Monte Carlo and discrete-ordinate simulations of spectral radiances in a coupled air-tissue system

We perform a detailed comparison study of Monte Carlo (MC) simulations and discrete-ordinate radiative-transfer (DISORT) calculations of spectral radiances in a 1D coupled air-tissue (CAT) system consisting of horizontal plane-parallel layers. The MC and DISORT models have the same physical basis, including coupling between the air and the tissue, and we use the same air and tissue input parameters for both codes. We find excellent agreement between radiances obtained with the two codes, both above and in the tissue. Our tests cover typical optical properties of skin tissue at the 280, 540, and 650 nm wavelengths. The normalized volume scattering function for internal structures in the skin is represented by the one-parameter Henyey-Greenstein function for large particles and the Rayleigh scattering function for small particles. The CAT-DISORT code is found to be approximately 1000 times faster than the CAT-MC code. We also show that the spectral radiance field is strongly dependent on the inherent optical properties of the skin tissue.     

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.     

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 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.     

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.     

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.     

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.     

Path integral Monte Carlo simulations of the melting of molecular hydrogen surfaces

We have used Path Integral Monte Carlo to study the surface melting of molecular hydrogen. Density profiles perpendicular and parallel to the bare H₂ surface are computed showing the formation of a liquid adlayer at 6 K, less than half the bulk melting temperature of para-hydrogen, 13.8 K. To estimate the onset temperature and depth of H₂ surface melting we determine the static structure factor within the individual H₂-layers for wave vectors in the plane and find no crystalline order down to 3 K in a partially filled H₂ adlayer at the free surface. We find quantum effects amplify the melting point depression at the free H₂ surface compared to bulk by a factor of five over classical Lennard-Jones solids and find that the zero-point fluctuations of molecules at the surface are much enhanced over their bulk values. We see vacancy formation in the solid before melting.     

Analytical solution of radiative transfer in the coupled atmosphere-ocean system with a rough surface

Using the computationally efficient discrete-ordinate method, we present an analytical solution for radiative transfer in the coupled atmosphere-ocean system with a rough air-water interface. The theoretical formulations of the radiative transfer equation and solution are described. The effects of surface roughness on the radiation field in the atmosphere and ocean are studied and compared with satellite and surface measurements. The results show that ocean surface roughness has significant effects on the upwelling radiation in the atmosphere and the downwelling radiation in the ocean. As wind speed increases, the angular domain of sunglint broadens, the surface albedo decreases, and the transmission to the ocean increases. The downward radiance field in the upper ocean is highly anisotropic, but this anisotropy decreases rapidly as surface wind increases and as ocean depth increases. The effects of surface roughness on radiation also depend greatly on both wavelength and angle of incidence (i.e., solar elevation); these effects are significantly smaller throughout the spectrum at high Sun. The model-observation discrepancies may indicate that the Cox-Munk surface roughness model is not sufficient for high wind conditions.     

Impulse response solution to the three-dimensional vector radiative transfer equation in atmosphere-ocean systems. I. Monte Carlo method

We have developed a powerful 3D Monte Carlo code, as part of the Radiance in a Dynamic Ocean (RaDyO) project, which can compute the complete effective Mueller matrix at any detector position in a completely inhomogeneous turbid medium, in particular, a coupled atmosphere-ocean system. The light source can be either passive or active. If the light source is a beam of light, the effective Mueller matrix can be viewed as the complete impulse response Green matrix for the turbid medium. The impulse response Green matrix gives us an insightful way to see how each region of a turbid medium affects every other region. The present code is validated with the multicomponent approach for a plane-parallel system and the spherical harmonic discrete ordinate method for the 3D scalar radiative transfer system. Furthermore, the impulse response relation for a box-type cloud model is studied. This 3D Monte Carlo code will be used to generate impulse response Green matrices for the atmosphere and ocean, which act as inputs to a hybrid matrix operator-Monte Carlo method. The hybrid matrix operator-Monte Carlo method will be presented in part II of this paper.     

Quantifying diffusion-controlled drug release from spherical devices using Monte Carlo simulations

We numerically calculate drug release profiles from simple spherical devices using Monte Carlo simulations, when diffusion is the dominant release mechanism. Release curves are accurately described by the stretched exponential function, also known as the Weibull function. The dependence of the two stretched exponential parameters on the size of the spherical device and the drug diffusion coefficient is investigated and simple analytical relations are provided. Release kinetics does not depend on the initial drug concentration. The obtained results are compared with predictions derived from the analytical solution of Fick's second law of diffusion.     

Monte Carlo simulations of the diffuse backscattering mueller matrix for highly scattering media

We have developed a Monte Carlo algorithm that computes all two-dimensional elements of the diffuse backscattering Mueller matrix for highly scattering media. Using the Stokes-Mueller formalism and scattering amplitudes calculated with Mie theory, we are able to consider polarization-dependent photon propagation in highly scattering media, including linearly and circularly polarized light. The numerically determined matrix elements are compared with experimental data for different particle sizes and show good agreement in both azimuthal and radial direction.     

Assessment of test duration effect in indoor radon measurement by Monte Carlo simulations

To better understand the effect of various test durations on indoor radon measurement results in Canada, Monte Carlo simulations were performed for test durations of 1 month (30 d), 2 months (61 d), 3 months (91 d) and 6 months (183 d). For each of the specified test durations, a total of 1500 Monte Carlo simulations were performed. Each simulation was compared with the result of a 1-y measurement. On average, the radon concentration estimated from a 30-d test differed by about ±22 % from the value of a 1-y measurement. The difference reduced to about ±17 % for a 61-d test, ±14 % for a 91-d test and ±9 % for a half-year test. Health Canada's recommendation of a 3-month radon test performed during the heating season resulted in an estimated radon concentration, on average, ～20 % higher than the value determined from a 1-y measurement. This ensures a conservative estimate of the annual average radon concentration, as there is some risk at any radon level. Therefore, to avoid an underestimation of radon exposure and to ensure appropriate levels of precision and accuracy are met, the results from this study suggest that a radon measurement duration of 3 months or longer during the heating season (from October through to April) is needed.