913 resultados para Least Energy Solutions


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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent (LI) hypergeometric functions of two variables F-4. This result is not physically acceptable when it is embedded in higher loops, because all four hypergeometric functions in the triangle result have the same region of convergence and further integration means going outside those regions of convergence. We could go outside those regions by using the well-known analytic continuation formulas obeyed by the F-4, but there are at least two ways we can do this. Which is the correct one? Whichever continuation one uses, it reduces a number of F-4 from four to three. This reduction in the number of hypergeometric functions can be understood by taking into account the fundamental physical constraint imposed by the conservation of momenta flowing along the three legs of the diagram. With this, the number of overall LI functions that enter the most general solution must reduce accordingly. It remains to determine which set of three LI solutions needs to be taken. To determine the exact structure and content of the analytic solution for the three-point function that can be embedded in higher loops, we use the analogy that exists between Feynman diagrams and electric circuit networks, in which the electric current flowing in the network plays the role of the momentum flowing in the lines of a Feynman diagram. This analogy is employed to define exactly which three out of the four hypergeometric functions are relevant to the analytic solution for the Feynman diagram. The analogy is built based on the equivalence between electric resistance circuit networks of types Y and Delta in which flows a conserved current. The equivalence is established via the theorem of minimum energy dissipation within circuits having these structures.

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

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Pós-graduação em Engenharia Mecânica - FEIS

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Purpose: To analyze whether immersion in sodium fluoride (NaF) solutions and/or common acidic beverages (test solutions) would affect the surface roughness or topography of lithium disilicate ceramic. Methods: 220 ceramic discs were divided into four groups, each of which was subdivided into five subgroups (n = 11). Control group discs were immersed in one of four test beverages for 4 hours daily or in artificial saliva for 21 days. Discs in the experimental groups were continuously immersed in 0.05% NaF, 0.2% NaF, or 1.23% acidulated phosphate fluoride (APF) gel for 12, 73, and 48 hours, respectively, followed by immersion in one of the four test beverages or artificial saliva. Vickers microhardness, surface roughness, scanning electron microscopy (SEM) associated with energy dispersive spectroscopy, and atomic force microscopy (AFM) assessments were made. Data were analyzed by nested analysis of variance (ANOVA) and Tukey's test (alpha = 0.05). Results: Immersion in the test solutions diminished the microhardness and increased the surface roughness of the discs. The test beverages promoted a significant reduction in the Vickers microhardness in the 0.05% and 0.2% NaF groups. The highest surface roughness results were observed in the 0.2% NaF and 1.23% APF groups, with similar findings by SEM and AFM. Acidic beverages affected the surface topography of lithium disilicate ceramic. Fluoride treatments may render the ceramic surface more susceptible to the chelating effect of acidic solutions.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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