Biomedical subjects

Freddy Bouchet

Publications and source records attributed to Freddy Bouchet.

5 recordsLinked to original sources

PubMed2005

Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics.

We explain the ubiquity and extremely slow evolution of non-Gaussian out-of-equilibrium distributions for the Hamiltonian mean-field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one also unambiguously explains and predicts striking slow algebraic relaxation of the momenta autocorrelation, previously found in numerical simulations. Finally, angular anomalous diffusion are predicted for a large class of initial distributions. Non-extensive statistical mechanics is shown to be unnecessary for the interpretation of these phenomena.

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PubMed2005

Thermodynamics of the self-gravitating ring model.

We present the phase diagram, in both the microcanonical and the canonical ensemble, of the self-gravitating-ring (SGR) model, which describes the motion of equal point masses constrained on a ring and subject to 3D gravitational attraction. If the interaction is regularized at short distances by the introduction of a softening parameter, a global entropy maximum always exists, and thermodynamics is well defined in the mean-field limit. However, ensembles are not equivalent and a phase of negative specific heat in the microcanonical ensemble appears in a wide intermediate energy region, if the softening parameter is small enough. The phase transition changes from second to first order at a tricritical point, whose location is not the same in the two ensembles. All these features make of the SGR model the best prototype of a self-gravitating system in one dimension. In order to obtain the stable stationary mass distribution, we apply an iterative method, inspired by a previous one used in 2D turbulence, which ensures entropy increase and, hence, convergence towards an equilibrium state.

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PubMed2004

Stochastic process of equilibrium fluctuations of a system with long-range interactions.

The relaxation towards equilibrium of systems with long-range interactions is not yet understood. As a step towards such a comprehension, we propose the study of dynamical equilibrium fluctuations in a model system with long-range interaction. We compute analytically, from the microscopic dynamics, the autocorrelation function of the order parameter. From this result, we derive analytically a Fokker-Planck equation which describes the stochastic process of the impulsion of a single particle in an equilibrium bath. The diffusion coefficient is explicitly computed.

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PubMed2004

Minimal stochastic model for Fermi's acceleration.

We introduce a simple stochastic system able to generate anomalous diffusion for both position and velocity. The model represents a viable description of the Fermi's acceleration mechanism and it is amenable to analytical treatment through a linear Boltzmann equation. The asymptotic probability distribution functions for velocity and position are explicitly derived. The diffusion process is highly non-Gaussian and the time growth of moments is characterized by only two exponents nu(x) and nu(v). The diffusion process is anomalous (non-Gaussian) but with a defined scaling property, i.e., P(|r|,t)=1/t(nu(x))Fx(|r|/t(nu(x))) and similarly for velocity.

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PubMed2002

Out-of-equilibrium states as statistical equilibria of an effective dynamics in a system with long-range interactions.

We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Nonequilibrium structures are shown to correspond to statistical equilibria of an effective dynamics, which is derived using averaging techniques. This simple behavior might be a prototype of others observed in more complicated systems with long-range interactions, such as two-dimensional incompressible fluids and wave-particle interaction in a plasma.

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