Analysis of an Energy Localization Approximation applied to three-dimensional Kinetic Monte Carlo simulations of heteroepitaxial growth

Heteroepitaxial growth involves depositing one material onto another with a different lattice spacing. This misfit leads to long-range elastic stresses that affect the behavior of the film. Previously, an Energy Localization Approximation was applied to Kinetic Monte Carlo simulations of two-dimensional growth in which the elastic field is updated using a sequence of nested domains. We extend the analysis of this earlier work to a three-dimensional setting and show that while it scales with the increase in dimensionality, a more intuitive Energy Truncation Approximation does not.     

An energy localization principle and its application to fast kinetic Monte Carlo simulation of heteroepitaxial growth

Simulation of heteroepitaxial growth using kinetic Monte Carlo (KMC) is often based on rates determined by differences in elastic energy between two configurations. This is computationally challenging due to the long range nature of elastic interactions. A new method is introduced in which the elastic field is updated using a local approximation technique. This involves an iterative method that is applied in a sequence of nested domains until a convergence criteria is satisfied. These localized calculations yield energy differences that are highly accurate despite the fact that the energies themselves are far less accurate: an effect referred to as the principle of energy localization. This is explained using the continuum analogue of the discrete model and error estimates are found. In addition, a rejection algorithm that relies on a computationally inexpensive estimate of hopping rates is used to avoid a substantial fraction of the elastic updates. These techniques are applied to 1+1-dimensional KMC simulations in physically interesting regimes.     

Dynamic Monte Carlo simulation of surface recombination

A dynamic model for the Monte Carlo method is developed to analyze the atom recombination on a catalytic surface. A numerical method for the study of this model is considered. The concentrations of physically and chemically adsorbed atoms obtained using this approach are in good agreement with experimental data and with the numerical results obtained on the basis of the phenomenological model and by other authors with the aid of the Monte Carlo method.     

Monte Carlo simulation of self-avoiding lattice chains under slit flow

This paper proposes a pseudo-potential describing slit flow in the formalism of lattice Monte Carlo simulation with the bond fluctuation algorithm as the unique basic micro-relaxation mode. The main characteristics of slit flow, such as the parabolic velocity profile and the pressure-flux relationship, are successfully reproduced in a three-dimensional self-avoiding multi-chain system. Both Newtonian and non-Newtonian regimes are revealed. The chain conformation and nonlinear rheological behavior are investigated. The simulation results agree with experimental measurements. This method can be used to investigate the viscoelastic properties at different layers as well as the global properties. Some peculiar phenomena in inhomogeneous flow are found to be consistent with previous theoretical predictions by others. Received: 20 April 1999/Accepted: 22 July 1999     

Two-component Brownian coagulation: Monte Carlo simulation and process characterization

The compositional distribution within aggregates of a given size is essential to the functionality of composite aggregates that are usually enlarged by rapid Brownian coagulation. There is no analytical solution for the process of such two-component systems. Monte Carlo method is an effective numerical approach for two-component coagulation. In this paper, the differentially weighted Monte Carlo method is used to investigate two-component Brownian coagulation, respectively, in the continuum regime, the free-molecular regime and the transition regime. It is found that (1) for Brownian coagulation in the continuum regime and in the free-molecular regime, the mono-variate compositional distribution, i.e., the number density distribution function of one component amount (in the form of volume of the component in aggregates) satisfies self-preserving form the same as particle size distribution in mono-component Brownian coagulation; (2) however, for Brownian coagulation in the transition regime the mono-variate compositional distribution cannot reach self-similarity; and (3) the bivariate compositional distribution, i.e., the combined number density distribution function of two component amounts in the three regimes satisfies a semi self-preserving form. Moreover, other new features inherent to aggregative mixing are also demonstrated; e.g., the degree of mixing between components, which is largely controlled by the initial compositional mass fraction, improves as aggregate size increases.     

Molecular models for simulation of rarefied gas flows using direct simulation Monte Carlo method

The direct simulation Monte Carlo (DSMC) method is a technique for the numerical simulation of the rarefied gas flows by employing simulated molecules in simulated physical spaces. In the procedures involved in DSMC, the accuracy of the simulation of intermolecular collisions depends on the collision model adopted in the collision routine. The simplest molecular model is the hard-sphere model. In order to improve the accuracy of the simulations, more and more refined collision models were introduced for the use in DSMC. Thus, the variable hard-sphere, the variable soft-sphere, the generalised hard-sphere, the generalised soft-sphere and the variable sphere models were put forward by various researchers. And, all these models have met with varying degrees of success. Meanwhile, the Borgnakke-Larsen model, statistical inelastic cross-section models for both continuous and discrete internal energy and the dynamic molecular collision model were proposed for the treatment of polyatomic molecules in which transfer of energy among translational, rotational and vibrational degrees of freedom is possible. This paper gives a brief introduction to the intermolecular potentials based on which the molecular models have been constructed. Then the various models are introduced in the chronological sequence; finally concluding with a brief summary of the progress that has been made so far in this area.     

Monte Carlo simulation of radiative transfer in a refractive layered medium

In this work, we adapted the Monte Carlo method to simulate radiative transfer in a two-layer scattering slab with continuously varying refractive index in each of the two layers and a jump of refractive index at the interface between the two layers. The hemispherical reflectance (R _h ) and transmittance (T _h ) of the slab are obtained by tracing photon bundles propagating along curved trajectories. There is a very satisfying correspondence between the present results and those obtained by numerical solution of integral radiative transfer equation for the special cases with constant refractive index in each of the layers. The magnitude of numerical uncertainty decreases with the increase of bundles. The results show that the R _h decreases with the increase of the positive gradient of the refractive index considered. For the cases with constant total thickness, the R _h and the T _h increase with the increase of the ratio of upper-layer thickness to lower-layer thickness.     

Effective hydraulic conductivities in unsaturated heterogeneous media by Monte Carlo simulation

When modeling flow and transport through unsaturated heterogeneous geological deposits, it may be neither computationally nor technically feasible to account for the actual heterogeneity in the simulations. One would fall short in terms of technical feasibility because there is simply no way that the entire spatial domain could be characterized (e.g., you cannot measure hydraulic conductivity at every location at a site). With respect to computational feasibility, the non-linear nature of the Richards equation (which is used to model the flow process) makes simulation of most sites extremely computationally intensive. The computational roadblock is being dismantled as computer hardware advances, but our inability to precisely characterize geological heterogeneity is expected to remain with us for a very long time. To address this problem, the analyst typically uses average or effective properties to model flow and transport behavior through heterogeneous media. In this paper, a variety of approaches for developing effective unsaturated flow properties are assessed. Computational results have been obtained which give the hydraulic conductivity ratios (K _parallel/K _nomal) for highly nonisotropic layered materials. These results are compared with analytical models. Good agreement was obtained for all soil saturation levels except for extremely dry conditions.This work was performed at Sandia National Laboratories, which is operated for the U.S. Department of Energy under contract number DE-AC04-76DP00789.     

Monte Carlo simulation of stage separation dynamics of a multistage launch vehicle

This paper provides the formulation used for studing the cold and hot separating stages of a multistage launch vehicle. Monte Carlo simulation is employed to account for the off nominal design parameters of the bodies undergoing separation to evaluate the risk of failure for the separation event. All disturbances, effect of dynamic unbalance, residual thrust, separation disturbance caused by the separation mechanism and misalignment in cold and hot separation are analyzed to find out nonoccurrence of collision between the separation bodies. The results indicate that the current design satisfies the separation requirements.     

Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials

A numerical method is developed to simulate complex two-dimensional crack propagation in quasi-brittle materials considering random heterogeneous fracture properties. Potential cracks are represented by pre-inserted cohesive elements with tension and shear softening constitutive laws modelled by spatially-varying Weibull random fields. Monte Carlo simulations of a concrete specimen under uni-axial tension were carried out with extensive investigation of the effects of important numerical algorithms and material properties on numerical efficiency and stability, crack propagation processes and load-carrying capacities. It was found that the homogeneous model led to incorrect crack patterns and load–displacement curves with strong mesh-dependence, whereas the heterogeneous model predicted realistic, complicated fracture processes and load-carrying capacity of little mesh-dependence. Increasing the variance of the tensile strength random fields with increased heterogeneity led to reduction in the mean peak load and increase in the standard deviation. The developed method provides a simple but effective tool for assessment of structural reliability and calculation of characteristic material strength for structural design.     

On the dynamics of grafted branched polymers—a Monte Carlo simulation study

A simplified model of grafted branched polymers was designed and investigated. The model consisted of star-branched chains constructed on a simple cubic lattice. The star polymers were built of three arms of equal lengths. The chains were attached to an impenetrable flat surface with one arm’s end. The arm attached to the surface (a stem) was built of segments different from those in two remaining arms (branches). During the Monte Carlo simulation of the system, the conformation of each chain was modified according to the metropolis sampling algorithm with local changes of chain conformations. The simulations were performed for different chain lengths and the temperature of the system (solvent conditions). The structure of a polymer film formed on the grafting surfaces depended strongly on the temperature and the low temperature films consisted of two separate layers with the insoluble layer located near the grafting surface. The short-time relaxation of the branches and stems of chains was also investigated. The analysis of the dynamics of the model system shows the influence of the structure of the system on relaxation times of various parameters. Paper presented at the AERC 2005 held on April 21–23, 2005 in Grenoble, France.     

Monte Carlo simulation of the heat flow in a dense hard sphere gas

The one-dimensional steady heat flow in a dense hard sphere gas is studied solving the Enskog equation numerically by a recently proposed DSMC-like particle scheme. The accuracy of the solutions is assessed through a comparison with solutions obtained from a semi-regular method which combines finite difference discretization with Monte Carlo quadrature techniques. It is shown that excellent agreement is found between the two numerical methods. The solutions obtained from the Enskog equation have also been found in good agreement with the results of molecular dynamics simulations.     

Differentially weighted direct simulation Monte Carlo method for particle collision in gas-solid flows

In gas-solid flows,particle-particle interaction(typical,particle collision) is highly significant,despite the small particles fractional volume.Widely distributed polydisperse particle population is a typical characteristic during dynamic evolution of particles(e.g.,agglomeration and fragmentation) in spite of their initial monodisperse particle distribution.The conventional direct simulation Monte Carlo(DSMC)method for particle collision tracks equally weighted simulation particles,which results in high statistical noise for particle fields if there are insufficient simulation particles in less-populated regions.In this study,a new differentially weighted DSMC(DW-DSMC) method for collisions of particles with different number weight is proposed within the framework of the general Eulerian-Lagrangian models for hydrodynamics.Three schemes(mass,momentum and energy conservation) were developed to restore the numbers of simulation particle while keeping total mass,momentum or energy of the whole system unchanged respectively.A limiting case of high-inertia particle flow was numerically simulated to validate the DW-DSMC method in terms of computational precision and efficiency.The momentum conservation scheme which leads to little fluctuation around the mass and energy of the whole system performed best.Improved resolution in particle fields and dynamic behavior could be attained simultaneously using DW-DSMC,compared with the equally weighted DSMC.Meanwhile,computational cost can be largely reduced in contrast with direct numerical simulation.     

Simulations for gas flows in microgeometries using the direct simulation Monte Carlo method

Micro gas flows are often encountered in MEMS devices and classical CFD could not accurately predict the flow and thermal behavior due to the high Knudsen number. Therefore, the gas flow in microgeometries was investigated using the direct simulation Monte Carlo (DSMC) method. New treatments for boundary conditions are verified by simulations of micro-Poiseuille flow, compared with the previous boundary treatments, and slip analytical solutions of the continuum theory. The orifice flow and the corner flow in microchannels are simulated using the modified DSMC codes. The predictions were compared with existing experimental phenomena as well as predictions using continuum theory. The results showed that the channel geometry significantly affects the microgas flow. In the orifice flow, the flow separation occurred at very small Reynolds numbers. In the corner flow, no flow separation occurred even with a high driving pressure. The DSMC results agreed well with existing experimental information.     

The direct simulation Monte Carlo method using unstructured adaptive mesh and its application

The implementation of an adaptive mesh‐embedding (h‐refinement) scheme using unstructured grid in two‐dimensional direct simulation Monte Carlo (DSMC) method is reported. In this technique, local isotropic refinement is used to introduce new mesh where the local cell Knudsen number is less than some preset value. This simple scheme, however, has several severe consequences affecting the performance of the DSMC method. Thus, we have applied a technique to remove the hanging node, by introducing the an‐isotropic refinement in the interfacial cells between refined and non‐refined cells. Not only does this remedy increase a negligible amount of work, but it also removes all the difficulties presented in the originals scheme. We have tested the proposed scheme for argon gas in a high‐speed driven cavity flow. The results show an improved flow resolution as compared with that of un‐adaptive mesh. Finally, we have used triangular adaptive mesh to compute a near‐continuum gas flow, a hypersonic flow over a cylinder. The results show fairly good agreement with previous studies. In summary, the proposed simple mesh adaptation is very useful in computing rarefied gas flows, which involve both complicated geometry and highly non‐uniform density variations throughout the flow field. Copyright © 2002 John Wiley & Sons, Ltd.     

Monte Carlo simulation of self-avoiding lattice chains subject to oscillatory shear flow in polymer solution

 This paper has introduced a pseudo-potential in bond-fluctuation model to simulate oscillatory shear flow of multiple self-avoiding chains in three dimensions following our previous work under simple shear flow. The oscillatory flow field was reasonably reproduced by lattice Monte Carlo simulation using this pseudo-potential neglecting hydrodynamic interaction. By sampling the configuration distribution functions, the macroscopic viscoelasticity of semi-concentrated polymer solution was determined. Both Newtonian and non-Newtonian regimes were studied. The complex modulus and dynamic viscosity exhibit a reasonable power relation with oscillatory frequency, which is consistent with present theories and experiments. Consequently, lattice Monte Carlo simulation has been extended to model free-draining self-avoiding multi chains subject to oscillatory shear flow and to investigate associated viscoelasticity on the molecular level. Received: 1 October 1999 Accepted: 19 October 1999     

Direct simulation Monte Carlo study of the formation and growth of clusters in the case of vapor expansion from a suddenly switched spherical source

The processes of formation of silicon clusters in the case of vapor expansion from a suddenly switched spherical source into an ambient inert gas are considered. Vapor expansion and condensation are described by the direct simulation Monte Carlo method. A model of clusterization is proposed, which describes reactions leading to the growth and decomposition of clusters and corresponding energytransfer processes. The main features of cluster formation in the case of vapor expansion into a gas are considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 101–109, January–February, 2009.     

Combined interval analysis - Monte Carlo simulation approach for the analysis of uncertainties in parallel manipulators

The quantification of the impact of uncertainties may increase the reliability and robustness of parallel manipulators. Monte Carlo simulation (MCS) and interval analysis are among the most common techniques used in uncertainty quantification. Interval analysis provides guaranteed performance since the interval evaluation of a function always contains the exact result. Nevertheless, interval analysis estimations are very conservative, frequently yielding overestimated results. Conversely, Monte Carlo Simulation avoids overestimation, but does not provide guaranteed performance. This paper proposes a novel hybrid algorithm combining the best features of interval analysis and Monte Carlo simulation for estimating probabilities of failure in the positioning error of parallel manipulators. A 3RRR manipulator is employed as case-study. The hybrid approach provides information on the bounds (minimum and maximum values) and estimated values of failure probabilities. The simulations herein compare the hybrid approach with pure interval analysis and pure Monte Carlo simulation. The results reveal that the hybrid technique may estimate not only the probability of failure in a continuous region, but also the worst and best case probabilities, much faster than interval analysis based approaches.

     

Calculation of radiative transfer In non Gris Gas using Narrow Band model and Monte Carlo simulation

 The radiation transfer is treated by the application of Narrow-Band Statistical Model (NBSM) which takes into account emissive and absorptive gas spectral structures. A Monte-Carlo method using radiative net exchange technique developed to determine the radiative balance in non grey gas. The proposed procedure is based on Net-Exchange Formulation (NEF). Such a formulation provides an efficient way of systematically fulfilling the reciprocity principle, which avoids some of the major problems usually associated with the Monte-Carlo method; numerical efficiency becomes independent of optical thickness, strongly nonuniform grid sizes can be used with no increase in computation time, and configurations with small temperature differences can be addressed with very good accuracy. It is shown that the radiation term is significant compared with conductive term in two specific regions in emitting and absorbing gas; in the immediate vicinity of the wall, and in the external part of the boundary layer. The Radiative Net-Exchange and Monte-Carlo method are detailed for a one dimensional slab. Received on 15 January 1999     

计算复杂边界渗流的蒙特卡罗方法

本文运用不规则游动网格的蒙特卡罗方法求解复杂边界渗流问题。与以往各种数值方法相比,蒙特卡罗方法在计算渗流问题时要更灵活、更方便,可以根据需要独立地计算出渗流区域内任意一点的渗透压力、渗流流速。