# Optimal search strategies of run-and-tumble walks

Source: [Optimal search strategies of run-and-tumble walks](<https://www.sota2.com/research/paper/68fa33ba1e209131ce892c5c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T20:14:57.378Z

Authors: Jean-Francois Rupprecht, Olivier B\\'enichou, Raphael Voituriez

Published: 2016-03-11T07:19:39.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1603.03544>)

[PDF](<https://arxiv.org/pdf/1603.03544.pdf>)