Monte Carlo and discrete-ordinate simulations of irradiances in the coupled atmosphere-ocean system

We compare Monte Carlo (MC) and discrete-ordinate radiative-transfer (DISORT) simulations of irradiances in a one-dimensional coupled atmosphere-ocean (CAO) system consisting of horizontal plane-parallel layers. The two models have precisely the same physical basis, including coupling between the atmosphere and the ocean, and we use precisely the same atmospheric and oceanic input parameters for both codes. For a plane atmosphere-ocean interface we find agreement between irradiances obtained with the two codes to within 1%, both in the atmosphere and the ocean. Our tests cover case 1 water, scattering by density fluctuations both in the atmosphere and in the ocean, and scattering by particulate matter represented by a one-parameter Henyey-Greenstein (HG) scattering phase function. The CAO-MC code has an advantage over the CAO-DISORT code in that it can handle surface waves on the atmosphere-ocean interface, but the CAO-DISORT code is computationally much faster. Therefore we use CAO-MC simulations to study the influence of ocean surface waves and propose a way to correct the results of the CAO-DISORT code so as to obtain fast and accurate underwater irradiances in the presence of surface waves.     

Dynamic bounds coupled with Monte Carlo simulations

For the reliability analysis of engineering structures a variety of methods is known, of which Monte Carlo (MC) simulation is widely considered to be among the most robust and most generally applicable. To reduce simulation cost of the MC method, variance reduction methods are applied. This paper describes a method to reduce the simulation cost even further, while retaining the accuracy of Monte Carlo, by taking into account widely present monotonicity. For models exhibiting monotonic (decreasing or increasing) behavior, dynamic bounds (DB) are defined, which in a coupled Monte Carlo simulation are updated dynamically, resulting in a failure probability estimate, as well as a strict (non-probabilistic) upper and lower bounds. Accurate results are obtained at a much lower cost than an equivalent ordinary Monte Carlo simulation. In a two-dimensional and a four-dimensional numerical example, the cost reduction factors are 130 and 9, respectively, where the relative error is smaller than 5%. At higher accuracy levels, this factor increases, though this effect is expected to be smaller with increasing dimension. To show the application of DB method to real world problems, it is applied to a complex finite element model of a flood wall in New Orleans.     

Monte Carlo simulations in zeolites

In this short review, the applications of Monte Carlo simulations to the study of the adsorption and diffusion of hydrocarbons in zeolites are discussed. We focus on those systems for which the conventional molecular simulation techniques, molecular dynamics and Monte Carlo, are not sufficiently efficient. In particular, to simulate the adsorption and diffusion of long-chain hydrocarbons, novel Monte Carlo techniques have been developed. Here we discuss configurational-bias Monte Carlo (CBMC) and kinetic Monte Carlo (KMC). CBMC was developed to compute the thermodynamic properties. KMC is applied to compute transport properties. The use of these methods is illustrated with examples of technological importance.     

Monte Carlo simulations of spectral albedo for artificial snowpacks composed of spherical and nonspherical particles

The optical properties of snowpacks composed of spherical and nonspherical particles artificially prepared in a cold laboratory are investigated by measuring spectral albedos. The measured spectral albedo in the spectral region lambda=0.35-2.5 microm is compared with the theoretically calculated albedo, for which a Monte Carlo radiative transfer model is employed for multiple scattering combined with the Mie theory and the ray-tracing technique for single scattering by snow particles. Since the spherical particles are a little aggregate, the effects of a cluster of the spheres on snow albedo are examined using a generalized multiparticle Mie-solution model [Appl. Opt. 34, 4573 (1995); J. Quant. Spectrosc. Radiat. Transf. 79-80, 1121 (2003)]. The snow albedo of a cluster of the spheres can be represented with that of the singe sphere slightly larger than its component of the cluster in case of small grains. The observed albedos for the spherical snow particles agree with the theoretically calculated ones for the snow grain size measured in the snow pit work. The snow albedos for the nonspherical particles, which were dendrites, are influenced by the branch width and the branch length, based on a comparison of the theoretically calculated albedo by using circular cylindrical snow particles and the observed albedo. The snow albedo in the near-infrared region depends on the branch width only when the branch length is sufficiently greater than the branch width. The comparison between the spherical and nonspherical snow particles indicates that the spectral albedo of the nonspherical particles can be represented by using an equal volume-area ratio sphere.     

Uncertainties beyond statistics in Monte Carlo simulations

The Monte Carlo method has become an essential tool for the simulation of radiation and particle transport problems. The combination of its ease of use and the power of the method can create a temptation to use Monte Carlo as a 'black box' tool. In this paper, we shall mention a number of important issues that any user of a Monte Carlo computer code should keep firmly in mind when attempting a transport simulation, and we shall present a recent practical example to show the potential significance of such issues.     

Monte Carlo simulations of magnetic properties in multilayers

A Monte Carlo method has been used to simulate Heisenberg multilayer systems (L × L × 4P) consisting of alternating P ferromagnetic layers A and B with antiferromagnetic interface coupling J_AB. Finite-size effects on the specific heat and magnetisation thermal variation for two kinds of boundary conditions at the top and bottom planes are investigated. In particular, our Monte Carlo data evidence that the specific heat exhibits two peaks and a single phase transition occurs at the temperature which corresponds to the location of the high temperature peak (as L → ∞).     

Monte Carlo simulations of magnetovolume instabilities in anti-Invar systems

We perform constant pressure Monte Carlo simulations of a spin-analogous model which describes coupled spatial and magnetic degrees of freedom on an fcc lattice. Our calculations qualitatively reproduce magnetovolume effects observed in some rare earth manganese compounds, especially in the anti-Invar material YMn₂. These are a sudden collapse of the magnetic moment which is connected with a huge volume change, and a largely enhanced thermal expansion coefficient.     

Quantum Monte Carlo simulations of Hubbard type models

We present a review of recent Quantum Monte-Carlo results for one- and twodimensional Hubbard models. In one-dimension spectral properties are calculated with the maximum entropy method. At small doping, the one-particle excitations are characterized by a dispersive cosine-like band. Two different velocities for charge and spin-excitations are obtained which lead to a conformal charge c = 0.98 ± 0.05. In two-dimensions, we concentrate on two methods to detect superconducting ground states without prior knowledge of the symmetry of the underlying pair-pair correlations: flux quantization and the temperature derivative of the superfluid density. Both methods are based on extensions of quantum Monte-Carlo algorithms to incorporate magnetic fields. Our main results include numerical data which a) confirm the Kosterlitz-Thouless transition in the attractive Hubbard model b) show the absence of superconductivity in the quarter filled repulsive Hubbard model, and finally c) show no sign of a Kosterlitz-Thouless type transition in the three-band Hubbard model up to t_pd = 12.5 and hole doping = 0.25.     

Computational steering in Monte Carlo simulations of thin film polystyrene

High molecular weight polymer systems show very long relaxation times, of the order of milliseconds or more. This time-scale proves practically inaccessible for atomic-scale dynamical simulation such as molecular dynamics. Even with a Monte Carlo (MC) simulation, the generation of statistically independent configurations is non-trivial. Many moves have been proposed to enhance the efficiency of MC simulation of polymers. Each is described by a proposal density Q(x'; x): the probability of selecting the trial state x' given that the system is in the current state x. This proposal density must be parametrized for a particular chain length, chemistry and temperature. Choosing the correct set of parameters can greatly increase the rate at which the system explores its configuration space. Computational steering (CS) provides a new methodology for a systematic search to optimize the proposal densities for individual moves, and to combine groups of moves to greatly improve the equilibration of a model polymer system. We show that monitoring the correlation time of the system is an ideal single parameter for characterizing the efficiency of a proposal density function, and that this is best evaluated by a distributed network of replicas of the system, with the operator making decisions based on the averages generated over these replicas. We have developed an MC code for simulating an anisotropic atomistic bead model which implements the CS paradigm. We report simulations of thin film polystyrene.     

Three-dimensional Monte Carlo simulations of electromigration in polycrystalline thin films

The effects of electromigration in metal thin films is studied by means of atomistic Monte Carlo simulations. The simulator is based on a model of atom diffusion particularly suited to deal with polycrystalline three-dimensional films. Interatomic interactions are estimated by means of a simplified Morse potential while the driving force exerted by the charge carrier flux is represented as a perturbation on the diffusion activation barrier. The local current density is calculated using an equivalent resistor network. The results of simulated stress applied to various samples including a triple point are presented demonstrating the possibility of reproducing the initial stage of void formation with an atomistic model.     

Comparison of Weibull small samples using Monte Carlo simulations

The evaluation of the functional reliability of different designs is a common task and times to failure can be compared using the likelihood ratio test. In the microelectronics industry, as in many others, the high cost of testing places severe restrictions on the sample size. Moreover, the products in these tests are often new and do not have previous reliability histories. These factors make the selection of the Type I and Type II errors in comparison tests very difficult. This paper presents the Monte Carlo simulation results of Type II errors for the likelihood ratio test of comparison as a function of the Type I error and the (small) sample size. Our conclusions are summarized as follows: (1) the common microelectronics industry standard sample size of 32 is often insufficient to reach satisfactory conclusions; (2) small sample tests should only be used for prescreening for significant differences; and (3) when only small samples are available, the Type I and the Type II errors must be selected carefully to prevent misleading conclusions. Copyright © 2006 John Wiley & Sons, Ltd.     

Monte Carlo simulations of the Galileo energetic particle detector

Monte Carlo radiation transport studies have been performed for the Galileo spacecraft energetic particle detector (EPD) in order to study its response to energetic electrons and protons. Three-dimensional Monte Carlo radiation transport codes, MCNP version 4B (for electrons) and MCNPX version 2.2.3 (for protons), were used throughout the study. The results are presented in the form of “geometric factors” for the high-energy channels studied in this paper: B1, DC2, and DC3 for electrons and B0, DC0, and DC1 for protons. The geometric factor is the energy-dependent detector response function that relates the incident particle fluxes to instrument count rates. The trend of actual data measured by the EPD was successfully reproduced using the geometric factors obtained in this study.     

Lanczos and recursion techniques for multiscale kinetic Monte Carlo simulations

We review an approach to the simulation of the class of microstructural and morphological evolution involving both relatively short-ranged chemical and interfacial interactions and long-ranged elastic interactions. The calculation of the anharmonic elastic energy is facilitated with Lanczos recursion. The elastic energy changes affect the rate of vacancy hopping, and hence the rate of microstructural evolution due to vacancy-mediated diffusion. The elastically informed hopping rates are used to construct the event catalog for kinetic Monte Carlo simulation. The simulation is accelerated using a second-order residence time algorithm. The effect of elasticity on the microstructural development has been assessed. This article is related to a talk given in honor of David Pettifor at the DGP60 Workshop in Oxford.     

Multiple discovery: Some Monte Carlo simulations and Gedanken experiments

Two major interpretations of multiples have been offered, the traditional one based on the scientific zeitgeist, the more recent one based on chance processes. To clarify the issues involved in any plausible explanation, six successive Monte Carlo simulations were developed. Though all models started with the same underlying probabilistic mechanism, several elaborations were introduced, including exhaustion, communication of both successes and failures, and variation in success probability. The models yield the same probability distribution for multiple grades, but they disagree on the frequency of nulltons. Additional Gedanken experiments dealt with the zeitgeist notions of a causal link between potential contributions.     

A spectral representation based model for Monte Carlo simulation

A new model is proposed for generating samples of real-valued stationary Gaussian processes. The model is based on the spectral representation theorem stating that a weakly stationary process can be viewed as a superposition of harmonics with random properties. The classical use of this theorem for Monte Carlo simulation is based on models consisting of a superposition of harmonics with fixed frequencies but random amplitude and phase. The resulting samples have the same period depending on the discretization of the frequency band. In contrast, the proposed model consists of a superposition of harmonics with random amplitude, phase, and frequency so that different samples have different periods depending on the particular sample values of the harmonic frequencies.

A band limited Gaussian white noise process is used to illustrate the proposed Monte Carlo simulation algorithm and demonstrate that the estimates of the covariance function based on the samples of the proposed model are not periodic.     

Monte Carlo simulations of very low pressure chemical vapor deposition

Summary Simulation strategies for chemical vapor deposition (CVD) of thin solid films are presented, with emphasis on direct simulation Monte Carlo methods for analyzing and predicting physical phenomena occurring at low pressures and in micron-sized substrate features. The Monte Carlo approach is placed in perspective, relative to standard continuum mechanics-based strategies for modeling of CVD systems. Design issues that may be addressed through the developed methods are exemplified with computations for a new, technologically important CVD process for epitaxy of Si and Si_xGe_1-x alloys. Specifically, radiative heat transfer, rarefied gas-flow characteristics, species separation caused by pressure and thermal diffusion, growth-rate uniformity vs. surface reactivity, and deposition in microscopic features are addressed as parts of the overall CVD reactor-design approach. Process implications of rarefied transport effects unique to very low pressure CVD conditions are described. A new profile evolution technique is also introduced which predicts film topology, as well as the microstructure of the film.     

Distributed Monte Carlo simulation of a dynamic expansion system

This paper presents a new approach to the implementation of the Monte Carlo (MC) method for the analysis of high vacuum metrological systems based on the principle of dynamic gas expansion. The main disadvantage of the Monte Carlo method, the very long time of computation, can be significantly reduced by using a distributed calculation schema. This paper describes the principles of the computation system and compares the computing times for some models of a chosen metrological system, performed using a network of Personal Computers.