We study a general class of nonlinear mean field Fokker-Planck equations in relation with an effective generalized thermodynamical (E.G.T.) formalism. We show that these equations describe several physical systems such as: chemotaxis of bacterial populations, Bose-Einstein condensation in the...

We derive the exact expression of the diffusion coefficient of a self-gravitating Brownian gas in two dimensions. Our formula generalizes the usual Einstein relation for a free Brownian motion to the context of two-dimensional gravity. We show the existence of a critical temperature T<Subscript>c</Subscript> at which...</subscript>

We present first elements of kinetic theory appropriate to the inhomogeneous phase of the Hamiltonian Mean Field (HMF) model. In particular, we investigate the case of strongly inhomogeneous distributions for T→0 and exhibit curious behaviour of the force auto-correlation function and friction...

We study the relaxation of a test particle immersed in a bath of field particles interacting via weak long-range forces. To order 1/N in the N→+∞ limit, the velocity distribution of the test particle satisfies a Fokker-Planck equation whose form is related to the Landau and Lenard-Balescu...

Systems with long-range interactions can reach a Quasi Stationary State (QSS) as a result of a violent collisionless relaxation. If the system mixes well (ergodicity), the QSS can be predicted by the statistical theory of Lynden-Bell (1967) based on the Vlasov equation. When the initial...

We develop the kinetic theory of point vortices in two-dimensional hydrodynamics and illustrate the main results of the theory with numerical simulations. We first consider the evolution of the system “as a whole” and show that the evolution of the vorticity profile is due to resonances...

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...