For my Ph.D. I am working with Dr. Mansoor Haider.
Current title: Lattice-based surrogate models for two-dimensional particle systems with internal collisions.
My thesis explores this idea in the context of two 2D model systems: (1) an interacting system of colliding particles in a closed domain, and (2) a representative volume in which a particle randomly walks in a representative volume element (RVE) with obstacles, assuming periodic boundary conditions. Both models are investigated on square domains in two spatial dimensions.
In Model 1, the boundaries of the domain are rigid, and there are twenty-seven circular particles following trajectories at constant speed until they collide with a boundary or another particle. In Model 2, a single circular particle randomly walks within a square RVE containing circular obstacles, and we incorporate periodic boundary conditions. We begin with direct simulation, tracking relevant state changes in a prescribed set of subdomains in order to build our surrogate models. We use our models to analyze the effects of particle size, obstacle size, and/or obstacle arrangement on stationary distributions of particle locations (Model 1), or the diffusivity of the particle (Model 2).
This project was inspired by cartilaginous systems, in which cells interact with the underlying scaffold.