From swarming and self-assembly to vortex interaction: Applications of nonlocal PDE

Start: 01/18/2012 - 1:15pm
End  : 01/18/2012 - 2:15pm

Applied Math Seminar

David Uminsky (UCLA)


I will survey results in applications of a large class of nonlocal PDEs. The problems are of active scalar type and the applications are dictated by the nonlocal interaction kernel. We will begin by considering nonlocal kernels with a gradient, attraction-repulsion structure which arise in minimal models of biological swarming and self-assembly. We use tools from dynamical systems and analysis to develop the mathematical theory for predicting which patterns will arise. We also discuss solving the inverse problem of designing kernels for a given ground state structure. We conclude by turning to kernels which are incompressible in nature and discuss the development of a new convergent, higher order deformable vortex method for simulating fluids.

RN 103