The work presented in this thesis was motivated by the large amount of experimental investigations of the phonons in quasicrystals. The generalized vibrational density of states (GVDOS) was measured for many quasicrystalline phases and in some cases at different temperatures [suck et al (1997), Dugain et al (1997)]. The progress achieved in the structure determination of approximants to some quasicrystals was a legitimate motivation for numerical investigations of lattice dynamics in these structures. Two different types of interatomic interactions were used: the spring model and the ab-initio pair potentials. The investigations explained the shape of some experimentally measured GVDOS (d-AlNiCo, o-Al13Co4 and i-ZnMgY) via the calculation of the partial vibrational densities of states. Both calculated and measured GVDOS of the d-AlNiCo phase showed an intensity excess at low energies relatively to the ideal Debye behaviour. This excess was found to be a consequence of the existence of special modes at theses energies which are called ``quasi-localized modes''. These modes seem to be characteristic of the lattice dynamics in the complex Al-TM structures. To calculate the frequency shift due to the shift of the GVDOS through low energies observed experimentally at high temperatures, a new method based on a Monte-Carlo simulation was developed. It was shown that the quasi-localized modes introduce large frequency shifts at low energies. Finally, the vibrational entropy was also investigated, and it was found that it contributes to the stabilization of the complex structures over the relatively simple structures at high temperatures. / Die Arbeit, die in dieser Dissertation präsentiert wird, wurde durch eine Vielzahl von experimentellen Beobachtungen von Phononen in Quasikristallen motiviert. Die verallgemeinerte vibrationelle Zustandsdichte (GVDOS, generalized vibrational density of states) wurde für viele quasikristalline Phasen gemessen und für einige auch bei verschiedener Temperatur [Suck et al. (1997), Dugain et al. (1997)]. Der Fortschritt, der in der Bestimmung von Näherungen für einige Quasikristalle erreicht wurde war eine legitime Motivation für numerische Untersuchungen der Gitterdynamik auf diesen Strukturen. Es wurden zwei unterschiedliche interatomare Wechselwirkungen verwendet: Das Federmodell und die ab-initio Paar Potentiale. Die Untersuchungen erklärten die Form einiger experimenteller GVDOS-Messungen (d-AlNiCo, o-Al13Co4 und i-ZnMgY) mittels der Berechnung der partiellen vibrationellen Zustandsdichte. Beide, berechnete und gemessene, GVDOS der d-AlNiCo Phase zeigten einen Intensitätsanstieg bei kleinen Energien relativ zum idealen Debye Verhalten. Dieser Anstieg stellte sich als Konsequenz der Existenz von besonderen Moden bei diesen Energien heraus, die quasi-lokalisierte Moden genannt werden. Diese Moden scheinen charakteristisch für die Gitterdynamik in den komplexen Al-TM Strukturen zu sein. Um die experimentell beobachtete Frequenzverschiebung aufgrund der Verschiebung der GVDOS durch niedrige Energien zu berechnen, wurde eine neue, auf Monte-Carlo Simulation beruhende, Methode entwickelt. Es wurde gezeigt, daß die quasi-lokalisierten Moden große Frequenzverschiebungen bei kleinen Energien hervorrufen. Letzt-lich wurde auch die vibrationelle Entropie untersucht und es stellte sich heraus, daß sie bei hohen Temperaturen dazu beiträgt die komplexen Strukturen gegenüber den relativ einfachen zu stabilisieren.

Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Bernd A. Berg, Florida State University, College of Arts and Sciences, Dept. of Physics. Title and description from dissertation home page (viewed June 16, 2004). Includes bibliographical references.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 86-88).

Thesis (Ph. D.)--University of Chicago, Department of Physics, December 2003. / Includes bibliographical references. Also available on the Internet.

Quasicrystal is the term used for a solid that possesses an essentially discrete diffraction pattern without having translational symmetry. Compared to periodic crystals, this difference in structure gives quasicrystals new properties that make them interesting to study -- both from a mathematical and from a physical point of view. In this thesis we review a mathematical description of quasicrystals that aims at generalizing the well-established theory of periodic crystals. We see how this theory can be connected to the cohomology of groups and how we can use this connection to classify quasicrystals. We also review an experimental method, NIXSW (Normal Incidence X-ray Standing Waves), that is ordinarily used for surface structure determination of periodic crystals, and show how it can be used in the study of quasicrystal surfaces. Finally, we define the reduced lattice and show a way to plot lattices in MATLAB. We see that there is a connection between the diffraction pattern and the reduced lattice and we suggest a way to describe this connection.

Laser beams with precisely controlled intensity profiles are essential for many areas. We developed a beam shaping system based on the digital micromirror device (DMD) for ultra-cold atom experiments and other potential applications. The binary DMD pattern was first designed by the error diffusion algorithm based on an accurate measurement of the quasi-Gaussian incident beam from a real-world laser. The DMD pattern was projected to the image plane by a bandwidth-limited 4f telescope that converted this pattern to the grayscale image. The system bandwidth determined the theoretical limit of image precision by the digitization error. In addition, it controlled the spatial shape of the point spread function (PSF) that reflected the tradeoff between image precision and spatial resolution. PSF was used as a non-orthogonal basis set for iterative pattern refinement to seek the best possible system performance. This feedback process, along with stable performance of DMD, the blue-noise spectrum of the error diffusion algorithm, and low-pass filtering, guaranteed high-precision beam shaping performance. This system was used to produce various beam profiles for different spatial frequency spectra. First, we demonstrated high-precision slowly-varying intensity beam profiles with an unprecedented high intensity accuracy. For flattop and linearly-tilted flattop beams, we achieved 0.20-0.34% root-mean-square (RMS) error over the entire measurement region. Second, two-dimensional sinusoidal-flattop beams were used to evaluate image precision versus system bandwidth. System evaluation confirmed that this system was capable of producing any spatial pattern with <3% RMS error for the most system bandwidth. This experiment extended the beam shaping to any system bandwidth and provided a reference to estimate the output image quality based on its spatial spectrum. Later experiment using a Lena-flattop beam profile demonstrated the arbitrary beam profile generation. We implemented this system for applications on the homogenous optical lattice and dynamic optical trap generation. The DMD pattern was optimized by the iterative refinement process at the image feedback arm, and projected through a two-stage imaging system to form the desired beam profile at the working plane. Experiments demonstrated a high-precision beam shaping as well as a fast and dynamic control of the generated beam profile. / text

The dynamics of mesoscopic two-boson systems that model an interacting pair of ultracold alkali atoms in the presence of electromagnetic potentials are considered. The translational degrees of freedom of such a system can be described by a simple reduced atom Hamiltonian. Introducing time modulations in the laser fields causes parametric variations of the Hamiltonian's Floquet eigenvalue spectrum. Broken symmetries cause level repulsion and avoided crossings in this spectrum that are quantum manifestations of the chaos in the underlying classical dynamics of the systems. We investigate the effects of this phenomenon in the coherent control of excitations in these systems. These systems can be coherently excited from their ground states to higher energy states via a Stimulated Raman Adiabatic Passage (STIRAP). The presence of avoided crossings alter the outcome of STIRAP. First, the classical dynamics of such two-boson systems in double wells is described and manifestations of the same to the quantum mechanical system are discussed. Second, the quantum dynamics of coherent control in the manner discussed above is detailed for a select choice(s) of system parameters. Finally, the same chaos-assisted adiabatic passage is demonstrated for optical lattice systems based on experiments on the same done with noninteracting atoms. / text

This dissertation focuses on two areas of garnet porphyroblast crystallization that have until now remained largely uninvestigated: epitaxial nucleation of garnet porphyroblasts and yttrium and rare earth (Y+REE) uptake in metamorphic garnet. The mechanism of epitaxial nucleation is explored as a step towards determining which aspects of interfaces are significant to interfacial energies and nucleation rates. Garnet from the aureole of the Vedrette di Ries tonalite, Eastern Alps, shows a clear case of epitaxial nucleation in which garnet nucleated on biotite with (110)grt / (001)bt with [100]grt / [100]bt. The occurrence is remarkable for the clear genetic relationships revealed by the microstructures and for its preservation of the mica substrate, which allows unambiguous determination of the coincident lattice planes and directions involved in the epitaxy. Not all epitaxial nucleation is conspicuous; to increase the ability to document epitaxial relationships between garnet and micas, I develop and apply a method for determining whether evidence for epitaxial nucleation of garnet is present in porphyroblasts containing an included fabric. Although the magnitude of uncertainties in orientation measurements for garnets from Passo del Sole (Switzerland), the Nevado Filabride Complex (Spain), and Harpswell Neck (USA) preclude definitive identification of epitaxial relationships, the method has potential to become a viable technique for creating an inventory of instances and orientations of epitaxial nucleation with appropriate sample selection. Using lattice-dynamics simulations, I explore the most commonly documented epitaxial relationship, (110)grt / (001)ms. The range of interfacial energies resulting from variations in the intracrystalline layer within garnet at the interface, the initial atomic arrangement at the interface, and the rotational orientation of the garnet structure relative to the muscovite structure shows that the intracrystalline layer within garnet has the greatest effect on interfacial energy. A complete understanding of the role of intergranular diffusion for yttrium and rare-earth-element uptake in porphyroblastic garnet is critical because the complexities of Y+REE zoning in garnets and the mechanisms of Y+REE uptake have implications for petrologic interpretations and garnet-based geochronology. Y+REE distributions in garnets from the Picuris Mountains (USA), Passo del Sole (USA), and the Franciscan Complex (USA) imply diverse origins linked to differing degrees of mobility of these elements through the intergranular medium during garnet growth. / text

Traditional Chinese architecture is one of the major historic building types in Hong Kong. Though the documentation on traditional Chinese building structure and form is extensive, the study on the decorative components is not as abundant. The deficiency is recognized particularly in timber components due to their high vulnerability to weather and fast deterioration under natural condition. Such situation is also observed in the design of traditional Chinese timber lattices in the partition doors and windows, which are regarded as unique artistic components in the traditional Chinese architecture. The objectives of the study are set to re-discover on the design, expression and associated cultural meanings of the traditional Chinese lattices in Hong Kong and its identity in the Lingnan context. Apart from being an artistic expression with high aesthetic value, the design of the lattice patterns and features are also recognized as symbolic means for the manifestation of collective and individual aspirations and beliefs of the people. They carry the hope for fortune, peace and longevity; and the influence of traditional Chinese thinking from Confucian and Taoist can also be traced. In the traditional Lingnan architecture, Hong Kong is closely related to its context, Guangzhou style. However variations in character of the local lattice design can still be found and the identity of Hong Kong is also to be sought. A field survey on the lattice design in the graded historic Chinese architecture in Hong Kong was carried out. As there is little research reference and the sampling is limited, the objective is set to establish a procedure for the collection of data for comparative analysis. By recording the results, finding out the characters and symbolic meanings, the associated intangible cultural significance can be established. The understanding of such intangible substances will be the essence for future conservation and the conserving of authenticity will rest on the inheritance of the intangible rather than the tangible form and material. / published_or_final_version / Conservation / Master / Master of Science in Conservation

Society is increasingly dependent on the correct operation of concurrent and distributed software systems. Examples of such systems include computer networks, operating systems, telephone switches and flight control systems. Model checking is a useful tool for ensuring the correctness of such systems, because it is a fully automatic technique whose use does not require expert knowledge. Additionally, model checking allows for the production of error trails when a violation of a desired property is detected. Error trails are an invaluable debugging aid, because they provide the programmer with the sequence of events that lead to an error. Model checking typically operates by performing an exhaustive exploration of the state space of the program. Exhaustive state space exploration is not practical for industrial use in the verification of concurrent systems because of the well-known phenomenon of state space explosion caused by the exploration of all possible interleavings of concurrent events. However, the exploration of all possible interleavings is not always necessary for verification. In this dissertation, we show that results from lattice theory can be applied to ameliorate state space explosion due to concurrency, and to produce short error trails when an error is detected. We show that many CTL formulae exhibit lattice-theoretic structure that can be exploited to avoid exploring multiple interleavings of a set of concurrent events. We use this structural information to develop efficient model checking techniques for both implicit (partial order) and explicit (interleaving) models of the state space. For formulae that do not exhibit the required structure, we present a technique called predicate filtering, which uses a weaker property with the desired structural characteristics to obtain a reduced state space which can then be exhaustively explored. We also show that lattice theory can be used to obtain a path of shortest length to an error state, thereby producing short error trails that greatly ease the task of debugging. We provide experimental results from a wide range of examples, showing the effectiveness of our techniques at improving the efficiency of verifying and debugging concurrent and distributed systems. Our implementation is based on the popular model checker SPIN, and we compare our performance against the state-of-the-art state space reduction strategies implemented in SPIN. / text