a new derivation of the quantum boltzmann transport equation for the fermion system from the quantum time evolution equation for the wigner distribution function is presented. the method exhibits the origin of the time - irreversibility of the boltzmann equation. in the present work, the spin dependent and indistinguishibility of particles are also considered.

A new derivation of the quantum Boltzmann transport equation for the Fermion system from the quantum time evolution equation for the wigner distribution function is presented. The method exhibits the origin of the time - irreversibility of the Boltzmann equation. In the present work, the spin dependent and indistinguishibility of particles are also considered.

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...

In this paper we analyze and compare the lattice-Boltzmann equation with the beam scheme in detail. We notice the similarity and differences between the lattice Boltzmann equation and the beam scheme. We show that the accuracy of the lattice-Boltzmann equation is indeed second order in space. We discuss the advantages and limitations of the lattice-Boltzmann equation and the beam scheme. Based ...

The inclusion of steric effects is important when determining the electrostatic potential near a solute surface. We consider a modified form of the Poisson-Boltzmann equation, often called the Poisson-Bikerman equation, in order to model these effects. The modifications lead to bounded ionic concentration profiles and are consistent with the Poisson-Boltzmann equation in the limit of zero-size ...

In this papcr we analyze and compare the lattice Boltzmann equation with the beam scheme in details. We notice the similarity and differences between the lattice Boltzmann equation and the beam scheme. We show that the accuracy of the lattice Boltzmann equation is indeed second order in space. We discuss the advantages and limitations of lattice Boltzmann equation and the beam scheme. Based on ...

In this paper a procedure for systematic a priori derivation of the lattice Boltzmann models for nonideal gases from the Enskog equation (the modified Boltzmann equation for dense gases) is presented. This treatment provides a unified theory of lattice Boltzmann models for nonideal gases. The lattice Boltzmann equation is systematically obtained by discretizing the Enskog equation in phase spac...

To develop and analyze new computational techniques for the Boltzmann equation based on model or approximation adaptivity, it is imperative to have disposal of a compliant model problem that displays the essential characteristics of the Boltzmann equation and that admits the extraction of highly accurate reference solutions. For standard collision processes, the Boltzmann equation itself fails ...