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Statistical mechanics of Beltrami flows in axisymmetric geometry: Theory reexamined
Aurore Naso, Romain Monchaux, Pierre-Henri Chavanis +1
A simplified thermodynamic approach of the incompressible axisymmetric Euler equations is considered based on the conservation of helicity, angular momentum and microscopic energy.…
Statistical mechanics of two-dimensional Euler flows and minimum enstrophy states
A. Naso, P. H. Chavanis, B. Dubrulle
A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical eq…
Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution
P. H. Chavanis, A. Naso, B. Dubrulle
Using a Maximum Entropy Production Principle (MEPP), we derive a new type of relaxation equations for two-dimensional turbulent flows in the case where a prior vorticity distributi…
Self-gravitating Brownian particles in two dimensions: the case of N=2 particles
P. H. Chavanis, R. Mannella
We study the motion of N=2 overdamped Brownian particles in gravitational interaction in a space of dimension d=2. This is equivalent to the simplified motion of two biological ent…
Dynamics and thermodynamics of systems with long-range interactions: interpretation of the different functionals
Pierre-Henri Chavanis
We discuss the dynamics and thermodynamics of systems with weak long-range interactions. Generically, these systems experience a violent collisionless relaxation in the Vlasov regi…
Statistical mechanics of 2D turbulence with a prior vorticity distribution
Pierre-Henri Chavanis
We adapt the formalism of the statistical theory of 2D turbulence in the case where the Casimir constraints are replaced by the specification of a prior vorticity distribution. A p…
Out-of-equilibrium phase re-entrance(s) in long-range interacting systems
F. Staniscia, P. H. Chavanis, G. De Ninno +1
Systems with long-range interactions display a short-time relaxation towards Quasi Stationary States (QSSs) whose lifetime increases with system size. The application of Lynden-Bel…
Virial theorem for rotating self-gravitating Brownian particles and two-dimensional point vortices
Pierre-Henri Chavanis
We derive the proper form of Virial theorem for a system of rotating self-gravitating Brownian particles. We show that, in the two-dimensional case, it takes a very simple form tha…