Karlstad Applied Analysis Seminar (KAAS)
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Future seminars:
TALK 161
When: 11 September 2026, 13:30-14:30
What: Two-temperature fluid models for a polyatomic gas based on kinetic theory
Who: Kazuo Aoki, Professor Emeritus, Kyoto University, Kyoto, Japan and Honorary Chair Professor, National Cheng Kung University, Tainan, Taiwan University
Where: offline in 21E205, online: https://kau-se.zoom.us/j/61616693592
A polyatomic gas with slow relaxation of internal modes is considered, and the fluid-dynamic equations (Euler and Navier-Stokes equations) with two temperatures, the translational and internal temperatures, are formally derived from the ellipsoidal-statistical (ES) model of the Boltzmann equation by the Chapman-Enskog procedure. As an application, the problem of shock-wave structure is investigated numerically.
It is shown that the two-temperature Navier-Stokes equations describe the shock-wave structure correctly even for a moderately strong shock wave. Finally, some remarks are made on the derivation of the two-temperature models from the Boltzmann equation.
TALK 162
When: 11 September 2026, 14:45-15:45
What: A model of gas surface interaction
Who: Francois Golse, Ecole Polytechnique, Paris, France
Where: offline in 21E205, online: https://kau-se.zoom.us/j/61616693592
The purpose of this talk is to present a new boundary condition for the Boltzmann equation of the kinetic theory of gases. While most boundary conditions used in the literature are phenomenological, this one is based on the mathematical analysis of a model including two physical effects: (a) physisorption near the surface (described by means of a Lennard-Jones potential) and (b) interaction between the gas molecules and the atoms in the crystalline structure of the solid (described in terms of a collision operator between gas molecules and phonons). Some numerical simulations based on this model will be presented. (Joint work with K. Aoki, V. Giovangigli, S. Kosuge)
TALK 163
When: 30 September 2026, 10:40-11:30
What: Mean-field games for traffic: modeling, numerics, and Nash equilibria
Who: Amal Machtalay. Mohammed VI Polytechnic University, Marrakesh, Morocco
Where: https://kau-se.zoom.us/j/61616693592
Mean-field games provide a powerful framework for describing systems with a very large number of interacting decision-making agents. A natural example is road traffic, where each driver makes individual choices while responding to the overall flow of vehicles around them.
In my talk, I will present the fundamental concepts of mean-field games through a multi-class traffic flow model involving different class of vehicles. Starting from the microscopic description of finitely many interacting agents, I will explain how a macroscopic mean-field game model arises and how the two descriptions are related. I will also discuss some of the numerical challenges associated with solving the resulting mean-field game system and present computational approaches to tackle them. Numerical experiments will illustrate how well the mean-field dynamics reproduce the finite-agent system and how mean-field strategies approximate Nash equilibria when the number of vehicles becomes large.