Aspects of Chiral Symmetry Breaking in Lattice QCD

Thesis (Ph.D.)--University of Washington, 2016-08

Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly

We investigate the phase behavior of a single-component system in three dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an intermediate distance, and a hard-core repulsion at a short distance, similar to potentials used to describe liquid systems such as colloids, protein solutions, or liquid metals. We showed [Nature (London) 409, 692 (2001)] that, even with no evidence of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gas¿low-density-liquid (LDL) critical point, and the other in a gas¿high-density-liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the three-parameter space of the soft-core potential and perform molecular dynamics simulations in the interesting region of parameters. For the equilibrium phase diagram, we analyze the structure of the crystal phase and find that, within the considered range of densities, the structure is independent of the density. Then, we analyze in detail the fluid metastable phases and, by explicit thermodynamic calculation in the supercooled phase, we show the absence of the density anomaly. We suggest that this absence is related to the presence of only one stable crystal structure.

TECTONICS OF THE HELVETIC NAPPE SYSTEM (W SWITZERLAND): CONTROL OF STRAIN LOCALIZATION AND BASEMENT-COVER DEFORMATION. Insights from models based on continuum mechanics

The Helvetic nappe system in Western Switzerland is a stack of fold nappes and thrust sheets em-placed at low grade metamorphism. Fold nappes and thrust sheets are also some of the most common features in orogens. Fold nappes are kilometer scaled recumbent folds which feature a weakly deformed normal limb and an intensely deformed overturned limb. Thrust sheets on the other hand are characterized by the absence of overturned limb and can be defined as almost rigid blocks of crust that are displaced sub-horizontally over up to several tens of kilometers. The Morcles and Doldenhom nappe are classic examples of fold nappes and constitute the so-called infra-Helvetic complex in Western and Central Switzerland, respectively. This complex is overridden by thrust sheets such as the Diablerets and Wildhörn nappes in Western Switzerland. One of the most famous example of thrust sheets worldwide is the Glariis thrust sheet in Central Switzerland which features over 35 kilometers of thrusting which are accommodated by a ~1 m thick shear zone. Since the works of the early Alpine geologist such as Heim and Lugeon, the knowledge of these nappes has been steadily refined and today the geometry and kinematics of the Helvetic nappe system is generally agreed upon. However, despite the extensive knowledge we have today of the kinematics of fold nappes and thrust sheets, the mechanical process leading to the emplacement of these nappe is still poorly understood. For a long time geologist were facing the so-called 'mechanical paradox' which arises from the fact that a block of rock several kilometers high and tens of kilometers long (i.e. nappe) would break internally rather than start moving on a low angle plane. Several solutions were proposed to solve this apparent paradox. Certainly the most successful is the theory of critical wedges (e.g. Chappie 1978; Dahlen, 1984). In this theory the orogen is considered as a whole and this change of scale allows thrust sheet like structures to form while being consistent with mechanics. However this theoiy is intricately linked to brittle rheology and fold nappes, which are inherently ductile structures, cannot be created in these models. When considering the problem of nappe emplacement from the perspective of ductile rheology the problem of strain localization arises. The aim of this thesis was to develop and apply models based on continuum mechanics and integrating heat transfer to understand the emplacement of nappes. Models were solved either analytically or numerically. In the first two papers of this thesis we derived a simple model which describes channel flow in a homogeneous material with temperature dependent viscosity. We applied this model to the Morcles fold nappe and to several kilometer-scale shear zones worldwide. In the last paper we zoomed out and studied the tectonics of (i) ductile and (ii) visco-elasto-plastic and temperature dependent wedges. In this last paper we focused on the relationship between basement and cover deformation. We demonstrated that during the compression of a ductile passive margin both fold nappes and thrust sheets can develop and that these apparently different structures constitute two end-members of a single structure (i.e. nappe). The transition from fold nappe to thrust sheet is to first order controlled by the deformation of the basement. -- Le système des nappes helvétiques en Suisse occidentale est un empilement de nappes de plis et de nappes de charriage qui se sont mis en place à faible grade métamorphique. Les nappes de plis et les nappes de charriage sont parmi les objets géologiques les plus communs dans les orogènes. Les nappes de plis sont des plis couchés d'échelle kilométrique caractérisés par un flanc normal faiblement défor-mé, au contraire de leur flanc inverse, intensément déformé. Les nappes de charriage, à l'inverse se caractérisent par l'absence d'un flanc inverse bien défini. Elles peuvent être définies comme des blocs de croûte terrestre qui se déplacent de manière presque rigide qui sont déplacés sub-horizontalement jusqu'à plusieurs dizaines de kilomètres. La nappe de Mordes et la nappe du Doldenhorn sont des exemples classiques de nappes de plis et constitue le complexe infra-helvétique en Suisse occidentale et centrale, respectivement. Ce complexe repose sous des nappes de charriages telles les nappes des Diablerets et du Widlhörn en Suisse occidentale. La nappe du Glariis en Suisse centrale se distingue par un déplacement de plus de 35 kilomètres qui s'est effectué à la faveur d'une zone de cisaillement basale épaisse de seulement 1 mètre. Aujourd'hui la géométrie et la cinématique des nappes alpines fait l'objet d'un consensus général. Malgré cela, les processus mécaniques par lesquels ces nappes se sont mises en place restent mal compris. Pendant toute la première moitié du vingtième siècle les géologues les géologues ont été confrontés au «paradoxe mécanique». Celui-ci survient du fait qu'un bloc de roche haut de plusieurs kilomètres et long de plusieurs dizaines de kilomètres (i.e., une nappe) se fracturera de l'intérieur plutôt que de se déplacer sur une surface frictionnelle. Plusieurs solutions ont été proposées pour contourner cet apparent paradoxe. La solution la plus populaire est la théorie des prismes d'accrétion critiques (par exemple Chappie, 1978 ; Dahlen, 1984). Dans le cadre de cette théorie l'orogène est considéré dans son ensemble et ce simple changement d'échelle solutionne le paradoxe mécanique (la fracturation interne de l'orogène correspond aux nappes). Cette théorie est étroitement lié à la rhéologie cassante et par conséquent des nappes de plis ne peuvent pas créer au sein d'un prisme critique. Le but de cette thèse était de développer et d'appliquer des modèles basés sur la théorie de la méca-nique des milieux continus et sur les transferts de chaleur pour comprendre l'emplacement des nappes. Ces modèles ont été solutionnés de manière analytique ou numérique. Dans les deux premiers articles présentés dans ce mémoire nous avons dérivé un modèle d'écoulement dans un chenal d'un matériel homogène dont la viscosité dépend de la température. Nous avons appliqué ce modèle à la nappe de Mordes et à plusieurs zone de cisaillement d'échelle kilométrique provenant de différents orogènes a travers le monde. Dans le dernier article nous avons considéré le problème à l'échelle de l'orogène et avons étudié la tectonique de prismes (i) ductiles, et (ii) visco-élasto-plastiques en considérant les transferts de chaleur. Nous avons démontré que durant la compression d'une marge passive ductile, a la fois des nappes de plis et des nappes de charriages peuvent se développer. Nous avons aussi démontré que nappes de plis et de charriages sont deux cas extrêmes d'une même structure (i.e. nappe) La transition entre le développement d'une nappe de pli ou d'une nappe de charriage est contrôlé au premier ordre par la déformation du socle. -- Le système des nappes helvétiques en Suisse occidentale est un emblement de nappes de plis et de nappes de chaînage qui se sont mis en place à faible grade métamoiphique. Les nappes de plis et les nappes de charriage sont parmi les objets géologiques les plus communs dans les orogènes. Les nappes de plis sont des plis couchés d'échelle kilométrique caractérisés par un flanc normal faiblement déformé, au contraire de leur flanc inverse, intensément déformé. Les nappes de charriage, à l'inverse se caractérisent par l'absence d'un flanc inverse bien défini. Elles peuvent être définies comme des blocs de croûte terrestre qui se déplacent de manière presque rigide qui sont déplacés sub-horizontalement jusqu'à plusieurs dizaines de kilomètres. La nappe de Morcles and la nappe du Doldenhorn sont des exemples classiques de nappes de plis et constitue le complexe infra-helvétique en Suisse occidentale et centrale, respectivement. Ce complexe repose sous des nappes de charriages telles les nappes des Diablerets et du Widlhörn en Suisse occidentale. La nappe du Glarüs en Suisse centrale est certainement l'exemple de nappe de charriage le plus célèbre au monde. Elle se distingue par un déplacement de plus de 35 kilomètres qui s'est effectué à la faveur d'une zone de cisaillement basale épaisse de seulement 1 mètre. La géométrie et la cinématique des nappes alpines fait l'objet d'un consensus général parmi les géologues. Au contraire les processus physiques par lesquels ces nappes sont mises en place reste mal compris. Les sédiments qui forment les nappes alpines se sont déposés à l'ère secondaire et à l'ère tertiaire sur le socle de la marge européenne qui a été étiré durant l'ouverture de l'océan Téthys. Lors de la fermeture de la Téthys, qui donnera naissance aux Alpes, le socle et les sédiments de la marge européenne ont été déformés pour former les nappes alpines. Le but de cette thèse était de développer et d'appliquer des modèles basés sur la théorie de la mécanique des milieux continus et sur les transferts de chaleur pour comprendre l'emplacement des nappes. Ces modèles ont été solutionnés de manière analytique ou numérique. Dans les deux premiers articles présentés dans ce mémoire nous nous sommes intéressés à la localisation de la déformation à l'échelle d'une nappe. Nous avons appliqué le modèle développé à la nappe de Morcles et à plusieurs zones de cisaillement provenant de différents orogènes à travers le monde. Dans le dernier article nous avons étudié la relation entre la déformation du socle et la défonnation des sédiments. Nous avons démontré que nappe de plis et nappes de charriages constituent les cas extrêmes d'un continuum. La transition entre nappe de pli et nappe de charriage est intrinsèquement lié à la déformation du socle sur lequel les sédiments reposent.

Critical behavior of a system with orientational and positional degrees of freedom: A Monte Carlo simulation study

The critical behavior of a system constituted by molecules with a preferred symmetry axis is studied by means of a Monte Carlo simulation of a simplified two-dimensional model. The system exhibits two phase transitions, associated with the vanishing of the positional order of the center of mass of the molecules and with the orientational order of the symmetry axis. The evolution of the order parameters and the specific heat is also studied. The transition associated with the positional degrees of freedom is found to change from a second-order to a first-order behavior when the two phase transitions are close enough, due to the coupling with the orientational degrees of freedom. This fact is qualitatively compared with similar results found in pure liquid crystals and liquid-crystal mixtures.

Finite-momentum condensate of magnetic excitons in a bilayer quantum Hall system

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Liquid-gas phase transition in Bose-Einstein condensates with time evolution

We study the effects of a repulsive three-body interaction on a system of trapped ultracold atoms in a Bose-Einstein condensed state. The stationary solutions of the corresponding s-wave nonlinear Schrödinger equation suggest a scenario of first-order liquid-gas phase transition in the condensed state up to a critical strength of the effective three-body force. The time evolution of the condensate with feeding process and three-body recombination losses has a different characteristic pattern. Also, the decay time of the dense (liquid) phase is longer than expected due to strong oscillations of the mean-squared radius.

First- and second-order stimulus length selectivity in New World monkey striate cortex

Motion is a powerful cue for figure-ground segregation, allowing the recognition of shapes even if the luminance and texture characteristics of the stimulus and background are matched. In order to investigate the neural processes underlying early stages of the cue-invariant processing of form, we compared the responses of neurons in the striate cortex (V1) of anaesthetized marmosets to two types of moving stimuli: bars defined by differences in luminance, and bars defined solely by the coherent motion of random patterns that matched the texture and temporal modulation of the background. A population of form-cue-invariant (FCI) neurons was identified, which demonstrated similar tuning to the length of contours defined by first- and second-order cues. FCI neurons were relatively common in the supragranular layers (where they corresponded to 28% of the recorded units), but were absent from layer 4. Most had complex receptive fields, which were significantly larger than those of other V1 neurons. The majority of FCI neurons demonstrated end-inhibition in response to long first- and second-order bars, and were strongly direction selective, Thus, even at the level of V1 there are cells whose variations in response level appear to be determined by the shape and motion of the entire second-order object, rather than by its parts (i.e. the individual textural components). These results are compatible with the existence of an output channel from V1 to the ventral stream of extrastriate areas, which already encodes the basic building blocks of the image in an invariant manner.

Optimization of co-current spray drying process of sugar-rich foods. Part I - Moisture and glass transition temperature profile during drying

A steady state mathematical model for co-current spray drying was developed for sugar-rich foods with the application of the glass transition temperature concept. Maltodextrin-sucrose solution was used as a sugar-rich food model. The model included mass, heat and momentum balances for a single droplet drying as well as temperature and humidity profile of the drying medium. A log-normal volume distribution of the droplets was generated at the exit of the rotary atomizer. This generation created a certain number of bins to form a system of non-linear first-order differential equations as a function of the axial distance of the drying chamber. The model was used to calculate the changes of droplet diameter, density, temperature, moisture content and velocity in association with the change of air properties along the axial distance. The difference between the outlet air temperature and the glass transition temperature of the final products (AT) was considered as an indicator of stickiness of the particles in spray drying process. The calculated and experimental AT values were close, indicating successful validation of the model. (c) 2004 Elsevier Ltd. All rights reserved.

[N]pT ensemble and finite-size-scaling study of the critical isostructural transition in the generalized exponential model of index 4.

First-order transitions of system where both lattice site occupancy and lattice spacing fluctuate, such as cluster crystals, cannot be efficiently studied by traditional simulation methods, which necessarily fix one of these two degrees of freedom. The difficulty, however, can be surmounted by the generalized [N]pT ensemble [J. Chem. Phys. 136, 214106 (2012)]. Here we show that histogram reweighting and the [N]pT ensemble can be used to study an isostructural transition between cluster crystals of different occupancy in the generalized exponential model of index 4 (GEM-4). Extending this scheme to finite-size scaling studies also allows us to accurately determine the critical point parameters and to verify that it belongs to the Ising universality class.

High-temperature X-ray powder diffraction study of the tetragonal-cubic phase transition in nanocrystalline, compositionally homogeneous ZrO2-CeO2 solid solutions

Crystal structure of compositionally homogeneous, nanocrystalline ZrO2-CeO2 solutions was investigated by X-ray powder diffraction as a function of temperature for compositions between 50 and 65 mol % CeO2 center dot ZrO2-50 and 60 mol % CeO2 solid solutions, which exhibit the t'-form of the tetragonal phase at room temperature, transform into the cubic phase in two steps: t'-to-t '' followed by t ''-to-cubic. But the ZrO2-65 mol % CeO2, which exhibits the t ''-form, transforms directly to the cubic phase. The results suggest that t'-to-t '' transition is of first order, but t ''-to-cubic seems to be of second order. (C) 2008 International Centre for Diffraction Data.

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: A statistical model

We propose a statistical model to account for the gel-fluid anomalous phase transitions in charged bilayer- or lamellae-forming ionic lipids. The model Hamiltonian comprises effective attractive interactions to describe neutral-lipid membranes as well as the effect of electrostatic repulsions of the discrete ionic charges on the lipid headgroups. The latter can be counterion dissociated (charged) or counterion associated (neutral), while the lipid acyl chains may be in gel (low-temperature or high-lateral-pressure) or fluid (high-temperature or low-lateral-pressure) states. The system is modeled as a lattice gas with two distinct particle types-each one associated, respectively, with the polar-headgroup and the acyl-chain states-which can be mapped onto an Ashkin-Teller model with the inclusion of cubic terms. The model displays a rich thermodynamic behavior in terms of the chemical potential of counterions (related to added salt concentration) and lateral pressure. In particular, we show the existence of semidissociated thermodynamic phases related to the onset of charge order in the system. This type of order stems from spatially ordered counterion association to the lipid headgroups, in which charged and neutral lipids alternate in a checkerboard-like order. Within the mean-field approximation, we predict that the acyl-chain order-disorder transition is discontinuous, with the first-order line ending at a critical point, as in the neutral case. Moreover, the charge order gives rise to continuous transitions, with the associated second-order lines joining the aforementioned first-order line at critical end points. We explore the thermodynamic behavior of some physical quantities, like the specific heat at constant lateral pressure and the degree of ionization, associated with the fraction of charged lipid headgroups.

Anelastic spectroscopy study of the metal-insulator transition of Nd(1-x)Eu(x)NiO(3)

Measurements are presented of the complex dynamic Young's modulus of NdNiO(3) and Nd(0.65)Eu(0.35)NiO(3) through the metal-insulator transition (MIT). Upon cooling, the modulus presents a narrow dip at the MIT followed by an abrupt stiffening of similar to 6%. The anomaly is reproducible between cooling and heating in Nd(0.65)Eu(0.35)NiO(3) but appears only as a slow stiffening during cooling in undoped NdNiO(3), in conformance with the fact that the MIT in RNiO(3) changes from strongly first order to second order when the mean R size is decreased. The elastic anomaly seems not to be associated with the antiferromagnetic transition, which is distinct from the MIT in Nd(0.65)Eu(0.35)NiO(3). It is concluded that the steplike stiffening is due to the disappearance or freezing of dynamic Jahn-Teller (JT) distortions through the MIT, where the JT active Ni(3+) is disproportionated into alternating Ni(3+delta) and Ni(3-delta). The fluctuating octahedral JT distortion necessary to justify the observed jump in the elastic modulus is estimated as similar to 3% but does not have a role in determining the MIT, since the otherwise-expected precursor softening is not observed.

Polaron liquid-gas crossover at the orthorhombic-rhombohedral transition of manganites

High-resolution synchrotron x-ray powder diffraction in La(0.7)Ca(0.3)MnO(3) shows in detail a first-order structural phase transition from orthorhombic (space-group Pnma) to rhombohedral (space-group R (3) over barc) crystal structures near T(S)=710 K. Magnetic susceptibility measurements show that the rhombohedral phase strictly obeys the Curie-Weiss law as opposed to the orthorhombic phase. A concomitant change in the electrical resistivity behavior, consistent with an alteration from nonadiabatic to adiabatic small polaron hopping regimes, was also observed at T(S). The simultaneous change in transport and magnetic properties are identified as a transition from a correlated polaron liquid for TT(S), driven by the change in the crystal symmetry.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.