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We first present the phase diffusion and mean drift equation which describe convective patterns in large aspect ratio containers and for arbitrary Rayleigh and Prandtl numbers. Some applications are presented such as the prediction of the selected wavenumber or the instability of foci. We propose in a second step a regularized form of the phase diffusion equation able to reproduce the formation and...
Hamiltonian systems with many degrees of freedom, like large assemblies of interacting particles in a box are described by the Gibbs-Boltzmann statistics, as far as their average properties are concerned. This does not hold for the long time behavior of classical nonlinear field equations, as noticed already by Jeans, because of the infinite heat capacity of this field. Thus nonlinear (and nonintegrable)...
We study the homoclinic tangle associated with the phase space flow of a particle in a cubic potential, subject to small and temporally periodic forcing. We construct a bifurcation diagram describing the changes in the Birkhoff signature of the tangle as the strength and frequency of the forcing are varied. From this diagram we find special regions in the parameter space for which we can approximate...
The qualitative features of large scale structures in the simplest case of kinetic plasma turbulence, the electron beam-plasma instability, are described. The corresponding theory is still unsatisfactory, and even paradoxical. The weaknesses of the traditional approach of microscopic plasma theory are analysed. A new approach is introduced, resting on a classical mechanics technique. It starts from...
Supersonic turbulence is observed in the giant molecular clouds in the galactic disk and may also occur at re-entry of space shuttles. Numerical simulations in three dimensions concerning compressible homogeneous non-stationary flows using the fluid equations with the Navier-Stokes formulation, a hyperviscosity method, and new simulations of the Euler equations using the PPM code are presented. Results...
The anisotropic kinetic alpha effect (AKA) and the (magnetic) alpha effect refer to large-scale instabilities which develop in low Reynolds number flows and lead to an exponential growth of a weak large-scale velocity or magnetic field respectively. When the nonlinearities become important, an inverse cascade is observed, yielding the formation of structures at larger and larger scales, up to the...
Some features and theoretical interpretations of the intermittency phenomenon observed in high-energy multi-particle production are recalled. One develops on the various connections found with fractal structuration of fluctuations in turbulence, spin-glass physics and aggregation phenomena described by the non-linear Smoluchowski equation. This may lead to a new approach to quantum field properties.
We review recent developments in the physics of the quark-gluon plasma. After giving a short account of results in lattice QCD at finite temperature, we describe briefly the Feynman rule at nonzero T. Then we discuss the spectrum of collective excitations (quasiparticles) in the quark-gluon plasma: fermionic as well as gluonic excitations. Finally we explain how a resummation method due to Braaten...
In this talk we introduce a new technique, called the delta expansion, which can be used to solve nonlinear problems in both classical and quantum physics. The idea of the delta expansion is to expand in the power of a nonlinear term. For example, to treat a y4 term, we introduce a small parameter delta and consider a (y2(1+δ)) term. When we expand in powers of delta,...
The properties of convection inside a spherical shell heated from within are studied by direct numerical simulations. A pseudo-spectral method is used. Both the compressible and the incompressible (Boussinesq) case are treated. We consider first a non rotating configuration. It is well known that the solutions of the linear problem are degenerate, due to the spherical symmetry, and that their...
We investigate, with the aid of three-dimensional direct-numerical simulations (using pseudo-spectral methods) at high resolution (up to 1283 grid points in a cubic box containing four fundamental longitudinal wavelengths), the origin and topology of the longitudinal vortex filaments which appear in temporally-growing mixing layers. The basic velocity field is a hyperbolic-tangent profile U tanh 2...
Atmospheric flows often produce organized structures in the presence of strong turbulence. This organization property of two-dimensional turbulence is also observed in laboratory experiments and numerical simulations. After introducing different examples, it is shown that this organization can be explained in terms of equilibrium statistical mechanics on Euler equations.
It is shown that when the stability spectrum of a system has degeneracies at critical values of a control parameter, below which the system is stable or marginally stable, it may develop instabilities due to the interaction of the degenerate critical eigenmodes. When the spectrum is discrete all instabilities close to criticality are expected to stem from such degeneracies, though not all degeneracies...
Formal solutions to a class of initial-value fluid problems are converted to explicit solutions given in terms of “continued functions”. Simplifications analogous to eikonal approximations of particle scattering theory are suggested, and an exact but implicit solution is constructed for a special situation of two-dimensional Euler flow.
We investigate the standard acoustical problem of sound decay in a room, due to a small absorption at the walls, both in the geometrical approximation (1) and for the full wave problem (2). The classical universal Sabine's law of reverberation is shown to rely on ergodic properties of both geometrical billiard-like trajectories (1) and eigenmodes (2). A paradigm of an ergodic auditorium is used to...
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