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Classification of self-organized vortices in two-dimensional turbulence : the case of a bounded domain
We calculate steady solutions of the Euler equations for any given value of energy and circulation (and angular momentum in the case of a circular domain). A linear relationship between vorticity and
Gravitational instability of finite isothermal spheres
We investigate the stability of bounded self-gravitating systems in the canonical ensemble by using a thermodynamical approach. Our study extends the earlier work of Padmanabhan ([CITE]) in the
Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions: II. Numerical results
Several recent astrophysical observations of distant type Ia supernovae have revealed that the content of the universe is made of about 70% of dark energy, 25% of dark matter and 5% of baryonic
Statistical Mechanics of Violent Relaxation in Stellar Systems
We discuss the statistical mechanics of violent relaxation in stellar systems following the pioneering work of (1967). The solutions of the gravitational Vlasov-Poisson system develop finer and finer
PHASE TRANSITIONS IN SELF-GRAVITATING SYSTEMS
We discuss the nature of phase transitions in self-gravitating systems. We show the connection between the binary star model of Padmanabhan, the thermodynamics of stellar systems and the
Kinetic theory of long-range interacting systems with angle–action variables and collective effects
We develop a kinetic theory of systems with long-range interactions taking collective effects and spatial inhomogeneity into account. Starting from the Klimontovich equation and using a quasilinear
Trapping of dust by coherent vortices in the solar nebula
We develop the idea proposed by Barge & Sommeria (1995) and Tanga et al. (1996) that large-scale vortices present in the solar nebula can concentrate dust particles and facilitate the formation of
Kinetic theory of spatially inhomogeneous stellar systems without collective effects
We review and complete the kinetic theory of spatially inhomogeneous stellar systems when collective effects (dressing of the stars by their polarization cloud) are neglected. We start from the BBGKY
Statistical Mechanics of Two-Dimensional Vortices and Collisionless Stellar Systems
In this article, we stress the analogy between two-dimensional vortices and collisionless stellar systems. This analogy is based on the similar morphology of the Euler and Vlasov equations. These
Generalized thermodynamics and Fokker-Planck equations: applications to stellar dynamics and two-dimensional turbulence.
  • P. Chavanis
  • Physics, Medicine
    Physical review. E, Statistical, nonlinear, and…
  • 4 September 2002
TLDR
A class of generalized Fokker-Planck equations that conserve energy and mass and increase a generalized entropy functional until a maximum entropy state is reached are introduced and the idea of a classification of generalized entropies in "classes of equivalence" is proposed.
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