Variational techniques in non-perturbative QCD

We review attempts to apply the variational principle to understand the vacuum of non-abelian gauge theories. In particular, we focus on the method explored by Ian Kogan and collaborators, which imposes exact gauge invariance on the trial Gaussian wave functional prior to the minimization of energy. We describe the application of the method to a toy model -- confining compact QED in 2+1 dimensions -- where it works wonderfully and reproduces all known non-trivial results. We then follow its applications to pure Yang-Mills theory in 3+1 dimensions at zero and finite temperature. Among the results of the variational calculation are dynamical mass generation and the analytic description of the deconfinement phase transition.Comment: 71 pages, 1 figure. To be published in the memorial volume "From Fields to Strings: Cirvumnavigating Theoretical Physics", World Scientific, 2004. Dedicated to the memory of Ian Koga

Variational analysis of the deconfinement phase transition

We study the deconfining phase transition in 3+1 dimensional pure SU(N) Yang-Mills theory using a gauge invariant variational calculation. We generalize the variational ansatz of Phys. Rev. D52, 3719 (1995) to mixed states (density matrices) and minimize the free energy. For N > 3 we find a first order phase transition with the transition temperature of T_C = 450 Mev. Below the critical temperature the Polyakov loop has vanishing expectation value, while above T_C, its average value is nonzero. According to the standard lore this corresponds to the deconfining transition. Within the accuracy of our approximation the entropy of the system in the low temperature phase vanishes. The latent heat is not small but, rather, is of the order of the nonperturbative vacuum energy.Comment: 15 pages, correction of minor typos only, submitted to JHE

METAPHYSICS AS A BASIS FOR DEEP ECOLOGY: AN ENQUIRY INTO SPINOZA’S SYSTEM

Recently, Deep Ecology has gained a new impetus because of the current state of affairs threatening the planet and because of intellectual changes in the field. One of these crucial intellectual changes came about as theorists gained a better understanding of what Naess meant by the concepts ‘Deep Ecology’ and ‘ecosophy’ in his talk in Bucharest in 1972 – the first part will focus on this. The second part will focus on the use by Deep Ecology supporters of Spinoza’s metaphysical system as a foundation to their own views, and it identifies problems and proposes solutions through an alternative reading of Spinoza’s metaphysics, especially his concepts of monism and conatus

Otimização de sistemas intervalares não lineares acíclicos

Resumo: Intervalos permitem uma representação aproximada de números reais, com a qual podemos modelar matematicamente problemas do mundo real de uma forma menos restritiva que a modelagem sobre restrições reais. Assim, podemos definir problemas intervalares de decisão e otimização que são relaxamentos da Programação Não Linear usual. Recentemente, técnicas utilizadas em algoritmos para o problema da Satisfatibilidade Booleana foram aplicadas na solução de problemas intervalares de decisão, utilizando a álgebra intervalar para refinar intervalos e obter soluções que satisfaçam um conjunto de restrições sob uma precisão preestabelecida. Embora essa abordagem não resolva problemas de otimização, ela apresenta um método para extrair uma solução real de uma solução intervalar, se o problema apresentar determinadas características. Neste trabalho, estendemos esse método, definindo uma classe de problemas para os quais é possível a extração de uma solução real mesmo sem a garantia de todas as condições exigidas pelos resolvedores anteriores. Além disso, mostramos que o método estendido pode ser utilizado para resolver algumas classes de problemas de otimização

Uma condição suficiente para otimização global sem retrocesso

Orientador: Fabiano SilvaTese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa : Curitiba, 04/05/2018Inclui referências: p.185-193Área de concentração: Ciência da ComputaçãoResumo: Um problema de satisfação de restrições (CSP, do inglês constraint satisfaction problem) consiste em encontrar uma atribuição de valores a um conjunto de variáveis que satisfaça uma rede de restrições. Técnicas de consistência local desempenham um papel central na resolução de CSPs, excluindo valores que certamente não constituem uma solução do problema. Muitos esforços vêm sendo aplicados na identificação de classes de CSPs relacionando a estrutura da rede (representada por um hipergrafo) com o nível de consistência local que garante uma solução livre de retrocesso, isto é, uma busca que encontra uma solução em um número polinomial de passos em relação ao tamanho da instância. Nesta tese, problemas de otimização global são representados por hipergrafos com um vértice raiz que representa a função objetivo a ser minimizada. Uma forma de decomposição de hipergrafos, chamada decomposição Epífita, é apresentada. Através da decomposição Epífita do hipergrafo de restrições, caracteriza-se uma classe de problemas de otimização onde a consistência de arco relacional direcionada garante uma solução livre de retrocesso. Alcançar consistência relacional exige a adição de novas restrições na rede, alterando a sua estrutura; por essa razão, um método de ramificação e poda intervalar para alcançar uma forma relaxada dessa consistência é proposto, encontrando uma aproximação do mínimo global de problemas de otimização. Um otimizador de código-fonte aberto que implementa esse método, chamado OGRe, é apresentado. A fim de generalizar o conceito de decomposição Epífita a todos os problemas de otimização, um parâmetro de largura de hipergrafos chamado largura epífita é introduzido. Como principal contribuição desta tese, mostra-se que problemas de otimização representados por hipergrafos com largura epífita k possuem decomposições k-Epífitas e são resolvidos sem retrocesso se alcançada k-consistência relacional direcionada forte. Palavras-chave: otimização global, consistência relacional, análise intervalar, decomposição epífita, hipergrafo.Abstract: A constraint satisfaction problem (CSP) consists of finding an assignment of values to a set of variables that satisfy a constraint network. Local consistency techniques play a central role in solving CSPs, pruning values that surely do not constitute a solution of the problem. Many efforts have been applied to identify classes of CSPs by linking the constraint network structure (represented by a hypergraph) to the level of local consistency that guarantees a backtrack-free solution, i.e., a search that finds a solution in a polynomial number of steps with relation to the size of the instance. In this thesis, global optimization problems are represented by hypergraphs with a root vertex that represents the objective function to be minimized. A form of hypergraph decomposition is introduced, called Epiphytic decomposition. By the Epiphytic decomposition of constraint hypergraphs a class of optimization problems is characterized, for which directional relational arc-consistency ensures a backtrack-free solution. Achieving relational consistency requires the addition of new constraints on the network, changing its structure; for this reason, an interval branch and bound method to enforce a relaxed form of this consistency is proposed, thus finding an approximation for the global minimum of optimization problems. An open-source optimizer that implements this method, namely OGRe, is introduced. In order to generalize the Epiphytic decomposition concept to cover all optimization problems, a hypergraph width parameter is introduced, called epiphytic width. As the main contribution of this thesis, it is shown that optimization problems represented by hypergraphs with epiphytic width k have k-Epiphytic decompositions and are solved in a backtrack-free manner if achieved strong directional relational k-consistency. Keywords: global optimization, relational consistency, interval analysis, epiphytic decomposition, hypergraph

Torque Control of a DC Motor with a State Space Estimator and Kalman Filter Applied in Electrical Vehicles

This work presents a study over a torque-generated speed control of free wheel attached to a DC motor, for use on traction of mobile vehicles. Also, it presents the discrete state space model of a DC model and the Kalman filter’s equations and applications. This work presents a hardware-in-the-loop (HIL) system for design of a torque controller noticed that this process produces a faster design, coding, and parameter optimization of any embedded systems. The hardware used for the implementation of the system is discussed as the hardware-in-the-loop environment which makes possible the fast tuning and design of the system. In the absence of a torque sensor, this work uses the Kalman filter’s estimated states torque and speed as feedbacks of the system

Comparison of Elastic Constants of Wood Determined by Ultrasonic Wave Propagation and Static Compression Testing

In Brazil, most reports on the elastic properties of wood include only the elastic modulus in the longitudinal direction. This is because of the difficulty in determining other properties through static testing. The purpose of this study was to evaluate the methodology for determining the three Young's moduli (EL, ER, ET), the three shear moduli (GLR, GLT, GRT), and the six Poisson ratios (VLR, VLT, VRL, VRT, VTL, VTR) using ultrasonic technology. For testing, we used specimens in the form of cubic prisms from the following species: Garapeira (Apuleia leiocarpa), Cupiuba (Goupia glabra), and Sydney Blue gum (Eucalyptus saligna). The ultrasonic tests were performed with plane transducers of longitudinal and transverse waves, both with a 1-MHz frequency. For comparison, the same specimens were tested by static compression. Based on the confidence intervals of the means, the results of the ultrasonic test produced values of longitudinal elasticity moduli (EL, ER, and ET) and shear moduli (GTR, GTL, and GLR) statistically equivalent to those obtained with static compression. In the case of the Poisson ratio, the results, using the confidence intervals, indicated that VRL, VLR, and VLT were not statistically equivalent to those obtained in static tests for any of the species. Conversely, VTL, VTR, VRT, were statistically equivalent to those obtained in static tests for all the species. In conclusion, the ultrasonic test for determining the Young's and shear moduli of wood was found to be simpler and less expensive than the static compression test, and the results are equally useful

Analysis of the Solar Tracking System for a Mobile Robot Prototype

Methods to detect the position of the sun and orientate a solar panel to its position are used in order to optimize the power generated. Two possible approaches are using light depending resistor (LDR) sensors, or using a GPS and equations that model the geometry between the Earth and the Sun. The main objective of this work is the proposal of a prototype system to optimize the harvesting of solar energy on photovoltaic panels. In this chapter, a mobile robot powered by a solar panel orientated by a LDR matrix and a GPS device was developed. The LDRs were used as the representation of vectors normal to a surface, where its sum resulted in the most lighted point. The GPS, in turn, provided location, date and time data, which were used in the calculations of the Sun?s azimuth and zenith, used to orientate the panel. The obtained results show that an orientated photovoltaic panel has a better performance when compared to a static panel. Possibilities and opportunities of research tend to grow for the next years with many possible works to be done in the future, both in mobile robotics and in other systems powered by photovoltaic panels