First, we study a Poisson model a polluted random screen. In this model, the defects on random screen are assumed Poisson-distribution and overlapped. The transmittance effects of overlapping defects are multiplicative. We can compute the autocorrelation function of the screen is obtained by defects' density, radius, and transmittance. Using the autocorrelation function, we then restore the telescope astronomy images. These image signals are generally degraded by their propagation through the random scattering in atmosphere. To restore the images, we estimate the three key parameters by three methods. They are expectation- maximization (EM) method and two Maximum-Entropy (ME) methods according to two different definitions. The restoration are successful and demonstrated in this thesis.

In recent years, series of high-entropy alloy have been well developed with high hardness and high temperature stability. These properties could apply in hard surface welding technology. The previous research showed that Al0.5CoCrCuFeNi based alloy contained excellent abrasive and adhesive wear resistant properties. According to the results of first year project, the post heat treatment is required for Type A (Al0.3CrFe1.5MnNi0.5 ) and B (Al0.5CrFe1.5MnNi0.5) alloys. It is not suitable for the industrial field service in certain repairing application. This research project will modify the Al0.5CrFe1.5MnNi0.5 base high-entropy alloy in the alloy content of Cr and Ni. These new alloy called Type D high entropy alloys include BCC and FCC two phases. We expect BCC part will provide the wear hardness and FCC part could improve the ductility during the wearing stage. The FCC phase may improve the manufacture of welding rods, also. The research contents include, (1) Type D high entropy alloys weld rod evaluation, (2) wear test, (3) microstructure analysis using electron micro-probe

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2010. / Committee Chair: Zhang, Zhuomin; Committee Member: Kumar, Satish; Committee Member: Peterson, G. P. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Static measures such as density and entropy, which are intimately connected to structure, have featured prominently in modern thinking about the dynamics of the liquid state. In this dissertation, we explore the connections between self-diffusivity, density, available space, and excess entropy in two non-trivial problems in liquid state theory, confined and supercooled liquids. We present exact simulation data for the relationship between self-diffusivity and excess entropy for a wide range of simple of simple fluids (i.e. hard-sphere, Lennard-Jones and square-well) confined to pores with a variety of different sizes and fluid-wall interations. Our main finding is that, at a given temperature, self-diffusivity of the confined fluids collapses onto the bulk behavior when plotted versus excess entropy. In other words, the only information required to "predict" the implications of confinement for the single-particle dynamics is the bulk fluid behavior at a given temperature and the excess entropy of the confined fluid. This should prove practically useful given that the bulk behavior is well known for these fluid systems, and the excess entropy of the confined fluids can be readily estimated from classical density functional theory. We also show that the self-diffusivity of the confined fluids approximately collapses onto the data for the corresponding bulk fluid when plotted versus the average packing fraction (which is based on total, rather than center accessible volume). For continuous interaction potentials such as Lennard-Jones, calculation of effective packing fraction requires knowledge of both the number density of the fluid and a temperature-dependent Boltzmann diameter associated with the repulsive part of the interparticle interactions. We suggest a way to calculate this effective diameter, which to a very good approximation, collapse the temperature- and density-dependent data for the self-diffusivity of the bulk Lennard-Jones fluid onto hard-sphere fluid data plotted versus the fluid's effective packing fraction. Finally, we found that the self-diffusivities of several model systems in their supercooled state also scale exponentially not only with the excess entropy, but also with the two-body contribution to the excess entropy obtained from the pair correlation function of the fluid. The latter observation is particularly interesting because it provides direct evidence of a quantitative link between the dynamics and the average structural order of supercooled liquids. Whether such a connection could indeed be discovered is part of a long-standing question in the study of liquids. / text

The goal of this thesis is to provide a unified framework in which to analyze the dynamics of two seemingly unrelated families of one-dimensional dynamical systems, namely the family of quadratic polynomials and continued fractions. We develop a combinatorial calculus to describe the bifurcation set of both families and prove they are isomorphic. As a corollary, we establish a series of results describing the behavior of entropy as a function of the parameter. One of the most important applications is the relation between the topological entropy of quadratic polynomials and the Hausdorff dimension of sets of external rays landing on principal veins of the Mandelbrot set. / Mathematics

Relationships between structure and dynamics have been well studied in molecular fluids, both in computer simulations and in experiments. However, the development of simple structure-dynamics relationships would also be useful in understanding colloidal fluids. Colloidal fluids display differentiated component dynamics, are made of polydisperse particles, have soft interactions and have a separation of length and time scales. In this dissertation work, we have used computer simulations to generalize some structure-dynamics scaling laws, originally formulated for molecular fluids, in a way that successfully accounts for these important aspects of colloidal suspensions. To begin, we examine a two-component mixture of ultrasoft Gaussian-core particles through molecular dynamics simulations. This fluid shows an anomalous dynamic crossover where the larger particles become more diffusive than the smaller particles. However, this dynamic crossover is accompanied by a corresponding structural crossover for a component-specific structural order metric. In the light of this structural order metric, the fluid is non-anomalous with respect to the relationship between static structuring and diffusivity. Next, we show that accounting for the many-component nature of even modestly polydisperse fluids is important for accurately characterizing their structure-dynamics relationships. We demonstrate this for colloids with short-range attractions through new Monte Carlo simulation techniques and through theoretical calculations carried out in the dilute limit. From here, we present a new generalized framework to non-dimensionalize diffusivity so that it will have an approximately one-to-one relationship with excess entropy. This method involves rescaling diffusivity with dilute-limit analyses that can be analytically and systematically executed. We tested this framework through a combination of molecular dynamics simulations, Brownian dynamics simulations and Monte Carlo simulations. The results of the simulations demonstrate that this framework can account for particle size asymmetry, particle additivity, interaction strength and some solvent effects. Finally, we present a new, simple equation that relates non-dimensionalized forms of diffusivity from molecular dynamics and Brownian dynamics simulations. This simple relationship is tested for inverse power law fluids, as well as a suite of ultrasoft fluids that show structural and dynamic anomalies. / text

This dissertation details the development and implementation of novel experimental techniques for cooling neutral atoms. Based on a method first proposed by Maxwell in a nineteenth century thought experiment, these techniques reduce the entropy of an ensemble by allowing unidirectional transmission through a barrier and thus compressing the ensemble without doing work or increasing its temperature. Because of their general nature, these techniques are much more broadly applicable than traditional laser and evaporative cooling methods, with the potential to cool the vast majority of the periodic table and even molecules. An implementation that cools in one dimension is demonstrated for an ensemble of magnetically trapped rubidium atoms which are irreversibly transferred to a gravito-optical trap. Analysis of the experimental results confirms that phase-space is completely compressed in one dimension. The results also indicate that the overall cooling performance is limited only by the dynamics of atoms in the magnetic trap and may be improved with a more ergodic system. Three-dimensional cooling may be accomplished with a modified technique which substitutes a radio-frequency-dressed magnetic trap for the gravito-optical trap. Application of this technique to atomic hydrogen and progress toward building an experimental apparatus are discussed. / text

Symmetrical multilevel diversity coding (SMDC) is a classical model for coding over distributed storage. In this setting, a simple separate encoding strategy known as superposition coding was shown to be optimal in terms of achieving the minimum sum rate and the entire admissible rate region of the problem in the literature. The proofs utilized carefully constructed induction arguments, for which the classical subset entropy inequality of Han played a key role. This thesis includes two parts. In the first part the existing optimality proofs for classical SMDC are revisited, with a focus on their connections to subset entropy inequalities. First, a new sliding-window subset entropy inequality is introduced and then used to establish the optimality of superposition coding for achieving the minimum sum rate under a weaker source-reconstruction requirement. Second, a subset entropy inequality recently proved by Madiman and Tetali is used to develop a new structural understanding to the proof of Yeung and Zhang on the optimality of superposition coding for achieving the entire admissible rate region. Building on the connections between classical SMDC and the subset entropy inequalities developed in the first part, in the second part the optimality of superposition coding is further extended to the cases where there is an additional all-access encoder, an additional secrecy constraint or an encoder hierarchy.

Entropy measures have been widely used to quantify the complexity of theoretical and experimental dynamical systems. In this thesis, two novel entropy measures are developed based on using coarse quantization to classify and compare dynamical features within a time series; quantized dynamical entropy (QDE) and a quantized approximation of sample entropy (QASE). Following this, comprehensive guidelines for the quantification of complexity are presented based on a detailed investigation of the performance characteristics of the two developed measures and three existing measures; permutation entropy, sample entropy and fuzzy entropy. The sensitivity of the considered entropy measures to changes in dynamics was assessed using the case study of characterizing bipedal walking gait dynamics. Based on the analysis conducted, it was found that sample entropy and fuzzy entropy, while computationally inefficient, provide the best overall performance. In instances where computational efficiency is vital, QDE and QASE serve as viable alternatives to existing methods.

Session ID: TH-F3-4 / SCIS & ISIS 2010, Joint 5th International Conference on Soft Computing and Intelligent Systems and 11th International Symposium on Advanced Intelligent Systems. December 8-12, 2010, Okayama Convention Center, Okayama, Japan