We investigate the capture dynamics of a Brownian particle in half-space above a reflecting plane with a periodic array of partially-absorbing patches. Prior work in this area has considered a reflecting surfaces with fully-absorbing disks. We do this via a hybrid numerical-asymptotic approach, performing matched asymptotic analysis on the survival probability partial differential equation in the limit of small patch size. This analysis relies on the numerical computation of a parameter depending on the reactivity of the patches. The numerical computation is obtained via a novel kinetic Monte Carlo method, which is an efficient particle-based simulation method relying on exact probability distributions. We use these results to derive a homogenized partial differential equation with a single Robin boundary condition to replace the equation with mixed Neumann-Robin boundary conditions. We also confirm these results with particle-based simulations.
Boundary Homogenization of Planes with Partially-Absorbing Patches
Claire E. Plunkett, University of UtahAuthors: Claire E. Plunkett and Sean D. Lawley
2022 AWM Research Symposium
Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows