Thesis (Ph.D.)--McMaster University (Canada), 1991. / Source: Dissertation Abstracts International, Volume: 54-02, Section: B, page: 0847.

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Mark G. Raizen. Vita. Includes bibliographical references. Also available from UMI.

No presente trabalho propomos e estudamos um modelo teórico que denominamos Cristal de Wigner Blindado. Assumindo para este sistema uma estrutura ordenada, nos foi possível verificar a ocorrência de uma transição de fase entre as estruturas bcc e fcc, para este modelo em função da densidade e/ou do parâmetro de blindagem. Após esta análise estática nos estendemos aos aspectos dinâmicos. Determinamos os modos normais para estas estruturas obtendo espectros de frequência para diversas blindagem e/ou densidade. Levando o parâmetro de blindagem para o limite zero, recuperamos diversos resultados conhecidos para o Cristal de Wigner. Isto era esperado urna vez que este modelo apenas difere do nosso pela natureza das interações, que neste caso são puramente coulombianas, sem blindagem. Além disto, nos foi possível efetuar comparação com sistemas reais formados por esferas de poliestireno em suspensão aquosa, permitindo-nos concluir que o modelo por nós proposto é aplicável aos mesmos / We present and develop a theoretical model which we designate Screened Wigner Lattice (SWL). In the ordered phase of this system we were able to predict a bcc-fcc transition, by varying the screening parameter and/or the density. After this static analysis we calculated the normal modes of such crystals and got the frequency spectra in function of the screening and/or density. Taking for the screening parameter the limit zero we reproduced several results already known for the Wigner Lattice (WL). This was expected since the only difference between the SWL and WL models consists on the nature of the interaction, some of our theoretical results with experimental data obtained for crystals formed by polystyrene spheres in aqueous suspension. The agreement allows us to conclude that the SWL model applies for such systems

Classical methods of analyzing heat capacity data for the characteristic moments of the frequency distribution are applied to iridium and rhodium. Impurity moments are determined from high and low temperature f values. These moments are combined by modern theory to estimate the magnitude of the host-host to host-impurity force constant ratio. Ratios of the various host moments are also examined.

No description available.

published_or_final_version / abstract / Mechanical Engineering / Doctoral / Doctor of Philosophy

The aim of this work has been to use atomistic computer simulation methods to calculate the thermal conductivity and investigate factors that will modify the behaviour when applied to three different oxide materials: MgO, SiO2 and SrTiO3. These were chosen as they represent distinct classes of materials and are substrates for thermoelectric devices, where one of the primary goals is to tailor the system to reduce the thermal conductivity. Chapter 1 introduces thermoelectric concepts, gives a background of the theory and a review of various important thermoelectric materials. In Chapter 2 an overview of the interatomic interactions is presented along with details on the implementation of these interactions in a simulation of a 3D periodic crystal. Chapter 3 outlines the importance of phonon processes in crystals and several approaches to the calculation of thermal conductivity are presented. MgO results are given in Chapter 4. Both the Green-Kubo and Boltzmann transport equation (BTE) methods of calculating thermal conductivity were used. The effect on thermal conductivity of two different grain boundary systems are then compared and finally extended to MgO nanostructures, thus identifying the role of surfaces and complex nanostructure architectures on thermal conductivity. In Chapter 5 two different materials with the formula unit SiO2 are considered. The two materials are quartz and silicalite which show interesting negative thermal expansion behaviour which may impact upon the thermal transport within the material. Chapter 6 presents results on the promising thermoelectric material STO. Once again the results from both Green-Kubo and BTE calculations are compared. Grain boundaries are also studied and the effect of inter-boundary distance and boundary type on the thermal conductivity is explored. Finally, a nanostructured STO system (assembled nanocubes) with promising thermoelectric applications is studied. Chapter 7 outlines the conclusions made from this work and suggests areas for future study.

This thesis provides a study of different aspects of the mechanical and vibrational properties of disordered and amorphous solids. Resorting to the theoretical framework of non-affine lattice dynamics the attention is focused on the analysis of disordered networks and lattices which serve as tractable model systems for real materials. Firstly, we discuss the static elastic response and the vibrational spectra of defective fcc crystals. The connection to different types of microstructural disorder in the form of bond-depletion and vacancies is described within the context of the inversion symmetry breaking of the local particle configurations. We identify the fluctuations of the local inversion symmetry breaking, which is directly linked to the non-affinity of the disordered solid, as the source of different scalings behaviours of the position of the boson peak. Furthermore, we describe the elastic heterogeneities occurring in a bond-depleted two- dimensional lattice with long-range interactions. The dependence of the concomitant correlations of the local elastic moduli are studied in detail in terms of the interaction range and the degree of disorder. An analytical scaling relation is derived for the radial part of the elastic correlations in the affine limit. Subsequently, we provide an argument for the change of the angular symmetry of the elastic correlation function which was observed in simulations and experiments on glasses and colloids, respectively. Moving to the dynamical behaviour of disordered solids, a framework is developed based on the kernel polynomial method for the approximate computation of the non- affine correlator of displacement fields which is the key requirement to describe the linear viscoelastic response of the system within the quasi-static non-affine formalism. This approach is then extended to the case of multicomponent polymer melts and validated against molecular dynamics simulations at low non-zero temperatures. We also consider the dynamical behaviour of metallic glasses in terms of its shear elasticity and viscosity. A theoretical scheme is suggested which links the repulsive strength of the interatomic potential to the viscoelasticity and fragility in metallic glasses in the quasi-affine limit.

In an attempt to achieve more efficient designs, the technological frontier is pushed further and further. Every year science probes for a better understanding of natural phenomena, discovering new and improved methods to perform the same task more efficiently and with better results. One of the new technologies is the nonlinear analysis of structural systems using inelastic post-buckling member performance. Inelastic post-buckling member performance is defined as the constitutive relationship between axial load and displacement after the ultimate member capacity has been exceeded. A nonlinear analysis is able to predict the failure behavior of a structural system under ultimate loads more accurately than the traditionally used linear elastic analysis. Consequently, designs can be improved and become more efficient, which reduces the realization cost of a project. An improved nonlinear analysis solution algorithm has been developed, that allows the analyst to perform a nonlinear analysis using post-buckling member performances faster than previously possible. Furthermore, the original post-buckling member performance database was expanded using results obtained from physical member compression tests. Based on the experimental results, new post-buckling member performance model curves were developed to be used together with the improved nonlinear solution algorithm. In addition, a program was developed that allows the analyst to perform a valid nonlinear analysis using a finite element program (LIMIT). The program combines a numerical pre-processor, and input and output data evaluation modules based on human expertise together with the LIMIT analysis package. Extensive on-line help facilities together with graphical pre- and post-processors were also integrated into the program. The resulting analysis package essentially combines all of the necessary components required to perform a nonlinear analysis using post-buckling member performances into one complete analysis package.

In the present work, we study wave phenomena in strongly nonlinear lattices. Such lattices are characterized by the absence of classical linear waves. We demonstrate that compactons – strongly localized solitary waves with tails decaying faster than exponential – exist and that they play a major role in the dynamics of the system under consideration. We investigate compactons in different physical setups. One part deals with lattices of dispersively coupled limit cycle oscillators which find various applications in natural sciences such as Josephson junction arrays or coupled Ginzburg-Landau equations. Another part deals with Hamiltonian lattices. Here, a prominent example in which compactons can be found is the granular chain. In the third part, we study systems which are related to the discrete nonlinear Schrödinger equation describing, for example, coupled optical wave-guides or the dynamics of Bose-Einstein condensates in optical lattices. Our investigations are based on a numerical method to solve the traveling wave equation. This results in a quasi-exact solution (up to numerical errors) which is the compacton. Another ansatz which is employed throughout this work is the quasi-continuous approximation where the lattice is described by a continuous medium. Here, compactons are found analytically, but they are defined on a truly compact support. Remarkably, both ways give similar qualitative and quantitative results. Additionally, we study the dynamical properties of compactons by means of numerical simulation of the lattice equations. Especially, we concentrate on their emergence from physically realizable initial conditions as well as on their stability due to collisions. We show that the collisions are not exactly elastic but that a small part of the energy remains at the location of the collision. In finite lattices, this remaining part will then trigger a multiple scattering process resulting in a chaotic state. / In der hier vorliegenden Arbeit werden Wellenphänomene in stark nichtlinearen Gittern untersucht. Diese Gitter zeichnen sich vor allem durch die Abwesenheit von klassischen linearen Wellen aus. Es wird gezeigt, dass Kompaktonen – stark lokalisierte solitäre Wellen, mit Ausläufern welche schneller als exponentiell abfallen – existieren, und dass sie eine entscheidende Rolle in der Dynamik dieser Gitter spielen. Kompaktonen treten in verschiedenen diskreten physikalischen Systemen auf. Ein Teil der Arbeit behandelt dabei Gitter von dispersiv gekoppelten Oszillatoren, welche beispielsweise Anwendung in gekoppelten Josephsonkontakten oder gekoppelten Ginzburg-Landau-Gleichungen finden. Ein weiterer Teil beschäftigt sich mit Hamiltongittern, wobei die granulare Kette das bekannteste Beispiel ist, in dem Kompaktonen beobachtet werden können. Im dritten Teil werden Systeme, welche im Zusammenhang mit der Diskreten Nichtlinearen Schrödingergleichung stehen, studiert. Diese Gleichung beschreibt beispielsweise Arrays von optischen Wellenleitern oder die Dynamik von Bose-Einstein-Kondensaten in optischen Gittern. Das Studium der Kompaktonen basiert hier hauptsächlich auf dem numerischen Lösen der dazugehörigen Wellengleichung. Dies mündet in einer quasi-exakten Lösung, dem Kompakton, welches bis auf numerische Fehler genau bestimmt werden kann. Ein anderer Ansatz, der in dieser Arbeit mehrfach verwendet wird, ist die Approximation des Gitters durch ein kontinuierliches Medium. Die daraus resultierenden Kompaktonen besitzen einen im mathematischen Sinne kompakten Definitionsbereich. Beide Methoden liefern qualitativ und quantitativ gut übereinstimmende Ergebnisse. Zusätzlich werden die dynamischen Eigenschaften von Kompaktonen mit Hilfe von direkten numerischen Simulationen der Gittergleichungen untersucht. Dabei wird ein Hauptaugenmerk auf die Entstehung von Kompaktonen unter physikalisch realisierbaren Anfangsbedingungen und ihre Kollisionen gelegt. Es wird gezeigt, dass die Wechselwirkung nicht exakt elastisch ist, sondern dass ein Teil ihrer Energie an der Position der Kollision verharrt. In endlichen Gittern führt dies zu einem multiplen Streuprozess, welcher in einem chaotischen Zustand endet.