Eur. Phys. J. B 54, 525-549 (2006)
https://doi.org/10.1140/epjb/e2007-00021-y

Phase separation of bacterial colonies in a limit of high degradation

Analogy with Jupiter's great red spot

Laboratoire de Physique Théorique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France

Corresponding author: ^a chavanis@irsamc.ups-tlse.fr

Received: 23 April 2006
Revised: 25 October 2006
Published online: 19 January 2007

Abstract

We discuss the structure of the equilibrium states of a regularized Keller-Segel model describing the chemotaxis of bacterial populations. We consider the limit of high degradation of the secreted chemical where analytical results can be obtained. Below a critical effective temperature, the system experiences a second order phase transition from a homogeneous phase to an inhomogeneous phase formed by two domains with uniform concentration separated by a thin interface (domain wall). We study the properties of the interface and determine the bifurcation between a circular shape (spot) and a rectangular shape (stripe) as a function of the control parameters. We show the analogy with the structure of Jupiter's great red spot which also consists in two phases with uniform potential vorticity separated by a thin annular jet.