Search of symmetric composition methods of symmetric integrators

Composition methods are useful when solving Ordinary Differential Equations (ODEs) as they increase the order of accuracy of a given basic numerical integration scheme. We will focus on sy-mmetric composition methods involving some basic second order symmetric integrator with different step sizes [17]. The introduction of symmetries into these methods simplifies the order conditions and reduces the number of unknowns. Several authors have worked in the search of the coefficients of these type of methods: the best method of order 8 has 17 stages [24], methods of order 8 and 15 stages were given in [29, 39, 40], 10-order methods of 31, 33 and 35 stages have been also found [24, 34]. In this work some techniques that we have built to obtain 10-order symmetric composition methods of symmetric integrators of s = 31 stages (16 order conditions) are explored. Given some starting coefficients that satisfy the simplest five order conditions, the process followed to obtain the coefficients that satisfy the sixteen order conditions is provided.

Diagnosing criticality in symmetric and chiral clock models

Quantum clock models are statistical mechanical spin models which may be regarded as a sort of bridge between the one-dimensional quantum Ising model and the one-dimensional quantum XY model. This thesis aims to provide an exhaustive review of these models using both analytical and numerical techniques. We present some important duality transformations which allow us to recast clock models into different forms, involving for example parafermions and lattice gauge theories. Thus, the notion of topological order enters into the game opening new scenarios for possible applications, like topological quantum computing. The second part of this thesis is devoted to the numerical analysis of clock models. We explore their phase diagram under different setups, with and without chirality, starting with a transverse field and then adding a longitudinal field as well. The most important observables we take into account for diagnosing criticality are the energy gap, the magnetisation, the entanglement entropy and the correlation functions.

Proposta de avaliação da simetria e transferencia de peso e a relação dessa condição com a atividade funcional do hemiplegico

Universidade Estadual de Campinas . Faculdade de Educação Física

Alterações dimensionais do côndilo mandibular em indivíduos de 3 a 20 anos de idade usando tomografia computadorizada de feixe cônico: um estudo preliminar

INTRODUÇÃO: o exame de tomografia computadorizada de feixe cônico (TCFC) oferece excelente representação dos tecidos duros da articulação temporomandibular (ATM). OBJETIVO: investigar as alterações morfológicas do côndilo mandibular, da infância à idade adulta, utilizando a TCFC. MÉTODOS: um estudo transversal foi conduzido envolvendo 36 côndilos de 18 indivíduos com idades variando entre 3 e 20 anos. As imagens dos côndilos foram obtidas por meio do sistema i-CAT e medidas com uma ferramenta do programa específica para ATM, que permite cortes perpendiculares à cabeça do côndilo, com correção individual em função das diferenças angulares de cada um. As maiores distâncias nas vistas lateral e frontal foram consideradas tanto para os côndilos do lado direto como para os do lado esquerdo. RESULTADOS: a dimensão lateral do côndilo mandibular parece ser estabelecida de maneira precoce, sofrendo poucas alterações com o passar dos anos, enquanto a dimensão frontal tende a aumentar. Assimetrias entre o côndilo esquerdo e o direito foram comumente observadas; no entanto, tais diferenças não apresentaram significância estatística para as vistas lateral (P=0,815) e frontal (P=0,374). CONCLUSÕES: os côndilos apresentaram simetria com relação ao tamanho, sendo observado crescimento apenas na dimensão frontal Os resultados sugerem que a TCFC constitui-se numa ferramenta útil na mensuração e avaliação das dimensões condilares.

Histological and radiological changes in cranial bone in the presence of bone wax

PURPOSE: To quantify the amount of bone formation in the calvarial region of Wistar rats after craniotomy using bone wax as a haemostatic agent. METHODS: Surgery to produce bilateral, symmetric, full-thickness cranial defects (area: 18 mm²) was performed in eight animals. The right side of the cranium remained open and the edges of the left side osseous defect was covered with bone wax. Calvaria were imaged immediately after surgery and 12 weeks postoperatively by computerized tomography. The areas of the bone defects were measured in three-dimensional images using Magics 13.0 (Materialise-Belgic, software CAD). RESULTS: The average amount of bone formation on the left and right side respectively was 4.85 mm² and 8.16 mm². Statistically significant differences between the amount of bone formation on the left and right sides were seen. CONCLUSIONS: Bone wax significantly diminishes the rate of bone formation in calvarial defects in a rat model.

Pulsar binary systems in a nonsymmetric theory of gravitation II. Dipole radiation

This paper deals with the emission of gravitational radiation in the context of a previously studied metric nonsymmetric theory of gravitation. The part coming from the symmetric part of the metric coincides with the mass quadrupole moment result of general relativity. The one associated to the antisymmetric part of the metric involves the dipole moment of the fermionic charge of the system. The results are applied to binary star systems and the decrease of the period of the elliptical motion is calculated.

Utilização de métodos acústicos em estudos de dinâmica costeira: exemplo na desembocadura lagunar de cananéia

Em função de suas condições de interface entre águas doces e salinas, desembocaduras estuarinas e lagunares constituem sistemas geomorfológicos altamente complexos e dinâmicos. Como conseqüência da variabilidade espacial e temporal dos fluxos de maré, o leito responde com uma grande variabilidade nas características morfológicas e sedimentares. Neste sentido, é possível relacionar diretamente a circulação de fundo e o transporte sedimentar com as feições submersas geradas. Perfis de ecossondagem, sonar de varredura lateral e sísmica de alta resolução, executados na desembocadura lagunar de Cananéia, revelaram a existência de uma dinâmica de fundo extremamente complexa, caracterizada por marcas onduladas e ondas de areia de alturas métricas. As maiores ondas de areia, localizadas em uma depressão na desembocadura lagunar, apresentam inversão de polaridade em sua assimetria, com a presença de ondas simétricas de grande tamanho no ponto de inversão. Este padrão morfológico não apresenta variação temporal em escala anual, sugerindo a persistência de um padrão de fluxos sobre o leito. Esta dinâmica revela, também, a constância de fluxos convergentes que aparentemente independem das condições de maré enchente ou vazante. Os resultados permitiram o estabelecimento de um primeiro modelo qualitativo de circulação de fundo na área, com aplicações potenciais na navegação e estudos de proteção da costa.

Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity

Dynamical Chern-Simons gravity is an extension of general relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard general relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.

Aging and fluctuation-dissipation ratio in a nonequilibrium q-state lattice model

A generalized version of the nonequilibrium linear Glauber model with q states in d dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the q states. Exact expressions for the two-time autocorrelation and response functions on a d-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

Disequilibrium Coefficient: A Bayesian Perspective

Hardy-Weinberg Equilibrium (HWE) is an important genetic property that populations should have whenever they are not observing adverse situations as complete lack of panmixia, excess of mutations, excess of selection pressure, etc. HWE for decades has been evaluated; both frequentist and Bayesian methods are in use today. While historically the HWE formula was developed to examine the transmission of alleles in a population from one generation to the next, use of HWE concepts has expanded in human diseases studies to detect genotyping error and disease susceptibility (association); Ryckman and Williams (2008). Most analyses focus on trying to answer the question of whether a population is in HWE. They do not try to quantify how far from the equilibrium the population is. In this paper, we propose the use of a simple disequilibrium coefficient to a locus with two alleles. Based on the posterior density of this disequilibrium coefficient, we show how one can conduct a Bayesian analysis to verify how far from HWE a population is. There are other coefficients introduced in the literature and the advantage of the one introduced in this paper is the fact that, just like the standard correlation coefficients, its range is bounded and it is symmetric around zero (equilibrium) when comparing the positive and the negative values. To test the hypothesis of equilibrium, we use a simple Bayesian significance test, the Full Bayesian Significance Test (FBST); see Pereira, Stern andWechsler (2008) for a complete review. The disequilibrium coefficient proposed provides an easy and efficient way to make the analyses, especially if one uses Bayesian statistics. A routine in R programs (R Development Core Team, 2009) that implements the calculations is provided for the readers.

HR Del REMNANT ANATOMY USING TWO-DIMENSIONAL SPECTRAL DATA AND THREE-DIMENSIONAL PHOTOIONIZATION SHELL MODELS

The HR Del nova remnant was observed with the IFU-GMOS at Gemini North. The spatially resolved spectral data cube was used in the kinematic, morphological, and abundance analysis of the ejecta. The line maps show a very clumpy shell with two main symmetric structures. The first one is the outer part of the shell seen in H alpha, which forms two rings projected in the sky plane. These ring structures correspond to a closed hourglass shape, first proposed by Harman & O'Brien. The equatorial emission enhancement is caused by the superimposed hourglass structures in the line of sight. The second structure seen only in the [O III] and [N II] maps is located along the polar directions inside the hourglass structure. Abundance gradients between the polar caps and equatorial region were not found. However, the outer part of the shell seems to be less abundant in oxygen and nitrogen than the inner regions. Detailed 2.5-dimensional photoionization modeling of the three-dimensional shell was performed using the mass distribution inferred from the observations and the presence of mass clumps. The resulting model grids are used to constrain the physical properties of the shell as well as the central ionizing source. A sequence of three-dimensional clumpy models including a disk-shaped ionization source is able to reproduce the ionization gradients between polar and equatorial regions of the shell. Differences between shell axial ratios in different lines can also be explained by aspherical illumination. A total shell mass of 9 x 10(-4) M(circle dot) is derived from these models. We estimate that 50%-70% of the shell mass is contained in neutral clumps with density contrast up to a factor of 30.

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.

Diffusion anomaly and dynamic transitions in the Bell-Lavis water model

In this paper we investigate the dynamic properties of the minimal Bell-Lavis (BL) water model and their relation to the thermodynamic anomalies. The BL model is defined on a triangular lattice in which water molecules are represented by particles with three symmetric bonding arms interacting through van der Waals and hydrogen bonds. We have studied the model diffusivity in different regions of the phase diagram through Monte Carlo simulations. Our results show that the model displays a region of anomalous diffusion which lies inside the region of anomalous density, englobed by the line of temperatures of maximum density. Further, we have found that the diffusivity undergoes a dynamic transition which may be classified as fragile-to-strong transition at the critical line only at low pressures. At higher densities, no dynamic transition is seen on crossing the critical line. Thus evidence from this study is that relation of dynamic transitions to criticality may be discarded. (C) 2010 American Institute of Physics. [doi:10.1063/1.3479001]

Stability, causality, and quasinormal modes of cosmic strings and cylinders

In this work we consider the evolution of a massive scalar field in cylindrically symmetric space-times. Quasinormal modes have been calculated for static and rotating cosmic cylinders. We found unstable modes in some cases. Rotating as well as static cosmic strings, i.e., without regular interior solutions, do not display quasinormal oscillation modes. We conclude that rotating cosmic cylinder space-times that present closed timelike curves are unstable against scalar perturbations.

Perturbative finiteness of three-dimensional supersymmetric QED to all orders

Within the superfield formalism, we study the ultraviolet properties of the three-dimensional super-symmetric quantum electrodynamics. The theory is shown to be finite at all loop orders in a particular gauge.