Markov chains are algorithms that can provide critical information from exponentially large sets efficiently through random sampling. These algorithms are ubiquitous across numerous scientific and engineering disciplines, including statistical physics, biology and operations research. In this thesis we solve sampling problems at the interface of theoretical computer science with applied computer science, discrete mathematics, statistical physics, chemistry and economics. A common theme throughout each of these problems is the use of bias. The first problem we study is biased permutations which arise in the context of self-organizing lists. Here we are interested in the mixing time of a Markov chain that performs nearest neighbor transpositions in the non-uniform setting. We are given "positively biased'' probabilities $\{p_{i,j} \geq 1/2 \}$ for all $i < j$ and let $p_{j,i} = 1-p_{i,j}$. In each step, the chain chooses two adjacent elements~$k,$ and~$\ell$ and exchanges their positions with probability $p_{ \ell, k}$. We define two general classes of bias and give the first proofs that the chain is rapidly mixing for both. We also demonstrate that the chain is not always rapidly mixing by constructing an example requiring exponential time to converge to equilibrium. Next we study rectangular dissections of an $n \times n$ lattice region into rectangles of area $n$, where $n=2^k$ for an even integer $k.$ We consider a weighted version of a natural edge flipping Markov chain where, given a parameter $\lambda > 0,$ we would like to generate each rectangular dissection (or dyadic tiling)~$\sigma$ with probability proportional to $\lambda^{|\sigma|},$ where $|\sigma|$ is the total edge length. First we look at the restricted case of dyadic tilings, where each rectangle is required to have the form $R = [s2^{u},(s+1)2^{u}]\times [t2^{v},(t+1)2^{v}],$ where $s, t, u$ and~$v$ are nonnegative integers. Here we show there is a phase transition: when $\lambda < 1,$ the edge-flipping chain mixes in time $O(n^2 \log n)$, and when $\lambda > 1,$ the mixing time is $\exp(\Omega({n^2}))$. The behavior for general rectangular dissections is more subtle, and we show the chain requires exponential time when $\lambda >1$ and when $\lambda <1.$ The last two problems we study arise directly from applications in chemistry and economics. Colloids are binary mixtures of molecules with one type of molecule suspended in another. It is believed that at low density typical configurations will be well-mixed throughout, while at high density they will separate into clusters. We characterize the high and low density phases for a general family of discrete interfering colloid models by showing that they exhibit a "clustering property" at high density and not at low density. The clustering property states that there will be a region that has very high area to perimeter ratio and very high density of one type of molecule. A special case is mixtures of squares and diamonds on $\Z^2$ which correspond to the Ising model at fixed magnetization. Subsequently, we expanded techniques developed in the context of colloids to give a new rigorous underpinning to the Schelling model, which was proposed in 1971 by economist Thomas Schelling to understand the causes of racial segregation. Schelling considered residents of two types, where everyone prefers that the majority of his or her neighbors are of the same type. He showed through simulations that even mild preferences of this type can lead to segregation if residents move whenever they are not happy with their local environments. We generalize the Schelling model to include a broad class of bias functions determining individuals happiness or desire to move. We show that for any influence function in this class, the dynamics will be rapidly mixing and cities will be integrated if the racial bias is sufficiently low. However when the bias is sufficiently high, we show the dynamics take exponential time to mix and a large cluster of one type will form.

Chemical reactions can be understood as transitions from basin to basin on a high dimensional potential energy landscape. Varying temperature only changes the average kinetic energy of the system. While applying voltages or external pressures directly tilts the landscape and drives the reactions in desired directions. In solids at relatively low temperature, where the entropy term is approximately invariant, the reaction spontaneity is determined by the energy difference between the reactant and product basins and the reaction rate can be calculated from the barriers in between. To achieve sufficient accuracy to explain experimental observations we are interested in, density functional theory (DFT) is usually employed to calculate energies. There are two types of reactions I have studied: the first type of reaction only involves a few number of individual atoms, corresponding to traveling in a small volume in the high dimensional configuration space; the other type involves a large amount of atoms moving in a concerted pattern, and the distance traveled in the configuration space is significantly longer. The scopes of these two in the energy landscapes are in different scales and thus proper metrics for distance measurements are required. In the first case, I have mainly studied Li/Na behaviors in the cathode materials of secondary batteries. Here resolving the energy landscape step by step with detailed information is possible and useful. By analyzing the energy landscapes with DFT plus the Hubbard U correction, I have explained several phenomena related to the degradation of lithium-rich layered oxides, rate performance of surface modified LiFePO₄, and capacity of vanadium-based fluorophosphates. Predictions on both thermodynamic and kinetic properties of materials are also made based on the calculation results and some are confirmed by experiments. In the second case, my focus is on solid-solid phase transitions. With a tremendous long reaction pathway, examining every possible atomic step is too expensive. By adopting periodic boundary conditions, a small supercell can represent the main feature of the energy landscape in a coarse grained way, where the connection between phases is easier to explore. After the big picture of a phase transition mechanism learned from this simplified model, details along the reaction pathway, like new phase nucleation and growth, could be resolved by using a larger supercell. In the above treatment, two types of variables, the cell vectors and atomic positions, span a generalized configuration space. Special consideration is required to balance these two to keep consistency under different supercells and avoid biases. A solid-state NEB (SSNEB) and a solid-state dimer (SSD) method are then developed to locate saddle points in the generalized configuration space. With the methodology well justified, we are able to efficiently find possible nucleation mechanisms, for examples the CdSe rock salt to wurtzite and Mo A15 to BCC phase transitions. SSNEB is also applied in studying phases transitions under pressures, including the graphite to diamond, and CaIrO₃ perovskite to post-perovskite transitions. Combined with the adaptive kinetic Monte Carlo (AKMC) algorithm, SSD shows the ability to find new polymorphs of CdSe and the connecting barriers between them. / text

Phase transitions abound in the physical world, from the subatomic length scales of quark condensation to the decoupling forces in the early universe. In the Bose-Einstein condensation phase transition, a gas of trapped bosonic atoms is cooled to a critical temperature. Below this temperature, a macroscopic number of atoms suddenly starts to occupy a single quantum state; these atoms comprise the Bose-Einstein condensate (BEC). The dynamics of the BEC phase transition are the focus of this dissertation and the experiments described here have provided new information on the details of BEC formation. New theoretical developments are proving to be valuable tools for describing BEC phase transition dynamics and interpreting new experimental results. With their amenability to optical manipulation and probing along with the advent of new microscopic theories, BECs provide an important new avenue for gaining insight into the universal dynamics of phase transitions in general.Spontaneous symmetry breaking in the system's order parameter may be one result of cooling through a phase transition. A potential consequence of this is the spontaneous formation of topological defects, which in a BEC appear as vortices. We experimentally observed and characterized the spontaneous formation of vortices during BEC growth. We attribute vortex creation to coherence length limitations during the initial stages of the phase transition. Parallel to these experimental observations, theory collaborators have used the Stochastic Gross-Pitaevski Equation formalism to simulate the growth of a condensate from a thermal cloud. The experimental and theoretical statistical results of the spontaneous formation of vortex cores during the growth of the condensate are in good quantitative agreement with one another, supporting our understanding of the dynamics of the phase transition. We believe that our results are also qualitatively consistent with the Kibble-Zurek mechanism, a universal model for topological defect formation.Ultimately, our understanding of the dynamics of the BEC phase transition may lead to a broader understanding of phase transitions in general, and provide new insight into the development of coherence in numerous systems.

Understanding the behaviour of nuclear materials in extreme conditions is of prime importance for the analysis of the operation limits of nuclear fuels, and prediction of possible nuclear reactor accidents, relevant to the general objectives of nuclear safety research. The main purpose of this thesis is the study of high temperature phase transitions in nuclear materials, with special attention to the candidate fuel materials for the reactors of the 4th Generation. In this framework, material properties need to be investigated at temperatures higher than 2500K, where equilibrium conditions are difficult to obtain. Laser heating combined with fast pyrometer is the method used at the European Institute for Transuranium Elements (JRC - ITU). It is associated to a novel process used to determine phase transitions, based on the detection, via a suited low-power (mW) probe laser, of changes in surface reflectivity that may accompany solid/liquid phase transitions. Fast thermal cycles, from a few ms up to the second, under almost container-free conditions and control atmosphere narrow the problem of vaporisation and sample interactions usually meet with traditional method. This new experimental approach has led to very interesting results. It confirmed earlier research for material systems known to be stable at high temperature (such as U-C) and allowed a refinement of the corresponding phase diagrams. But it was also feasible to apply this method to materials highly reactive, thus original results are presented on PuO2, NpO2, UO2-PuO2 and Pu-C systems.

In this thesis several classes of directed paths are considered as models of linear polymers in a dilute solution. We obtain the generating functions for each model by considering factorization arguments. Information about the polymer behaviour can be extracted from the singularity structure of the associated generating functions. By using modified versions of these models we study the adsorption and localization of polymer molecules, the behaviour of polymers subject to a tensile force, the effects of stiffness, as well as the behaviour of polymers in confined geometries. In each of these situations the resulting generating functions contain at least two physical singularities. We identify the phase transitions in these systems by a changeover in the dominant singularity of the generating function. In the study of localization and polymers subject to a force, we utilize both homopolymer and random copolymer models. For copolymers, the physically relevant properties are obtained by considering a quenched average of the free energy over all possible monomer sequences. This procedure is intractable even for the simplest models. By considering the Morita approximation for several walk models we obtain results which give a bound on the corresponding features of the quenched system. We use a mapping between a simple model of duplex DNA and an adsorbing Motzkin path in order to study the mechanical unzipping of duplex DNA. From this model, we obtain force-temperature diagrams which show re-entrant behaviour of the force. We also develop a simple low temperature theory to describe the behaviour of the force close to T=0 and find that the shape of the force-temperature curve is associated with entropy in the ground state of the system. We consider the effect of stiffness on polymer adsorption and find that the phase transition is second order for all finite stiffness parameters. For systems of polymers in confined geometries, we find that the behaviour of the polymer depends on the distance between the confining surfaces and the associated interactions with each surface. In this problem, there exist regimes where the polymer exerts a force on the surfaces which can be attractive, repulsive or zero.

In this thesis, assuming that higher spatial dimensions existed only during the inflationary prematter phases of the universe, we construct a (1+D)-dimensional (D&gt / 3), nonsingular, homogeneous and isotropic Friedmann model for dimensional reduction. In this model, dimensional reduction occurs in the form of a phase transition that follows from a purely thermodynamical consideration that the universe heats up during the inflationary prematter phases. When the temperature reaches its Planck value Tpl,D, which is taken as the maximum attainable physical temperature, the phase of the universe changes from one prematter era with D space dimensions to another prematter era with ( D-1) space dimensions where T_pl,D is higher. In this way, inflation gets another chance to continue in the lower dimension and the reduction process stops when we reach D=3 ordinary space dimensions. As a specific model, we investigate the evolution of a (1+4)-dimensional universe and see that dimensional reduction occurs when a critical length parameter l_4,3 reaches the Planck length of the lower dimension. Although the predictions of our model for the cosmological parameters are beyond the ranges accepted by recent measurements for closed geometry, for a broad range of initial conditions they are within the acceptable ranges for open geometry

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23728号 / 理博第4818号 / 新制||理||1689(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)教授 北川 宏, 教授 吉村 一良, 教授 竹腰 清乃理 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

xviii, 124 p. : ill. (some col.) / This dissertation discusses three topics on scenarios beyond the Standard Model. Topic one is the effects from a fourth generation of quarks and leptons on electroweak baryogenesis in the early universe. The Standard Model is incapable of electroweak baryogenesis due to an insufficiently strong enough electroweak phase transition (EWPT) as well as insufficient CP violation. We show that the presence of heavy fourth generation fermions solves the first problem but requires additional bosons to be included to stabilize the electroweak vacuum. Introducing supersymmetric partners of the heavy fermions, we find that the EWPT can be made strong enough and new sources of CP violation are present. Topic two relates to the lepton avor problem in supersymmetry. In the Minimal Supersymmetric Standard Model (MSSM), the off-diagonal elements in the slepton mass matrix must be suppressed at the 10-3 level to avoid experimental bounds from lepton avor changing processes. This dissertation shows that an enlarged R-parity can alleviate the lepton avor problem. An analysis of all sensitive parameters was performed in the mass range below 1 TeV, and we find that slepton maximal mixing is possible without violating bounds from the lepton avor changing processes: μ [arrow right] eγ; μ [arrow right] e conversion, and μ [arrow right] 3e. Topic three is the collider phenomenology of quirky dark matter. In this model, quirks are particles that are gauged under the electroweak group, as well as a \dark" color SU (2) group. The hadronization scale of this color group is well below the quirk masses. As a result, the dark color strings never break. Quirk and anti-quirk pairs can be produced at the LHC. Once produced, they immediately form a bound state of high angular momentum. The quirk pair rapidly shed angular momentum by emitting soft radiation before they annihilate into observable signals. This dissertation presents the decay branching ratios of quirkonia where quirks obtain their masses through electroweak symmetry breaking. This dissertation includes previously published and unpublished co-authored material. / Committee in charge: Dr. Davison Soper: Chair; Dr. Graham Kribs: Advisor; Dr. Ray Frey: Member; Dr. Michael Kellman: Outside Member

Submitted by IDALCI CRUVINEL DOS REIS null (idalcireis@yahoo.com.br) on 2016-01-27T19:12:31Z No. of bitstreams: 1 Tese_Idalci Cruvinel dos Reis.pdf: 11534800 bytes, checksum: bebcb1750beb5d5066bead83c37b196a (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-01-28T18:47:45Z (GMT) No. of bitstreams: 1 reis_ic_dr_ilha.pdf: 11534800 bytes, checksum: bebcb1750beb5d5066bead83c37b196a (MD5) / Made available in DSpace on 2016-01-28T18:47:45Z (GMT). No. of bitstreams: 1 reis_ic_dr_ilha.pdf: 11534800 bytes, checksum: bebcb1750beb5d5066bead83c37b196a (MD5) Previous issue date: 2015-12-18 / Fundação de Amparo à Pesquisa do Estado de Goiás (FAPEG) / Neste trabalho, as características estruturais, microestruturais, ferroelétricas e dielétricas de materiais ferroelétricos com estruturas laminares de bismuto (BLSFs), conhecidos como Aurivillius, foram investigadas. Os sistemas objetos de estudo foram compostos bicamadas (SrBi2Nb2O9, SrBi2Ta2O9, BaBi2Nb2O9) e tricamadas (Bi4Ti3O12), onde foi considerada a dopagem do sítio A da estrutura com lantânio (La3+). As propriedades físicas, portanto, foram investigadas considerando a influência do La3+ para várias concentrações. As cerâmicas foram preparadas pelo método de reação de estado sólido com sinterização em temperaturas acima de 1000 °C, para todos os casos. Para o estudo das propriedades estruturais e microestruturais, foram utilizadas as técnicas de difração de raios-x, Espectroscopia Raman, Microscopia Eletrônica de Varredura (MEV) e Espectrometria de Dispersão de Energia (EDS). As propriedades ferroelétricas e dielétricas foram investigadas a partir da dependência da polarização com o campo elétrico e resposta dielétrica com temperatura, respectivamente. Fases puras foram verificadas para todos os sistemas e analisadas com refinamento pelo método de Reitveld. Os resultados apresentaram indícios de alterações nas estruturas das cerâmicas, o que pode ser associado à influência do lantânio na estrutura. Essas alterações foram confirmadas nas medidas de MEV, onde foi possível observar um aumento significativo dos tamanhos médios dos grãos com aumento do dopante para os sistemas bicamadas e uma redução para o sistema tri-camadas. As medidas de Raman identificaram os modos ativos característicos dos sistemas Aurivillius para todos os sistemas estudados, com influência do conteúdo de lantânio na estrutura. As propriedades ferroelétricas foram confirmadas para todos os casos com uma pequena contribuição da condutividade, que pode ser a causa da obtenção de ciclos de histerese aquém da saturação para alguns casos. Em particular, o sistema SrBi2Ta2O9 revelou ciclos bem característicos e definidos, enquanto o sistema BaBi2Nb2O9 mostrou o comportamento esperado para os ferroelétricos relaxores. Picos bem definidos foram observados na resposta dielétrica para todos os casos, observando uma forte influência do conteúdo de dopante nos parâmetros dielétricos. As características da transição de fases revelam comportamentos associados tanto a um ferroelétrico normal quanto ao comportamento típico de relaxores. Este efeito foi discutido detalhadamente para cada caso. É importante destacar que, para todos os casos, baixos valores de perdas dielétricas foram obtidos, muito abaixo dos reportados na literatura para sistemas Aurivillius. Diante destes resultados, os sistemas aqui estudados são fortes candidatos para aplicações tecnológicas. / In this work the structural, microstructural, ferroelectric and dielectric characteristics of ferroelectric materials with bismuth layer structures (BLSFs), known as Aurivillius, were investigated. The studied materials were based on bi-layers (SrBi2Nb2O9, SrBi2Ta2O9, BaBi2Nb2O9) and tri-layer (Bi4Ti3O12) systems, where the lanthanum (La3+) doping in the A-site of the structure has been considered. The physical properties where, therefore, investigated considering the influence of La3+ at various concentrations. The ceramics were prepared by the solid state reaction method for temperatures above 1000 °C for all the cases. For the investigation of the structural and microstructural properties the x-ray diffraction technique, as well as Raman spectroscopy, Scanning Electron Microscopy (SEM) and Energy Dispersive of Spectrometry (EDS) were used. The ferroelectric and dielectric properties were investigated from the electric field dependence of the polarization and dielectric response with temperature, respectively. Pure phases were found for all the systems and analyzed with structural refinement by the Reitveld’s method. The results showed changes in the structure of the ceramics, which can be associated with the influence of the lanthanum content in the structure. These changes were confirmed in the SEM measurements, where a significant increase in average grain size with the increase of the doping content for bi-layer systems, as well as a reduction in average grain size for the tri-layer system, has been observed. The Raman measurements showed the characteristic bands of the Aurivillius systems, with influence of the lanthanum content in the structure, for all the cases. The ferroelectric properties were confirmed in all cases, with a small contribution of the conductivity, which can be the cause for the observation of unsaturated loops in some cases. Particularly, the SrBi2Ta2O9 system showed very well defined hysteresis loops and the BaBi2Nb2O9 system showed the expected behavior for relaxor ferroelectrics. On the other hand, well defined peaks were observed in the dielectric response for all cases, showing a strong influence of the dopant content in the dielectric parameters. The phase transition characteristics revealed behaviors associated with both normal and relaxor ferroelectrics. This effect has been discussed in details for all the cases. Very low values of the dielectric losses were found, when compared to those reported in the literature for typical Aurivillius systems. This result makes the materials studied here promissory systems for practical applications. / FAPEG: 201310267000048

Orientador: Elso Drigo Filho / Banca: Carla Goldman / Banca: José Roberto Ruggiero / Resumo: Neste trabalho foi analisada uma rede unidimensional composta por sistemas massamola com um potencial de Rosen-Morse on site. Esse tipo de rede é usado para estudar propriedades termodinâmicas do DNA, particularmente sua desnaturação térmica. No contexto do presente trabalho, o potencial de Rosen-Morse simula as ligações de hidrogênio entre a dupla fita da molécula. A partir do gráfico do estiramento médio dos pares de base versus temperatura se observou a desnaturação térmica do sistema. Esse resultado mostra que é possível obter transição de fase com um potencial sem uma barreira infinita, porém assimétrico. Outro resultado obtido é a forma da curva, que mostrou uma transição ligeiramente mais abrupta em comparação com a curva de transição feita para o potencial de Morse on site usado no modelo original de Peyrard-Bishop. Esse comportamento é encontrado em modelos que buscam uma melhor aproximação entre o modelo e os resultados experimentais de desnaturação térmica para o DNA / Abstract: In this work, it was analyzed a one-dimensional lattice formed by mass-spring systems with an additional Rosen-Morse potential on site. This kind of lattice is used to study thermodynamic properties of DNA, in particular the thermal denaturation. In the context of this work, the Rosen-Morse potential simulates the hydrogen bounds between the double helix of the DNA. The graphic of the average base pairs stretching in function of temperature gives information about the thermal denaturation of the macromolecule. This result shows that it is possible to obtain phase transition using an asymmetric potential on site without an infinite barrier. The graphic also showed a sharp denaturation in comparison with the transition curve obtained when the Morse potential on site is used in the original Peyrard- Bishop model. This behavior improves the model / Mestre