This thesis presents the results from Monte Carlo calculations on classical vector spins in face-centered-cubic (FCC) lattices. The goal of the study was to understand the effect of interlayer coupling, dilution of magnetic atoms in the lattice, and symmetry-changing strain. Experimental work by T. M. Giebultowicz et al. and J. A. Borchers et al. greatly inspired my work [1, 2]. J. A. Borchers's group studied NiO/CoO superlattices and observed that the magnetic order of CoO persisted above its Neel temperature due to the effect of interlayer coupling with NiO, which has a higher Neel temperature than CoO [1]. Simulating on a model of NiO/CoO bilayer reproduced the experimental results from Borchers et al. [1]. I concluded that exchange pinning on the NiO/CoO interface preserves the magnetic order of CoO above its Neel temperature significantly. Building on this initial result, a ferromagnet/antiferromagnet/ferromagnet (FM/AFM/FM) trilayer model was studied, where the ferromagnetic (FM) layers were antiferromagnetically coupled. First, I calculated the strength of the AF coupling as a function of the number of antiferromagnetic (AFM) spacer monolayers and concluded that the strength of AFM coupling decreases as the number of AFM spacer monolayers increases. Secondly, I added a uniaxial anisotropy to the model and obtained magnetization curves which exhibited hysteresis-like features with an external field and a first order magnetic transition. Lastly, I diluted the AFM spacer layer in the FM/AFM/FM trilayer by replacing magnetic spins with zero spins in the model. The dilution of AFM spacer layer caused fluctuations in the magnetization curves with external field but the strength of AFM coupling decreases as the number of AFM monolayers increases as in the nondiluted cases. The experimental results from T.M. Giebultowicz's group on MnSe/ZnTe superlattices by neutron scattering showed incommensurate helical spin order in MnSe, where MnSe layers were under tensile strain due to a small mismatching in the lattice parameter [2]. In addition, they observed that the pitch of the spin helix increased as the temperature increased [2]. I modeled the MnSe/ ZnTe system with Monte Carlo method and found that the pitch of the spin helix increased with temperature. In fact, the dependence of helix pitch on temperature was present regardless of the thickness of the sample, so I concluded that this pitch increase is not from the weakening of coupling of surface spins / Graduation date: 2013 / Access restricted to the OSU Community at author's request from Jan. 18, 2013 - July 18, 2013

In this paper, the coarse mesh transport method is extended to hexagonal geometry. This stochastic-deterministic hybrid transport method calculates the eigenvalue and explicit pin fission density profile of hexagonal reactor cores. It models the exact detail within complex heterogeneous cores without homogenizing regions or materials, and neither block-level nor core-level asymmetry poses any limitations to the method. It solves eigenvalue problems by first splitting the core into a set of coarse meshes, and then using Monte Carlo methods to create a library of response expansion coefficients, found by expanding the angular current in phase-space distribution using a set of polynomials orthogonal on the angular half-space defined by mesh boundaries. The coarse meshes are coupled by the angular current at their interfaces. A deterministic sweeping procedure is then used to iteratively construct the solution. The method is evaluated using benchmark problems based on a gas-cooled, graphite-moderated high temperature reactor. The method quickly solves problems to any level of detail desired by the user. In this paper, it is used to explicitly calculate the fission density of individual fuel pins and determine the reactivity worth of individual control rods. In every case, results for the core multiplication factor and pin fission density distribution are found within several minutes. Results are highly accurate when compared to direct Monte Carlo reference solutions; errors in the eigenvalue calculations are on the order of 0.02%, and errors in the pin fission density average less than 0.1%.

The seabed is envisaged to meet the increased future demands for minerals from the rapidly growing industrialized societies of the world. Shipboard analysis of cores can significantly reduce the cost and time spent at the exploratory drilling stage by obviating the need to go back to land for analysis. It can further speed the exploration process by enabling a quick modification of the exploration plan based on the results of the shipboard analysis. A ²⁵²Cf-based analyzer utilizing the prompt gamma neutron activation analysis technique has been designed. The analyzer is a spherical iron shell with the source at its center. The seabed core is passed through a hollow composite tube which is positioned a short distance directly below the source and the resulting prompt gamma rays are collimated to a HPGe detector. The rest of the sphere is filled with paraffin. The gamma ray flux at the detector is converted into a count rate by using a semi-empirical detector response function. This count rate data are then used to determine the sensitivity and detection limits for the chosen elements (Mg, Al, Ti, Cr, Mn, Fe, Ni and Cu). Monte Carlo simulations using the Monte Carlo neutron photon coupled transport code, MCNP, were carried out for a parametric study of important variables influencing the design of the analyzer. These parameters included the moderator type, source to sample distance and sample porosity. MCNP was then used to model the analyzer and to generate the neutron flux profiles in the sample and the prompt gamma flux at the detector. Due to the non-availability of the prompt gamma data for most of the elements of economic interest in the ENDF/B-V cross section libraries associated with MCNP, the point kernel photon transport code ISOSHLD-II (modified for high energy gamma rays) was used to generate the gamma flux at the detector for specific elements. The ISOSHLD-II source term was calculated based on known gamma production data (thermal capture only) and the thermal neutron flux in the sample obtained from MCNP computations. The sensitivity and detection limits obtained from the isotopic source based analyzer were compared for the case of aluminum with values reported from reactor facilities. The results obtained indicate that the analyzer designed in this work could prove suitable for the on-line analysis of many elements of economic interest in seabed cores at the 1 weight percent level. / Graduation date: 1992

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.

[Abstract] This thesis is divided into two parts, both containing algorithms for dealing with matrices and matrix groups. Part I is concerned with individual matrices over an arbitrary field. Our algorithms make use of a sequence called the rank profile which is related to the linear dependence relations between the columns of a matrix. First we look at LSP decompositions of matrices as defined by Ibarra et al. in 1982. This decomposition is related to, and a little more general than, the LUP decomposition. The algorithm given by Ibarra et al. to compute an LSP decomposition was only defined for m?n matrices where m ≤ n and is claimed to have the same asymptotic cost as matrix multiplication. We prove that their cost analysis overlooked some aspects of the computation and present a new version of the algorithm which finds both an LSP decomposition and the rank profile of any matrix. The cost of our algorithm is the same as that claimed by Ibarra et al. when m ≤ n and has a similar cost when m > n. One of the steps in the Ibarra et al. algorithm is not completely explicit, so that any one of several choices can be made. Our algorithm is designed so that the particular choice made at this point allows for the simultaneous calculation of the rank profile. Next we study algorithms to find the characteristic polynomial of a square matrix. The current fastest algorithm to find the characteristic polynomial of a square matrix was developed by Keller-Gehrig in 1985. We present a new, simpler version of this algorithm with the same cost which makes the algorithm?s reliance on the rank profile explicit. In Part II we present generalised sifting, a scheme for creating Monte Carlo black box constructive group recognition algorithms. Generalised sifting is designed to facilitate computation in a known group, specifically re-writing arbitrary elements as words or straight-line programs in a standard generating set. It can also be used to create membership tests in black-box groups. Generalised sifting was inspired by the subgroup sifting techniques originally introduced by Sims in 1970 but uses a chain of subsets rather than subgroups. We break the problem down into a sequence of separately analysed and proven steps which sift down into each subset in turn ... All of the algorithms in Parts I and II are given with a theoretical proof and (where appropriate) complexity analysis. The LSP decomposition, characteristic polynomial and generalised sifting algorithms have all been implemented and tested in the computer algebra package GAP.

Thesis (M.S.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on March 19, 2008) Includes bibliographical references.

Thesis (doctoral)--Universität Konstanz, 1988. / Includes bibliographical references (p. 180-187).

Thesis (Ph. D.)--McMaster University (Canada), 1990. / Source: Dissertation Abstracts International, Volume: 52-10, Section: B, page: 5290. Supervisor: M.F. Collins.

Thesis (Ph.D.)--McMaster University (Canada), 1991. / Source: Dissertation Abstracts International, Volume: 53-01, Section: B, page: 0178. Supervisor: John A. Davies.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.