Spatially extended stationary and traveling states in the strongly nonlinear regime of convection in layers of binary fluid mixtures heated from below are described by a few–mode–model. It is derived from the proper hydrodynamic balance equations including experimentally relevant boundary conditions with a non–standard Galerkin approximation that uses numerically obtained, symmetry decomposed m...

Although the foundations of the hydrodynamical formulation of quantum mechanics were laid over 50 years ago, it has only been within the past few years that viable computational implementations have been developed. One approach to solving the hydrodynamic equations uses quantum trajectories as the computational tool. The trajectory equations of motion are described and methods for implementatio...

We establish the global existence of smooth solutions to the Cauchy problem for the one{dimensional isentropic Euler{Poisson (or hydrodynamic) model for semiconductors for small initial data. In particular we show that, as t ! 1, these solutions converge to the stationary solutions of the drift{diiusion equations. The existence and uniqueness of stationary solutions to the drift-diiusion equati...

This paper is devoted to hydrodynamic limits for collisional linear kinetic equations. It is a classical result that under certain conditions on the collision operator, the long time/small mean free path asymptotic behavior of the density of particles can be described by diffusion type equations. We are interested in situations in which the degeneracy of the collision frequency for small veloci...

Abstract. Many numerical solution alternatives based on Navier Stokes equations or Reynolds equations with single or double phase closure turbulence model were proposed. These have the drawback of : i) High computational cost, ii) The detailed complexity of the flow are partially accounted for, iii) Parameters estimation is still an open problem. In this paper, we proceeded by depth averaging o...

High volume production flows are modeled by nonlinear hyperbolic partial differential equations representing conservation laws. These models have Little’s law explicitly built into the formulation. Borrowing from concepts in gas dynamics and vehicular traffic models we derive several prototypical equations representing linear as well as reentrant factories. Multiple products, dispatch polices a...

In this paper, we construct a hierarchy of hybrid numerical methods for multi-scale kinetic equations based on moment realizability matrices, a concept introduced by Levermore, Morokoff and Nadiga in [15]. Following such a criterion, one can consider hybrid scheme where the hydrodynamic part is given either by the compressible Euler or Navier-Stokes equations, or even with more general models, ...

Hydrodynamics is one of the main tools for studying the collective flow in high-energy nuclear collisions. Here, we shall examine some of the main ingredients of such a description and see how likely more realistic treatment of these elements may affect some of the observable quantities. The main components of any hydrodynamic model are the initial conditions, the equations of motion, equations...

A weakly ionized plasma under the influence of a strong electric field is considered. Supposing a local Maxwellian distribution for the electron momenta the plasma is described by hydrodynamic equations for the pair distribution functions. These equations are solved and the relaxation field is calculated for an arbitrary field strength. It is found that the relaxation effect becomes lower with ...

The relativistic kinetic equations for two domains separated by a hypersurface with both spacelike and timelike parts are derived. The particle exchange between the domains separated by timelike boundaries generates source terms and modifies the collision term of the kinetic equation. The correct hydrodynamic equations for the "hydro+cascade" models are obtained and their differences from exist...