This thesis describes Monte-Carlo computer simulations of binary alloys, with comparisons between small angle neutron scattering (SANS) data, and numerically integrated solutions to the Cahn-Hilliard-Cook (CHC) equation. Elementary theories for droplet growth are also compared with computer simulated data. Monte-Carlo dynamical algorithms are investigated in detail, with special regard for universal dynamical times. The computer simulated systems are Fourier transformed to yield partial structure functions which are compared with SANS data for the binary Iron-Chromium system. A relation between real time and simulation time is found. Cluster statistics are measured in the simulated systems, and compared to droplet formation in the Copper-Cobalt system. Some scattering data for the complex steel PE16 is also discussed. The characterisation of domain size and its growth with time are investigated, and scaling laws fitted to real and simulated data. The simple scaling law of Lifshitz and Slyozov is found to be inadequate, and corrections such as those suggested by Huse, are necessary. Scaling behaviour is studied for the low-concentration nucleation regime and the high-concentration spinodal-decomposition regime. The need for multi-scaling is also considered. The effect of noise and fluctuations in the simulations is considered in the MonteCarlo model, a cellular-automaton (CA) model and in the Cahn-Billiard-Cook equation. The Cook noise term in the CHC equation is found to be important for correct growth scaling properties.

Lam, Kwok Hap. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 68-72). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Two-level NSEM with outcomes from Exponential Family --- p.6 / Chapter 2.1 --- Basic Model Description --- p.7 / Chapter 2.2 --- Generalization from Normal Distribution to Exponential Family Distributions --- p.9 / Chapter 2.3 --- Bayesian Analysis of the Model --- p.10 / Chapter 2.3.1 --- Posterior Analysis and Gibbs Sampler --- p.10 / Chapter 2.3.2 --- Prior Distributions --- p.11 / Chapter 2.3.3 --- Bayesian Estimation --- p.13 / Chapter 2.3.4 --- Bayesian Model Selection --- p.14 / Chapter 2.4 --- A Simulation Study --- p.15 / Chapter 3 --- Two-level NSEM with mixed continuous and ordered categorical data --- p.28 / Chapter 3.1 --- Model Description --- p.29 / Chapter 3.2 --- Bayesian Analysis of the Model --- p.30 / Chapter 3.2.1 --- Posterior Analysis and Gibbs Sampler --- p.30 / Chapter 3.2.2 --- Bayesian Estimation --- p.31 / Chapter 3.3 --- A Simulation Study --- p.31 / Chapter 4 --- "Two-level NSEM with mixed continuous, count and binomial data" --- p.36 / Chapter 4.1 --- Model Description --- p.37 / Chapter 4.2 --- Bayesian Estimation --- p.38 / Chapter 4.3 --- A Simulation Study --- p.39 / Chapter 5 --- Two-level NSEM with mixed continuous and unordered categorical data --- p.43 / Chapter 5.1 --- Basic Model Description --- p.44 / Chapter 5.2 --- Bayesian Analysis of the Model --- p.47 / Chapter 5.2.1 --- Posterior Analysis and Gibbs Sampler --- p.47 / Chapter 5.2.2 --- Prior Distributions --- p.48 / Chapter 5.3 --- A Simulation Study --- p.49 / Chapter 6 --- Conclusion and Discussion --- p.53 / Chapter A --- Technical Details for Chapter 2 --- p.56 / Chapter A.1 --- Full conditional distributions --- p.56 / Chapter A.2 --- Implementation of the Metropolis-Hastings (MH) Algorithm --- p.59 / Chapter A.3 --- Gelman-Rubin statistic --- p.61 / Chapter B --- Technical Details for Chapter 3 --- p.63 / Chapter B.1 --- Full conditional distributions --- p.63 / Chapter B.2 --- Implementation of the Metropolis-Hastings (MH) Algorithm --- p.64 / Chapter C --- Technical Details for Chapter 5 --- p.66 / Chapter C.l --- Full conditional distributions --- p.66 / Bibliography --- p.68

Chan, Tsz Him. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 94-96). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Monte Carlo method in Finance --- p.6 / Chapter 2.1 --- Principle of MC and pricing theory --- p.6 / Chapter 2.2 --- An illustrative example --- p.9 / Chapter 3 --- Discretization method --- p.15 / Chapter 3.1 --- The Euler scheme and Milstein scheme --- p.16 / Chapter 3.2 --- Convergence of Mean Square Error --- p.19 / Chapter 4 --- Quasi Monte Carlo method --- p.22 / Chapter 4.1 --- Basic idea of QMC --- p.23 / Chapter 4.2 --- Application of QMC in Finance --- p.29 / Chapter 4.3 --- Another illustrative example --- p.34 / Chapter 5 --- Our Methodology --- p.42 / Chapter 5.1 --- Measure decomposition --- p.43 / Chapter 5.2 --- QMC in SDE simulation --- p.51 / Chapter 5.3 --- Towards a workable algorithm --- p.58 / Chapter 6 --- Numerical Result --- p.69 / Chapter 6.1 --- Case I Generalized Wiener Process --- p.69 / Chapter 6.2 --- Case II Geometric Brownian Motion --- p.76 / Chapter 6.3 --- Case III Ornstein-Uhlenbeck Process --- p.83 / Chapter 7 --- Conclusion --- p.91 / Bibliography --- p.96

A braquiterapia é a modalidade de tratamento radioterápico que utiliza fontes radioativas seladas a uma distância curta do tumor, diminuindo o risco de aplicação de uma dose indesejável em tecidos sadios adjacentes. Para que a braquiterapia seja confiável, é necessário estabelecer um programa de práticas dosimétricas visando a determinação da dose ideal de radiação para esta prática radioterápica. Neste trabalho apresenta a aplicação de duas metodologias destinadas à dosimetria utilizando filmes radiocrômicos. Medidas experimentais foram realizadas com filmes EBT3 em objetos simuladores composto de material homogêneo e heterogêneo (pulmão, osso e tecidos moles) construídos especialmente para medidas de dose em braquiterapia. Os processamentos e analises das imagens resultantes do procedimento experimental foram realizados com o software IMAGEJ e MATLAB. Os resultados foram avaliados a partir de comparações medidas experimentais de dose e obtidas por simulações pelo Método de Monte Carlo. / Brachytherapy is a radiotherapy treatment modality using radioactive sealed sources within walking distance of the tumor, reducing the risk of applying an unwanted dose to adjacent healthy tissues. For brachytherapy is reliable, it is necessary to establish a dosimetric practices program aimed at determining the optimal dose of radiation for this radiotherapy practice. This paper presents the application of two methodologies for the dosimetry using radiochromic movies. Experimental measurements were performed with EBT3 movies phantoms consisting of homogeneous and heterogeneous material (lung, bone and soft tissue) built especially for dose measurements in brachytherapy. The processing and analysis of the resulting images of the experimental procedure were performed with ImageJ software and MATLAB. The results were evaluated from comparisons dose of experimental measurements and simulations obtained by the Monte Carlo method.

Barrier options have become increasingly popular financial instruments due to the lower costs and the ability to more closely match speculating or hedging needs. In addition, barrier options play a significant role in modeling and managing risks in insurance and finance as well as in refining insurance products such as variable annuities and equity-indexed annuities. Motivated by these immediate applications arising from actuarial and financial contexts, the thesis studies the pricing of barrier options and some exotic variations, assuming that the underlying asset price follows the Black-Scholes model or jump-diffusion processes. Barrier options have already been well treated in the classical Black-Scholes framework. The first part of the thesis aims to develop a new valuation approach based on the technique of exponential stopping and/or path counting of Brownian motions. We allow the option's boundaries to vary exponentially in time with different rates, and manage to express our pricing formulas properly as combinations of the prices of certain binary options. These expressions are shown to be extremely convenient in further pricing some exotic variations including sequential barrier options, immediate rebate options, multi-asset barrier options and window barrier options. Many known results will be reproduced and new explicit formulas will also be derived, from which we can better understand the impact on option values of various sophisticated barrier structures. We also consider jump-diffusion models, where it becomes difficult, if not impossible, to obtain the barrier option value in analytical form for exponentially curved boundaries. Our model assumes that the logarithm of the underlying asset price is a Brownian motion plus an independent compound Poisson process. It is quite common to assign a particular distribution (such as normal or double exponential distribution) for the jump size if one wants to pursue closed-form solutions, whereas our method permits any distributions for the jump size as long as they belong to the exponential family. The formulas derived in the thesis are explicit in the sense that they can be efficiently implemented through Monte Carlo simulations, from which we achieve a good balance between solution tractability and model complexity.

The exact and phaseless variants of auxiliary-field quantum Monte Carlo (AFQMC) have been shown to be capable of producing accurate ground-state energies for a wide variety of systems including those which exhibit substantial electron correlation effects. The first chapter of this thesis will provide an overview of the relevant electronic structure problem, and the phaseless AFQMC (ph-AFQMC) methodology. The computational cost of performing these calculations has to date been relatively high, impeding many important applications of these approaches. In Chapter 2 we present a correlated sampling methodology for AFQMC which relies on error cancellation to dramatically accelerate the calculation of energy differences of relevance to chemical transformations. In particular, we show that our correlated sampling-based ph-AFQMC approach is capable of calculating redox properties, deprotonation free energies, and hydrogen abstraction energies in an efficient manner without sacrificing accuracy. We validate the computational protocol by calculating the ionization potentials and electron affinities of the atoms contained in the G2 test set and then proceed to utilize a composite method, which treats fixed-geometry processes with correlated sampling-based AFQMC and relaxation energies via MP2, to compute the ionization potential, deprotonation free energy, and the O-H bond dissociation energy of methanol, all to within chemical accuracy. We show that the efficiency of correlated sampling relative to uncorrelated calculations increases with system and basis set size and that correlated sampling greatly reduces the required number of random walkers to achieve a target statistical error. This translates to reductions in wall-times by factors of 55, 25, and 24 for the ionization potential of the K atom, the deprotonation of methanol, and hydrogen abstraction from the O-H bond of methanol, respectively. In Chapter 3 we present an implementation of ph-AFQMC utilizing graphical processing units (GPUs). The AFQMC method is recast in terms of matrix operations which are spread across thousands of processing cores and are executed in batches using custom Compute Unified Device Architecture kernels and the hardware-optimized cuBLAS matrix library. Algorithmic advances include a batched Sherman-Morrison-Woodbury algorithm to quickly update matrix determinants and inverses, density-fitting of the two-electron integrals, an energy algorithm involving a high-dimensional precomputed tensor, and the use of single-precision floating point arithmetic. These strategies result in dramatic reductions in wall-times for both single- and multi-determinant trial wavefunctions. For typical calculations we find speed-ups of roughly two orders of magnitude using just a single GPU card. Furthermore, we achieve near-unity parallel efficiency using 8 GPU cards on a single node, and can reach moderate system sizes via a local memory-slicing approach. We illustrate the robustness of our implementation on hydrogen chains of increasing length, and through the calculation of all-electron ionization potentials of the first-row transition metal atoms. We compare long imaginary-time calculations utilizing a population control algorithm with our previously published correlated sampling approach, and show that the latter improves not only the efficiency but also the accuracy of the computed ionization potentials. Taken together, the GPU implementation combined with correlated sampling provides a compelling computational method that will broaden the application of ph-AFQMC to the description of realistic correlated electronic systems. In Chapter 4 the bond dissociation energies of a set of 44 3d transition metal-containing diatomics are computed with ph-AFQMC utilizing the correlated sampling technique. We investigate molecules with H, N, O, F, Cl, and S ligands, including those in the 3dMLBE20 database first compiled by Truhlar and co-workers with calculated and experimental values that have since been revised by various groups. In order to make a direct comparison of the accuracy of our ph-AFQMC calculations with previously published results from 10 DFT functionals, CCSD(T), and icMR-CCSD(T), we establish an objective selection protocol which utilizes the most recent experimental results except for a few cases with well-specified discrepancies. With the remaining set of 41 molecules, we find that ph-AFQMC gives robust agreement with experiment superior to that of all other methods, with a mean absolute error (MAE) of 1.4(4) kcal/mol and maximum error of 3(3) kcal/mol (parenthesis account for reported experimental uncertainties and the statistical errors of our ph-AFQMC calculations). In comparison, CCSD(T) and B97, the best performing DFT functional considered here, have MAEs of 2.8 and 3.7 kcal/mol, respectively, and maximum errors in excess of 17 kcal/mol (for the CoS diatomic). While a larger and more diverse data set would be required to demonstrate that ph-AFQMC is truly a benchmark method for transition metal systems, our results indicate that the method has tremendous potential, exhibiting unprecedented consistency and accuracy compared to other approximate quantum chemical approaches. The energy gap between the lowest-lying singlet and triplet states is an important quantity in chemical photocatalysis, with relevant applications ranging from triplet fusion in optical upconversion to the design of organic light-emitting devices. The ab initio prediction of singlet-triplet (ST) gaps is challenging due to the potentially biradical nature of the involved states, combined with the potentially large size of relevant molecules. In Chapter 5, we show that ph-AFQMC can accurately predict ST gaps for chemical systems with singlet states of highly biradical nature, including a set of 13 small molecules and the ortho-, meta-, and para- isomers of benzyne. With respect to gas-phase experiments, ph-AFQMC using CASSCF trial wavefunctions achieves a mean averaged error of ~1 kcal/mol. Furthermore, we find that in the context of a spin-projection technique, ph-AFQMC using unrestricted single-determinant trial wavefunctions, which can be readily obtained for even very large systems, produces equivalently high accuracy. We proceed to show that this scalable methodology is capable of yielding accurate ST gaps for all linear polyacenes for which experimental measurements exist, i.e. naphthalene, anthracene, tetracene, and pentacene. Our results suggest a protocol for selecting either unrestricted Hartree-Fock or Kohn-Sham orbitals for the single-determinant trial wavefunction, based on the extent of spin-contamination. These findings provide a reliable computational tool with which to investigate specific photochemical processes involving large molecules that may have substantial biradical character. We compute the ST gaps for a set of anthracene derivatives which are potential triplet-triplet annihilators for optical upconversion, and compare our ph-AFQMC predictions with those from DFT and CCSD(T) methods. We conclude with a discussion of ongoing projects, further methodological improvements on the horizon, and future applications of ph-AFQMC to chemical systems of interest in the fields of biology, drug-discovery, catalysis, and condensed matter physics.

Abstract not available

Masters Research - Master of Philosophy (Engineering) / Thermal conduction properties are of major concern for those metal/ceramic composite materials having applications in semiconductor devices and electronic packaging materials. A higher thermal conductivity to coefficient of thermal expansion ratio is an advantage for such materials employed in electronic devices due to the subjective high thermal loads. It is well known that the shape, size and distribution of the insulating phase have an effect on the overall thermal conductivity properties. But the details are lacking and well deserving of study. Metal/ceramic oxide interfaces are important in the strengthening mechanisms of dispersion strengthened materials. Accordingly, considerable attention has been given to recent investigations of oxygen diffusion characteristics and the bonding mechanisms at such interfaces. Susceptibility to oxidation can be studied by analysing several thicknesses of material. As an example, studying a thin film and a semi-infinite material subjected to a high oxygen partial pressure environment and a vacuum condition would help to determine the oxidation (in-diffusion) and de-oxidation (out-diffusion) processes respectively. Since metal/ceramic internal interfaces play a very important role in controlling the mechanical, thermal and electrical properties, it is timely to consider these diffusion processes for detailed study. In this Thesis, the two areas mentioned above were selected for detailed investigation. The Thesis also addresses the further development of a method for solving complex phenomenological diffusion problems. This method makes use of lattice-based random walks of virtual particles, directed according to the Monte Carlo method (the Lattice Monte Carlo method) which is then used to address various mass and thermal diffusion processes. Chapter 2 is concerned with using this method to determine the thermal conductivity of model composites. In that chapter, the Lattice Monte Carlo method is used to calculate the effective thermal conductivity of several models of a composite, where inclusions are arranged in square planar and cubic arrangements with periodic boundary conditions. Excellent agreement is found of the effective thermal conductivity with the century-old Maxwell-Garnett Equation. Chapter 3 is concerned with a phenomenological representation of oxygen diffusion and segregation in a model composite based on Ag/MgO. The Lattice Monte Carlo method is employed to address mass diffusion in this composite. Square and randomly distributed multiple inclusions were considered as shapes of the MgO inclusion phase. The time-dependence of oxygen concentration depth profiles and contour maps were determined. First, oxygen in-diffusion is considered from a constant surface source solely into the Ag metal matrix: oxygen depth profiles were in excellent agreement with exact results. Next, oxygen in-diffusion/segregation is simulated in the composite by permitting and restricting the mobility of oxygen in different scenarios involving the Ag-MgO interface. The (higher temperature) out-diffusion of oxygen from the composite was also simulated and corresponding results obtained for the oxygen depth profiles. In both cases, very good agreement was found between the results from the Lattice Monte Carlo method and analytical expressions.

Mass transfer processes in food systems, such as solute infusion, are poorly understood because of their complex nature. Food systems contain porous matrices and a variety of continuous phases within cellular tissues. Mass transfer processes are generally not pure diffusion: often convection, binding and obstructing diffusion will occur. Monte Carlo (MC) simulation has been increasingly used in life science and engineering to elucidate molecular transport in biological systems. However, there are few articles available discussing MC simulation in food processing, especially mass transfer. The main goal of this study was to show the inherent simplicity of the MC approach and its potential when combined with traditional experimental and theoretical approaches to better describe and understand mass transfer processes. A basic framework for MC random walk - simulation applied to a diffusion problem - is developed in this project. Infusion of two sizes of dextran macromolecules in fish muscle cells is used to apply the MC framework in combination with Fluorescence Recovery After Photobleaching experiments. Effective diffusivity coefficients within cells, considering the degree of obstruction due to the myofibrilar matrix, are assessed. Then, the results are used as input in a mathematical model that was developed for theoretical simulation of mass transfer in the multi-cellular tissue. Diffusivity values obtained by the MC framework had an SD of ±0.02 [µm²/s] around the true value of 0.25 [µm²/s]. MC results for degree of obstruction were 0.29 and 0.34 for dextran FD1OS and FD2OS, respectively, and the Devalues were 23.7 and 11.2 [µm2/s]. The statistical error in the estimation of D was estimated to be [22.8-24.6] and [9.7-12.7] (95% CI), where average experimental values of 24.3 [µm²/s] for FD1OS and 11.4 [µm²/s] for FD2OS were captured by the respective interval. The theoretical model showed a significant influence of the cell membrane characteristics and tissue porosity in both the degree of solute penetration and the solute distribution between intra- and extra-cellular space. The combined approach was successfully applied to a diffusion problem. Overall, it is expected that the present work will contribute towards the application of MC simulation in the field of Food Science and Engineering. / Graduation date: 2006

For over 30 years, the Implicit Monte Carlo (IMC) method has been used to solve challenging problems in thermal radiative transfer. These problems are typically optically thick and di ffusive, as a consequence of the high degree of "pseudo-scattering" introduced to model the absorption and reemission of photons from a tightly-coupled, radiating material. IMC has several well-known features which could be improved: a) it can be prohibitively computationally expensive, b) it introduces statistical noise into the material and radiation temperatures, which may be problematic in multiphysics simulations, and c) under certain conditions, solutions can be unphysical and numerically unstable, in that they violate a maximum principle - IMC calculated temperatures can be greater than the maximum temperature used to drive the problem. We have developed a variant of IMC called "iterative thermal emission" IMC, which is designed to be more stable than IMC and have a reduced parameter space in which the maximum principle is violated. ITE IMC is a more implicit method version of the IMC in that it uses the information obtained from a series of IMC photon histories to improve the estimate for the end of time-step material temperature during a time step. A better estimate of the end of time-step material temperature allows for a more implicit estimate of other temperature dependent quantities: opacity, heat capacity, Fleck Factor (probability that a photon absorbed during a time step is not reemitted) and the Planckian emission source. The ITE IMC method is developed by using Taylor series expansions in material temperature in a similar manner as the IMC method. It can be implemented in a Monte Carlo computer code by running photon histories for several sub-steps in a given time-step and combining the resulting data in a thoughtful way. The ITE IMC method is then validated against 0-D and 1-D analytic solutions and compared with traditional IMC. We perform an in finite medium stability analysis of ITE IMC and show that it is slightly more numerically stable than traditional IMC. We find that significantly larger time-steps can be used with ITE IMC without violating the maximum principle, especially in problems with non-linear material properties. We also compare ITE IMC to IMC on a two-dimensional, orthogonal mesh, x-y geometry problem called the "crooked pipe" and show that our new method reproduces the IMC solution. The ITE IMC method yields results with larger variances; however, the accuracy of the solution is improved in comparison with IMC, for a given choice of spatial and temporal grid. / Graduation date: 2013