Transport Models for Collective Dynamics in Biological Systems

Analysis and simulation of active liquid crystals using both kinetic and continuum models

Qi Wang

University of South Carolina

Collective dynamics for active particles and molecules can be described by models for active liquid crystals. In this talk, I will discuss a kinetic model and simulational results using the model in space-time to explore the potentially important, polar as well as excluded volume interaction among the active anisotropic molecules in addition to the self-propelled molecular motions in semi-dilute regime of the active liquid crystal. To explore the genesis of the pattern formation in this class of materials, a detailed analysis on a coarse-grain model based on the polarity vector will be given in which both asymptotic solutions and numerical ones are obtained in simple geometries subject to a set of chosen boundary conditions for the active liquid crystal. Applications of these models to cytoskeletal modeling will be mentioned if time permits.