We study a proposed statistical explanation for the Bekenstein-Hawking entropy of a black hole in which entropy arises quantum-mechanically as a result of entanglement. Arguments for the identification of black hole entropy with entanglement entropy are reviewed in the framework of quantum field theory, emphasizing the role of renormalization and the need for a physical short-distance cutoff. Our main novel contribution is a calculation of entanglement entropy in loop quantum gravity. The kinematical Hilbert space and spin network states are introduced, and the entanglement entropy of these states is calculated using methods from quantum information theory. The entanglement entropy is compared with the density of states previously computed for isolated horizons in loop quantum gravity, and the two are found to agree up to a topological term. We investigate a conjecture due to Sorkin that the entanglement entropy must be a monotonically increasing function of time under the assumption of causality. For a system described by a finite-dimensional Hilbert space, the conjecture is found to be trivial, and for a system described by an infinite-dimensional Hilbert space a counterexample is provided. For quantum states with Euclidean symmetry, the area scaling of the entanglement entropy is shown to be equivalent to the strong additivity condition on the entropy. The strong additivity condition is naturally interpreted in information-theoretic terms as a continuous analog of the Markov property for a classical random variable. We explicitly construct states of a quantum field theory on the one-dimensional real line in which the area law is exactly satisfied.

There is now ample evidence to support the notion that a lack of oxygen (hypoxia) within the tumour adversely affects the outcome of radiotherapy and whether a patient is able to remain disease free. Thus, there is increasing interest in accurately determining oxygen concentration levels within a tumour. Hypoxic regions arise naturally in cancerous tumours because of their abnormal vasculature and it is believed that oxygen is necessary in order for radiation to be effective in killing cancer cells. One method of measuring oxygen concentration within a tumour is the Eppendorf polarographic needle electrode; a method that is favored by many clinical researchers because it is the only device that is inserted directly into the tumour, and reports its findings in terms of oxygen partial pressure (PO2). Unfortunately, there are often anomalous readings in the Eppendorf measurements (negative and extremely high values) and there is little consensus as to how best to interpret the data. In this thesis, Bayesian methods are applied to estimate two measures commonly used to quantify oxygen content within a tumour in the current literature: the median PO2, and Hypoxic Proportion (HP5), the percentage of readings less than 5mmHg. The results will show that Bayesian methods of parameter estimation are able to reproduce the standard estimate for HP5 while providing an additional piece of information, the error bar, that quantifies how uncertain we believe our estimate to be. Furthermore, using the principle of Maximum Entropy, we will estimate the true median PO2 of the distribution instead of simply relying on the sample median, a value which may or may not be an accurate indication of the actual median PO2 inside the tumour. The advantage of the Bayesian method is that it takes advantage of probability theory and presents its results in the form of probability density functions. These probability density functions provide us with more information about the desired quantity than the single number that is produced in the current literature and allows us to make more accurate and informative statements about the measure of hypoxia that we are trying to estimate.

The detection for phase locking in a forced oscillator with dual attractors and ill-defined phase structure is hard until a quantitative approach was constructed for detecting phase locking via stroboscopic method. We study the route to weak phase locking in a chaotic system ¡§Chua oscillator¡¨ with complex attractor structure by analyzing the stroboscopic points. The onset of weak phase locking detected by using this statistical approach and the critical coupling strength calculated by conditional Lyapunov exponent are matched well. Detailed structure of phase locking intensity is described by the Arnold tongue diagram. Moreover, we apply this approach on three hyper-chaotic systems with multi-scroll attractor, including hyper-chaotic Rössler system, hyper-chaotic Lorenz system, and modified MCK oscillator. The weak phase locking between hyper-chaotic system and a periodic or a chaotic driving force is observable following the condition of stroboscopic point concentration.

We investigate the genericity of measure-preserving actions of the free group Fn, on possibly countably infinitely many generators, acting on a standard probability space. Specifically, we endow the space of all measure-preserving actions of Fn acting on a standard probability space with the weak topology and explore what properties may be verified on a comeager set in this topology. In this setting we show an analog of the classical Rokhlin Lemma. From this result we conclude that every action of Fn may be approximated by actions which factor through a finite group. Using this finite approximation we show the actions of Fn, which are rigid and hence fail to be mixing, are generic. Combined with a recent result of Kerr and Li, we obtain that a generic action of Fn is weak mixing but not mixing. We also show a generic action of Fn has sigma-entropy at most zero. With some additional work, we show the finite approximation result may be used to that show for any action of Fn, the crossed product embeds into the tracial ultraproduct of the hyperfinite II1 factor. We conclude by showing the finite approximation result may be transferred to a subspace of the space of all topological actions of Fn on the Cantor set. Within this class, we show the set of actions with sigma-entropy at most zero is generic.

Materials like asphalt, asphalt concrete and polyimides that are used in the transportation and aerospace industry show viscoelastic behavior. These materials in the working environment are subject to degradation due to temperature, diffusion of moisture and chemical reactions (for instance, oxidation) and there is need for a good understanding of the various degradation mechanisms. This work focuses on: 1) some topics related to development of viscoelastic fluid models that can be used to predict the response of materials like asphalt, asphalt concrete, and other geomaterials, and 2) developing a framework to model degradation due to the various mechanisms (such as temperature, diffusion of moisture and oxidation) on polyimides that show nonlinear viscoelastic solid-like response. Such a framework can be extended to model similar degradation phenomena in the area of asphalt mechanics and biomechanics. The thermodynamic framework that is used in this work is based on the notion that the 'natural configuration' of a body evolves as the body undergoes a process and the evolution is determined by maximizing the rate of entropy production. The Burgers' fluid model is known to predict the non-linear viscoelastic fluid-like response of asphalt, asphalt concrete and other geomaterials. We first show that different choices for the manner in which the body stores energy and dissipates energy and satisfies the requirement of maximization of the rate of entropy production that leads to many three dimensional models. All of these models, in one dimension, reduce to the model proposed by Burgers. A thermodynamic framework to develop rate-type models for viscoelastic fluids which do not possess instantaneous elasticity (certain types of asphalt show such a behavior) is developed next. To illustrate the capabilities of such models we make a specific choice for the specific Helmholtz potential and the rate of dissipation and consider the creep and stress relaxation response associated with the model. We then study the effect of degradation and healing due to the diffusion of a fluid on the response of a solid which prior to the diffusion can be described by the generalized neo-Hookean model. We show that a generalized neo-Hookean solid - which behaves like an elastic body (i.e., it does not produce entropy) within a purely mechanical context - creeps and stress relaxes when infused with a fluid and behaves like a body whose material properties are time dependent. A framework is then developed to predict the viscoelastic response of polyimide resins under different temperature conditions. The developed framework is further extended to model the phenomena of swelling due to diffusion of a fluid through a viscoelastic solid using the theory of mixtures. Finally, degradation due to oxidation is incorporated into such a framework by introducing a variable that represents the extent of oxidation. The data from the resulting models are shown to be in good agreement with the experiments for polyimide resins.

<p>The arrival of microarray technology has produced a lot of expression profiles of genes. The amount of data now available is so huge that new alternate and efficient methods are needed to analyse it. One of the approaches that have been taken is the use of reverse engineering to build up a picture of how the genes are interacting, where one of the obstacles is the amount of calculations needed. Liang et al. (1998) introduced an algorithm called REVEAL, where reverse engineering with entropy and mutual information are used in an attempt to generate the rules of regulation in genetic networks.</p><p>In this dissertation it was investigated if it was possible to compliment the REVEAL algorithm with heuristics. The heuristic approach probed consists of setting a threshold on mutual information values, thereby dismissing combinations of input genes producing values below the threshold value as being non-relevant.</p><p>Four experiments were performed, where each consisted of a different combination of rule complexity, size of network and number of inputs per gene tested.</p><p>The findings of this study are that applying a threshold on mutual information is a realistic option that can reduce the number of calculations and also act as a filter that divides the important information from the irrelevant information. However this method has its limitations; since it is not known in advance where to place the threshold it will always be a chance that true connections fall below the threshold and therefore will be disregarded and not further analysed.</p>

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 (M.S. in Software Engineering)--Naval Postgraduate School, June 2003. / Thesis advisor(s): Mantak Shing, Christopher D. Miles. Includes bibliographical references (p. 69-70). Also available online.

The standard material by which all materials exhibiting magnetocaloric effect are measured is Gadnolinium. In this work we are attempting to understand how nanostructuring can impact the magnetocaloric effect, to this end we have grown Gd in various thin film structures. The samples made were grown via magnetron sputtering on MgO(100) substrates. Samples of thick Gd (2000 A) were grown and sandwiched between two layers of Cr or W and annealed at increasing temperatures to study how this can perturb the magnetic and structural properties of the Gd. Another set of samples was grown in which Gd (at various thicknesses) is in a multilayer system with W. Here the purpose is to explore how changing the thickness of the Gd can change its magnetic properties. Using the appropriate Maxwell relation, the magnetic entropy change was observed to increase with increasing annealing temperature. In a 0-4T magnetic field change, the peak entropy was found to go from approximately 1.5 J/kg-K for the unannealed sample to 4.4 J/kg-K when annealed to 600°C. The multilayers were found to all have a T C near 280 K, in contrast with what is predicted by finite size scaling. This is likely due to pinholes in the W layers allowing the Gd to act as one magnetic material.

Nuclear fuel cycles (NFC) are the collection of interconnected processes which generate electricity through nuclear power. Due to the high degree of coupling between components even in the simplest cycles, the need for a dynamic fuel cycle simulator and analysis framework arises. The work presented herein develops essential physics models of nuclear power reactors and incorporate them into a NFC simulation framework. First, a one-energy group reactor model is demonstrated. This essential physics model is then to simulate a sampling fuel cycles which are perturbations of well known base-case cycles. Because the NFC may now be simulated quickly, stochastically modeling many fuel cycle realizations dramatically expands the parameter space which may be analyzed. Finally, a multigroup reactor model which incorporates spectral changes as a function of burnup is presented to increase the fidelity of the original one-group reactor. These methods form a suite of modeling technologies which reach from the lowest levels (individual components) to the highest (inter-cycle comparisons). Prior to the development of this model suite, such broad-ranging analysis had been unrealistic to perform. The work here thus presents a new, multi-scale approach to fuel cycle system design. / text