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Kinetic theory of two-dimensional point vortices at order and
Jean-Baptiste Fouvry, Pierre-Henri Chavanis
We investigate the long-term relaxation of a distribution of point vortices in two-dimensional hydrodynamics. To focus on the regime of weak collective amplification, we embed…
Kinetic theory of stellar systems and two-dimensional vortices
Pierre-Henri Chavanis
We discuss the kinetic theory of stellar systems and two-dimensional vortices and stress their analogies. We recall the derivation of the Landau and Lenard-Balescu equations from t…
The Boltzmann-Poisson equation with a central body: analytical solutions in one and two dimensions
Pierre-Henri Chavanis
We consider an isothermal self-gravitating system surrounding a central body. This model can represent a galaxy or a globular cluster harboring a central black hole. It can also re…
Kinetic theory of inhomogeneous systems with long-range interactions and fluctuation-dissipation theorem
Pierre-Henri Chavanis
We complete the kinetic theory of inhomogeneous systems with long-range interactions initiated in previous works. We use a simpler and more physical formalism. We consider a system…
Phase transitions in self-gravitating systems and bacterial populations surrounding a central body
P. H. Chavanis, J. Sopik, C. Sire
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…
Kinetic theory of two-dimensional point vortices and fluctuation-dissipation theorem
Pierre-Henri Chavanis
We complete the kinetic theory of two-dimensional (2D) point vortices initiated in previous works. We use a simpler and more physical formalism. We consider a system of 2D point vo…
Long-term relaxation of self-gravitating systems
Mathieu Roule, Jean-Baptiste Fouvry, Christophe Pichon +1
We investigate the long-term relaxation of one-dimensional () self-gravitating systems, using both kinetic theory and -body simulations. We consider thermal and Plummer eq…
Kinetic theory of collisionless relaxation for systems with long-range interactions
Pierre-Henri Chavanis
We develop the kinetic theory of collisionless relaxation for systems with long-range interactions in relation to the statistical theory of Lynden-Bell. We treat the multi-level ca…
Self-gravitating clusters of Fermi-Dirac gas with planar, cylindrical, or spherical symmetry: evolution of density profiles with temperature
Michael Kirejczyk, Gerhard Müller, Pierre-Henri Chavanis
We calculate density profiles for self-gravitating clusters of an ideal Fermi-Dirac gas with nonrelativistic energy-momentum relation and macroscopic mass at thermal equilibrium. O…
Self-gravitating clusters of Bose-Einstein gas with planar, cylindrical, or spherical symmetry: gaseous density profiles and onset of condensation
Michael Kirejczyk, Gerhard Müller, Pierre-Henri Chavanis
We calculate density profiles for self-gravitating clusters of an ideal Bose-Einstein gas with nonrelativistic energy-momentum relation and macroscopic mass at thermal equilibrium.…
Kinetic theory of one-dimensional homogeneous long-range interacting systems with an arbitrary potential of interaction
Jean-Baptiste Fouvry, Pierre-Henri Chavanis, Christophe Pichon
Finite- effects unavoidably drive the long-term evolution of long-range interacting -body systems. The Balescu-Lenard kinetic equation generically describes this process sour…
Kinetic theory of homogeneous long-range interacting systems sourced by effects
Jean-Baptiste Fouvry, Ben Bar-Or, Pierre-Henri Chavanis
The long-term dynamics of long-range interacting -body systems can generically be described by the Balescu-Lenard kinetic equation. However, for homogeneous systems, this…
Generalized Euler, Smoluchowski and Schrödinger equations admitting self-similar solutions with a Tsallis invariant profile
Pierre-Henri Chavanis
The damped isothermal Euler equations, the Smoluchowski equation and the damped logarithmic Schrödinger equation with a harmonic potential admit stationary and self-similar solutio…
Secular dynamics of long-range interacting particles on a sphere in the axisymmetric limit
Jean-Baptiste Fouvry, Ben Bar-Or, Pierre-Henri Chavanis
We investigate the secular dynamics of long-range interacting particles moving on a sphere, in the limit of an axisymmetric mean field potential. We show that this system can be de…
The quasilinear theory in the approach of long-range systems to quasi-stationary states
Alessandro Campa, Pierre-Henri Chavanis
We develop a quasilinear theory of the Vlasov equation in order to describe the approach of systems with long-range interactions to quasi-stationary states. We derive a diffusion e…
Functional integral derivation of the kinetic equation of two-dimensional point vortices
Jean-Baptiste Fouvry, Pierre-Henri Chavanis, Christophe Pichon
We present a brief derivation of the kinetic equation describing the secular evolution of point vortices in two-dimensional hydrodynamics, by relying on a functional integral forma…
Gravitational phase transitions with an exclusion constraint in position space
Pierre-Henri Chavanis
We discuss the statistical mechanics of a system of self-gravitating particles with an exclusion constraint in position space in a space of dimension . The exclusion constraint…
Random transitions described by the stochastic Smoluchowski-Poisson system and by the stochastic Keller-Segel model
P. H. Chavanis, L. Delfini
We study random transitions between two metastable states that appear below a critical temperature in a one dimensional self-gravitating Brownian gas with a modified Poisson equati…
Explicit formula of energy-conserving Fokker-Planck type collision term for single species point vortex systems with weak mean flow
Yuichi Yatsuyanagi, Tadatsugu Hatori, Pierre-Henri Chavanis
This paper derives a kinetic equation for a two-dimensional single species point vortex system. We consider a situation (different from the ones considered previously) of weak mean…
Initial value problem for the linearized mean field Kramers equation with long-range interactions
Pierre-Henri Chavanis
We solve the initial value problem for the linearized mean field Kramers equation describing Brownian particles with long-range interactions in the limit. We…
The Brownian Mean Field model
Pierre-Henri Chavanis
We discuss the dynamics and thermodynamics of the Brownian Mean Field (BMF) model which is a system of N Brownian particles moving on a circle and interacting via a cosine potentia…
Kinetic theory of spatially homogeneous systems with long-range interactions: III. Application to power-law potentials, plasmas, stellar systems, and to the HMF model
Pierre-Henri Chavanis
We apply the general results of the kinetic theory of systems with long-range interactions to particular systems of physical interest. We consider repulsive and attractive power-la…
Kinetic theory of spatially homogeneous systems with long-range interactions: II. Basic equations
Pierre-Henri Chavanis
We provide a short historic of the early development of kinetic theory in plasma physics and synthesize the basic kinetic equations describing the evolution of systems with long-ra…
Caloric curves fitted by polytropic distributions in the HMF model
A. Campa, P. H. Chavanis
We perform direct numerical simulations of the HMF model starting from non-magnetized initial conditions with a velocity distribution that is (i) gaussian, (ii) semi-elliptical, an…