Eur. Phys. J. E (2012) 35: 84
https://doi.org/10.1140/epje/i2012-12084-y

Regular Article

Probability distributions for the run-and-tumble bacterial dynamics: An analogy to the Lorentz model

¹ LPMCN, Université Lyon 1 and UMR CNRS 5586, 69622, Villeurbanne, France
² CNR-IPCF UOS Roma, Dipartimento di Fisica, Università Sapienza, I-00185, Roma, Italy

^* e-mail: lyderic.bocquet@univ-lyon1.fr

Received: 1 May 2012
Revised: 22 June 2012
Accepted: 16 July 2012
Published online: 14 September 2012

Abstract

In this paper, we exploit an analogy of the run-and-tumble process for bacterial motility with the Lorentz model of electron conduction in order to obtain analytical results for the intermediate scattering function. This allows to obtain an analytical result for the van Hove function in real space for two-dimensional systems. We furthermore consider the 2D circling motion of bacteria close to solid boundaries with tumbling, and show that the analogy to electron conduction in a magnetic field allows to predict the effective diffusion coefficient of the bacteria. The latter is shown to be reduced by the circling motion of the bacteria.