Kyushu University Academic Staff Educational and Research Activities Database
List of Papers
Matsue Kaname Last modified date:2023.10.12

Professor / Division of Strategic Liaison / Institute of Mathematics for Industry


Papers
1. 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..
2. 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..
3. 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..
4. 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].
5. 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..
6. 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..
7. 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].
8. 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..
9. 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..
10. 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..
11. 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].
12. 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.
13. 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.
14. 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.
15. 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.
16. 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.
17. 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.
18. Kaname Matsue, Osamu Ogurisu and Etsuo Segawa, Quantum walks on simplicial complexes, Quantum Information Processing, 15, 5, 1865-1896, 2016.02.
19. 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.
20. 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.
21. Kaname Matsue, Rigorous numerics for stationary solutions of dissipative PDEs - Existence and local dynamics -, NOLTA, 4, 1, 62-79, 2013.07.
22. 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.