Transport of Charged Particles in Biological Environment: An Energetic Variational Approach(5)
10:20:00 - 11:10:00
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
Almost all biological activities involve transport of ions through biological environments. The nature of these problems makes it necessary to couple effects from different scales, both spatial and temporal. Motivated by the seminal work of Rayleigh and Onsarger, together with the developments in the past 50 years on chemical engineering and soft matter physics, the general framework of energetic variational approaches is developed specifically to be consistent with the basic principles of statistical physics and non-equilibrium thermodynamics, and at the same time, incorporate the specific physical and biological ingredients/considerations in the models.
In this mini-course, I will go over some of the basic approaches in related to modern mathematical analysis and numerical techniques. In particular, due to the time constraint, I will focus on the derivation of some basic systems and the relation to the classical theories for idea materials.
Some of the topics that I wish to cover in the course:
1. General energetic variational framework for complex fluids:
least action principle and maximum dissipation principle.
Navier-Stokes equations and elasticity.
3. Multiscale modeling and analysis:
basis of stochastic differential equations: Fokker-Planck equations, diffusion, Smoluchowski coagulation equations, variational formulations, kinetic theory.
micro-macro models for polymeric materials.
moment closure methods, Mori-Zwanzig formulation and other coarse grain methods.
4. Ionic fluids and ion channels:
generalized diffusion, nonlocal diffusion.
electroeheological (ER) fluids: Poisson-Boltzman fluids, steric effects of ion particles, equation of states.
ionic fluids in ion channels.