Rozprawy doktorskie na temat „Geometric Phase Transition”

The theory of thermodynamic phase transitions has played a central role both in theoretical physics and in dynamical systems for several decades. One of its fundamental results is the classification of various physical models into equivalence classes with respect to the scaling behavior of solutions near the critical manifold. From that point of view, systems characterized by the same set of critical exponents are equivalent, regardless of how different the original physical models might be. For non-equilibrium phase transitions, the current theoretical framework is much less developed. In particular, an equivalent classification criterion is not available, thus requiring a specific analysis of each model individually. In this thesis, we propose a potential classification method for time-dependent dynamical systems, namely comparing the possible deformations of the original problem, and identifying dynamical systems which share the same deformation space. The specific model on which this procedure is developed is the Kuramoto model for interacting, disordered oscillators. Studied in the mean-field limit by a variety of methods, its associated synchronization phase transition appears as an appropriate model for cooperative phenomena ranging from coupled Josephson junctions to self-ordering patterns in biological and social systems. We investigate the geometric deformation of the dynamical system into the space of univalent maps of the unit disk, related to the Douady-Earle extension and the Denjoy-Wolff theory, and separately the algebraic deformation into the space of nonlinear sigma models for unitary operators. The results indicate that the Kuramoto model is representative for a large class of non-equilibrium synchronization models, with a rich phase-space diagram.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this thesis, we deal with a particular geometric scalar tensor theory, which is a version of the Brans-Dicke gravitation, formulated in aWeyl integrable space-time. This formulation is done using the Palatini's variation procedure. The main point of our work is to perform two particular applications of the geometrical Brans-Dicke theory. The rst one is the study of geometric fase transition phenomena, that's related to a continuous change in the space-time structure of the universe from a Riemann's geometry to a Weyl's geometry, or in the inverse sense, from Weyl's geometry to Riemann's geometry. This phenomena seems to take place when the universe starts to expand in a accelerated rate. The second one is the investigation of classical and quantum behaviour of a anisotropic n-dimensional universe . To nd solutions that display the dynamical compacti cation of non observed extra dimensions is the main motivation to study such universe.
Nesta tese, reapresentamos uma teoria escalar tensorial geométrica, que é uma versão da gravitação de Brans-Dicke formulada em um espaço-tempo de Weyl integrável. Com esta teoria fazemos duas aplicações especí cas. Uma delas para o estudo de um fenômeno, que chamamos de transição de fase geométrica, uma mudança contínua na estrutura geom étrica do espaço-tempo. Este fenômeno parece ocorrer quando o universo se expande aceleradamente. A segunda aplicação reside no estudo clássico e quântico do comportamento de um modelo de universo n-dimensional anisotrópico. A motivação para esta investigação é a busca de soluções que exibem o compactação dinâmica das dimensões extras, que não são observadas.

Les études et les résultats présentés dans ce manuscrit ont pour but de développer une meilleure compréhension des principes à la base de l'auto-organisation dans les systèmes biologiques. La théorie topologique des transitions de phase est l'un des approches possibles pour fournir une généralisation de la description des transitions de phase dans les systèmes petits ou mésoscopiques. Cette théorie a été rigoureusement enracinée dans deux théorèmes: un contre exemple à l'un de ces théorèmes a été récemment découvert. La première partie de ce manuscrit est donc consacré à mieux comprendre ce «contre-exemple » pour verifier si et comment la théorie peut être sauvé.Dans la deuxieme parte de ce manuscrit les résultats des recherches théoriques, numériques et expérimentales sur la condensation à la Fr "ohlich sont reportés. Ceci est une condition préalable à l'activation des oscillations dipolaires géantes qui entraînent des interactions électrodynamiques à long portée entre les molécules coresonnantes. Dans cette thèse, on montre que les interactions à longue portée affectent sensiblement les propriétés de diffusion des molécules en solution. Une empreinte des interactions à long portée pourrait être un phénomène de «transition» en ce qui concerne le coefficient de diffusion en fonction d'un paramètre de contrôle proportionnel à l’intensité d'interaction. Simulations analogues ont été réalisées afin de valider une approche expérimentale visant à trouver une telle «empreinte» dans les systèmes avec interactions à longue portée
The studies and results reported in this manuscript are aimed to develop a deeper understanding of the principles at the basis of self-organization in biological system.The Topological Theory of phase transitions is one of the possible approaches to provide a generalization of description of phase transitions in small or mesoscopic systems. This theory has been rigorously rooted in two theorems: a counterexample to one of these theorems has been recently found. The first part of this manuscript is devoted to investigation of the "counterexample" to understand if and how the theory can be saved. In the second part of this manuscript the results of theoretical, numerical and experimental investigations on Fr"ohlich-like condensation for normal modes of biomolecules are reported. This is a prerequisite for the activation of giant dipole oscillations in biomolecules which entail long-range electrodynamic interactions between coresonant molecules. In this thesis is shown that long-range interactions markedly affect the self-diffusion properties of molecules in solution. A fingerprint of long-range interactions could be a "transitional" phenomenon concerning the self-diffusion coefficient as a function of a control parameter proportional to interaction strength. Analogous simulations have been performed to validate an experimental approach aimed at finding such "fingerprint" in systems with built-in long-range interactions

Orientador: Patricio Anibal Letelier Sotomayor
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin
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Resumo: São apresentadas soluções numéricas do sistema de equações diferenciais de Tolman-Oppenheimer- Volkov para um gás de partículas em transição de fases, no contexto da relatividade geral, encontrando a estrutura do espaço-tempo associada com a transição de fases. Para isto assumimos que o gás está formado por partículas autogravitantes, idênticas, com simetria esférica, e cujo tensor de energia-momentum é do tipo fluido perfeito. As interações internas do gás são representadas por uma equação de estado capaz de descrever uma transição de fase do tipo gás-Iíquido. Um gás estacionário deste tipo poderia representar uma estrela em equilíbrio hidrodinâmico. Concluímos que a termo dinâmica não perde sentido no contexto da relatividade geral, apresentando claramente que a transição de fases acontece só numa superfície esférica e concêntrica no interior da estrela, na qual a curvatura do espaço-tempo reflete, mais uma vez, o mesmo comportamento que a distribuição interna de matéria na estrela, neste caso, uma descontinuidade na região de coexistência de fases
Abstract: We present numerical solutions for the differencial equations the Tolman-Oppenheimer-Voltov for a gas particles in phase transition in the general relativity background, obtaining the space-time structure involved in the phase transition. For this purpouse, we consider the gas as formed by identical self-gravitating particles with spherical simetry and whose momentum- energy tensor is do like perfect fluid type. The internal interactions of the gas are represented by a state equation that has the property of describing gas-liquid phases transition. A stacionary gas like this is supposed to represent a star in hydrodynamic equilibrium. We conclude that there is no conflict of using thermodynamics in general relativity context, showing cleary that the phase transtition happens only in a spherical shell centered in the star geometrical center, about what the space-time curvature ilustrates, once more, the same behaviour expect by the distribution of matter inside the star, in such case, a descontinuity in the region of phase's coexistence
Mestrado
Física
Mestre em Física

Mott insulator to superfluid phase transitions and unconventional superfluid phases in spin-orbit coupled Bose-Einstein condensate in one dimensional, square and hexagonal optical lattices are investigated using decoupling approximation and variational Gutzwiller wave function. We considered a system with two components. In the first part, we used decoupling approximation along side perturbation to chart the phase diagrams of the system in the absence of spin-orbit coupling. Our results show that the occupation number of the species, interspecies interaction and the ratio of the hopping matrix of the species dictate the critical point and the separation of the insulating phases. Applying decoupling approximation to spin-orbit coupled Bose-Einstein condensate in one dimensional optical we find that spin-orbit coupling reduces the phase boundary of Mott insulator-superfluid transition and also modifies the critical point in a way that the critical point reduces as the coupling strength increases. In the second part, we applied the variational Gutzwiller wave function to spin-orbit coupled Bose-Einstein condensate in square and hexagonal lattice. Our results show that the geometry of the optical lattice plays a role in the transition. We find that the mean-field Mott insulator-superfluid phase transition boundary of hexagonal lattice is smaller than that of square lattice for the same system. Finally, we showed that the Gutzwiller variational approach gives us access to the twisted superfluid phase realized in the system. The nonuniformity of the superfluid phase is different for the two lattices.

The knowledge of physicochemical properties of organic compounds becomes increasingly important. In this study, we developed UPPER (Unified Physical Property Estimation Relationships), a comprehensive model for the estimation of 20 physicochemical properties of organic compounds. UPPER is a system of thermodynamically sound relationships that relate the various phase-transition properties to one another, which includes transition heats, transition entropies, transition temperatures, molar volume, vapor pressure, solubilities and partition coefficients in different solvents and etc. UPPER integrates group contributions with the molecular geometric factors that affect transition entropies. All of the predictions are directly based on molecular structure. As a result, the proposed model provides a simple and accurate prediction of the properties studied. UPPER is designed to predict industrially, environmentally and pharmaceutically relevant physicochemical properties of organic compounds. It also can be an aid for the efficient design and synthesis of compounds with optimal physicochemical properties.

Nous avons étudié, par RPE impulsionnelle, la cohérence quantique et des spins électroniques des ions de transition Mn2+, Co2+, Fe3+, et des complexes Fe3+/Cs+ et Fe3+/Na+, tous présents dans le ZnO monocristallin. Nous avons trouvé que l’anisotropie magnétique peut altérer la cohérence de la phase dynamique des qubits des spins électroniques. Nous avons mesuré une faible décohérence pour les spins d’ions Mn2+et Fe3+ dans ZnO, qui ont tous deux une faible anisotropie magnétique uniaxiale, tandis que les ions Co2+ isolés avec une très forte anisotropie magnétique uniaxiale, une décohérence rapide a été mis en évidence. Nous avons trouvé que les spins électroniques des complexes de type Fe3+/Cs+, ayant un tenseur d’anisotropie magnétique plus complexe que la simple anisotropie uniaxiale des ions Fe3+ isolés, possèdent presque le même temps de décohérence. Par la méthode des perturbations, nous avons mis en évidence théoriquement un terme supplémentaire à la phase habituelle de Berry, dû à l’anisotropie magnétique et qui existe dans tout système ayant un spin S>1/2
We studied by pulsed EPR (p-EPR), the quantum coherence of electronic spins qubits of isolated transition metal ions of Mn2+, Co2+, Fe3+ and Fe3+/Cs+ as well as Fe3+/Na+ complexes, all found as traces in mono-crystalline ZnO. Indeed, we experimentally demonstrated that the magnetic anisotropy can alter the coherence of the dynamic phase of electronic spins qubits. We found a small decoherence for Mn2+ and Fe3+, spins having a small uniaxial magnetic anisotropy, and on the contrary, we found a very strong decoherence for Co2+ spins having a very strong uniaxial magnetic anisotropy. We found that the electronic spins of the Fe3+/Cs+ complex, having a more complex tensor magnetic anisotropy compared to the simplest uniaxial one of isolated Fe3+ spins in ZnO, have almost the same coherence time. By the perturbation method, we have found theoretically an additional term to the usual geometric Berry phase, due to the magnetic anisotropy which exists in any system having a spin S>1/2

This thesis focusses on the properties of, and relationships between, several fundamental objects arising from critical physical models. In particular, we consider Schramm--Loewner evolutions, the Gaussian free field, Liouville quantum gravity and the Brownian continuum random tree. We begin by considering branching diffusions in a bounded domain $D\subset$ $R^{d}$, in which particles are killed upon hitting the boundary $\partial D$. It is known that such a system displays a phase transition in the branching rate: if it exceeds a critical value, the population will no longer become extinct almost surely. We prove that at criticality, under mild assumptions on the branching mechanism and diffusion, the genealogical tree associated with the process will converge to the Brownian CRT. Next, we move on to study Gaussian multiplicative chaos. This is the rigorous framework that allows one to make sense of random measures built from rough Gaussian fields, and again there is a parameter associated with the model in which a phase transition occurs. We prove a uniqueness and convergence result for approximations to these measures at criticality. From this point onwards we restrict our attention to two-dimensional models. First, we give an alternative, ``non-Gaussian" construction of Liouville quantum gravity (a special case of Gaussian multiplicative chaos associated with the 2-dimensional Gaussian free field), that is motivated by the theory of multiplicative cascades. We prove that the Liouville (GMC) measures associated with the Gaussian free field can be approximated using certain sequences of ``local sets" of the field. This is a particularly natural construction as it is both local and conformally invariant. It includes the case of nested CLE$_{4}$, when it is coupled with the GFF as its set of ``level lines". Finally, we consider this level line coupling more closely, now when it is between SLE$_{4}$ and the GFF. We prove that level lines can be defined for the GFF with a wide range of boundary conditions, and are given by SLE$_{4}$-type curves. As a consequence, we extend the definition of SLE$_{4}(\rho)$ to the case of a continuum of force points.

In this thesis we develop a mathematically rigorous framework of the so-called ''classical limit'' of quantum systems and their semi-classical properties. Our methods are based on the theory of strict, also called C*- algebraic deformation quantization. Since this C*-algebraic approach encapsulates both quantum as classical theory in one single framework, it provides, in particular, an excellent setting for studying natural emergent phenomena like spontaneous symmetry breaking (SSB) and phase transitions typically showing up in the classical limit of quantum theories. To this end, several techniques from functional analysis and operator algebras have been exploited and specialised to the context of Schrödinger operators and quantum spin systems. Their semi-classical properties including the possible occurrence of SSB have been investigated and illustrated with various physical models. Furthermore, it has been shown that the application of perturbation theory sheds new light on symmetry breaking in Nature, i.e. in real, hence finite materials. A large number of physically relevant results have been obtained and presented by means of diverse research papers.

Le nombre croissant de nanostructures physiques et biologiques sont caractérisées par l'ordre non-cristallin et par les propriétés physiques et biologiques non-conventionnels. Parmi ses systèmes il faut distinguer les capsides virales. Ces coquilles solides qui sont formées par un certain nombre dec opies de la même protéine protègent le virus des agressions et facilitent le processus d'infection de la cellule hôte. La distribution des positions de protéines dans une capside est très régulière et montre un degré très élevé d'ordre, aussi bien orientationnel que positionnel. Les capsides virales de topologie sphérique possèdent la symétrie icosaédrique compatible avec l'ordre cristallin local, mais incompatible avec la symétrie cristalline globale et interdite dans les structures périodiques.Ici, sur l'exemple des Papovavirus, nous montrons l'existence d'un nouveau type d'organisation qui résulte dans l'ordre quasicristallin pentagonal chiral de protéines dans des capsides de topologie sphérique et géométrie dodécaédrique. La formation de cet ordre est décrite dans le cadre de la théorie de Landau de cristallisation. Les particularités de la structure sont élucidées grâce à la théorie d'élasticité des quasicristaux comme le résultat de la déformation phason nonlinéaire.La généralisation de la théorie de Landau de cristallisation que nous proposons permet également de décrire des structures quasicristallines octogonales et décagonales grâce à la minimisation contrainte de l'énergie libre, et donne un nouveau sens physique à la notion de " fenêtre de projection " utilisée dans la cristallographie multidimensionnelle.

The present thesis is devoted to the investigation of modulated structures as well as the direct measurement of magnetocaloric effect (MCE) in Ni-Mn based magnetic shape memory (MSM) Heusler compounds in pulsed magnetic fields after analyzing isothermal entropy data taken in static magnetic fields. The emphasis is on the modulated structure of MSM Heusler compounds because of lower twinning stress which facilitates the easy transformation from austenite to martensite structure. Synchrotron x-ray powder diffraction (SXRPD) was carried out to study the modulated structure and NPD for antisite disorder as Ni and Mn have easily the same atomic scattering factor. Direct measurement of the adiabatic temperature change ΔTad was done in pulsed magnetic fields, because of fast response of ~10 to 100 ms to the sample temperature on magnetic field, providing adiabatic conditions. It also gives an opportunity of very high magnetic fields up to 70 T because of short pulse duration during the measurement. The modulated structure has been studied for the off-stoichiometric Ni2Mn1.4In0.6 and Ni1.9Pt0.1MnGa MSM Heusler compounds from SXRPD and NPD. Ni2Mn1.4In0.6 exhibits martensitic transition at TM ~ 295 K and Curie temperature TC ~ 315 K. Rietveld refinement reveals uniform atomic displacement in the modulated structure of martensite phase and the absence of premartensite phase and phason broadening of the satellite peaks which was further confirmed by HRTEM study. Therefore, the structural modulation in Ni2Mn1.4In0.6 can be successfully explained in term of the adaptive phase model. Whereas, Ni1.9Pt0.1MnGa shows the premartensite phase in addition to the martensite and austenite phases and follows the soft phonon model. The temperature dependent ac-susceptibility shows the change in slope at different temperatures 365, 265, 230 and 220 K corresponding to the Curie temperature TC, first premartensite T1, second premartensite T2 and martensite temperature TM, respectively. Temperature-dependent high resolution SXRPD data analysis shows first, a nearly 3M modulated premartensite phase with an average cubic-like feature i.e. negligible Bain distortion of the elementary L21 unit cell results from the austenite phase. This phase then undergoes an isostructural phase transition 3M like premartensite phase with robust Bain distortion in the temperature range from 220 to 195 K. Below 195 K, the martensite phase appears which results from the larger Bain-distorted premartensite phase. In this work, the magnetocaloric properties of Ni2.2Mn0.8Ga and Ni1.8Mn1.8In0.4 magnetic shape memory (MSM) Heusler compounds were studied. Ni2.2Mn0.8Ga exhibits the reversible conventional MCE, measured from isothermal entropy change ΔSM and adiabatic temperature change ΔTad because of the geometric compatibility condition (GCC) for cubic austenite phase to tetragonal martensite phase as a consequence of low thermal hysteresis of the martensite phase transition. The reversible MCE has been confirmed by applying more than one pulse in the hysteresis region at 317 K. Ni1.8Mn1.8In0.4 possess improved reversible behavior of inverse MCE due to the closely satisfying of GCC from cubic austenite to modulated monoclinic martensite structure. The maximum value of ΔSM has been found to the same for both heating and cooling curves measured from isothermal magnetization M(T) curves until a magnetic field of 5 T. The adiabatic temperature change ΔTad results in a value of -10 K by applying a magnetic field of 20 T in a pulsed magnetic field. Furthermore, reversible magnetostriction of 0.3% was observed near the first-order martensite phase transition temperatures 265, 270 and 280 K. A reduction of thermal hysteresis has been found in MSM Heusler compounds Ni2Mn1.4In0.6 and Ni1.8Co0.2Mn1.4In0.6 with the application of hydrostatic pressure followed by GCC from pressure dependent x-ray diffraction in both austenite and martensite phase. By increasing pressure, the lattice parameters of both phases change in such a way that they increasingly satisfy the GCC. The approach of GCC for different kind of martensite structures (tetragonal, orthorhombic and monoclinic) will help to design new MSM Heusler compounds taking advantage of first-order martensite phase transition.

This study consists of an experimental investigation into the fluid flow and heat transfer aspects of microchannels. Rectangular copper microchannels of hydraulic diameters 1.05 mm, 0.85 mm and 0.57 mm were considered. Using water as the working fluid, heat transfer and pressure drop characteristics were determined under a constant surface heat flux for different inlet configurations in the laminar and transitional regimes. Three inlet geometries were experimentally investigated: a sudden contraction inlet, a bellmouth inlet and a swirl-generating inlet. The influence of the inlet conditions on the pressure drop, Nusselt number and critical Reynolds number was determined experimentally. Pressure drop results showed good agreement with existing correlations for adiabatic conditions. Diabatic friction factor results for the sudden contraction and bellmouth inlets were overpredicted when using the friction factor results from literature. It is noted that a relationship between the pressure drop and heat flux existed in the laminar regime, where an increase in the heat input resulted in a decrease in the friction factor. The bellmouth inlet condition showed an enhancement of the heat transfer in the transition regime compared with the sudden contraction inlet. The critical Reynolds number for the onset of transition for the sudden contraction inlet was found to be approximately 1 950, with a sharp rise to the turbulent regime thereafter. The bellmouth inlet influenced the originating point of the transition regime, which commenced at a Reynolds number of approximately 1 600. A smoother and more gradual increase to the turbulent regime was observed as an effect of the bellmouth inlet over the sudden contraction inlet. The swirl-generating inlet condition produced higher friction factor results in all three flow regimes. Transition occurred at a Reynolds number of approximately 1 500 and the turbulent regime was quickly ii reached thereafter. The turbulent regime friction factor was found to be significantly higher with the swirl inlet compared with both the sudden contraction and bellmouth inlets. Nusselt numbers continued to increase until the onset of the transition regime, and did not converge to a constant value as stated in theory. Similar enhancement of the transition regime with the bellmouth inlet was observed for the Nusselt numbers as with the friction factors. The initial turbulent regime results followed the trend of the theory for both the sudden contraction and bellmouth inlet conditions for most of the data sets, with deviation occurring in some of the 0.57 mm test cases. The swirl inlet Nusselt number results were significantly underpredicted by the theory in the early turbulent regime.
Dissertation (MEng)--University of Pretoria, 2014.
gm2014
Mechanical and Aeronautical Engineering
unrestricted