arXiv subjects

P. H. Chavanis

Publications and source records attributed to P. H. Chavanis.

43 records · Page 3Linked to original sources

arXiv2002

The self-gravitating Fermi gas

We discuss the nature of phase transitions in the self-gravitating Fermi gas at non-zero temperature. This study can be relevant for massive neutrinos in Dark Matter models and for collisionless self-gravitating systems experiencing a ``violent relaxation''. Below a critical energy (in the microcanonical ensemble) or below a critical temperature (in the canonical ensemble), the system undergoes a gravitational collapse leading to a compact object with a massive degenerate nucleus (fermion ball).

astro-ph↗

arXiv2002

Phase diagram of self-attracting systems

Phase diagram of microcanonical ensembles of self-attracting particles is studied for two types of short-range potential regularizations: self-gravitating fermions and classical particles interacting via attractive soft $-(r^2+r_0^2)^{-1/2}$ Coulomb potential. When the range of regularization is sufficiently short, the self-attracting systems exhibit gravitational or collapse-like transition. As the fermionic degeneracy or the softness radius increases, the gravitational phase transition crosses over to a normal first-order phase transition, becomes second-order at a critical point, and finally disappears. Applicability of a commonly used saddle-point or mean-field approximation and importance of metastable states is discussed.

cond-mat.stat-mech↗

arXiv2002

Phase transitions in self-gravitating systems. Self-gravitating fermions and hard spheres models

We discuss the nature of phase transitions in self-gravitating systems both in the microcanonical and in the canonical ensemble. We avoid the divergence of the gravitational potential at short distances by considering the case of self-gravitating fermions and hard spheres models. Three kinds of phase transitions (of zeroth, first and second order) are evidenced. They separate a ``gaseous'' phase with a smoothly varying distribution of matter from a ``condensed'' phase with a core-halo structure. We propose a simple analytical model to describe these phase transitions. We determine the value of energy (in the microcanonical ensemble) and temperature (in the canonical ensemble) at the transition point and we study their dependance with the degeneracy parameter (for fermions) or with the size of the particles (for a hard spheres gas). Scaling laws are obtained analytically in the asymptotic limit of a small short distance cut-off. Our analytical model captures the essential physics of the problem and compares remarkably well with the full numerical solutions.

cond-mat.stat-mech↗

arXiv2001

Gravitational instability of polytropic spheres and generalized thermodynamics

We complete the existing literature on the structure and stability of polytropic gas spheres reported in the classical monograph of Chandrasekhar (1942). For isolated polytropes with index $1<n<5$, we provide a new, alternative, proof that the onset of instability occurs for $n=3$ and we express the perturbation profiles of density and velocity at the point of marginal stability in terms of the Milne variables. Then, we consider the case of polytropes confined within a box of radius $R$ (an extension of the Antonov problem for isothermal gas spheres). For $n\ge 3$, the mass-density relation presents some damped oscillations and there exists a limiting mass above which no hydrostatic equilibrium is possible. Like for isothermal gas spheres, the onset of instability occurs precisely at the point of maximum mass. Analytical results are obtained for the particular index $n=5$. We also discuss the relation of our study with extended thermodynamics (Tsallis entropy) recently investigated by Taruya & Sakagami (cond-mat/0107494).

astro-ph↗

arXiv2001

Kinetic theory of point vortices: diffusion coefficient and systematic drift

We develop a kinetic theory for point vortices in two-dimensional hydrodynamics. Using standard projection operator technics, we derive a Fokker-Planck equation describing the relaxation of a ``test'' vortex in a bath of ``field'' vortices at statistical equilibrium. The relaxation is due to the combined effect of a diffusion and a drift. The drift is shown to be responsible for the organization of point vortices at negative temperatures. A description that goes beyond the thermal bath approximation is attempted. A new kinetic equation is obtained which respects all conservation laws of the point vortex system and satisfies a H-theorem. Close to equilibrium this equation reduces to the ordinary Fokker-Planck equation.

cond-mat.stat-mech↗

arXiv2000

Statistical mechanics of the shallow water system

We extend the formalism of the statistical theory developed for the 2D Euler equation to the case of shallow water system. Relaxation equations towards the maximum entropy state are proposed, which provide a parametrization of sub-grid scale eddies in 2D compressible turbulence.

physics.flu-dyn↗

arXiv1999

Particle Aggregation in a turbulent Keplerian flow

In the problem of planetary formation one seeks a mechanism to gather small solid particles together into larger accumulations of solid matter. Here we describe a scenario in which turbulence mediates this process by aggregating particles into anticyclonic regions. If, as our simulations suggest, anticyclonic vortices form as long-lived coherent structures, the process becomes more powerful because such vortices trap particles effectively. Even if the turbulence is decaying, following the upheaval that formed the disk, there is enough time to make the dust distribution quite lumpy.

astro-ph↗