Random search in fluid flow aided by chemotaxis

TL;DR

This paper studies how a 2D agent searching for a target in fluid flow with chemical attraction behaves, revealing optimal flow conditions that minimize search time through analysis and numerical simulations.

Contribution

It provides a rigorous analysis of the expected hit time limit under large flow and identifies the existence of an optimal shear flow for efficient target search.

Findings

Expected hit time limit characterized in large flow regime

Numerical simulations reveal an optimal shear flow minimizing search time

Flow conditions outperform the large flow limit in search efficiency

Abstract

In this paper, we consider the dynamics of a 2D target-searching agent performing Brownian motion under the influence of fluid shear flow and chemical attraction. The analysis is motivated by numerous situations in biology where these effects are present, such as broadcast spawning of marine animals and other reproduction processes or workings of the immune systems. We rigorously characterize the limit of the expected hit time in the large flow amplitude limit as corresponding to the effective one-dimensional problem. We also perform numerical computations to characterize the finer properties of the expected duration of the search. The numerical experiments show many interesting features of the process, and in particular existence of the optimal value of the shear flow that minimizes the expected target hit time and outperforms the large flow limit.