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A functional Analytic method which was first introduced by Larsen and Habetler for the one-speed isotropic case in 1973 is applied to full and half-space multigroup problems in one dimension with a constant and invertible transfer matrix. The Case-type eigenfunction expansion formulas for the solutions of these problems are explicitly obtained. For the half-space case, the formulas are expressed in terms of two matrices X and Y which provide the Wiener-Hopf factorization of the dispersion matrix. The method applied yields compact results avoiding the calculation of adjoint solutions and normalization integrals to determine the expansion coefficients. Since the method proves to be amenable to further generalization, the case of a degenerate transfer kernel is also considered along the same lines, yielding the expansion formulas for that problem in the full and half-space cases. The expansion formulas are shown to be valid at least for subcritical media, but an extension to critical problems is expected. / Doctor of Philosophy

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

The fundamental definitions of radiative transfer theory are given and the two-dimensional equation of transfer is derived, density of radiation is defined, and two-dimensional two-intensity transfer model is presented. An operational interpretation of the latter model is given interms of military truck transport supply and the functional dependencies of the terms in the transfer equations are evaluated. For this interpretation the density equations are given and the study state and time dependent solutions of the density equations are discussed in polar coordinates. This work was conducted for the U. S. Army Transportation Research Command, Fort Eustis, Virginia, 1961, Task 9R38-11-009-02. / Master of Science

Transport of muonic hydrogen and deuterium atoms in gaseous hydrogen and deuterium is studied in the diffusion approximation and by means of the multiple collision expansion. The diffusion coefficient is derived. Scattering kernels are computed from the kinematics of an inelastic binary collision. The effect of rotations of the target molecules is treated by defining and computing an effective inelastic energy transfer Q_eff. The Doppler effect is taken into account by averaging the cross sections over the Maxwellian velocity distribution of the target molecules. Numerical results of the time-dependent problem in slab geometry are presented. In part two we construct a candidate for a realistic four generation Calabi-Yau manifold by dividing an algebraic variety in CP₄ x CP₄ with the Z₂ x Z₂ symmetry. A nontrivial embedding of Z₂ x Z₂ in E(6) allows the physically interesting intermediate symmetry, based on Pati-Salam SU(2)_L x SU(2)_R x SU(4)_C group. The group of honest symmetries G_H of the manifold is identified and the transformations properties of quark and lepton fields under G_H are given. / Ph. D.

The Coarse-Mesh Transport Method (COMET) is a method developed by the Computational Reactor and Medical Physics Group at Georgia Tech. Its original application was neutron transport for nuclear reactor modeling. COMET has since been shown to be effective for coupled photon-electron transport calculations where the goal is to determine the energy deposition of a photon beam. So far COMET can simulate a mono-directional, mono-energetic, spatially-flat photon beam. The goal of this thesis will be to extend COMET by adding a generalized source treatment. The new source will be able to simulate beams that vary in intensity as a function of position, angle, and energy. EGSnrc will be used to verify the accuracy of the new method for 3D photon kerma calculations.

Thesis (MScEng)--University of Stellenbosch, 2002 / ENGLISH ABSTRACT: A Representative Unit Cell (RUC) model for flow through two-dimensional porous media is presented and applied to two industrial related problems. The first application is to that of cross-flow in tube banks. Both staggered and square (inline) configurations are investigated and the model results are compared to experimental data. The second application is to flow through a stack in a timber-drying kiln. The RUC model is applied to the anisotropic timber stack ends and the centre part is modelled with a standard duct flow solution. The results of the models applied to a timber stack are compared to experimental data obtained from model tests undertaken in a wind tunnel. The results of the RUC and duct flow models are found to be in excellent agreement with the data of the experimental models. These models may be used to optimize kiln designs. / AFRIKAANSE OPSOMMING: 'n Verteenwoordigende Eenheid Sel (VES) model vir vloei deur twee-dimensionele poreuse media word weergegee en toegepas op twee industriële toepassings. Die eerste toepassing is op dwarsvloei deur banke van buise. Beide gestapelde en inlyn konfigurasies word ondersoek waarvan die model resulte met eksperimentele data vergelyk word. Die tweede toepassing is op vloei deur 'n stapel in 'n hout-droogoond. Die VES model word toegepas op die anisotropiese ente van houtstapels en die middelste seksie word gemodelleer deur 'n standaard kanaalvloei oplossing. Die resultate van die modelle toegepas op n 'houtstapel word vergelyk met eksperimentele data verkry uit model toetse wat in 'n wind-tonnel uitgevoer is. Die VES en kanaalvloei modelle se resultate stem uitstekend ooreen met die data van die eksperimentele modelle. Hierdie modelle kan gebruik word om die ontwerp van droogoonde te optimeer.

A hybrid stochastic-deterministic method, COMET-PE, is developed for dose calculation in radiotherapy. Fast, accurate dose calculation is a key component of successful radiotherapy treatment. To calculate dose, COMET-PE solves the coupled Boltzmann Transport Equations for photons and electrons. The method uses a deterministic iteration to compose response functions that are pre-computed using Monte Carlo. Thus, COMET-PE takes advantage of Monte Carlo physics without incurring the computational costs typically required for statistical convergence. This work extends the method to 3-D problems with realistic source distributions. Additionally, the performance of the deterministic solver is improved, taking advantage of both shared-memory and distributed-memory parallelism to enhance efficiency. To verify the method’s accuracy, it is compared with the DOSXYZnrc (Monte Carlo) method using three different benchmark problems: a heterogeneous slab phantom, a water phantom, and a CT-based lung phantom. For the slab phantom, all errors are less than 1.5% of the maximum dose or less than 3% of local dose. For both the water phantom and the lung phantom, over 97% of voxels receiving greater than 10% of the maximum dose pass a 2% (relative error) / 2 mm (distance-to-agreement) test. Timing comparisons show that COMET-PE is roughly 10-30 times faster than DOSXYZnrc. Thus, the new method provides a fast, accurate alternative to Monte Carlo for dose calculation in radiotherapy treatment planning.

English abstract Hydrothermal systems related to highly evolved granitic magmas host diverse mineralization styles and provide an important source of economic metals. This master thesis concentrates on description and interpretation of geological structure, petrographic and textural variability, alteration zoning and calculation of time-integrated fluid fluxes recorded in highly evolved granites and tin-mineralized greisens of the Horní Blatná massif in the Western Krušné hory pluton. The massif is a composite intrusion, which consists of a large number of intrusive units emplaced during two stages. The first stage is represented by sparsely porphyritic fine-grained low-lithian annite granites that can be correlated with marginal granites (G2) of the Fichtelgebirge (Smrčiny) batholith or with intermediate granites (Walfischkopf type) of the Western Krušné hory (Erzgebirge) pluton. Intrusive batches of the second stage progressively evolve from medium- to coarse-grained serial high-lithian annite and zinnwaldite granites with topaz and rare tourmaline towards aphyric fine-grained zinnwaldite (or trilithionite) granites. This suite corresponds to the EIB2 and EIB3 facies of the younger intrusive complex in the Western Krušné hory (Erzgebirge) pluton and it can be compared to the G3 Waldstein and G4 units in...

Call number: LD2668 .T4 1986 J66 / Master of Science / Chemical Engineering