We studied the nonlocal effects of intraspecific prey competition on the stability of the critical points of the Rosenzweig-MacArthur model and the Holling-Tanner model, respectively, using linear stability analysis. In particular we focused on the study of the stability of the coexistence state influenced by the nonlocality for both models....
Mixing of granular materials is an important engineering process, and a very complex problem. In this thesis, I use granular mixing in a half-full biaxial spherical tumbler (BST), a spherical container that rotates sequentially about two orthogonal axes, to motivate the study of mixing with piecewise isometries (PWIs), a rich...
The behavior of type-II superconductors is modeled using the time-dependent Ginzburg Landau equations (TDGLE). Pinning centers (inclusions) and geometries which maximize the critical current that can be passed through a superconductor are numerically obtained. Previous analytical results are summarized and new results are obtained for the critical current in one...