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〈Dynamical Systems / Verified Numerical Computation〉
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A lab that uses dynamical systems and verified numerical computation to uncover the singular behavior of differential equations.
AboutAbout the lab
What looks strange becomes simple when viewed differently.
The lab of Professor Kaname Matsue studies applied mathematics, grounded in dynamical systems theory, differential equations, and numerical analysis.
Its basic spirit is to unravel the fundamental properties of the "strange" or "singular" behavior hidden in phenomena generated by differential equations and the like.
With applied mathematics at its core, the lab also tackles problems arising from combustion and related energy issues.
Key terms
- Dynamical systems
- The mechanisms generated by differential equations in which a state changes over time
- Finite-time singularity
- When a solution of a differential equation shows abrupt behavior such as blow-up, extinction, quenching, or collision in finite time
- Verified numerical computation
- Numerical computation that uses computers while mathematically and rigorously guaranteeing things such as the existence of solutions and blow-up times
- Dynamics at infinity
- An approach that reformulates the phase space to include infinity and investigates the behavior of solutions there
NewsLab news
Professor Matsue's paper accepted for publication in Oyo Suri, the journal of the Japan Society for Industrial and Applied Mathematics
Co-authored paper published in Japan Journal of Industrial and Applied Mathematics
Co-authored paper published in SIAM Journal on Applied Mathematics
A doctoral student received the Kyushu Young Mathematician Presentation Award at the Kyushu Branch Meeting of the Mathematical Society of Japan
Paper published in Discrete and Continuous Dynamical Systems
ResearchResearch themes
Grounded in dynamical systems theory, differential equations, and numerical analysis, the lab seeks to clarify the fundamental properties of the "strange" or "singular" behavior of phenomena generated by differential equations. Its main focus is finite-time singularities, and it also works on verified numerical computation and on combustion science and engineering.
*Illustrative imageFinite-Time Singularities and Dynamical Systems
Targeting phenomena in which solutions of differential equations blow up, go extinct, quench, or collide in finite time, the lab focuses on building a unified framework for characterizing them, centered on analyzing the dynamics at infinity of systems of ordinary differential equations.
*Illustrative imageVerified Numerical Computation for Dynamical Systems
The lab investigates solutions that undergo abrupt changes using verified numerical computation. Its targets are fast-slow systems, which mix fast and slow motions, and finite-time singularities such as blow-up solutions; the existence of solutions is guaranteed mathematically.
*Illustrative imageCombustion Science and Engineering
With applied mathematics at its core, the lab aims to find guiding principles for how the motion of a flame changes through its interactions with thermal expansion, gravity, mass diffusion, and sound, and to lead to the development of highly efficient, stable, and safe combustion technologies.
MembersFaculty
- ProfessorKaname Matsue
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “FitzHugh-Nagumo Model” Cosmia Nebula / CC BY-SA 4.0 (cropped)
- Finite-Time Singularities and Dynamical Systems: “Airplane vortex edit” NASA Langley Research Center (NASA-LaRC), Edited by Fir0002 / Public domain (cropped)
- Verified Numerical Computation for Dynamical Systems: “Interval multiplication” 作者不詳 / Public domain (cropped)
- Combustion Science and Engineering: “Close-up of a Fire” Thomas Kirchel / CC BY 4.0 (cropped)
- Related lab (Dynamical Systems and Verified Numerical Computation Lab (Kaname Matsue)): “Flow and orbit of vector field (dynamical system)” Yapparina / CC0 (cropped)
- Related lab (Numerical Analysis and Computational Fluid Dynamics Lab): “Biomechanics-Femur-Fracture-Nail-Internal Fixation-CAD-FEM” Fry72 Karel Frydrýšek, Tomáš Halo, Daniel Čepica / CC BY-SA 4.0 (cropped)
- Related lab (Numerical Analysis and Computational Fluid Dynamics Lab): “AbsoluteErrorNumericalDifferentiationExample” Berland / Public domain (cropped)
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