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The subgroup decomposition method (SDM) has recently been developed as an improvement over the consistent generalized energy condensation theory for treatment of the energy variable in deterministic particle transport problems. By explicitly preserving reaction rates of the fine-group energy structure, the SDM directly couples a consistent coarse-group transport calculation with a set of fixed-source "decomposition sweeps" to provide a fine-group flux spectrum. This paper will outline the implementation of the SDM into the three-dimensional, discrete ordinates (SN) deterministic transport code TITAN. The new version of TITAN, TITAN-SDM, is tested using 1-D and 2-D benchmark problems based on the Japanese designed High Temperature Engineering Test Reactor (HTTR). In addition to accuracy, this study examines the efficiency of the SDM algorithm in a 3-D SN transport code. / Master of Science

Yes / The aim of this research is to determine the extent of online and offline acculturation preferences affecting purchase intentions within a minority ethnic community. This study investigates the role of social media as an agent in terms of how it influences acculturation and consumption. It also investigates the moderating role of education level. The findings highlight the significance of investigating language and friendship orientations and subsequent acculturation preferences. Empirical results confirm the impact of language and friendship orientations on enculturation/acculturation, which in turn impact purchase intentions. The results suggest differences among three groups in terms of their education level. The study discusses contribution to theory and provides future research directions, while offering useful practical implications for marketers.

A condensed multigroup formulation is developed which maintains direct consistency with the continuous energy or fine-group structure, exhibiting the accuracy of the detailed energy spectrum within the coarse-group calculation. Two methods are then developed which seek to invert the condensation process turning the standard one-way condensation (from fine-group to coarse-group) into the first step of a two-way iterative process. The first method is based on the previously published Generalized Energy Condensation, which established a framework for obtaining the fine-group flux by preserving the flux energy spectrum in orthogonal energy expansion functions, but did not maintain a consistent coarse-group formulation. It is demonstrated that with a consistent extension of the GEC, a cross section recondensation scheme can be used to correct for the spectral core environment error. A more practical and efficient new method is also developed, termed the "Subgroup Decomposition (SGD) Method," which eliminates the need for expansion functions altogether, and allows the fine-group flux to be decomposed from a consistent coarse-group flux with minimal additional computation or memory requirements. In addition, a new whole-core BWR benchmark problem is generated based on operating reactor parameters in 2D and 3D, and a set of 1D benchmark problems is developed for a BWR, PWR, and VHTR core.

The problem of inferring or reconstructing the material properties (cross sections) of a domain through noninvasive techniques, methods using only input and output at the domain boundary, is attempted using the governing laws of neutron diffusion theory as an optimization constraint. A standard Lagrangian was formed consisting of the objective function and the constraints to satisfy, which was minimized through optimization using a line search method. The chosen line search method was Newton's method with the Armijo algorithm applied for step length control. A Gaussian elimination procedure was applied to form the Schur complement of the system, which resulted in greater computational efficiency. In the one energy group and multi-group models, the limits of parameter reconstruction with respect to maximum reconstruction depth, resolution, and number of experiments were established. The maximum reconstruction depth for one-group absorption cross section or multi-group removal cross section were only approximately 6-7 characteristic lengths deep. After this reconstruction depth limit, features in the center of a domain begin to diminish independent of the number of experiments. When a small domain was considered and size held constant, the maximum reconstruction resolution for one group absorption or multi-group removal cross section is approximately one fourth of a characteristic length. When finer resolution then this is considered, there is simply not enough information to recover that many region's cross sections independent of number of experiments or flux to cross-section mesh refinement. When reconstructing fission cross sections, the one group case is identical to absorption so only the multi-group is considered, then the problem at hand becomes more ill-posed. A corresponding change in fission cross section from a change in boundary flux is much greater then change in removal cross section pushing convergence criteria to its limits. Due to a more ill-posed problem, the maximum reconstruction depth for multi-group fission cross sections is 5 characteristic lengths, which is significantly shorter than the removal limit. To better simulate actual detector readings, random signal noise and biased noise were added to the synthetic measured solutions produced by the forward models. The magnitude of this noise and biased noise is modified and a dependency of the maximum magnitude of this noise versus the size of a domain was established. As expected, the results showed that as a domain becomes larger its reconstruction ability is lowered which worsens upon the addition of noise and biased noise.

In this work, we propose, implement and test two fully automated mesh adaptation methods for 1-D multigroup eigenproblems. The first method is the standard hp-adaptive refinement strategy and the second technique is a goal-oriented hp-adaptive refinement strategy. The hp-strategies deliver optimal guaranteed solutions obtained with exponential convergence rates with respect to the number of unknowns. The goal-oriented method combines the standard hp-adaptation technique with a goal-oriented adaptivity based on the simultaneous solution of an adjoint problem in order to compute quantities of interest, such as reaction rates in a sub-domain or point-wise fluxes or currents. These algorithms are tested for various multigroup 1-D diffusion problems and the numerical results confirm the optimal, exponential convergence rates predicted theoretically.

A hybrid Quasi-diffusion/Monte Carlo Method for solving multigroup criticality problems in slab geometry was investigated. Analog Monte Carlo was used to calculate functionals (Eddington Factors) that were then used in solution of the quasi-diffusion equations. The hybrid method was shown to accurately and precisely predict the k-eigenvalue and fission source distribution for loosely coupled problems with high dominance ratios and significant spatial gradients. The hybrid method was also shown to be computationally more efficient than analog Monte Carlo. / Graduation date: 2012