We obtain compact, exact, analytical expressions for the first-passage-time distribution for a particle diffusing on a planar wedge for special values of the wedge angle. Specifically, we calculate the first-passage-time distribution for the diffusing particle through a planar wedge of angle pi/n, where n is an integer. For the cases n=2 and n odd, we provide an exact closed-form expression to the first-passage-time distribution while for the remaining cases, we provide it in integral form and evaluate numerically using quadratures. We then show that our results are in good agreement with Markovian simulations in the continuum limit.
We obtain compact, exact, analytical expressions for the first-passage-time distribution for a particle undergoing biased diffusion in a planar wedge for wedge angles π/p, where p is a positive integer. We then provide the long-time limit of the first-passage time and found it to be dependent on the drift direction and wedge angle. We finally provide exact expressions for the mean first-passage time for specific cases.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.