An attempt is made for the first time to solve the quadratic and cubic model of magneto hydrodynamic Poiseuille flow of Phan-Thein-Tanner (PTT). A series solution of magneto hydrodynamic (MHD) flow is developed by using homotopy perturbation method (HPM). The results are presented graphically and the effects of non-dimensional parameters on the flow field are analyzed. The results reveal many i...

Hydrodynamics is the appropriate “effective theory” for describing any fluid medium at sufficiently long length scales. This paper treats the vacuum as such a medium and derives the corresponding hydrodynamic equations. Unlike a normal medium the vacuum has no linear sound-wave regime; disturbances always “propagate” nonlinearly. For an “empty vacuum” the hydrodynamic equations are familiar one...

We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N = 2 and N = 3 containing the equations of shallow water waves and its generalizations with their first two higher symmetries and their recursion operators. We also discuss a reduction of N + 1 systems to N systems of so...

We present a simple method for the solution of one-component and multicomponent hydrodynamic equations based on the NewtonRaphson method. We show that this method can be used for the solution of stationary hydrodynamic equations. This method has been used for the calculation of the low density stellar wind models for which the multicomponent nature of the wind influences the overall wind struct...

For a system consisting of a large collection of particles, a set of variables that will generally become effectively classical are the local densities (number, momentum, energy). That is, in the context of the decoherent histories approach to quantum theory, it is expected that histories of these variables will be approximately decoherent, and that their probabilites will be strongly peaked ab...

We present some results on the mathematical analysis of kinetic equations for modelling transport processes in semiconductors. We focus our attention on the connection between the kinetic models and the fluids ones based on driftdiffusion or hydrodynamic equations. Asymptotic analysis gives hydrodynamic coefficients in, terms of microscopic quantities and allows to derive accurate boundary cond...

New quantum hydrodynamic equations are derived from a Wigner-Boltzmann model, using the quantum entropy minimization method recently developed by Degond and Ringhofer. The model consists of conservation equations for the carrier, momentum, and energy densities. The derivation is based on a careful expansion of the quantum Maxwellian in powers of the Planck constant. In difference to the standar...

A set of hydrodynamic equations modeling strong ionization in semiconductors is formally derived from a kinetic framework. To that purpose, a system of Boltzmann transport equations governing the distribution functions of conduction electrons and holes is considered. The charge carriers obey a degenerate gas statistics and their kinetic energy relations are arbitrary. The umklapp collisions are...