Self-gravitating Brownian systems and bacterial populations with two or more types of particles

Abstract

We study the thermodynamical properties of a self-gravitating gas with two or more types of particles. Using the method of linear series of equilibria, we determine the structure and stability of statistical equilibrium states in both microcanonical and canonical ensembles. We show how the critical temperature (Jeans instability) and the critical energy (Antonov instability) depend on the relative mass of the particles and on the dimension of space. We then study the dynamical evolution of a multi-components gas of self-gravitating Brownian particles in the canonical ensemble. Self-similar solutions describing the collapse below the critical temperature are obtained analytically. We find particle segregation, with the scaling profile of the slowest collapsing particles decaying with a non universal exponent that we compute perturbatively in different limits. These results are compared with numerical simulations of the two-species Smoluchowski-Poisson system. Our model of self-attracting Brownian particles also describes the chemotactic aggregation of a multi-species system of bacteria in biology.

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• Post-collapse dynamics of self-gravitating Brownian particles in D dimensions
• Estimate of blow-up and relaxation time for self-gravitating Brownian particles and bacterial populations
• Statistical Mechanics of the Self-gravitating gas with two or more kinds of Particles

Cited by in corpus (18)

• Virial theorem and dynamical evolution of self-gravitating Brownian particles and bacterial populations in an unbounded domain
• Dynamics of a microorganism moving by chemotaxis in its own secretion
• Logotropic distributions
• Critical dynamics of self-gravitating Langevin particles and bacterial populations
• Critical mass of bacterial populations and critical temperature of self-gravitating Brownian particles in two dimensions
• Exact diffusion coefficient of self-gravitating Brownian particles in two dimensions
• Nonlinear mean-field Fokker-Planck equations and their applications in physics, astrophysics and biology
• Self-gravitating Brownian particles in two dimensions: the case of N=2 particles
• Gravothermal Catastrophe: the dynamical stability of a fluid model
• Charged Brownian Particles: Kramers and Smoluchowski Equations and the Hydrothermodynamical Picture
• Newtonian gravity in d dimensions
• Phase separation of bacterial colonies in a limit of high degradation. Analogy with Jupiter's great red spot
• Ensemble inequivalence in a mean-field XY model with ferromagnetic and nematic couplings
• Scaling quasi-stationary states in long range systems with dissipation
• Statistical mechanics of two-dimensional point vortices: relaxation equations and strong mixing limit
• Virial theorem for rotating self-gravitating Brownian particles and two-dimensional point vortices
• Finite $N$ corrections to Vlasov dynamics and the range of pair interactions
• Stability of steady states in kinetic Fokker-Planck equations for Bosons and Fermions