complexes, Quantum Information Processing, 15, 5, 1865-1896, 2016.02.
10. 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.
11. 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.
1. Kaname Matsue, Rigorous numerics of blow-up solutions for autonomous ODEs, CRM CAMP in Nonlinear Analysis, 2021.05, [URL].
2. , [URL].
3. Kaname Matsue, On numerical and Mathematical description of premixed flame dynamics , I2CNER Hydrogen Materials Compatibility Division Winter Retreat, 2020.02.
4. Kaname Matsue, On numerical and Mathematical description of premixed flame dynamics , I2CNER-IMI International Joint Workshop "Applied Math for Energy: Future Directions", 2020.01.
5. Kaname Matsue, On numerical and Mathematical description of premixed flame dynamics , I2CNER Institute Interest Seminar Series, 2020.01.
6. Kaname Matsue, Premixed Flame Dynamics: Modeling, Numerical and Mathematical Studies , Mathematical Science Workshop in Yamaguchi 2019 Presented by RITS, 2019.11.
7. , [URL].
8. Kaname Matsue, Shikhar Mohan, Moshe Matalon, Effect of gravity on hydrodynamically unstable flames , The 12th Asia-Pacific Conference on Combustion, 2019.07, [URL].
9. Kaname Matsue, Blow-up solutions for ODEs from the viewpoint of dynamical systems : theory and applications, HADES (Harmonic Analysis and Differential Equations Seminar), 2018.11.
10. Kaname Matsue, Rigorous numerics and asymptotic analysis of finite-time singularities : qualitative and quantitative natures , SCAN2018, 2018.09.
11. Walls and Doors : Dynamical Systems and Rigorous Numerics.
12. Kaname Matsue, Rigorous numerics of finite-time singularity for ODEs , EASIAM2018, 2018.06, [URL].
13. Kaname Matsue, Finite-time singularity for ODEs from the viewpoint of dynamical systems, EASIAM2018, 2018.06, [URL].
14. Kaname Matsue, Mathematical treatment of flame dynamics toward foundation of combustion, FMfI2017 (Forum of Mathematics for Industry), 2017.10.
15. Kaname Matsue, Rigorous numerics of blow-up solutions for autonomous ODEs, A3 workshop on Fluid Dynamics and Materials Science in CSIAM 2017, 2017.10.
16. , [URL].
17. Kaname Matsue, Mathematics in Combustion -Fundamentals and Trends- , I2CNER Hydrogen Materials Compatibility Research Division Summer Retreat 2017, 2017.06.
18. Kaname Matsue, Technology for New Energy Generation - Mathematics of Combustion - , I2CNER Site Visit, 2017.06.
Membership in Academic Society
  • Combustion Society of Japan
  • The Japan Society for Industrial and Applied Mathematics
  • Mathematical Society of Japan
Educational Activities
Exercise for freshmen and sophomores, and relay-style lectures for graduate students (topic : mathematics in combustion).
In FY2019, Matsue has given a teaching class "Complex Functions" for the 2nd grade undergraduate students (Engineering).
From FY2020, he also gives a class "Numerical analysis: lecture and exercises" for graduate students.
From FY2021, he also gives a class in "Graduate Program for Mathematics for Innovation".