Thesis (Ph. D.)--Chemistry and Biochemistry, Georgia Institute of Technology, 2006. / Dr. C. P. Wong, Committee Member ; Dr. C. David Sherrill, Committee Member ; Dr. Thomas M. Orlando, Committee Member ; Dr. Mostafa A. El-Sayed, Committee Member ; Dr. Robert M. Dickson, Committee Chair.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 191-207). Also available in electronic version.

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<p> The theoretical formulation of the electronic transport properties (in the absence of a magnetic field) of pure single crystals of simple metals is extended to incorporate the effect of a non~spherical Fermi surface, using a multiple orthogonalized plane wave description of the conduction electrons. Two approaches are considered, one using a variational principle, and the other employing a scattering time approximation. </p> <p> Formal results for the electrical resistivity and the electronic contribution to the thermal resistivity are expressed in terms of effective phonon frequency distributions. These distributions are particularly convenient for numerical computations and are generalization: of those previously used for the case of a spherical Fermi surface. </p> <p> The generalization of the scattering time method to dilute nonmagnetic substitutional alloys is applied to hexagonal close~packed metalsc It is shown that the addition of small amounts of impurities to pure Zn leads to measurable changes in the temperature dependence of the electrical resistivity ratio (see text for ratio with symbols). The corresponding deviations front Matthiessen's rule for polycrystalline samples are also calculated. </p> / Thesis / Master of Science (MSc)

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The calculation of neutron-nuclei reaction rates in the lower resolved resonance region (167 ev - l.855 ev) is considered in this dissertation. Particular emphasis is placed on the calculation of these reaction rates for tight lattices where their accuracy is most important. The results of the continuous energy Monte Carlo code, VIM, are chosen as reference values for this study. The primary objective of this work is to develop a method for calculating resonance reaction rates which agrees well with the reference solution, yet is efficient enough to be used by nuclear reactor fuel cycle designers on a production basis. A very efficient multigroup solution of the two spatial region energy dependent integral transport equation is developed. This solution, denoted the "Broad Group Integral Method'' (BGIM), uses escape probabilities to obtain the spatial coupling between regions and uses an analytical flux shape within a multigroup to obtain weighted cross sections which account for the rapidly varying resonance cross sections. The multigroup lethargy widths chosen for the numerical integration of the two region energy-dependent neutron continuity equations can be chosen much wider (a factor of 30 larger) than in the direct numerical integration methods since the analytical f1ux shape is used to account for fine structure effects. The BGIM solution is made highly efficient through the use of these broad groups. It is estimated that for a 10 step unit cell fuel cycle depletion calculation, the computer running time for a production code such as EPRI-LEOPARD would be increased by only 6% through the use of the more accurate and intricate BGIM method in the lower resonance energy region. A comprehensive numerical verification of the proposed method is performed. Numerous comparisons are made to VIM for an infinite repeating lattice. These comparisons consider isotopic changes caused by burnup and enrichment variations, cold and hot temperatures in fuel and moderator, and lattice geometry variations. These results show the "Broad Group Integral Method" (BGIM) to be an efficient and accurate solution of the Energy dependent integral Boltzmann transport equation in the resolved resonance energy region. / Ph. D.

The purpose of this thesis is to examine the accuracy of the RAPID (Real-Time Analysis for Particle Transport and In-situ Detection) eigenvalue algorithm based on a few problems from the ICSBEP (International Criticality Safety Benchmark Evaluation Project) Handbook. RAPID is developed based on the MRT (Multi-Stage Response-Function Transport) methodology and it uses the fission matrix (FM) method for performing eigenvalue calculations. RAPID has already been benchmarked based on several real-world problems including spent fuel pools and casks, and reactor cores. This thesis examines the accuracy of the RAPID eigenvalue algorithm for modeling the physics of problems with unique geometric configurations. Four problems were selected from the ICSBEP Handbook; these problems differ by their unique configurations which can effectively examine the capability of the RAPID code system. For each problem, a reference Serpent Monte Carlo calculation has been performed. Using the same Serpent model in the pRAPID (pre- and post-processing for RAPID) utility code, a series of fixed-source Serpent calculations are performed to determine spatially-dependent FM coefficients. RAPID calculations are performed using these FM coefficients to obtain the axially-dependent, pin-wise fission density distribution and system eigenvalue for each problem. It is demonstrated that the eigenvalues calculated by RAPID and Serpent agree with the experimental data within the given experimental uncertainty. Further, the detailed 3-D pin-wise fission density distribution obtained by RAPID agrees with the reference prediction by Serpent which itself has converged to less than 1% weighted uncertainty. While achieving accurate results, RAPID calculations are significantly faster than the reference Serpent calculations, with a calculation time speed-up of between 4x and 34x demonstrated in this thesis. In addition to examining the accuracy of the RAPID algorithm, this thesis provides useful information on the use of the FM method for simulation of nuclear systems. / Master of Science / In the modeling and simulation of nuclear systems, two parameters are of key importance: the system eigenvalue and the fission distribution. The system eigenvalue, known as kef f , is the ratio of neutron production from fission in the current neutron generation compared with the absorption and leakage of neutrons from the system in the previous neutron generation. When this ratio is equal to one, the system is critical and is a self-sustaining chain reaction. Knowledge of the fission distribution is important in the nuclear power industry, as it enables engineers to determine the best reactor core assembly configuration to maintain an even power distribution. Several methods have been developed over the years to effectively solve for a nuclear systems fission distribution and system eigenvalue. Aspects of both Monte Carlo and deterministic transport methods have been combined into RAPID’s MRT methodology. It is capable of accurately determining the system eigenvalue and fission distribution in real time. This thesis examines the accuracy of the RAPID algorithm using four unique problems from the ICSBEP handbook. These problems help us to test the limits of the FM method in RAPID through the modeling of small, unique geometric configurations not seen in large, uniformly configured power reactor cores and spent fuel pools. For comparison, each problem is modeled using the Serpent Monte Carlo code, an accurate code meant to serve as the industry standard for determination of the fission distribution of each problem. This model is then used to generate a set of FM coefficients for use in RAPID calculations. It is demonstrated that the eigenvalues calculated by RAPID and Serpent agree with the experimental data within the given experimental uncertainty. The fission distribution obtained by RAPID is also in agreement with the Serpent reference model. Finally, the RAPID eigenvalue calculation is significantly faster than the corresponding Serpent reference model, with speed-ups ranging from 4x to 34x demonstrated.

A novel collision source method has been developed to solve the Linear Boltzmann Equation (LBE) more efficiently by adaptation of the angular quadrature order. The angular adaptation method is unique in that the flux from each scattering source iteration is obtained, with potentially a different quadrature order used for each. Traditionally, the flux from every iteration is combined, with the same quadrature applied to the combined flux. Since the scattering process tends to distribute the radiation more evenly over angles (i.e., make it more isotropic), the quadrature requirements generally decrease with each iteration. This method allows for an optimal use of processing power, by using a high order quadrature for the first few iterations that need it, before shifting to lower order quadratures for the remaining iterations. This is essentially an extension of the first collision source method, and is referred to as the adaptive collision source (ACS) method. The ACS methodology has been implemented in the 3-D, parallel, multigroup discrete ordinates code TITAN. This code was tested on a variety of test problems including fixed-source and eigenvalue problems. The ACS implementation in TITAN has shown a reduction in computation time by a factor of 1.5-4 on the fixed-source test problems, for the same desired level of accuracy, as compared to the standard TITAN code. / Ph. D.