High resolution computer simulations of two-dimensional convection using the anelastic approximation are presented. These calculations span Rayleigh numbers from 10 10 for Prandtl number equal to unity, with the uid density decreasing by a factor of 12 from the bottom to the top of the convection region. This range covers several decades in the \hard" turbulent regime. While many studies of thi...

in present paper, a numerical analysis for a rectangular cavity filled with a anisotropic porous media has been studied. it is assumed that the horizontal walls are adiabatic and impermeable, while the side walls of the cavity are maintained at constant temperatures and concentrations. the buoyancy force that induced the fluid motion are assumed to be cooperative. in the two extreme cases of he...

The first consistent phenomenological theory for two- and three-dimensional Rayleigh-Taylor (RT) turbulence has recently been presented by Chertkov [Phys. Rev. Lett. 91, 115001 (2003)]. By means of direct numerical simulations, we confirm the spatiotemporal prediction of the theory in two dimensions and explore the breakdown of the phenomenological description due to intermittency effects. We s...

We present a Rayleigh-Schrödinger-Goldstone perturbation formalism for many fermion systems. Based on this formalism, variational perturbation scheme which goes beyond the Gaussian approximation is developed. In order to go beyond the Gaussian approximation, we identify a parent Hamiltonian which has an effective Gaussian vacuum as a variational solution and carry out further perturbation with ...

The Navier-Stokes equation driven by heat conduction is studied. As a prototype we consider Rayleigh-Bénard convection, in the Boussinesq approximation. Under a large aspect ratio assumption, which is the case in Rayleigh-Bénard experiments with Prandtl number close to one, we prove the existence of a global strong solution to the 3D NavierStokes equation coupled with a heat equation, and the e...

This review summarizes results for Rayleigh-Bénard convection that have been obtained over the past decade or so. It concentrates on convection in compressed gases and gas mixtures with Prandtl numbers near one and smaller. In addition to the classical problem of a horizontal stationary fluid layer heated from below, it also briefly covers convection in such a layer with rotation about a vertic...

The linear stability of a horizontal layer of fluid heated from below and above is considered. In addition to a steady temperature difference between the walls of the fluid layer, a time-dependent periodic perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. Numerical results for the critical Rayleigh number are obtained at various Prandtl numbers an...

Modified Rayleigh conjecture (MRC) in scattering theory is proposed and justified. MRC allows one to develop numerical algorithms for solving direct scattering problems related to acoustic wave scattering by soft and hard obstacles of arbitrary shapes. It gives an error estimate for solving the direct scattering problem. It suggests a numerical method for finding the shape of a star-shaped obst...

Rayleigh-Bénard convection with internal heat sources and a variable gravity field is treated with no-slip boundary conditions. It is proved that the principle of exchange of stabilities holds at all Prandtl numbers, as long as the gravity field and the integral of the heat sources both have the same sign. The proof is based on the idea of a positive operator, and uses the positivity properties...

Abstract—In this paper, we derive the exact symbol error probability for coherent detection of MPSK signals with optimum combining in the presence of multiple uncorrelated equal power co-channel interferers and thermal noise in a Rayleigh fading environment. The expression is general and valid for arbitrary numbers of receiving antennas or co-channel interferers. The complexity of the analytica...