Optimal search strategies of run-and-tumble walks

TL;DR

This paper analyzes the efficiency of run-and-tumble search strategies in confined spaces, revealing optimal run durations that minimize search time across different boundary conditions and distributions.

Contribution

It provides a comprehensive evaluation of mean search times for run-and-tumble walks, identifying optimal parameters and contrasting with ballistic motion strategies.

Findings

Mean search time has a minimum at specific run durations.

Optimal strategies depend on boundary conditions and run duration distributions.

Pure ballistic motion is not always optimal for target search.

Abstract

The run-and-tumble walk, consisting in randomly reoriented ballistic excursions, models phenomena ranging from gas kinetics to bacteria motility. We evaluate the mean time required for this walk to find a fixed target within a 2D or 3D spherical confinement. We find that the mean search time admits a minimum as a function of the mean run duration for various types of boundary conditions and run duration distributions (exponential, power-law, deterministic). Our result stands in sharp contrast to the pure ballistic motion, which is predicted to be the optimal search strategy in the case of Poisson distributed targets.