Numerical Analysis and Modeling in Nonlinear Dynamics

Dear Colleagues, 

Nonlinear dynamics with multiscale variables are common phenomena in physics and chemistry. The connections between microscopic stochastic models and macroscopic continuum models are built by statistical mechanics and probability limiting theory, including the law of large numbers, the central limit theory and the large deviation principles. The resulting nonlinear dynamics usually possess some generic structures, such as the gradient flow dissipation structure and the conservative Hamiltonian flow structure. Applied mathematicians can understand these complicated nonlinear dynamics in physics and biochemical reactions using various methods, including numerical analysis and modelling. Any related methods, new ideas and practical algorithms are welcome to solve those nonlinear dynamics for fundamental scientific problems.

Topics of interest include, but are not limited to: 

• Multiscale modelling: microscopic stochastic models and fast–slow nonlinear dynamics;
• Continuum limit theory: thermodynamic limit, large population mean field limit, and convergence analysis for interacting particle systems;
• Numerical simulation for stochastic differential equations and macroscopic partial differential equations;
• Stochastic algorithms: ensembled statistical properties, rare event simulation, important sampling, Bayesian inference, variational methods for structure-preserving schemes, stochastic optimal control simulation and deep learning for dynamic systems. 

Dr. Yuan Gao
Guest Editor

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