63 resultados para linear and nonlinear differential and integral equations


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This work deals with nonlinear geometric plates in the context of von Karman`s theory. The formulation is written such that only the boundary in-plane displacement and deflection integral equations for boundary collocations are required. At internal points, only out-of-plane rotation, curvature and in-plane internal force representations are used. Thus, only integral representations of these values are derived. The nonlinear system of equations is derived by approximating all densities in the domain integrals as single values, which therefore reduces the computational effort needed to evaluate the domain value influences. Hyper-singular equations are avoided by approximating the domain values using only internal nodes. The solution is obtained using a Newton scheme for which a consistent tangent operator was derived. (C) 2009 Elsevier Ltd. All rights reserved.

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This paper proposes a boundary element method (BEM) model that is used for the analysis of multiple random crack growth by considering linear elastic fracture mechanics problems and structures subjected to fatigue. The formulation presented in this paper is based on the dual boundary element method, in which singular and hyper-singular integral equations are used. This technique avoids singularities of the resulting algebraic system of equations, despite the fact that the collocation points coincide for the two opposite crack faces. In fracture mechanics analyses, the displacement correlation technique is applied to evaluate stress intensity factors. The maximum circumferential stress theory is used to evaluate the propagation angle and the effective stress intensity factor. The fatigue model uses Paris` law to predict structural life. Examples of simple and multi-fractured structures loaded until rupture are considered. These analyses demonstrate the robustness of the proposed model. In addition, the results indicate that this formulation is accurate and can model localisation and coalescence phenomena. (C) 2010 Elsevier Ltd. All rights reserved.

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The objective of the present work is to propose a numerical and statistical approach, using computational fluid dynamics, for the study of the atmospheric pollutant dispersion. Modifications in the standard k-epsilon turbulence model and additional equations for the calculation of the variance of concentration are introduced to enhance the prediction of the flow field and scalar quantities. The flow field, the mean concentration and the variance of a flow over a two-dimensional triangular hill, with a finite-size point pollutant source, are calculated by a finite volume code and compared with published experimental results. A modified low Reynolds k-epsilon turbulence model was employed in this work, using the constant of the k-epsilon model C(mu)=0.03 to take into account the inactive atmospheric turbulence. The numerical results for the velocity profiles and the position of the reattachment point are in good agreement with the experimental results. The results for the mean and the variance of the concentration are also in good agreement with experimental results from the literature. (C) 2009 Elsevier Ltd. All rights reserved.

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Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.

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BACKGROUND: The interaction between lipoxygenase-active soybean flour (LOX) and ascorbic acid (AA), on colour, rheological and sensory properties of wheat bread was studied with the aim of reducing the applied quantity of additives in bread formulations. RESULTS: The ascorbic acid (0-500 ppm) and active soybean flour (0-1%) mixture improved bread-crumb colour by lowering the yellow hue in a higher proportion than those expressed by the components alone, characterising a synergistic mechanism ((y) over cap (b) = 15.1- (1.7 x LOX) - (0.5 x AA) - (5.8 x LOX x AA), where : (y) over cap (b) represent the estimated value for the yellow hue parameter). No differences in flavour and porosity were seen between the samples. As supported by the instrumental methods, breads made with active soybean flour and ascorbic acid (LOX + AA) had whiter crumbs and were softer and springier than controls as assessed by a trained sensory panel. In summary, the combination of both active soybean flour and ascorbic acid showed synergism, promoting a greater bleaching effect than when used alone. CONCLUSION: These results suggest the potential use of active soybean flour as a synergistic ingredient in the substitution of artificial additives in bread making. Since the interaction on the bleaching response was not linear and active soybean flour showed a higher iron concentration (66.40 +/- 4.23 mu g g(-1)) than non-active soybean flour (52.30 +/- 0.40 mu g g(-1)), more studies are warranted to establish the biochemical mechanisms involved in this interaction. (c) 2007 Society of Chemical Industry.

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Conidia are responsible for reproduction, dispersal, environmental persistence and host infection of many fungal species. One of the main environmental factors that can kill and/or damage conidia is solar UV radiation. Cyclobutane pyrimidine dimers (CPD) are the major DNA photoproducts induced by UVB. We examined the conidial germination kinetics and the occurrence of CPD in DNA of conidia exposed to different doses of UVB radiation. Conidia of Aspergillus fumigatus, Aspergillus nidulans and Metarhizium acridum were exposed to UVB doses of 0.9, 1.8, 3.6 and 5.4 kJ m-2. CPD were quantified using T4 endonuclease V and alkaline agarose gel electrophoresis. Most of the doses were sublethal for all three species. Exposures to UVB delayed conidial germination and the delays were directly related both to UVB doses and CPD frequencies. The frequencies of dimers also were linear and directly proportional to the UVB doses, but the CPD yields differed among species. We also evaluated the impact of conidial pigmentation on germination and CPD induction on Metarhizium robertsii. The frequency of dimers in an albino mutant was approximately 10 times higher than of its green wild-type parent strain after exposure to a sublethal dose (1.8 kJ m-2) of UVB radiation.

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Selenium (Se) is an essential element and deficit or excess of dietary Se is associated with health disorders. Relatively elevated Se levels have been reported in the Brazilian Amazon, where there are also important annual variations in the availability of different foods. The present study was conducted among six riparian communities of the Tapajos River to evaluate seasonal variations in blood and sequential hair cm Se concentrations, and to examine the relationships between Se in blood and hair, and blood and urine. Two cross-sectional studies were conducted, at the descending water (DWS, n = 259) and the rising water (RWS, n = 137) seasons, with repeated measures for a subgroup (n = 112). Blood Se (B-Se), hair Se (H-Se) and urine Se (U-Se) were determined. Match-paired analyses were used for seasonal comparisons and the method of best fit was used to describe the relationships between biomarkers. B-Se levels presented a very large range (142-2447 mu g/l) with no overall seasonal variation (median 284 and 292 mu g/l, respectively). Sequential analysis of 13 cm hair strands showed significant variations over time: Se concentrations at the DWS were significantly lower compared with the rising water season (medians: 0.7 and 0.9 mu g/g; ranges: 0.2-4.3 mu g/g and 0.2-5.4 mu g/g, respectively). At both seasons, the relationships between B-Se and H-Se were linear and highly significant (r(2) = 67.9 and 63.6, respectively), while the relationship between B-Se and U-Se was best described by a sigmoid curve. Gender, age, education and smoking did not influence Se status or biomarker relationships. Variations in H-Se suggest that there may be seasonal availability of Se sources in local food. For populations presenting a large range and/or elevated Se exposure, sequential analyses of H-Se may provide a good reflection of variations in Se status.

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Analytical and bioanalytical methods of high-performance liquid chromatography with fluorescence detection (HPLC-FLD) were developed and validated for the determination of chloroaluminum phthalocyanine in different formulations of polymeric nanocapsules, plasma and livers of mice. Plasma and homogenized liver samples were extracted with ethyl acetate, and zinc phthalocyanine was used as internal standard. The results indicated that the methods were linear and selective for all matrices studied. Analysis of accuracy and precision showed adequate values, with variations lower than 10% in biological samples and lower than 2% in analytical samples. The recoveries were as high as 96% and 99% in the plasma and livers, respectively. The quantification limit of the analytical method was 1.12 ng/ml, and the limits of quantification of the bioanalytical method were 15 ng/ml and 75 ng/g for plasma and liver samples, respectively. The bioanalytical method developed was sensitive in the ranges of 15-100 ng/ml in plasma and 75-500 ng/g in liver samples and was applied to studies of biodistribution and pharmacokinetics of AlClPc. (C) 2011 Elsevier B.V. All rights reserved.

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Objective. The objective of this study was to evaluate, using computed tomography, correlations between Hyrax appliance opening and post-SARPE skeletal changes. Study design. Fifteen patients underwent SARPE according to a specific protocol and were followed. Linear and angular measurements of the anterior, intermediate, and posterior portions of the maxilla were evaluated. The correlation between maxillary expansion and appliance opening was investigated. Results. Significant overall expansion was observed. In the anterior and intermediate portions of the maxilla, the increase in maxillary width was greater than that observed in the posterior portion. The degree of appliance opening was significantly greater than that of the skeletal expansion. Also, no linear correlation between appliance opening and regional maxillary expansion was established. Conclusion. The transverse expansion of the maxilla was less than uniform. The lack of linear correlation between appliance opening and skeletal expansion is attributable to multiple factors, including those related to the device, the surgical technique, and the craniofacial deformity itself. (Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2008; 106: 812-819)

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The aims of this study were: (1) to correlate surface (SH) and cross-sectional hardness (CSH) with microradiographic parameters of artificial enamel lesions; (2) to compare lesions prepared by different protocols. Fifty bovine enamel specimens were allocated by stratified randomisation according to their initial SH values to five groups and lesions produced by different methods: MC gel (methylcellulose gel/lactic acid, pH 4.6, 14 days); PA gel (polyacrylic acid/lactic acid/hydroxyapatite, pH 4.8, 16 h); MHDP (undersaturated lactate buffer/methyl diphosphonate, pH 5.0, 6 days); buffer (undersaturated acetate buffer/fluoride, pH 5.0, 16 h), and pH cycling (7 days). SH of the lesions (SH(1)) was measured. The specimens were longitudinally sectioned and transverse microradiography (TMR) and CSH measured at 10- to 220-mu m depth from the surface. Overall, there was a medium correlation but non-linear and variable relationship between mineral content and root CSH. root SH(1) was weakly to moderately correlated with surface layer properties, weakly correlated with lesion depth but uncorrelated with integrated mineral loss. MHDP lesions showed the highest subsurface mineral loss, followed by pH cycling, buffer, PA gel and MC gel lesions. The conclusions were: (1) CSH, as an alternative to TMR, does not estimate mineral content very accurately, but gives information about mechanical properties of lesions; (2) SH should not be used to analyse lesions; (3) artificial caries lesions produced by the protocols differ, especially considering the method of analysis. Copyright (C) 2009 S. Karger AG, Basel

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The objective of this study was to identify and quantify the influence of F (inbreeding coefficient) on weaning weight (WW), weight gain from weaning to 18 months of age (WG345), finishing visual score (precocity) at 18 months of age, muscling visual score at 18 months of age (MUS), hip height (HH), scrotal circumference at 18 months of age (SC), heifer probability of pregnancy at 14 months of age (PP14), and stayability (STAY) in Brazilian Nellore cattle. The complete pedigree included 417,552 animals born between 1984 and 2007 on 12 farms located in the states of Mato Grosso do Sul, Sao Paulo and Bahia. Following the observation of a statistically significant effect (P<0.05) of the covariates individual inbreeding coefficient (F) and maternal inbreeding coefficient, regression analysis of each trait, adjusted for all other effects, was performed as a function of the linear and quadratic effect of F and maternal F (when significant). Inbreeding negatively affected all traits studied (P<0.05), except for muscling. A quadratic effect of individual F on WW, WG345, HH and PP14, and a quadratic effect of maternal F on WG345 and HH were observed. Levels of inbreeding higher than 7-11% affected negatively growth and reproductive performance of Nellore cattle. Therefore, inbreeding should be avoided, except for purposes of genetic breeding whose main objective is the fixation of certain alleles in the population. (C) 2010 Elsevier B.V. All rights reserved.

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The kinematic expansion history of the universe is investigated by using the 307 supernovae type Ia from the Union Compilation set. Three simple model parameterizations for the deceleration parameter ( constant, linear and abrupt transition) and two different models that are explicitly parametrized by the cosmic jerk parameter ( constant and variable) are considered. Likelihood and Bayesian analyses are employed to find best fit parameters and compare models among themselves and with the flat Lambda CDM model. Analytical expressions and estimates for the deceleration and cosmic jerk parameters today (q(0) and j(0)) and for the transition redshift (z(t)) between a past phase of cosmic deceleration to a current phase of acceleration are given. All models characterize an accelerated expansion for the universe today and largely indicate that it was decelerating in the past, having a transition redshift around 0.5. The cosmic jerk is not strongly constrained by the present supernovae data. For the most realistic kinematic models the 1 sigma confidence limits imply the following ranges of values: q(0) is an element of [-0.96, -0.46], j(0) is an element of [-3.2,-0.3] and z(t) is an element of [0.36, 0.84], which are compatible with the Lambda CDM predictions, q(0) = -0.57 +/- 0.04, j(0) = -1 and z(t) = 0.71 +/- 0.08. We find that even very simple kinematic models are equally good to describe the data compared to the concordance Lambda CDM model, and that the current observations are not powerful enough to discriminate among all of them.

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In this article, we present a generalization of the Bayesian methodology introduced by Cepeda and Gamerman (2001) for modeling variance heterogeneity in normal regression models where we have orthogonality between mean and variance parameters to the general case considering both linear and highly nonlinear regression models. Under the Bayesian paradigm, we use MCMC methods to simulate samples for the joint posterior distribution. We illustrate this algorithm considering a simulated data set and also considering a real data set related to school attendance rate for children in Colombia. Finally, we present some extensions of the proposed MCMC algorithm.

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In this article we address decomposition strategies especially tailored to perform strong coupling of dimensionally heterogeneous models, under the hypothesis that one wants to solve each submodel separately and implement the interaction between subdomains by boundary conditions alone. The novel methodology takes full advantage of the small number of interface unknowns in this kind of problems. Existing algorithms can be viewed as variants of the `natural` staggered algorithm in which each domain transfers function values to the other, and receives fluxes (or forces), and vice versa. This natural algorithm is known as Dirichlet-to-Neumann in the Domain Decomposition literature. Essentially, we propose a framework in which this algorithm is equivalent to applying Gauss-Seidel iterations to a suitably defined (linear or nonlinear) system of equations. It is then immediate to switch to other iterative solvers such as GMRES or other Krylov-based method. which we assess through numerical experiments showing the significant gain that can be achieved. indeed. the benefit is that an extremely flexible, automatic coupling strategy can be developed, which in addition leads to iterative procedures that are parameter-free and rapidly converging. Further, in linear problems they have the finite termination property. Copyright (C) 2009 John Wiley & Sons, Ltd.

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We study the propagation of perturbations in the energy density in a quark gluon plasma. Expanding the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations we obtain a nonlinear differential equation called the breaking wave equation. We solve it numerically and follow the time-evolution of initially localized pulses. We find that, quite unexpectedly, these pulses live for a very long time (compared to the reaction time-scales) before breaking. In practice, they mimick the Korteweg-de Vries solitons. Their existence may have some observable consequences.