On the Kinetic Description of Objective Molecular Dynamics (OMD): multiscale modeling, numerics, data-driven applications
数学专题报告
报告题目(Title)：On the Kinetic Description of Objective Molecular Dynamics (OMD): multiscale modeling, numerics, data-driven applications
报告人(Speaker)：綦昆仑 明尼苏达大学
地点(Place)：后主楼1225
时间(Time)：2024年12月25日（周三）11:00-12:00
邀请人(Inviter)：陈华杰
报告摘要
In the first part of this talk, a multiscale modeling framework for objective molecular dynamics (OMD), a reduced molecular dynamics approach with inherent symmetries, will be presented. 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 spectral method for numerically solving the derived kinetic equations, supported by convergence analysis and numerical simulations to confirm its effectiveness. If time permits, I will discuss our recent progress in applying data-driven methodologies to kinetic theory.
主讲人简介
綦昆仑2017年本科毕业于华南理工大学数学学院，2021年7月博士毕业于香港城市大学，师从杨彤教授。2021年7月-2022年7月于香港中文大学进行博士后研究工作，并与2022年8月至今加入明尼苏达大学数学学院担任Dunham-Jackson助理教授(non-tenure track)。其研究方向集中于动理学理论(Kinetic Theory)，尤其是玻尔兹曼方程及其相关流体、材料模型的多尺度建模，数值模拟和误差分析，相关成果发表在SIAM J. Numer. Anal., SIAM J. Appl. Math., SIAM Multiscale Model. Simul., M3AS, JCP等期刊。
