A Finite Element Numerical Algorithm for Modelling and Data Fitting in Complex Systems

Numerical modelling methodologies are important by their application to engineering and scientific problems, because there are processes where analytical mathematical expressions cannot be obtained to model them. When the only available information is a set of experimental values for the variables that determine the state of the system, the modelling problem is equivalent to determining the hyper-surface that best fits the data. This paper presents a methodology based on the Galerkin formulation of the finite elements method to obtain representations of relationships that are defined a priori, between a set of variables: y = z(x1, x2,...., xd). These representations are generated from the values of the variables in the experimental data. The approximation, piecewise, is an element of a Sobolev space and has derivatives defined in a general sense into this space. The using of this approach results in the need of inverting a linear system with a structure that allows a fast solver algorithm. The algorithm can be used in a variety of fields, being a multidisciplinary tool. The validity of the methodology is studied considering two real applications: a problem in hydrodynamics and a problem of engineering related to fluids, heat and transport in an energy generation plant. Also a test of the predictive capacity of the methodology is performed using a cross-validation method.

Penalized Least Squares Fitting

* Supported by the Army Research Office under grant DAAD-19-02-10059.

H(infinity) filtering for rectangular discrete-time descriptor systems

This paper deals with the H(infinity) recursive estimation problem for general rectangular time-variant descriptor systems in discrete time. Riccati-equation based recursions for filtered and predicted estimates are developed based on a data fitting approach and game theory. In this approach, the nature determines a state sequence seeking to maximize the estimation cost, whereas the estimator tries to find an estimate that brings the estimation cost to a minimum. A solution exists for a specified gamma-level if the resulting cost is positive. In order to present some computational alternatives to the H(infinity) filters developed, they are rewritten in information form along with the respective array algorithms. (C) 2009 Elsevier Ltd. All rights reserved.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Kinetics of phosphorus sorption in soils in the state of Paraíba¹

The soil P sorption capacity has been studied for many years, but little attention has been paid to the rate of this process, which is relevant in the planning of phosphate fertilization. The purpose of this experiment was to assess kinetics of P sorption in 12 representative soil profiles of the State of Paraíba (Brazil), select the best data fitting among four equations and relate these coefficients to the soil properties. Samples of 12 soils with wide diversity of physical, chemical and mineralogical properties were agitated in a horizontal shaker, with 10 mmo L-1 CaCl2 solution containing 6 and 60 mg L-1 P, for periods of 5, 15, 30, 45, 60, 90, 120, 420, 720, 1,020, and 1,440 min. After each shaking period, the P concentration in the equilibrium solution was measured and three equations were fitted based on the Freundlich equation and one based on the Elovich equation, to determine which soil had the highest sorption rate (kinetics) and which soil properties correlated to this rate. The kinetics of P sorption in soils with high maximum P adsorption capacity (MPAC) was fast for 30 min at the lower initial P concentration (6 mg L-1). No difference was observed between soils at the higher initial P concentration (60 mg L-1). The P adsorption kinetics were positively correlated with clay content, MPAC and the amount of Al extracted with dithionite-citrate-bicarbonate. The data fitted well to Freundlich-based equations equation, whose coefficients can be used to predict P adsorption rates in soils.

Caracterização ácido-base da superfície de espécies mistas da alga Spirulina através de titulação potenciométrica e modelo de distribuição de sítios discretos

Acid base properties of mixed species of the microalgae Spirulina were studied by potentiometric titration in medium of 0.01 and 0.10 mols L-1 NaNO3 at 25.0±0.10 C using modified Gran functions or nonlinear regression techniques for data fitting. The discrete site distribution model was used, permitting the characterization of five classes of ionizable sites in both ionic media. This fact suggests that the chemical heterogeneity of the ionizable sites on the cell surface plays a major role on the acid-base properties of the suspension in comparison to electrostatic effects due to charge-charge interactions. The total of ionizable sites were 1.75±0.10 and 1.86±0.20 mmolsg-1 in ionic media of 0.01 and 0.10 mols L-1 NaNO3, respectively. A major contribution of carboxylic groups was observed with an average 34 and 22% of ionizable sites being titrated with conditional pcKa of 4.0 and 5.4, respectively. The remaining 44% of ionizable sites were divided in three classes with averaged conditional pcKa of 6.9, 8.7 and 10.12, which may be assigned respectively to imidazolic, aminic, and phenolic functionalities.

Modelling oil absorption during post-frying cooling - I: model development

Several studies have highlighted the importance of the cooling period in oil absorption in deep-fat fried products. Specifically, it has been established that the largest proportion of oil which ends up into the food, is sucked into the porous crust region after the fried product is removed from the oil bath, stressing the importance of this time interval. The main objective of this paper was to develop a predictive mechanistic model that can be used to understand the principles behind post-frying cooling oil absorption kinetics, which can also help identifying the key parameters that affect the final oil intake by the fried product. The model was developed for two different geometries, an infinite slab and an infinite cylinder, and was divided into two main sub-models, one describing the immersion frying period itself and the other describing the post-frying cooling period. The immersion frying period was described by a transient moving-front model that considered the movement of the crust/core interface, whereas post-frying cooling oil absorption was considered to be a pressure driven flow mediated by capillary forces. A key element in the model was the hypothesis that oil suction would only begin once a positive pressure driving force had developed. The mechanistic model was based on measurable physical and thermal properties, and process parameters with no need of empirical data fitting, and can be used to study oil absorption in any deep-fat fried product that satisfies the assumptions made.

Modelling the interdependence between the stoichiometry of receptor oligomerization and ligand binding for a coexisting dimer/tetramer receptor system

Many G protein-coupled receptors have been shown to exist as oligomers, but the oligomerization state and the effects of this on receptor function are unclear. For some G protein-coupled receptors, in ligand binding assays, different radioligands provide different maximal binding capacities. Here we have developed mathematical models for co-expressed dimeric and tetrameric species of receptors. We have considered models where the dimers and tetramers are in equilibrium and where they do not interconvert and we have also considered the potential influence of the ligands on the degree of oligomerization. By analogy with agonist efficacy, we have considered ligands that promote, inhibit or have no effect on oligomerization. Cell surface receptor expression and the intrinsic capacity of receptors to oligomerize are quantitative parameters of the equations. The models can account for differences in the maximal binding capacities of radioligands in different preparations of receptors and provide a conceptual framework for simulation and data fitting in complex oligomeric receptor situations.

Número mínimo de tensões para determinação da curva característica de retenção de água de um latossolo vermelho eutrófico sob sistema de semeadura direta

Para o conhecimento do comportamento físico-hídrico do solo, é fundamental a determinação da curva de retenção de água (CRA). A aquisição de dados para obtenção da CRA envolve processos demorados e custos elevados. A hipótese deste estudo foi a de que é possível determinar a CRA com menor número de tensões, reduzindo seu tempo de obtenção, sem, contudo, comprometer a acurácia dos resultados. Assim, o objetivo deste trabalho foi determinar quais tensões podem ser utilizadas para determinação da CRA de Latossolo Vermelho eutrófico de maneira acurada e em menor tempo. Foram determinados os conteúdos de água retidos em amostras de um Latossolo Vermelho eutrófico sob sistema de semeadura direta (SSD). As tensões utilizadas na determinação dos conteúdos de água foram: 0, 10, 20, 40, 60, 80, 100, 200, 300, 500, 700, 1.000, 3.000, 5.000 e 15.000 hPa. Os dados foram combinados e determinaram-se 450 CRAs ajustadas pelo modelo de van Genuchten. Os parâmetros α, m, n e Ug res, gerados pelo modelo, foram submetidos à análise de variância (teste F) e as médias comparadas pelo teste de Scott-Knott (p = 0,05). A hipótese deste estudo foi confirmada, ou seja, é possível determinar a CRA com menor número de tensões, reduzindo seu tempo de obtenção em até cinco vezes, sem, contudo, comprometer a acurácia dos resultados. A tensão de 15.000 hPa deve estar contida na combinação de tensões a serem utilizadas para determinação da curva característica de retenção de água, quando se emprega o modelo matemático de van Genuchten para ajuste dos dados. As curvas características de retenção de água do solo, definidas com as combinações de tensões (0, 60, 700 e 15.000 hPa), (0, 80, 700 e 15.000 hPa), (0, 100, 1.000 e 15.000 hPa), (0, 20, 60, 100, 700 e 15.000 hPa), (0, 80, 300, 700 e 15.000 hPa) e (0, 100, 300, 1.000 e 15.000 hPa), sendo os dados ajustados ao modelo de van Genuchten, proporcionaram estimativas dos conteúdos de água, retidos no Latossolo Vermelho eutrófico sob sistema de semeadura direta, com a mesma acurácia, quando comparada à curva de referência partindo-se de um conjunto de 15 valores de tensões.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

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

Análise dos Processos de Flotação e Oxidação Avançada para o Tratamento de Efluente Modelo da Indústria do Petróleo

The generation of wastes in most industrial process is inevitable. In the petroleum industry, one of the greatest problems for the environment is the huge amount of produced water generated in the oil fields. This wastewater is a complex mixture and present great amounts. These effluents can be hazardous to the environmental without adequate treatment. This research is focused in the analysis of the efficiencies of the flotation and photo-oxidation processes to remove and decompose the organic compounds present in the produced water. A series of surfactants derivated from the laurilic alcohol was utilized in the flotation to promote the separation. The experiments have been performed with a synthetic wastewater, carefully prepared with xylene. The experimental data obtained using flotation presented a first order kinetic, identified by the quality of the linear data fitting. The best conditions were found at 0.029 g.L-1 for the surfactant EO 7, 0.05 g.L-1 for EO 8, 0.07 g.L-1 for EO 9, 0.045 g.L-1 for EO 10 and 0.08 g.L-1 for EO 23 with the following estimated kinetic constants: 0.1765, 0.1325, 0.1210, 0.1531 and 0.1699 min-1, respectively. For the series studied, the most suitable surfactant was the EO 7 due to the lower reagent onsumption, higher separation rate constant and higher removal efficiency of xylene in the aqueous phase (98%). Similarly to the flotation, the photo-Fenton process shows to be efficient for degradation of xylene and promoting the mineralization of the organic charge around 90% and 100% in 90 min

Análise dos Processos de Flotação e Oxidação Avançada para o Tratamento de Efluente Modelo da Indústria do Petróleo

The generation of wastes in most industrial process is inevitable. In the petroleum industry, one of the greatest problems for the environment is the huge amount of produced water generated in the oil fields. This wastewater is a complex mixture and present great amounts. These effluents can be hazardous to the environmental without adequate treatment. This research is focused in the analysis of the efficiencies of the flotation and photo-oxidation processes to remove and decompose the organic compounds present in the produced water. A series of surfactants derivated from the laurilic alcohol was utilized in the flotation to promote the separation. The experiments have been performed with a synthetic wastewater, carefully prepared with xylene. The experimental data obtained using flotation presented a first order kinetic, identified by the quality of the linear data fitting. The best conditions were found at 0.029 g.L-1 for the surfactant EO 7, 0.05 g.L-1 for EO 8, 0.07 g.L-1 for EO 9, 0.045 g.L-1 for EO 10 and 0.08 g.L-1 for EO 23 with the following estimated kinetic constants: 0.1765, 0.1325, 0.1210, 0.1531 and 0.1699 min-1, respectively. For the series studied, the most suitablesurfactant was the EO 7 due to the lower reagent consumption, higher separation rate constant and higher removal efficiency of xylene in the aqueous phase (98%). Similarly to the flotation, the photo-Fenton process shows to be efficient for degradation of xylene and promoting the mineralization of the organic charge around 90% and 100% in 90 min

Influence from the free volume on the photoinduced birefringence in azocompound-containing polymers

The photoinduced birefringence is analyzed in a guest-host azobenzene-containing polymer in the temperature range from 20 to 330 K. An anomalous behavior arises in the low-temperature range, suggesting strong influence from the free volume for the chromophores in the polymer. This influence is so strong that quenched samples have a photoinduced signal ca. 5 times greater than the annealed ones at room temperature. An extended free volume model is presented based on two assumptions about thermal fluctuations in the cavities and their size distribution. This model, which is an extension of the model by Mita et al., can explain the main features of the photoinduced birefringence as a function of time, temperature, and initial free volume state. To account for the influence of free volume on the photoorientation, the detailed reorientation model by Sekkat's was used. We show that Sekkat's model leads to an exponential behavior at small orientation regimes, which simplifies the mathematical treatment and allows the mean free volume to be obtained from the data fitting.

Strong and fast phase modulation for quantitative analysis of photorefractive gratings

A new approach for studying photorefractive gratings in two-wave mixing experiments by a phase modulation technique is presented. The introduction of a large-amplitude, high-frequency sinusoidal phase modulation in one of the input beams blurs the interference pattern and provides powerful harmonic signals for accurate measurements of the grating diffraction efficiency eta and the output phase shift rho between the transmitted and diffracted waves. The blurring of the light fringes can be used to suppress the higher spatial harmonics of the grating, allowing a space-charge field with sinusoidal profile to be recorded. Although the presence of such a strong phase modulation affects the beam coupling in a rather complicated way, it is shown that for the special case of equal intensity input beams, the effect of the phase modulation on eta and rho is reduced to a weakening of the coupling strength. The potentialities of the technique are illustrated in a study of refractive-index waves excited by running interference patterns in a Bi12TiO20 crystal. Expressions for the diffraction efficiency and the output phase shift are derived and used to match numerically calculated curves to the experimental data. The theoretical model is supported by the very good data fitting and allows the computation of important material parameters.

Descrição da resposta germinativa de cultivares de Phaseolus vulgaris L. (Fabaceae) à temperatura e ao potencial osmótico

Pós-graduação em Ciências Biológicas (Biologia Vegetal) - IBRC