A non-autonomous scalar one-dimensional dissipative parabolic problem: The description of the dynamics

The purpose of this paper is to give a characterization of the structure of non-autonomous attractors of the problem $u_t= u_{xx} + \lambda u - \beta(t)u^3$ when the parameter $\lambda > 0$ varies. Also, we answer a question proposed in [11], concerning the complete description of the structure of the pullback attractor of the problem when $1<\lambda <4$ and, more generally, for $\lambda \neq N^2$, $2 \leq N \in \mathbb{N}$. We construct global bounded solutions , "non-autonomous equilibria", connections between the trivial solution these "non-autonomous equilibria" and characterize the $\alpha$-limit and $\omega$-limit set of global bounded solutions. As a consequence, we show that the global attractor of the associated skew-product flow has a gradient structure. The structure of the related pullback an uniform attractors are derived from that.Comment: 32 pages, 04 figure

Cosmological constant constraints from observation-derived energy condition bounds and their application to bimetric massive gravity

Among the various possibilities to probe the theory behind the recent accelerated expansion of the universe, the energy conditions (ECs) are of particular interest, since it is possible to confront and constrain the many models, including different theories of gravity, with observational data. In this context, we use the ECs to probe any alternative theory whose extra term acts as a cosmological constant. For this purpose, we apply a model-independent approach to reconstruct the recent expansion of the universe. Using Type Ia supernova, baryon acoustic oscillations and cosmic-chronometer data, we perform a Markov Chain Monte Carlo analysis to put constraints on the effective cosmological constant $\Omega^0_{\rm eff}$. By imposing that the cosmological constant is the only component that possibly violates the ECs, we derive lower and upper bounds for its value. For instance, we obtain that $0.59 < \Omega^0_{\rm eff} < 0.91$ and $0.40 < \Omega^0_{\rm eff} < 0.93$ within, respectively, $1\sigma$ and $3\sigma$ confidence levels. In addition, about 30\% of the posterior distribution is incompatible with a cosmological constant, showing that this method can potentially rule it out as a mechanism for the accelerated expansion. We also study the consequence of these constraints for two particular formulations of the bimetric massive gravity. Namely, we consider the Visser's theory and the Hassan and Roses's massive gravity by choosing a background metric such that both theories mimic General Relativity with a cosmological constant. Using the $\Omega^0_{\rm eff}$ observational bounds along with the upper bounds on the graviton mass we obtain constraints on the parameter spaces of both theories.Comment: 11 pages, 4 figures, 1 tabl

Correlations around an interface

We compute one-loop correlation functions for the fluctuations of an interface using a field theory model. We obtain them from Feynman diagrams drawn with a propagator which is the inverse of the Hamiltonian of a Poschl-Teller problem. We derive an expression for the propagator in terms of elementary functions, show that it corresponds to the usual spectral sum, and use it to calculate quantities such as the surface tension and interface profile in two and three spatial dimensions. The three-dimensional quantities are rederived in a simple, unified manner, whereas those in two dimensions extend the existing literature, and are applicable to thin films. In addition, we compute the one-loop self-energy, which may be extracted from experiment, or from Monte Carlo simulations. Our results may be applied in various scenarios, which include fluctuations around topological defects in cosmology, supersymmetric domain walls, Z(N) bubbles in QCD, domain walls in magnetic systems, interfaces separating Bose-Einstein condensates, and interfaces in binary liquid mixtures.Comment: RevTeX, 13 pages, 6 figure

A mathematical framework for reducing the domain in the mechanical analysis of periodic structures

A theoretical framework is developped leading to a sound derivation of Periodic Boundary Conditions (PBCs) for the analysis of domains smaller then the Unit Cells (UCs), named reduced Unit Cells (rUCs), by exploiting non-orthogonal translations and symmetries. A particular type of UCs, Offset-reduced Unit Cells (OrUCs) are highlighted. These enable the reduction of the analysis domain of the traditionally defined UCs without any loading restriction. The relevance of the framework and its application to any periodic structure is illustrated through two practical examples: 3D woven and honeycomb.Comment: 18 page

Estrutura de uma floresta de terra firme na região de Marabá-PA: a posição do mogno em relação ás outras espécies da comunidade.

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Processing and characterization of extruded breakfast meal formulated with broken rice and bean flour.

O objetivo deste trabalho foi elaborar um produto matinal extrusado de quirera de arroz e bandinha de feijão, além de verificar a influência do processo de extrusão nas suas características físico-químicas, nutricionais, tecnológicas e sensoriais. O produto final apresentou teor considerável de proteínas (9,9 g.100 g–1), podendo ser considerado uma boa fonte desse nutriente para crianças e adolescentes. Para a fibra alimentar, observou-se teor de 3,71 g.100 g–1 do produto pronto para o consumo. Dessa forma, o floco matinal de arroz e feijão pode receber a alegação de alimento fonte de fibras, de acordo com a legislação brasileira. Com relação às propriedades tecnológicas, o extrusado estudado apresentou índice de expansão de 8,89 e densidade aparente de 0,25 g.cm-3. Quanto à análise sensorial, o floco matinal avaliado obteve notas médias de aceitação, situadas no intervalo de 6,8 a 7,7, que corresponde às categorias “gostei ligeiramente” e “gostei muito”. Para a intenção de compra, 79% dos provadores opinaram que certamente ou possivelmente comprariam o produto. O emprego de quirera de arroz e bandinha de feijão é uma interessante alternativa para a elaboração de produto matinal extrusado, apresentando boas qualidades de ordem nutricional, tecnológica e sensorial

Assessment of carotenoids in pumpkins after different home cooking conditions.

The aim of this study was to assess the total carotenoid, a- and B-carotene, and 9 and 13-Z- B-carotene isomer contents in C. moschata after different cooking processes