Analytical solution of diffusion probability for a flat potential with a gaussian sink

TL;DR

This paper presents a straightforward analytical method to solve the diffusion probability problem for a particle on a flat potential with a Gaussian sink, using the Smoluchowski equation and Laplace transforms.

Contribution

It introduces a simple, exact analytical solution for diffusion with a Gaussian sink on a flat potential, applicable to various diffusion-reaction systems.

Findings

Provides an explicit Laplace domain solution.

Derives an analytical expression for the time-averaged rate constant.

Enables analysis of related diffusion-reaction problems.

Abstract

We give a very simple method for finding the exact analytical solution for the problem of a particle undergoing diffusive motion on a flat potential in the presence of a gaussian sink function. The diffusion process is modelled by using one dimensional Smoluchowski equation. Our method provides solution in Laplace domain, which is used to derive an analytical expression for time average rate constant. Our solution can be used to analyze several related problems involving diffusion-reaction systems.