Survival of a Diffusing Particle in a Transverse Flow Field

TL;DR

This paper analyzes the survival probability of a diffusing particle in the y-direction under a transverse flow field, exploring how different flow functions affect the particle's likelihood of absorption over time.

Contribution

It provides a theoretical framework for understanding particle survival in complex flow fields with sign-changing functions f(y).

Findings

Derived expressions for survival probability over time.

Identified conditions under which survival probability decays or persists.

Analyzed specific classes of flow functions with positive and negative regions.

Abstract

We consider a particle diffusing in the y-direction, dy/dt=\eta(t) where \eta(t) is Gaussian white noise, and subject to a transverse flow field in the x-direction, dx/dt=f(y), where x \ge 0 and x=0 is an absorbing boundary. We discuss the time-dependence of the survival probability of the particle for a class of functions f(y) that are positive in some regions of space and negative in others.