On algebraic damping close to inhomogeneous Vlasov equilibria in multi-dimensional spaces

We investigate the asymptotic damping of a perturbation around inhomogeneous stable stationary states of the Vlasov equation in spatially multi-dimensional systems. We show that branch singularities of the Fourier-Laplace transform of the perturbation yield algebraic dampings. In two spatial dimensions, we classify the singularities and compute the associated damping rate and frequency. This 2D setting also applies to spherically symmetric self-gravitating systems. We validate the theory using a toy model and an advection equation associated with the isochrone model, a model of spherical self-gravitating systems.Comment: 37 pages, 10 figure

Dynamical pattern formations in two dimensional fluid and Landau pole bifurcation

A phenomenological theory is proposed to analyze the asymptotic dynamics of perturbed inviscid Kolmogorov shear flows in two dimensions. The phase diagram provided by the theory is in qualitative agreement with numerical observations, which include three phases depending on the aspect ratio of the domain and the size of the perturbation: a steady shear flow, a stationary dipole, and four traveling vortices. The theory is based on a precise study of the inviscid damping of the linearized equation and on an analysis of nonlinear effects. In particular, we show that the dominant Landau pole controlling the inviscid damping undergoes a bifurcation, which has important consequences on the asymptotic fate of the perturbation.Comment: 9 pages, 7 figure

Enhanced low-energy spin dynamics with diffusive character in the iron-based superconductor (La0.87Ca0.13)FePO: Analogy with high Tc cuprates (A short note)

In a recent NMR investigation of the iron-based superconductor (La0.87Ca0.13)FePO [Phys. Rev. Lett. 101, 077006 (2008)] Y. Nakai et al. reported an anomalous behavior of the nuclear spin-lattice relaxation of 31P nuclei in the superconducting state: The relaxation rate 1/T1 strongly depends on the measurement frequency and its T dependence does not show the typical decrease expected for the superconducting state. In this short note, we point out that these two observations bear similarity with the situation is some of the high Tc cuprates.Comment: To appear in J. Phys. Soc. Jpn. (Short Note

The Vlasov equation and the Hamiltonian Mean-Field model

We show that the quasi-stationary states observed in the $N$-particle dynamics of the Hamiltonian Mean-Field (HMF) model are nothing but Vlasov stable homogeneous (zero magnetization) states. There is an infinity of Vlasov stable homogeneous states corresponding to different initial momentum distributions. Tsallis $q$-exponentials in momentum, homogeneous in angle, distribution functions are possible, however, they are not special in any respect, among an infinity of others. All Vlasov stable homogeneous states lose their stability because of finite $N$ effects and, after a relaxation time diverging with a power-law of the number of particles, the system converges to the Boltzmann-Gibbs equilibrium

Motion of sediment particles in a Rankine combined vortex

CER84-85PYJ6.Includes bibliographical references (page 28).May 1985

Planform geometry of meandering alluvial channels

CER84-85PYJ5.Includes bibliographical references (pages 32-49).May 1985