Volume 39, Issue 3

In this paper, we present three algorithms for simulation of intervals of stationary vector and scalar sequences with partial distributions of their subsequences of fixed length in the form of a mixture of Gaussian distributions. The first algorithm is based on superposition of two Gaussian vector processes and the second and third ones use the method of conditional distributions and the method of superpositions to simulate the mixtures and to select realizations for approximate construction of conditional realizations. Some properties of these algorithms are presented.

The paper deals with Monte Carlo simulation of polarized radiative transfer and lidar returns in sensing of atmospheric clouds. The Stokes parameters were used to describe the transfer of polarized radiation, and computation of the lidar returns was based on flux-at-point estimators. We consider modifications of the numerical algorithm with scattering according to the phase function for unpolarized light and with scattering depending on polarization. Numerical experiments were performed for lidar sensing of waterdrop clouds.

Stochastic simulation algorithm for solving exciton transport in a 3D layered semiconductor heterostructure is developed. The problem is governed by a transient drift-diffusion-recombination equation with Dirichlet and Neumann mixed boundary conditions. The semiconductor is represented as an infinite multilayer of finite thickness along the transverse coordinate z . The multilayer is composed by a set of sublayers of different materials so that the excitons have different diffusion and recombination coefficients in each layer. Continuity of solutions and fluxes at the plane interfaces between layers are imposed. The stochastic simulation algorithm solves the transport problem by tracking exciton trajectories in accordance with the probability distributions represented through the Green function of the problem in each sublayer. The method is meshless, the excitons jump only over the plane boundaries of the layers. This explains the high efficiency of the method. Simulation results for transport problems with different mixed boundary conditions are presented.

The paper demonstrates two approaches to constructing monotonic difference schemes for the transfer equation in divergent form from the family of semi-Lagrangian methods: Eulerian–Lagrangian and Lagrangian–Eulerian. Within each approach, a monotonic conservative difference scheme is proposed. It is shown that within the framework of the Lagrangian–Eulerian approach, based on the use of curvilinear grids formed by the characteristics of the approximated transfer operator, it is possible to construct monotonic difference schemes of second order accuracy.

The paper deals with an Eulerian model for heterogeneous multiphase (multi-material) elasto-plastic media based on the diffuse interface method in the one-dimensional uniaxial strain approximation. In this approximation, an equilibrium hypoelastic Wilkins bi-material model is derived. This is carried out on the basis of an analogy between the elasto-plastic Wilkins and hydrodynamic Euler models. For the obtained model, a Godunov-type numerical method is developed based on the approximate Riemann solver HLLC. The results of the proposed Eulerian diffuse interface model are compared with reference solutions on moving grids with explicit tracking interfaces. It is shown that the present diffuse interface numerical model describes with good accuracy strong shock-wave processes in heterogeneous multiphase elasto-plastic media.