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.
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Chavanis, P. Phase separation of bacterial colonies in a limit of high degradation. Eur. Phys. J. B 54, 525–549 (2006). https://doi.org/10.1140/epjb/e2007-00021-y
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DOI: https://doi.org/10.1140/epjb/e2007-00021-y