Boltzmann-Poisson equation with a central body: Analytical solutions in one and two dimensions.

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 represent a gaseous atmosphere surrounding a protoplanet.

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).

Long-term relaxation of one-dimensional self-gravitating systems.

We investigate the long-term relaxation of one-dimensional (1D) self-gravitating systems, using both kinetic theory and N-body simulations. We consider thermal and Plummer equilibria, with and without collective effects. All combinations are found to be in clear agreement with respect to the Balescu-Lenard and Landau predictions for the diffusion coefficients.

Self-gravitating clusters of Fermi-Dirac gas with planar, cylindrical, or spherical symmetry: Evolution of density profiles with temperature.

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. Our study includes clusters with planar symmetry in dimensions D=1,2,3, clusters with cylindrical symmetry in D=2,3, and clusters with spherical symmetry in D=3. Wall confinement is imposed where needed for stability against escape.

Self-gravitating clusters of Bose-Einstein gas with planar, cylindrical, or spherical symmetry: Gaseous density profiles and onset of condensation.

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. Our study includes clusters with planar symmetry in dimensions D=1,2,3, clusters with cylindrical symmetry in D=2,3, and clusters with spherical symmetry in D=3. Wall confinement is imposed where needed to prevent escape.

Kinetic theory of one-dimensional homogeneous long-range interacting systems with an arbitrary potential of interaction.

Finite-N effects unavoidably drive the long-term evolution of long-range interacting N-body systems. The Balescu-Lenard kinetic equation generically describes this process sourced by 1/N effects but this kinetic operator exactly vanishes by symmetry for one-dimensional homogeneous systems: such systems undergo a kinetic blocking and cannot relax as a whole at this order in 1/N. It is therefore only through the much weaker 1/N^{2} effects, sourced by three-body correlations, that these systems can relax, leading to a much slower evolution.

Caloric curves of classical self-gravitating systems in general relativity.

We determine the caloric curves of classical self-gravitating systems at statistical equilibrium in general relativity. In the classical limit, the caloric curves of a self-gravitating gas depend on a unique parameter ν=GNm/Rc^{2}, called the compactness parameter, where N is the particle number and R the system's size. Typically, the caloric curves have the form of a double spiral.

Kinetic theory of one-dimensional homogeneous long-range interacting systems sourced by 1/N^{2} effects.

The long-term dynamics of long-range interacting N-body systems can generically be described by the Balescu-Lenard kinetic equation. However, for one-dimensional homogeneous systems, this collision operator exactly vanishes by symmetry. These systems undergo a kinetic blocking, and cannot relax as a whole under 1/N resonant effects.

First Star-Forming Structures in Fuzzy Cosmic Filaments.

In hierarchical models of structure formation, the first galaxies form in low-mass dark matter potential wells, probing the behavior of dark matter on kiloparsec scales. Even though these objects are below the detection threshold of current telescopes, future missions will open an observational window into this emergent world. In this Letter, we investigate how the first galaxies are assembled in a "fuzzy" dark matter (FDM) cosmology where dark matter is an ultralight ∼10^{-22}  eV boson and the primordial stars are expected to form along dense dark matter filaments.

Secular dynamics of long-range interacting particles on a sphere in the axisymmetric limit.

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 described by the general kinetic equation, the inhomogeneous Balescu-Lenard equation. We use this approach to compute long-term diffusion coefficients, that are compared with direct simulations.

Supernovae: an example of complexity in the physics of compressible fluids.

Because the collapse of massive stars occurs in a few seconds, while the stars evolve on billions of years, the supernovae are typical complex phenomena in fluid mechanics with multiple time scales. We describe them in the light of catastrophe theory, assuming that successive equilibria between pressure and gravity present a saddle-center bifurcation. In the early stage we show that the loss of equilibrium may be described by a generic equation of the Painlevé I form.

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.

Instability of a uniformly collapsing cloud of classical and quantum self-gravitating Brownian particles.

We study the growth of perturbations in a uniformly collapsing cloud of self-gravitating Brownian particles. This problem shares analogies with the formation of large-scale structures in a universe experiencing a "big-crunch" or with the formation of stars in a molecular cloud experiencing gravitational collapse. Starting from the barotropic Smoluchowski-Poisson system, we derive a new equation describing the evolution of the density contrast in the comoving (collapsing) frame.

Noise-induced dynamical phase transitions in long-range systems.

In the thermodynamic limit, the time evolution of isolated long-range interacting systems is properly described by the Vlasov equation. This equation admits nonequilibrium dynamically stable stationary solutions characterized by a zero order parameter. We show that the presence of external noise sources, such as a heat bath, can reduce their lifetime and induce at a specific time a dynamical phase transition marked by a nonzero order parameter.

Exact analytical solution of the collapse of self-gravitating Brownian particles and bacterial populations at zero temperature.

We provide an exact analytical solution of the collapse dynamics of self-gravitating Brownian particles and bacterial populations at zero temperature. These systems are described by the Smoluchowski-Poisson system or Keller-Segel model in which the diffusion term is neglected. As a result, the dynamics is purely deterministic.

Statistical mechanics of Beltrami flows in axisymmetric geometry: theory reexamined.

A simplified thermodynamic approach of the incompressible axisymmetric Euler equations is considered based on the conservation of helicity, angular momentum, and microscopic energy. Statistical equilibrium states are obtained by maximizing the Boltzmann entropy under these sole constraints. We assume that these constraints are selected by the properties of forcing and dissipation.

Microcanonical quasistationarity of long-range interacting systems in contact with a heat bath.

On the basis of analytical results and molecular dynamics simulations, we clarify the nonequilibrium dynamics of a long-range interacting system in contact with a heat bath. For small couplings with the bath, we show that the system can first be trapped in a Vlasov quasistationary state, then a microcanonical one follows, and finally canonical equilibrium is reached at the bath temperature. We demonstrate that, even out of equilibrium, Hamiltonian reservoirs microscopically coupled with the system and Langevin thermostats provide equivalent descriptions.

Critical dynamics of self-gravitating Langevin particles and bacterial populations.

We study the critical dynamics of the generalized Smoluchowski-Poisson system (for self-gravitating Langevin particles) or generalized Keller-Segel model (for the chemotaxis of bacterial populations). These models [P. H.

Fluctuation-dissipation relations and statistical temperatures in a turbulent von Kármán flow.

We experimentally characterize the fluctuations of the nonhomogeneous nonisotropic turbulence in an axisymmetric von Kármán flow. We show that these fluctuations satisfy relations, issued from the Euler equation, which are analogous to classical fluctuation-dissipation relations in statistical mechanics. We use these relations to estimate statistical temperatures of turbulence.

Dynamical phase transitions in long-range Hamiltonian systems and Tsallis distributions with a time-dependent index.

We study dynamical phase transitions in systems with long-range interactions, using the Hamiltonian mean field model as a simple example. These systems generically undergo a violent relaxation to a quasistationary state (QSS) before relaxing towards Boltzmann equilibrium. In the collisional regime, the out-of-equilibrium one-particle distribution function (DF) is a quasistationary solution of the Vlasov equation, slowly evolving in time due to finite- N effects.

Maximum entropy principle explains quasistationary states in systems with long-range interactions: the example of the Hamiltonian mean-field model.

A generic feature of systems with long-range interactions is the presence of quasistationary states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian mean-field model, we demonstrate that a maximum entropy principle applied to the associated Vlasov equation explains known features of such states for a wide range of initial conditions. We are able to reproduce velocity distribution functions with an analytic expression which is derived from the theory with no adjustable parameters.

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.

Virial theorem and dynamical evolution of self-gravitating Brownian particles in an unbounded domain. II. Inertial models.

We propose a general kinetic and hydrodynamic description of self-gravitating Brownian particles in d dimensions. We go beyond the usual approximations by considering inertial effects and finite-N effects while previous works use a mean-field approximation valid in a proper thermodynamic limit (N --> +infinity) and consider an overdamped regime (xi --> +infinity). We recover known models in some particular cases of our general description.

Virial theorem and dynamical evolution of self-gravitating Brownian particles in an unbounded domain. I. Overdamped models.

We derive the virial theorem appropriate to the generalized Smoluchowski-Poisson (GSP) system describing self-gravitating Brownian particles in an overdamped limit. We extend previous works by considering the case of an unbounded domain and an arbitrary equation of state. We use the virial theorem to study the diffusion (evaporation) of an isothermal Brownian gas above the critical temperature Tc in dimension d = 2 and show how the effective diffusion coefficient and the Einstein relation are modified by self-gravity.