Phase transitions in self-gravitating systems and bacterial populations surrounding a central body.

We study the nature of phase transitions in a self-gravitating classical gas in the presence of a central body. The central body can mimic a black hole at the center of a galaxy or a rocky core (protoplanet) in the context of planetary formation. In the chemotaxis of bacterial populations, sharing formal analogies with self-gravitating systems, the central body can be a supply of "food" that attracts the bacteria (chemoattractant).

Effective merging dynamics of two and three fluid vortices: application to two-dimensional decaying turbulence.

We present a kinetic theory of two-dimensional decaying turbulence in the context of two-body and three-body vortex merging processes. By introducing the equations of motion for two or three vortices in the effective noise due to all the other vortices, we demonstrate analytically that a two-body mechanism becomes inefficient at low vortex density n<<1. When the more efficient three-body vortex mergings are considered (involving vortices of different signs), we show that n~t(-ξ), with ξ=1.

Dynamics of the Bose-Einstein condensation: analogy with the collapse dynamics of a classical self-gravitating Brownian gas.

We consider the dynamics of a gas of free bosons within a semiclassical Fokker-Planck equation for which we give a physical justification. In this context, we find a striking similarity between the Bose-Einstein condensation in the canonical ensemble, and the gravitational collapse of a gas of classical self-gravitating Brownian particles. The paper is mainly devoted to the complete study of the Bose-Einstein "collapse" within this model.

Distance traveled by random walkers before absorption in a random medium.

We consider the penetration length l of random walkers diffusing in a medium of perfect or imperfect absorbers of number density rho. We solve this problem on a lattice and in the continuum in all dimensions D, by means of a mean-field renormalization group. For a homogeneous system in D > 2, we find that l is similar to max(xi,rho(-1/2)), where is the absorber density correlation length.

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

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.