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Y Elskens

Publications and source records attributed to Y Elskens.

7 recordsLinked to original sources
PubMed2001

Long-time discrete particle effects versus kinetic theory in the self-consistent single-wave model.

The influence of the finite number N of particles coupled to a monochromatic wave in a collisionless plasma is investigated. For growth as well as damping of the wave, discrete particle numerical simulations show an N-dependent long time behavior resulting from the dynamics of individual particles. This behavior differs from the one due to the numerical errors incurred by Vlasov approaches. Trapping oscillations are crucial to long time dynamics, as the wave oscillations are controlled by the particle distribution inhomogeneities and the pulsating separatrix crossings drive the relaxation towards thermal equilibrium.

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PubMed2000

Phase transition in the collisionless damping regime for wave-particle interaction

Gibbs statistical mechanics is derived for the Hamiltonian system coupling a wave to N particles self-consistently. This identifies Landau damping with a regime where a second order phase transition occurs. For nonequilibrium initial data with warm particles, a critical initial wave intensity is found: above it, thermodynamics predicts a finite wave amplitude in the limit N-->infinity; below it, the equilibrium amplitude vanishes. Simulations support these predictions providing new insight into the long-time nonlinear fate of the wave due to Landau damping in plasmas.

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PubMed1986

From instability to irreversibility.

A canonical procedure transforming the unitary evolution group U(t) in a contracting semigroup W(t) for phase-space ensembles has been developed for Kolmogorov dynamical systems in a series of recent papers. This paper investigates the physical meaning of this transformation. We stress that, for sufficiently unstable dynamical systems in which phase-space points are identified with an arbitrary but finite precision, one must take into account the undiscernibility of trajectories having the same asymptotic behavior in the future. The fundamental objects of our description are thus bundles of converging trajectories. We show that such an ensemble, corresponding to initial conditions whose support has finite measure, is then represented by a distribution function (called a Boltzmann ensemble) that evolves to equilibrium under the action of a markovian semigroup. The usual Gibbs-Koopman ensembles satisfying the Liouville equation are recovered as a singular limit. This work validates Boltzmann's intuition for a class of unstable dynamical systems and appears as a step toward the derivation of equations exhibiting irreversibility at a microscopic level.

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