Volume 24, Issue 3

Through the direct simulation Monte Carlo, the Boltzmann equation is solved numerically for dilute hard spheres gas between two infinite parallel plates in relative motion and at the same time the particles feel the action of a uniform body force along the same direction as the moving plate. The study is conducted on the effect of the external force on the nonlinear properties of the Poiseuille–Couette flow. We have been interested in the bulk properties, to inhibit the influence of finite-size effects, while ignoring linear effects like Knudsen boundary layer to investigate the generalised transport coefficients depending on the shear rate nonlinearly: the two nonlinear thermal conductivity function of normal heat flux and parallel one, the viscosity function, the tangential friction function, and the thermal curvature. The results indicate that the effect of the external force is significant on the nonlinear functions, where the viscosity function and normal thermal conductivity are increasing functions of this field.

This paper deals with Monte Carlo simulation and focuses on the use of the concepts of variance reduction, relative error and bias in testing the performance of stationary M/G/1 retrial queues estimators using either Random Sampling (RS) or Refined Descriptive Sampling (RDS) to generate input samples. For this purpose, a software under Linux system using the C compiler was designed and realized providing the performance measures of such system and the statistical concepts of bias, relative error and accuracy using both sampling methods. As a conclusion, it has been shown that the performance of stationary M/G/1 retrial queues estimators is better using RDS than RS and sometimes by a substantial variance reduction factor.

In this paper, we construct the model of a generalized fractional Brownian motion with parameter α∈(0,2){\alpha\in(0,2)}, which approximates such a process with given reliability 1-δ{1-\delta}, 0<δ<1{0<\delta<1}, and accuracy ε>0{\varepsilon>0} in the space C⁢([0,T]){C([0,T])}. An Example of a simulation in C⁢([0,1]){C([0,1])} is given.

We develop in this paper a hybrid kinetic Monte Carlo and continuous thermodynamically based model for the simulation of homogeneous nucleation under burst regime when a long incubation time is followed by rapid nucleation of stable nuclei. In this model we assume that the kinetics of particle nucleation and disaggregation is governed by a Smoluchowski equation while the size of a stable nuclei is taken from the thermodynamic theory of nucleation with varying supersaturation under metastable conditions. We show that the Smoluchowski equations without the metastable conditions cannot describe the regime of burst nucleation showing the following general feature: the longer the incubation time, the slower the nucleation rate even if a multiple disaggregation is assumed. In contrast, a combined hybrid Monte Carlo and metastable thermodynamic model suggested is able to predict a long incubation time followed by rapid nucleation regime. A series of numerical simulations presented supports this conclusion.

We consider the problem of sampling from high-dimensional likelihood functions with large amounts of non-identifiabilities via Markov-Chain Monte-Carlo algorithms. Non-identifiabilities are problematic for commonly used proposal densities, leading to a low effective sample size. To address this problem, we introduce a regularization method using an artificial prior, which restricts non-identifiable parts of the likelihood function. This enables us to sample the posterior using common MCMC methods more efficiently. We demonstrate this with three MCMC methods on a likelihood based on a complex, high-dimensional blood coagulation model and a single series of measurements. By using the approximation of the artificial prior for the non-identifiable directions, we obtain a sample quality criterion. Unlike other sample quality criteria, it is valid even for short chain lengths. We use the criterion to compare the following three MCMC variants: The Random Walk Metropolis Hastings, the Adaptive Metropolis Hastings and the Metropolis adjusted Langevin algorithm.

The energy and the angular distribution of atoms are considered like two parameters most influent in the optimization of the sputtering and subsequently on the deposit, resulting in films having the desired properties (homogeneity in thickness, composition identical to that of the evaporated material). Moreover, a great influence on the shape and quality of thin films is obtained. In this work, a simulation with a Monte Carlo (MC) method is used to calculate the sputtering yield for different energies and angular distributions of atoms of metals (Cu, Al and Ag) and semiconductors (Ge, Si and Te) bombarded by different gas particles (Ar, Xe and Ne). Our results showed that when arriving at a certain energy value EmaxE_{\rm max}, sputtering yield will be in maximum Y⁢1maxY1_{\rm max}. Applying this EmaxE_{\rm max} and with variation in the angular distribution, we will obtain θmax\theta_{\rm max} corresponding to the maximum of sputtering yield Y⁢2maxY2_{\rm max}. These two values (EmaxE_{\rm max}, θmax\theta_{\rm max}) give the maximum of atoms sputtered and as a result, the films will be uniform. The obtained results are in very high agreement with other works, which validates our calculations.