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
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.
PACS: 05.20.-y – Classical statistical mechanics / 05.45.-a – Nonlinear dynamics and chaos / 05.40.Jc – Brownian motion / 87.10.+e – General theory and mathematical aspects
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007