Lattice Boltzmann equations for the isothermal Navier-Stokes equations have been constructed systematically using a truncated moment expansion of the equilibrium distribution function from continuum kinetic theory. Applied to the shallow water equations, with its different equation of state, the same approach yields discrete equilibria that are subject to a grid scale computational instability....

We present the derivation of the perturbation equations governing the oscillations of relativistic nonrotating neutron star models using the (3+1)-decomposition. We show that the perturbation equations can always be written in terms of spacetime variables only, regardless of any particular gauge. We demonstrate how to obtain the Regge-Wheeler gauge, by choosing appropriate shift and lapse. In a...

In this paper we investigate the stability and instability of boundary layers of incompressible Euler equations. Dans cet article on etudie la stabilit e et l'instabilit e de couches limites des equations d'Euler.

We first review the known mathematical results concerning the KP type equations. Then we perform numerical simulations to analyze various qualitative properties of the equations : blow-up versus long time behavior, stability and instability of solitary waves.

The Eckhaus instability of hexagonal patterns is studied within the model of three coupled envelope equations for the underlying roll systems. The regions of instability in the parameter space are found analytically from both the phase approximation and a full system of amplitude equations. Beyond the stability limits of hexagons two different modes go unstable. Both provide symmetry breaking o...

We propose a novel type of color magnetic condensation originating from magnetic monopoles so that it provides the mass of off-diagonal gluons in the Yang-Mills theory. This dynamical mass generation enables us to explain the infrared Abelian dominance and monopole dominance by way of a non-Abelian Stokes theorem, which supports the dual superconductivity picture of quark confinement. Moreover,...