In this paper we propose a numerical scheme to solve the Kac model of the Boltzmann equation for multiscale rarefied gas dynamics. This scheme is uniformly stable with respect to the Knudsen number, consistent with the fluid-diffusion limit for small Knudsen numbers, and with the Kac equation in the kinetic regime. Our approach is based on the micro-macro decomposition which leads to an equival...

It is shown how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to yield the empirical Havriliak-Negami (HN) equation of anomalous dielectric relaxation from a microscopic model based on a kinetic equation just a...

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to fast variable is used. The main assumption is that the correlator of probability densities of particles to make a step has a power-law dependence. As a result,...

A sequence of approximate linear collision models for hard-sphere and inverse-power-law gases is introduced. These models are obtained by expanding the linearized Boltzmann collision operator into a Hermite series, and a practical algorithm is proposed for evaluating the coefficients in the series. The sequence approximates the linearized Boltzmann operator to high accuracy, and it establishes ...

Platinum extraction from spent reforming catalysts in iodine solutions under atmospheric pressure at different temperatures, acid concentration, and iodine spices concentration, catalyst particle size, and impeller agitation speed have been studied in our group. In this system, platinum is oxidized from spent catalyst with I3¯ that is formed ...

Till now, different constitutive models have been applied to model the hot deformation flow curves of different materials. In this research, the hot deformation flow stress of API X65 pipeline steel was modeled using the power law equation with strain dependent constants. The results was compared with the results of the other previously examined constitutive equations including the Arrhenius eq...

for preventing groundwater and soil from heavy metal contamination and/or to decrease contamination, and to clean up the former disposal sites from these metals, one must be beforehand able to predict the movement of these pollutants in soils. in this research in order to describe cadmium [cd (ii)] transport in soils, we incorporated an equilibrium-kinetic two-site model into the convection-dis...

Batch experiments were conducted to study the adsorption behaviors of lead ion (Pb2+) onto ferrihydrites prepared using three different procedures which were characterized  by textural analysis (BET). The adsorption removal of Pb2+ by the three ferrihydrites (called FH-1, FH-2 and FH-3, respectively) were compared, and FH-3 shows fast adsorption kinetics as well as hig...

Abstract. In this work we derive a hierarchy of new mathematical models for describing the motion of phototactic bacteria, i.e., bacteria that move towards light. These models are based on recent experiments suggesting that the motion of such bacteria depends on the individual bacteria, on group dynamics, and on the interaction between bacteria and their environment. Our first model is a collis...

In this paper, the lattice vehicular model, which is in the form the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. A 3-bit approximation, which describe uncongested traffic flow, for the discretization of the Boltzmann equation in both time and phase space is di...