An atomistic simulation of solid state sintering using Monte Carlo methods

This paper presents results on the simulation of the solid state sintering of copper wires using Monte Carlo techniques based on elements of lattice theory and cellular automata. The initial structure is superimposed onto a triangular, two-dimensional lattice, where each lattice site corresponds to either an atom or vacancy. The number of vacancies varies with the simulation temperature, while a cluster of vacancies is a pore. To simulate sintering, lattice sites are picked at random and reoriented in terms of an atomistic model governing mass transport. The probability that an atom has sufficient energy to jump to a vacant lattice site is related to the jump frequency, and hence the diffusion coefficient, while the probability that an atomic jump will be accepted is related to the change in energy of the system as a result of the jump, as determined by the change in the number of nearest neighbours. The jump frequency is also used to relate model time, measured in Monte Carlo Steps, to the actual sintering time. The model incorporates bulk, grain boundary and surface diffusion terms and includes vacancy annihilation on the grain boundaries. The predictions of the model were found to be consistent with experimental data, both in terms of the microstructural evolution and in terms of the sintering time. (C) 2002 Elsevier Science B.V. All rights reserved.

Genetic assignment methods for the direct, real-time estimation of migration rate: a simulation-based exploration of accuracy and power

Genetic assignment methods use genotype likelihoods to draw inference about where individuals were or were not born, potentially allowing direct, real-time estimates of dispersal. We used simulated data sets to test the power and accuracy of Monte Carlo resampling methods in generating statistical thresholds for identifying F-0 immigrants in populations with ongoing gene flow, and hence for providing direct, real-time estimates of migration rates. The identification of accurate critical values required that resampling methods preserved the linkage disequilibrium deriving from recent generations of immigrants and reflected the sampling variance present in the data set being analysed. A novel Monte Carlo resampling method taking into account these aspects was proposed and its efficiency was evaluated. Power and error were relatively insensitive to the frequency assumed for missing alleles. Power to identify F-0 immigrants was improved by using large sample size (up to about 50 individuals) and by sampling all populations from which migrants may have originated. A combination of plotting genotype likelihoods and calculating mean genotype likelihood ratios (D-LR) appeared to be an effective way to predict whether F-0 immigrants could be identified for a particular pair of populations using a given set of markers.

Numerical methods for strong solutions of stochastic differential equations: an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Grand canonical Monte Carlo simulation study of methane adsorption at an open graphite surface and in slitlike carbon pores at 273 K

Grand canonical Monte Carlo (GCMC) simulation was used for the systematic investigation of the supercritical methane adsorption at 273 K on an open graphite surface and in slitlike micropores of different sizes. For both considered adsorption systems the calculated excess adsorption isotherms exhibit a maximum. The effect of the pore size on the maximum surface excess and isosteric enthalpy of adsorption for methane storage at 273 K is discussed. The microscopic detailed picture of methane densification near the homogeneous graphite wall and in slitlike pores at 273 K is presented with selected local density profiles and snapshots. Finally, the reliable pore size distributions, obtained in the range of the microporosity, for two pitch-based microporous activated carbon fibers are calculated from the local excess adsorption isotherms obtained via the GCMC simulation. The current systematic study of supercritical methane adsorption both on an open graphite surface and in slitlike micropores performed by the GCMC summarizes recent investigations performed at slightly different temperatures and usually a lower pressure range by advanced methods based on the statistical thermodynamics.

Numerical modeling of 11.1 T MRI of a human head using MoM/FDTD methods

In a recent study, severe distortions in the proton images of an excised, fixed, human brain in an 11.1 Tesla/40 cm MR instrument have been observed, and the effect modeled on phantom images using a finite difference time domain (FDTD) model. in the present study, we extend these simulations to that of a complete human head, employing a hybrid FDTD and method of moments (MoM) approach, which provides a validated method for simulating biological samples in coil structures. The effect of fixative on the image distortions is explored. importantly, temperature distributions within the head are also simulated using a bioheat method based on parameters derived from the electromagnetic simulations. The MoM/FDTD simulations confirm that the transverse magnetic field (B,) from a ReCav resonator exhibits good homogeneity in air but strong inhomogeneity when loaded with the head with or without fixative. The fixative serves to increase the distortions, but they are still significant for the in vivo simulations. The simulated signal intensity (SI) distribution within the sample confirm the distortions in the experimental images are caused by the complex interactions of the incident electromagnetic fields with tissue, which is heterogeneous in terms of conductivity and permittivity. The temperature distribution is likewise heterogeneous, raising concerns regarding hot spot generation in the sample that may exceed acceptable levels in future in vivo studies. As human imaging at 11.1 T is some time away, simulations are important in terms of predicting potential safety issues as well as evaluating practical concerns about the quality of images. Simulation on a whole human head at 11.1 T implies the wave behavior presents significant engineering challenges for ultra-high-field (UHF) MRI. Novel strategies will have to be employed in imaging technique and resonator design for UHF MRI to achieve the theoretical signal-to-noise ratio (SNR) improvements it offers over lower field systems. (C) 2005 Wiley Periodicals, Inc.

Simulation of binary mixture adsorption of methane and CO2 at supercritical conditions in carbons

Knowledge of the adsorption behavior of coal-bed gases, mainly under supercritical high-pressure conditions, is important for optimum design of production processes to recover coal-bed methane and to sequester CO2 in coal-beds. Here, we compare the two most rigorous adsorption methods based on the statistical mechanics approach, which are Density Functional Theory (DFT) and Grand Canonical Monte Carlo (GCMC) simulation, for single and binary mixtures of methane and carbon dioxide in slit-shaped pores ranging from around 0.75 to 7.5 nm in width, for pressure up to 300 bar, and temperature range of 308-348 K, as a preliminary study for the CO2 sequestration problem. For single component adsorption, the isotherms generated by DFT, especially for CO2, do not match well with GCMC calculation, and simulation is subsequently pursued here to investigate the binary mixture adsorption. For binary adsorption, upon increase of pressure, the selectivity of carbon dioxide relative to methane in a binary mixture initially increases to a maximum value, and subsequently drops before attaining a constant value at pressures higher than 300 bar. While the selectivity increases with temperature in the initial pressure-sensitive region, the constant high-pressure value is also temperature independent. Optimum selectivity at any temperature is attained at a pressure of 90-100 bar at low bulk mole fraction of CO2, decreasing to approximately 35 bar at high bulk mole fractions. (c) 2005 American Institute of Chemical Engineers.

User guide for shock and blast simulation with the OctVCE code (version 3.5+), Department of Mechanical Engineering Report 2007/13

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel as it is simple to code and sufficient for practical engineering design problems. This also makes the code much more ‘user-friendly’ than structured grid approaches as the gridding process is done automatically. The CFD methodology relies on a finite-volume formulation of the unsteady Euler equations and is solved using a standard explicit Godonov (MUSCL) scheme. Both octree-based adaptive mesh refinement and shared-memory parallel processing capability have also been incorporated. For further details on the theory behind the code, see the companion report 2007/12.

Improving wheat simulation capabilities in Australia from a cropping systems perspective - II. Testing simulation capabilities of wheat growth

To simulate cropping systems, crop models must not only give reliable predictions of yield across a wide range of environmental conditions, they must also quantify water and nutrient use well, so that the status of the soil at maturity is a good representation of the starting conditions for the next cropping sequence. To assess the suitability for this task a range of crop models, currently used in Australia, were tested. The models differed in their design objectives, complexity and structure and were (i) tested on diverse, independent data sets from a wide range of environments and (ii) model components were further evaluated with one detailed data set from a semi-arid environment. All models were coded into the cropping systems shell APSIM, which provides a common soil water and nitrogen balance. Crop development was input, thus differences between simulations were caused entirely by difference in simulating crop growth. Under nitrogen non-limiting conditions between 73 and 85% of the observed kernel yield variation across environments was explained by the models. This ranged from 51 to 77% under varying nitrogen supply. Water and nitrogen effects on leaf area index were predicted poorly by all models resulting in erroneous predictions of dry matter accumulation and water use. When measured light interception was used as input, most models improved in their prediction of dry matter and yield. This test highlighted a range of compensating errors in all modelling approaches. Time course and final amount of water extraction was simulated well by two models, while others left up to 25% of potentially available soil water in the profile. Kernel nitrogen percentage was predicted poorly by all models due to its sensitivity to small dry matter changes. Yield and dry matter could be estimated adequately for a range of environmental conditions using the general concepts of radiation use efficiency and transpiration efficiency. However, leaf area and kernel nitrogen dynamics need to be improved to achieve better estimates of water and nitrogen use if such models are to be use to evaluate cropping systems. (C) 1998 Elsevier Science B.V.