Trapping of an active Brownian particle at a partially absorbing wall

Active matter concerns the self-organization of energy consuming elements such as motile bacteria or self-propelled colloids. A canonical example is an active Brownian particle (ABP) that moves at a constant speed while its direction motion undergoes rotational diffusion. When ABPs are confined within channel, they tend to accumulate channel walls, even when inter-particle interactions ignored. Each pushes on boundary until tumble event reverses direction. The wall thus acts sticky boundary. In this article, we consider natural extension boundaries allow for be permanently absorbed (killed) whilst attached wall. particular, investigate first passage time (FPT) problem ABP in two-dimensional where one walls partially permeable. Calculating exact FPT statistics requires solving non-trivial two-way diffusion value problem. We follow different approach by separating out dynamics away from absorbing absorption and escape By using probabilistic methods, derive explicit expression mean absorption, assuming arrival particles known. Our method also allows us incorporate more general encounter-based model absorption.