In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...

      In this article, the crystallization of polyethylene is investigated by the modified weighted density approximation. Also, a direct correlation function of polyethylene based on the RISM theory is used. The free energy of a polyethylene is calculated using the density functional theory. The crystallization and also the solid and liquid densities of polyethylene are calculated and compared...

We investigate the stochastic Direct Simulation Monte Carlo method (DSMC) for numerically solving the collision-term in heavy-ion transport theories of the Boltzmann-Uehling-Uhlenbeck (BUU) type. The first major modification we consider is changes in the collision rates due to excluded volume and shadowing/screening effects (Enskog theory). The second effect studied by us is the inclusion of an...

In this paper, we provide the O(ε) corrections to the hydrodynamic model derived by Degond &Motsch from a kinetic version of the model by Vicsek & coauthors describing flocking biological agents. The parameter ε stands for the ratio of the microscopic to the macroscopic scales. The O(ε) corrected model involves diffusion terms in both the mass and velocity equations as well as terms which are q...

In numerous applications, a hierarchy of models is available to describe the phenomenon under consideration. We focus in this work on general hyperbolic systems with stiff relaxation source terms together with the corresponding hyperbolic equilibrium systems. The goal is to determine the regions of the computational domain where the relaxation model (so-called fine model) can be replaced by the...

Abstract. The Enskog-Landau kinetic equation is considered to describe non-equilibrium processes of a mixture of charged hard spheres. This equation has been obtained in our previous papers by means of the non-equilibrium statistical operator method. The normal solution of this kinetic equation found in the first approximation using the standard Chapman-Enskog method is given. On the basis of t...

Particular solutions that correspond to inhomogeneous driving terms in the linearized Boltzmann equation for the case of a binary mixture of rigid spheres are reported. For flow problems (in a plane channel) driven by pressure, temperature, and density gradients, inhomogeneous terms appear in the Boltzmann equation, and it is for these inhomogeneous terms that the particular solutions are devel...

The nonlocal scattering-in and scattering-out integrals of the Enskog equation have reversed displacements of colliding particles reflecting that the scattering-in and -out processes are conjugated by the space and time inversions. Generalizations of the Enskog equation to Fermi liquid systems are hindered by the need for particle-hole symmetry which contradicts the reversed displacements. We r...