Phase separation of bacterial colonies in a limit of high degradation. Analogy with Jupiter's great red spot

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 stripe as a function of the control parameters. We show the analogy with the structure of Jupiter's Great red spot which also consists of two phases with uniform potential vorticity separated by a thin annular jet.

References in corpus (28)

• Theory of Phase Ordering Kinetics
• Non Linear Kinetics underlying Generalized Statistics
• Percolation, Morphogenesis, and Burgers Dynamics in Blood Vessels Formation
• Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics, two-dimensional turbulence and Jupiter's great red spot
• Thermodynamics of self-gravitating systems
• Phase transitions in self-gravitating systems. Self-gravitating fermions and hard spheres models
• Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions
• Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions
• Aggregation of finite size particles with variable mobility
• Generalized thermodynamics and kinetic equations: Boltzmann, Landau, Kramers and Smoluchowski
• Formation of clumps and patches in self-aggregation of finite size particles
• Hamiltonian and Brownian systems with long-range interactions
• Chapman-Enskog derivation of the generalized Smoluchowski equation
• Strong-coupling dynamics of a multi-cellular chemotactic system
• Post-collapse dynamics of self-gravitating Brownian particles in D dimensions
• Statistical mechanics of the shallow water system
• Virial theorem and dynamical evolution of self-gravitating Brownian particles and bacterial populations in an unbounded domain
• Generalized Fokker-Planck equations and effective thermodynamics
• Logotropic distributions
• Numerical renormalization group of vortex aggregation in 2D decaying turbulence: the role of three-body interactions
• Dynamics of the Bose-Einstein condensation: analogy with the collapse dynamics of a classical self-gravitating Brownian gas
• Brownian theory of 2D turbulence and generalized thermodynamics
• Self-gravitating Brownian systems and bacterial populations with two or more types of particles
• Relaxation of a test particle in systems with long-range interactions: diffusion coefficient and dynamical friction
• Accurate discretization of advection-diffusion equations
• Estimate of blow-up and relaxation time for self-gravitating Brownian particles and bacterial populations
• Nonlinear mean-field Fokker-Planck equations and their applications in physics, astrophysics and biology
• Jeans type instability for a chemotactic model of cellular aggregation

Cited by in corpus (12)

• Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
• Kinetic and hydrodynamic models of chemotactic aggregation
• Critical dynamics of self-gravitating Langevin particles and bacterial populations
• Jeans type analysis of chemotactic collapse
• Exact diffusion coefficient of self-gravitating Brownian particles in two dimensions
• Critical mass of bacterial populations and critical temperature of self-gravitating Brownian particles in two dimensions
• Exact analytical solution of the collapse of self-gravitating Brownian particles and bacterial populations at zero temperature
• Generalized Euler, Smoluchowski and Schrödinger equations admitting self-similar solutions with a Tsallis invariant profile
• Entropy-driven phase transitions with influence of the field-dependent diffusion coefficient
• Universality and self-similar behaviour of non-equilibrium systems with non-Fickian diffusion
• Critical mass of bacterial populations in a generalized Keller-Segel model. Analogy with the Chandrasekhar limiting mass of white dwarf stars
• The role of advection in phase-separating binary liquids