Dissertation (Ph.D.) -- Worcester Polytechnic Institute. / Keywords: Activated carbons; Hydrogen cyanide; Methyl ethyl ketone; Adsorption; Mercury; Monte-Carlo; Solvents; Molecular simulations; Zeolites; Water; Methanol; Nanopores. Includes bibliographical references (leaves 147-150).

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by Lee Siu-keung. / Parallel title in Chinese. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 162-164). / Chapter Chapter 1 --- Introduction --- p.5 / Chapter Chapter 2 --- Path Integrals / Chapter 2.1 --- Path´ؤIntegral Approach to Quantum Mechanics --- p.8 / Chapter 2.2 --- Path´ؤIntegral Approach to Statistical Mechanics --- p.14 / Chapter 2.3 --- Variational Principle --- p.18 / Chapter 2.4 --- "Variational Method Proposed by Giachetti and Tognetti, and by Feynman and Kleinert" / Chapter 2.4.1 --- Effective Classical Partition Function --- p.24 / Chapter 2.4.2 --- Particle Distribution Function From Effective Classical Potential --- p.34 / Chapter Chapter 3 --- Systematic Perturbation Corrections to the Variational Approximation Proposed in Section2.4 / Chapter 3.1 --- Formalism / Chapter 3.1.1 --- Free Energy --- p.38 / Chapter 3.1.2 --- Particle Distribution Function --- p.49 / Chapter 3.2 --- Second Order Correction to Free Energy --- p.53 / Chapter 3.3 --- First Order Correction to Particle Distribution Function --- p.60 / Chapter Chapter 4 --- Examples and Results / Chapter 4.1 --- Quartic Anharmonic Oscillator / Chapter 4.1.1 --- "Free Energy, Internal Energy and Specific Heat" --- p.69 / Chapter 4.1.2 --- Particle Distribution Function --- p.87 / Chapter 4.2 --- Symmetric Double-well Potential / Chapter 4.2.1 --- "Free Energy, Internal Energy and Specific Heat" --- p.88 / Chapter 4.2.2 --- Particle Distribution Function --- p.106 / Chapter 4.3 --- Quartic-cubic Anharmonic Potential / Chapter 4.3.1 --- Free Energy --- p.108 / Chapter 4.3.2 --- Particle Distribution Function --- p.115 / Chapter Chapter 5 --- Application to the One-dimensional Ginzburg-Landau Model / Chapter 5.1 --- Introduction --- p.120 / Chapter 5.2 --- Exact Partition Function and Free Energy Per Unit Length --- p.123 / Chapter 5.3 --- Zeroth Order Approximation to Free Energy Per Unit Length --- p.126 / Chapter 5.4 --- Exact Specific Heat --- p.133 / Chapter 5.5 --- Zeroth Order Approximation to Specific Heat --- p.139 / Chapter Chapter 6 --- Conclusion --- p.141 / Chapter Appendix I --- Functional Calculus - Differentiation --- p.145 / Chapter Appendix II --- Evaluation of Feynman Propagator Δf(τ) --- p.147 / Chapter Appendix III --- Vanishing of the First Order Correction-βf1 --- p.150 / Chapter Appendix IV --- Numerical Method for the Energy Eigenvalues and Eigenfunctions of the One-dimensional Schroedinger Equation with ax2 + bx4 Potential --- p.153 / Chapter Appendix V --- Numerical Integrations with imaginary Ω --- p.158 / References --- p.162 / Figures --- p.165

Statistical Mechanics describes the macroscopic behavior of a system through the analysis of its microscopic components. It is therefore a framework to move from a probabilistic, high-dimensional description of a system to its macroscopic description through averaging. This approach, now one of the pillars of physics, has seen successes in other fields, such as statistics or mathematical finance. This broadening of the applications of statistical physics has opened new avenues of research in the field itself. Ideas from information theory, differential geometry, and approximate computation are making their way into modern statistical physics. The research presented in this dissertation straddles this boundary: we start by showing how concepts from statistical physics can be applied to statistical learning, then show how modern statistical physics can provide insights into molecular transport phenomena. The first three chapters focus on building an understanding of statistical learning as a thermodynamic relaxation process in a high-dimensional space: in the same way that a statistical mechanical system is composed of a large number of particles relaxing to their equilibrium distribution, a statistical learning system is a parametric function whose optimal parameters minimize an empirical loss. We present this process as a trajectory in a high-dimensional probability Riemannian manifold, and show how this conceptual framework can lead to practical improvements in learning algorithms for large scale neural networks. The second part of this thesis focuses on two applications of modern statistical mechanics to molecular transport. First, I propose a statistical mechanical interpretation of metabolon formation through cross-diffusion, a generalization of the reaction-diffusion framework to multiple reacting species with non-diagonal terms in the diffusion matrix. These theoretical results are validated by experimental results obtained using a microfluidic system. Second, I demonstrate how fluctuation analysis in motility assays can allow us to infer nanoscale properties from microscale measurements. I accomplish this using computational Langevin dynamics simulations and show how this setup can be used to simplify the testing of theoretical non-equilibrium statistical mechanics hypotheses.

As teorias existentes para o estudo do fenômeno de envelhecimento biológico são divididas basicamente em duas categorias: teorias bioquímicas e teorias evolucionárias. As teorias bioquímicas associam o envelhecimento a danos que podem ocorrer nas células, tecidos, órgãos e às imperfeições dos mecanismos bioquímicos responsáveis pela manutenção da vida. As teorias evolucionárias, por sua vez, explicam o envelhecimento sem recorrerem a mecanismos bioquímicos específicos. Elas são de natureza hipotético-dedutiva associando o envelhecimento ao resultado de uma história de vida, ajustada pelo processo de seleção natural que garante a perpetuação de uma espécie. Por apresentar estas características, as teorias evolucionárias são mais adequadas à utilização dos métodos da Física. Todo nosso trabalho será desenvolvido à luz destas teorias. Na primeira parte deste trabalho fazemos uma rápida discussão acerca das dificuldades em se determinar com rigor, propriedades biológicas que possam ser usadas com eficiência no processo de quantificação do envelhecimento. Mostramos que uma das formas mais eficientes para a detecção do envelhecimento é por meio da análise das taxas de mortalidade, realizadas com a ajuda de tabelas atuarias. Estas tabelas apontam para a existência de uma lei de mortalidade, responsável por padrões específicos de mortalidade, em população nas quais se observa o envelhecimento. Expomos as hipóteses centrais sobre as quais se baseiam tanto as teorias bioquímicas quanto as teorias evolucionárias e, ainda, os mecanismos de envelhecimento utilizados por estas duas teorias. Propomos um modelo para populações estruturadas por idade contendo os principais ingredientes das teorias evolucionárias de envelhecimento a saber, mutações benéficas e deletérias, hereditariedade, taxas reprodutivas e seleção natural. Encontramos uma solução exata para este modelo e mostramos que o mesmo não apresenta envelhecimento. Calculamos as probabilidades de sobrevivência médias e o expoente de crescimento Malthusiano cujos resultados indicam que o modelo pode exibir extinção populacional. Acreditamos que este modelo possa ser aplicado no estudo de população de protozoários e celenterados. Por meio de um formalismo matricial, encontramos uma solução exata para a evolução temporal do modelo de Partridge e Barton na presença do vínculo pleiotrópico, mutações somáticas e fecundidades arbritárias. São determinados valores de estado estacionário para as probabilidades de sobrevivência médias e para o expoente de crescimento Malthusiano. A idade média da população também é calculada e exibe um decaimento tipo lei de potências. Por último estudamos o modelo de envelhecimento proposto por Heumann e Hötzel. Por meio de pequenas modificações neste modelo, mostramos, que ao contrário do que se acreditava, ele é capaz de sustentar populações com mais de três idades. Além disso, nossas simulações mostram que este modelo apresenta uma grande quantidade de resultados interessantes, tais como, senescência catastrófica, lei de mortalidade de Grompertz e a influência que diferentes estratégias reprodutivas têm sobre a longevidade da população. / There are two kinds of aging theories: biochemical and evolutionary. Biochemical theories invoke damage to cells, tissues, and organs and connect senescence with imperfections of the biochemical processes responsible for the maintenance of life. The evolutionary theories, on the other hand, explain senescence without any especific biochemical mechanisms. Aging evolutionary theories are hypothetico-dedutive and assume that senescence is a consequence of na optimal life history, controlled by natural selection, which guarantees perpetuation of the species. Such characteristics make the evolutionary theories more suited for the application of Physics methods. In our work, we will consider only this kind of theory. In the first part of this thesis, we present a brief discussion on the difficulties to obtain rigorously biological properties which can be efficiently used in the quantificaion of the aging process. One way to measure senescence is through an analysis of the so called table of life. These tables indicate the existence of a mortality Law which is responsible for a specific mortality pattern. We explain the main ideas on which the biochemical and evolutionary theories are based. We propose a simple age-structured population model containing all the relevant features of the evolutionary aging theories: beneficial and deleterious mutations, reproductive rates, and natural selection. An exact solution for this model is found and, to our surprise, it does not exhibit senescence. Average survival probabilities and Malthusian growth exponents are calculated and they indicate that the system may have a mutational meltdown. We believe that this model is a good candidate to appropriately describe some coelenterate and prokaryote groups. In the presence of the pleiotropic constraint and deleterious somatic mutations, the time evolution of the Partridge-Barton model is exactly solved for na arbitrary fecundity using a matricial formalism. The steady state values for the mean survival probabilities and the Malthusian growth exponent are obtained. The mean age of the population shows a Power Law decay. Finally, we study the aging model proposed by Heumann and Hötzel. By introducing a minor change in this model, we show that it is able to keep many age intervals in disagreement with previous ideas. Moreover, our numerical simulations show a plethora of new interesting features, namely catastrophic senescence, the Gompertz Law and the effects that different reproductive strategies may have on life expectancy.

Usando um método proposto por van Hemmen nós computamos a energia livre da versão Curie-Weiss do modelo de Ising antiferromagnético com diluição de sítio na presença de um campo magnético uniforme. A solução apresenta uma correspondência exata entre as termodinâmicas deste modelo de Ising ferromagnético na presença de um campo magnético aleatório. Os diagramas de fase são discutidos e mostra-se a existência de um ponto tricrítico. Apresentamos também uma derivação alternativa dos resultados de van Hemmen a qual permite uma comparação com os métodos usuais de campo médio contidos na literatura. A solução obtida a partir da transformação de Hubbard-Stratorovich permite o cálculo das flutuações do parâmetro de ordem dos respectivos modelos e a constatação de uma equivalência também a este nível, em particular com a igualdade dos expoentes críticas relevantes. / Using a method proposed by van Hemmen we compute the free energy of the Curie-Wiess version of the site-dilute antiferromagnetic Ising model in the presence of a uniform magnetic field. The solution displays an exact thermodynamic correspondence between this model and the Curie-Weiss version of the Ising model in the presence of a random magnetic field. The phase diagrams are discussed and a tricritical point is shown to exist. We present also an alternative derivation of van Hemmens results which allows an easy comparison with the usual mean-field methods used in the literature. The solution obtained via Hubbard-Stratorovich transformation allows the computation of the fluctuations of the order parameter in both models as to display their equivalence with equality of the relevant critical exponents.

Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves [87]-89).

published_or_final_version / Physics / Master / Master of Philosophy