912 resultados para Power Law Distribution


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

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

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

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The rheological parameters of raisins were obtained after three different drying methods: convective, osmo-convective and solar drying. Compression tests were applied to rehydrated samples by using a Texture Analyzer TAXT2i. A mathematical trick was used to determine the stress and area was calculated along the deformation. A power law model could adequately fit stress-true strain curves and parameters; K (measure of stiffness) and n (solid behavior index) were obtained as a function of water activity between 0.755 to 0.432. Results showed that these parameters were strongly dependent on water activity for all drying methods. The constant K, which indicates the resistance against deformation, increased with decreasing water activity. on the other hand, increasing water activity resulted in higher solid behavior indexes, showing a large deviation from the Hookean behavior.

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This article presents empirical correlations to predict the density, specific heat, thermal conductivity and rheological power-law parameters of liquid egg yolk over a temperature range compatible with its industrial thermal processing (0-61 C). Moreover, a mathematical model for a pasteurizer that takes into account the spatial variation of the overall heat transfer coefficient throughout the plate heat exchanger is presented, as are two of its simplified forms. The obtained correlations of thermophysical properties are applied for the simulation of the egg yolk pasteurization, and the obtained temperature profiles are used for evaluating the extent of thermal inactivation. A detailed simulation example shows that there is a considerable deviation between the designed level of heat treatment and that this is predicted through process simulation. It is shown that a reliable mathematical model, combined with specialized thermophysical property correlations, provide a more accurate design of the pasteurization equipment that ensures effective inactivation, while preserving nutritional and sensorial characteristics.

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The physicochemical (pH, fat and total solids content), sensory (appearance, consistency and taste), and rheological characteristics of five different commercial brands of lactic beverages were determined. Rheological measurements were obtained at 5 degreesC and 25 degreesC using a Brookfield rheometer. The experimental data were described by the power law and Herschel-Bulkley models. The ANOVA of the results were conducted using an incomplete block design, and using Tukey test. Samples showed a significant difference (P less than or equal to 0.05%) for fat content and pH. There was a significant difference in total solids content only among Nestle (A), Batavo (C), and Parmalat (D) samples. Sensory evaluation showed more global acceptability for Nestle; however, Nestle and Vigor (E) lactic beverages obtained better results for appearance than for consistency and taste. Batavo obtained the best score for taste. All test samples exhibited non-Newtonian behavior, with thixotropy. Upward curves showed pseudoplastic behavior, while downward curves showed dilatant behavior with the exception of the Nestle sample, at 25 degreesC. Lactic beverages from all brands analyzed showed similar rheological behavior. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

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The properties of edible films are influenced by several factors, including thickness. The purpose of this paper was to study the influence of thickness on the viscoelasticity properties, water vapor permeability, color and opacity of cassava starch edible films. These films were prepared by a casting technique, the film-forming solutions were 1, 2, 3 and 4% (w/v) of starch, heated to 70degreesC. Different thicknesses were obtained by putting 15 to 70 g of each solution on plexiglass plates. After drying at 30degreesC and ambient relative humidity, these samples were placed for 6 days at RH of 75%, at 22degreesC. The sample thicknesses were determined by a digital micrometer (+/-0.001 mm), as the average of nine different points. The viscoelasticity properties were determined by stress relaxation tests with a texture analyser TA.XT2i (SMS), being applied the Burgers model of four parameters. The water vapor permeability was determined with a gravimetric method, and color and opacity were determined using a Miniscan XE colorimeter, operated according to the Hunterlab method. All the tests were carried out in duplicate at 22degreesC. Practically, the four visco-elasticity properties calculated by the Burgers model had the same behavior, increasing with the thickness of all films, according to a power law model. The water vapor permeability and the color difference increased linearly with the thickness (0.013-0.144 mm) of all films prepared with solution of 1 to 4% of starch. on the other hand, the effect of the variation of the thickness over the opacity, was more important in the films with 1 and 2% of starch. It can be concluded that the control of the thickness in the elaboration of starch films by the casting technique is of extreme importance.

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For the configuration optimization of plate heat exchangers (PHEs), the mathematical models for heat transfer and pressure drop must be valid for a wide range of operational conditions of all configurations of the exchanger or the design results may be compromised. In this investigation, the thermal model of a PHE is adjusted to fit experimental data obtained from non-Newtonian heat transfer for eight different configurations, using carboxymethylcellulose solutions (CMC) as test fluid. Although it is possible to successfully adjust the model parameters, Newtonian and non-Newtonian heat transfer cannot be represented by a single generalized correlation. In addition, the specific heat, thermal conductivity and power-law rheological parameters of CMC solutions were correlated with temperature, over a range compatible with a continuous pasteurization process.

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An analytical approximate method for the Dirac equation with confining power law scalar plus vector potentials, applicable to the problem of the relativistic quark confinement, is presented. The method consists in an improved version of a saddle-point variational approach and it is applied to the fundamental state of massless single quarks for some especial cases of physical interest. Our treatment emphasizes aspects such as the quantum-mechanical relativistic Virial theorem, the saddle-point character of the critical point of the expectation value of the total energy, as well as the Klein paradox and the behaviour of the saddle-point variational energies and wave functions.

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We investigate the Heston model with stochastic volatility and exponential tails as a model for the typical price fluctuations of the Brazilian São Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for inflation and a period spanning 15 years characterized by memoryless returns is chosen for the analysis. Model parameters are estimated by observing volatility scaling and correlation properties. We show that the Heston model with at least two time scales for the volatility mean reverting dynamics satisfactorily describes price fluctuations ranging from time scales larger than 20min to 160 days. At time scales shorter than 20 min we observe autocorrelated returns and power law tails incompatible with the Heston model. Despite major regulatory changes, hyperinflation and currency crises experienced by the Brazilian market in the period studied, the general success of the description provided may be regarded as an evidence for a general underlying dynamics of price fluctuations at intermediate mesoeconomic time scales well approximated by the Heston model. We also notice that the connection between the Heston model and Ehrenfest urn models could be exploited for bringing new insights into the microeconomic market mechanics. (c) 2005 Elsevier B.V. All rights reserved.

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The rheological behavior of egg yolk was studied at a range of temperatures (277-333 K) using a concentric cylinder viscometer. Rheological behavior was pseudoplastic and flow curves fitted by the power law model. The consistency and behavior indexes, dependent on temperature, were expressed by an Arrhenius-type equation. The rheological parameters, together with experimental values of pressure loss in tube flow were used to calculate friction factors. The good agreement between predicted and observed values confirmed the reliability of the equations proposed for describing the flow behavior of the egg yolk. (c) 2005 Published by Elsevier Ltd.

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Data on flow properties of Frozen Concentrated Orange Juice (FCOJ) produced from oranges cv. Pera-Rio (65.04 Brix, 8.8% w/w pulp content, 2.5% w/w pectin, 3.84% citric acid, 1.293 g cm(-3)) from -18 to 0 degrees C were fitted with appropriate predictive models. The power law model was found to be the most appropriate to fit the flow curves obtained for FCOJ between 46.56 and 65.04 degrees Brix. In higher concentrations, thixotropy was observed and showed more temperature dependence. A single equation combining Arrhenius and exponential relationships was applied to describe the temperature effect and shear rate on the quantity of breakdown of FCOJ.

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Laminar axial flow of a pseudoplastic fluid food (soursop, juice) in annular ducts has been experimentally investigated. In the first part of the manuscript, the rheological behavior of soursop juice, being essential for the annular flow analysis, was completely determined from 9.3 to 49.4 degrees Brix and temperatures from 0.4 degrees C to 68.8 degrees C, using a rotational rheometer equipped with coaxial cylinders. In order to test the adequacy of the rheology results, pressure loss data in the laminar pipe flow were collected and then experimental and theoretical friction factors were compared, showing excellent agreement, which indicated the reliability of the Power-Law model for describing the soursop juices. In the second part, pressure loss in annular regions was measured and used to estimate friction factors, which were then compared to those resulted from analytical and semi-analytical equations. The principal contributions of this article are to provide a review on the determination of friction factors-Reynolds number of pseudoplastic fluids in annuli, and also supply extensive new experimental data on the rheological properties and pressure loss of an important shear-thinning fluid food, which is of particular interest for the food engineering process design. (c) 2006 Elsevier Ltd. All rights reserved.

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We present atomic force microscopic images of the interphase morphology of vertically segregated thin films spin coated from two-component mixtures of poly[2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylene-vinylene] (MEH-PPV) and polystyrene (PS). We investigate the mechanism leading to the formation of wetting layers and lateral structures during spin coating using different PS molecular weights, solvents and blend compositions. Spinodal decomposition competes with the formation of surface enrichment layers. The spinodal wavelength as a function of PS molecular weight follows a power-law similar to bulk-like spinodal decomposition. Our experimental results indicate that length scales of interface topographical features can be adjusted from the nanometer to micrometer range. The importance of controlled arrangement of semiconducting polymers in thin film geometries for organic optoelectronic device applications is discussed. (c) 2007 Elsevier Ltd. All rights reserved.

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We present the zero-temperature phase diagram of the one-dimensional t(2g)-orbital Hubbard model, obtained using the density-matrix renormalization group and Lanczos techniques. Emphasis is given to the case of the electron density n=5 corresponding to five electrons per site, while several other cases for electron densities between n=3 and 6 are also studied. At n=5, our results indicate a first-order transition between a paramagnetic (PM) insulator phase, with power-law slowly decaying correlations, and a fully polarized ferromagnetic (FM) state by tuning the Hund's coupling. The results also suggest a transition from the n=5 PM insulator phase to a metallic regime by changing the electron density, either via hole or electron doping. The behavior of the spin, charge, and orbital correlation functions in the FM and PM states are also described in the text and discussed. The robustness of these two states against varying parameters suggests that they may be of relevance in quasi-one-dimensional Co-oxide materials, or even in higher dimensional cobaltite systems as well.