Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
On the Kinetic Description of Objective Molecular Dynamics (OMD): multiscale model reduction, numerics and data-driven application
In the first part of this talk, a multiscale framework for objective molecular dynamics (OMD), a reduced molecular dynamics approach with inherent symmetries, will be presented as a typical example to do model reduction. This hierarchical framework bridges OMD with statistical kinetic equations and macroscopic hydrodynamic models. In the kinetic regime, we identify two distinct interaction scalings, leading to either a Mean-Field-type or Boltzmann-type equation. At the macroscopic level, we derive reduced Euler and Navier-Stokes systems through a detailed asymptotic analysis. The second part of the talk introduces a fast Fourier spectral method for numerically solving the derived kinetic equations (also recent progress for wave kinetic equations), supported by convergence analysis and numerical tests to confirm its effectiveness. As an outlook, I will discuss our recent progress in applying data-driven and machine-learning methodologies to kinetic theory.
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