It is well known that for increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier–Stokes equations lose accuracy. For the high speed diatomic molecular flow in the transitional regime, the inaccuracies are partially attributed to the single temperature approximations in the Navier–Stokes equations. Here, we propose a continuum multiple temperature model ...

We offer a new form for the Snl term in the Hasselmann kinetic equation for squared wave amplitudes of wind-driven gravity wave. This form of Snl makes possible to rewrite in differential form the conservation laws for energy, momentum, and wave action, and introduce their fluxes by a natural way. We show that the stationary kinetic equation has a family of exact Kolmogorov-type solutions gover...

Aqueous-phase edsorption equilibrium and kinetic mechanism of phenol, 3-chlorophenol rnd o-cresol onto Norit Granular Activaied Caibon (NAC 1240) were studied in a batch system at temperature of 30 oC, agitation speed of 120 rpm, initial phenol concentrations of 25-200 mg/t. The elfects of initid phenol concentration and time of adsorption on phenol adsorption process were lnvestigated. The ads...

In this paper we derive diffusive relaxation schemes for the linear semiconductor Boltzmann equation that work in both the kinetic and diffusive regimes. Similar to our earlier approach for multiscale transport equations, we use the evenand oddparity formulation of the kinetic equation, and then reformulate it into the diffusive relaxation system (DRS). In order to handle the implicit anisotrop...

A comprehensive description of methods, suitable for solving the kinetic equation for fast ions and impurity species in tokamak plasmas using Monte Carlo approach, is presented. The described methods include Hamiltonian orbit-following in particle and guiding center phase space, test particle or guiding center solution of the kinetic equation applying stochastic differential equations in the pr...

Alexander, Garcia and Alder [1] introduced the Consistent Boltzmann Algorithm (CBA) as a simple variant of Direct Simulation Monte Carlo (DSMC) for dense gases. In CBA, collisions alter both the positions and velocities of the particles. In the present work the limiting kinetic equation for CBA is derived; the formulation is similar to the proof that the Boltzmann equation is the limiting kinet...

The so-called renormalization group (RG) method is applied to derive kinetic and transport equations from the respective microscopic equations. The derived equations include Boltzmann equation in classical mechanics, Fokker-Planck equation, a rate equation in a quantum field theoretical model. Utilizing the formulation of the RG method which elucidates the important role played by the choice of...

‎we study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{r}}^2$ with critical exponential growth‎. ‎this model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.