Volume 29, Issue 4

Lagrangian stochastic methods are widely used to model turbulent flows. Scarce consideration has, however, been devoted to the treatment of the near-wall region and to the formulation of a proper wall-boundary condition. With respect to this issue, the main purpose of this paper is to present an in-depth analysis of such flows when relying on particle/mesh formulations of the probability density function (PDF) model. This is translated into three objectives. The first objective is to assess the existing an-elastic wall-boundary condition and present new validation results. The second objective is to analyse the impact of the interpolation of the mean fields at particle positions on their dynamics. The third objective is to investigate the spatial error affecting covariance estimators when they are extracted on coarse volumes. All these developments allow to ascertain that the key dynamical statistics of wall-bounded flows are properly captured even for coarse spatial resolutions.

In this paper we develop a stochastic simulation algorithm for electron transport in a DA-pHEMT heterostructure. Mathematical formulation of the problem of electron gas transport in the heterostructure in the form of a coupled system of Poisson, Schrödinger and kinetic Boltzmann equations is given. A Monte Carlo model of electron transport in DA-pHEMT heterostructures which accounts for multivalley parabolic band structure, as well as relevant formulas for calculating electron scattering rates and scattering phase functions on polar optical, intervalley phonons and on impurities are developed. The results of a computational experiment involving the solution of the system of Poisson–Schrödinger–Boltzmann equations for the AlGaAs / GaAs / InGaAs / GaAs / AlGaAs heterostructure are presented. The distribution of electrons by energy subband in the main and satellite valleys and the field dependences of the electron drift velocity in each valley are calculated. It was discovered that there is no spatial transfer of electrons into wide-gap AlGaAs layers due to high barriers created by modulated-doped impurities. A comparative analysis of the electron drift velocities in the studied DA-pHEMT heterostructures and in the unstrained layer of the InGaAs is given.

In this paper we suggest randomized linear solvers with a focus on refinement issue to achieve a high precision while maintaining all the advantages of the Monte Carlo method for solving systems of large dimension with dense matrices. It is shown that each iterative refinement step reduces the error by one order of magnitude. The crucial point of the suggested method is, in contrast to the standard Monte Carlo method, that the randomized vector algorithm computes the entire solution column at once, rather than a single component. This makes it possible to efficiently construct the iterative refinement method. We apply the developed method for solving a system of elasticity equations.

In this paper, we will consider periodic EGARCH ⁡ ( p , p ) {\operatorname{EGARCH}(p,p)} (exponential generalized autoregressive conditional heteroscedastic) processes denoted by PEGARCH ⁡ ( p , p ) {\operatorname{PEGARCH}(p,p)} . These processes are similar to the standard EGARCH processes, but include seasonally varying coefficients. We examine the probabilistic structure of an EGARCH-type stochastic difference equation with periodically-varying parameters. We propose necessary and sufficient conditions ensuring the existence of stationary solutions (in a periodic sense) based on a Markovian representation. The closed forms of higher moments are, under these conditions, established. Furthermore, the expressions for the Kurtosis coefficient and the autocorrelations of squared observations are derived. The general theory is illustrated by considering special cases such as the symmetric and the asymmetric cases of the second order PEGARCH model.

In this work, we considered the parametric estimation of the characteristics of the M / M / 1 / N {M/M/1/N} waiting model with Bernoulli feedback. Through a Monte-Carlo simulation study, we have illustrated the effect of the estimation of the starting parameters of the considered waiting system on the statistical properties of its performance measures estimates, when these latter are obtained using the plug-in method. In addition, several types of convergence (bias, variance, MSE, in law) of these performance measure estimators have also been showed by simulation.