Stochastic and Multiscale Modeling and Computation Seminar by Bryan Quaife: Boundary Integral Methods for Particle Diffusion in Complex Geometries: Shielding, Confinement, and Escape
Speaker: , associate professor of scientific computing, Florida State University
Title: Boundary Integral Methods for Particle Diffusion in Complex Geometries: Shielding, Confinement, and Escape
Abstract: Many problems in engineering and biology involve the first passage time problem, which addresses questions such as the expected time for a Brownian particle in unbounded space to reach an absorbing body. In many applications, this process occurs in the presence of a complex network of reflecting bodies that the Brownian particle must navigate. I will present a boundary integral equation method for computing statistics of the first passage time in complex geometries involving absorbing and reflecting bodies. The method applies the Laplace transform to the time-dependent problem, yielding a modified Helmholtz equation that is solved using a boundary integral formulation. This approach avoids the limitations of traditional time-stepping methods and effectively captures the long equilibrium timescales associated with diffusion in unbounded domains. The solution is then returned to the time domain by applying quadrature along the so-called Talbot contour. I will demonstrate the method on complex geometries composed of reflecting and absorbing bodies of arbitrary shape. Examples include geometries that guide diffusion toward specific absorbing sites and configurations in which reflecting bodies shield absorbing sites. If time permits, I will also discuss a stochastic cyclic pursuit project that generalizes the classical 'N Bugs on a Square' problem.
Multiscale Modeling and Computation