京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20189号 / 理博第4274号 / 新制||理||1614(附属図書館) / 京都大学大学院理学研究科地球惑星科学専攻 / (主査)准教授 三宅 亮, 教授 平島 崇男, 教授 山 明 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

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Steepest-entropy-ascent quantum thermodynamics (SEAQT) is a mathematical and theoretical framework for intrinsic quantum thermodynamics (IQT), a unified theory of quantum mechanics and thermodynamics. In the theoretical framework, entropy is viewed as a measure of energy load sharing among available energy eigenlevels, and a unique relaxation path of a system from an initial non-equilibrium state to a stable equilibrium is determined from the greatest entropy generation viewpoint. The SEAQT modeling has seen a great development recently. However, the applications have mainly focused on gas phases, where a simple energy eigenstructure (a set of energy eigenlevels) can be constructed from appropriate quantum models by assuming that gas-particles behave independently. The focus of this research is to extend the applicability to solid phases, where interactions between constituent particles play a definitive role in their properties so that an energy eigenstructure becomes quite complicated and intractable from quantum models. To cope with the problem, a highly simplified energy eigenstructure (so-called ``pseudo-eigenstructure") of a condensed matter is constructed using a reduced-order method, where quantum models are replaced by typical solid-state models. The details of the approach are given and the method is applied to make kinetic predictions in various solid-state phenomena: the thermal expansion of silver, the magnetization of iron, and the continuous/discontinuous phase separation and ordering in binary alloys where a pseudo-eigenstructure is constructed using atomic/spin coupled oscillators or a mean-field approximation. In each application, the reliability of the approach is confirmed and the time-evolution processes are tracked from different initial states under varying conditions (including interactions with a heat reservoir and external magnetic field) using the SEAQT equation of motion derived for each specific application. Specifically, the SEAQT framework with a pseudo-eigenstructure successfully predicts: (i) lattice relaxations in any temperature range while accounting explicitly for anharmonic effects, (ii) low-temperature spin relaxations with fundamental descriptions of non-equilibrium temperature and magnetic field strength, and (iii) continuous and discontinuous mechanisms as well as concurrent ordering and phase separation mechanisms during the decomposition of solid-solutions. / Ph. D. / Many engineering materials have physical and chemical properties that change with time. The tendency of materials to change is quantified by the field of thermodynamics. The first and second laws of thermodynamics establish conditions under which a material has no tendency to change; these conditions are called equilibrium states. When a material is not in an equilibrium state, it is able to change spontaneously. Classical thermodynamics reliably identifies whether a material is susceptible to change, but it is incapable of predicting how change will take place or how fast it will occur. These are kinetic questions that fall outside the purview of thermodynamics. A relatively new theoretical treatment developed by Hatsopoulos, Gyftopoulos, Beretta and others over the past forty years extends classical thermodynamics into the kinetic realm. This framework, called steepest-entropy-ascent quantum thermodynamics (SEAQT), combines the tools of thermodynamics with quantum mechanics through a postulated equation of motion. Solving the equation of motion provides a kinetic description of the path a material will take as it changes from a non-equilibrium state to stable equilibrium. To date, the SEAQT framework has been applied primarily to systems of gases. In this dissertation, solid-state models are employed to extend the SEAQT approach to solid materials. The SEAQT framework is used to predict the thermal expansion of silver, the magnetization of iron, and the kinetics of atomic clustering and ordering in binary solid-solutions as a function of time or temperature. The model makes it possible to predict a unique kinetic path from any arbitrary, non-equilibrium, initial state to a stable equilibrium state. In each application, the approach is tested against experimental data. In addition to reproducing the qualitative kinetic trends in the cases considered, the SEAQT framework shows promise for modeling the behavior of materials far from equilibrium.

We investigate the dynamics of a three-state stochastic lattice gas, consisting of holes and two oppositely "charged" species of particles, under the influence of an "electric" field, at zero total charge. Interacting only through an excluded volume constraint, particles can hop to nearest neighbor empty sites, but particle-particle exchange between oppositely charged particles is also allowed on a separate time scale. Controlled by this relative time scale, particle density and drive, the system orders into a charge-segregated state. Using a combination of Monte Carlo simulations and continuum field theory techniques, we study the order of these transitions and map out the steady state phase diagram of the system. On a single sheet of transitions, a line of multicritical points is found, separating the first order and continuous transitions. Furthermore, we study the steady-state structure factors in the disordered phase where homogeneous configurations are stable against small harmonic perturbations. The average structure factors show a discontinuity singularity at the origin which in real space predicts an intricate crossover between power laws of different kinds. We also seek for generic statistical properties of these quantities. The probability distributions of the structure factors are universal asymmetric exponential distributions. This research was supported in part by grants from the National Science Foundation through the Division of Materials Research. / Ph. D.

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Earth and Planetary Sciences. / Bibliography: leaves 124-128. / by James R. Besancon. / Ph.D.

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Lipídios em solução aquosa formam uma variedade de estruturas diferentes que incluem monocamadas de surfactantes na interface água-ar, conhecidas como monocamadas de Langmuir, como também vesículas unilamelares ou plurilamelares no interior da solução. Sob variação de temperatura, estas estruturas apresentam diferentes fases, observadas através de calorimetria ou variação isotérmica de pressão lateral. Entre as fases apresentadas por estas estruturas, as duas mais importantes se diferenciam pela ordem das cadeias lipídicas. Entendemos que do ponto de vista das fases termodinâmicas, simplificado e qualitativo, monocamadas de Langmuir e bicamadas lipídicas constituem o mesmo sistema físico sob vínculos diferentes. Neste trabalho, desenvolvemos um modelo estatístico para o estudo da transição ordem-desordem destes sistemas, que inclui flutuações de densidade, estas ausentes no modelo de Doniach, de 1980, a base para muitos estudos teóricos para transições de fase de sistemas lipídicos. Flutuações de densidade são fundamentais na descrição de vesículas lipídicas carregadas, compostas de surfactante cuja cabeça polar se dissocia em água. O estudo em laboratório das propriedades térmicas e estruturais de membranas artificiais de lipídios carregados _e relativamente recente, e foi desenvolvido em grande parte no Laboratório de Biofísica do IFUSP. Tais membranas apresentam comportamento distinto das membranas neutras, notoriamente influenciado pela concentração de sal na solução. Isto motivou o desenvolvimento de uma segunda versão do modelo, na qual passamos a descrever a cabeça polar do lipídio em termos de um par de cargas opostas, sendo que a camada lipídica foi acoplada ao modelo primitivo restrito na rede, que desempenha o papel da solução salina. O primeiro modelo foi estudado por aproximação de campo médio e por simulações de Monte Carlo, e o segundo modelo foi investigado apenas através de simulações numéricas. O estudo do modelo carregado foi precedido por uma investigação criteriosa das técnicas de simulação de sistemas com interação Coulombiana, resultando no desenvolvimento de uma metodologia adequada a condições de contorno não isotrópicas e com custo computacional reduzido. Os modelos estatísticos propostos por nós levaram a dois resultados importantes. O modelo para camadas lipídicas neutras é, até hoje, o único modelo estatístico que descreve tanto a transição gel-fluido de bicamadas lipídicas, como a transição líquido condensado - líquido expandido\" de monocamadas de Langmuir, além de descrever também a transição líquido expandido gás na interface água-ar. O modelo para camadas lipídicas que se dissociam em água reproduz a variação abrupta na dissociação, concomitante com a transição ordem-desordem, propriedade que permite interpretar estudos experimentais relativos à condutividade das soluções lipídicas correspondentes. / Lipids in aqueous solution form a variety of different structures which include monolayers of surfactants at the water-air interface, known as Langmuir monolayers, as well as unilamellar or plurilamellar vesicles within the solution. Under temperature variation, these structures display different phases, observed through calorimetry or isothermal variation of lateral pressure. Among the phases presented by these structures, the two most important differ in the order of the lipid chains. From the point of view of the thermodynamic phases, our understanding is that Langmuir monolayers and lipid bilayers constitute the same physical system under different constraints. In this work, we develop a statistical model for the order - disorder transition of lipid bilayers which adds density fluctuations to Doniach\'s 1980 model, which has been considered the basis for many theoretical studies for lipid systems phase transitions. Density fluctuations are essential in the description of the properties of charged vesicles in solution, which consist of surfactants whose polar head dissociates in water. The study in the laboratory of thermal and structural properties of artificial charged lipid membranes is relatively new, and was developed largely in the IFUSP Laboratory of Biophysics. Such membranes exhibit distinct behavior if compared to neutral membranes, notoriously influenced by the solution salt concentration. The experimental investigations motivated us to develop a second model, in which we describe the polar headgroups through a pair of opposite charges. The lipid layer is attached to the lattice restricted primitive model, which plays the role of the saline solution. The first model was studied both through a mean-field approximation as well as through Monte Carlo simulations, whereas the second model was investigated only through numerical simulations. The study of the charged model was preceded by a thorough investigation of the simulation techniques for Coulomb interaction systems, leading to the development of a methodology suitable for non isotropic boundary conditions and with reduced computational cost. The statistical models proposed by us led to two important results. To our knowledge, our model for neutral lipid layers is the only statistical model which, aside from describing simultaneously both the gel-fluid transition of lipid bilayers and the condensed liquid - expanded liquid transition of Langmuir monolayers, also describes the gas- expanded liquid transition at the air-water interface. The model for lipid layers that dissociate in water reproduces the abrupt change in dissociation, concomitant with the order-disorder transition, a property that allows us to interpret experimental studies related to conductivity of the corresponding lipid solutions.

Thesis: Ph. D., Massachusetts Institute of Technology. Department of Materials Science and Engineering, 1975. / Vita. / Includes bibliographical references. / The discrepancy between two recent phase diagram determinations of the Fe-Al system is resolved experimentally. Both diagrams are correct, but-one is a metastable coherent phase diagram. The iron-aluminum system possesses a tricritical point where a line of [lambda]- transitions ends at a miscibility gap at about 23 atom percent aluminum and 615°C. Rules of general applicability governing phase separation within the miscibility gap are developed. Application of the rules to the iron-aluminum system results in detailed predictions about the mechanisms of decomposition and their sequences in this system. Electron microscopy is used to study the reactions experimentally and the results are in agreement with theoretical predictions. / by Samuel Miller Allen. / Ph. D.

Thesis (Ph. D.)--University of Oregon, 1999. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 165-166). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9948028.