Numerical study of Petrov-Galerkin formulations for the shallow water wave equations

The behavior of Petrov-Galerkin formulations for shallow water wave equations is evaluated numerically considering typical one-dimensional propagation problems. The formulations considered here use stabilizing operators to improve classical Galerkin approaches. Their advantages and disadvantages are pointed out according to the intrinsic time scale (free parameter) which has a particular importance in this kind of problem. The influence of the Courant number and the performance of the formulation in dealing with spurious oscillations are adressed.

Covalidation of Integral Transforms and Method of Lines in Nonlinear Convection-Diffusion with Mathematica

The Mathematica system (version 4.0) is employed in the solution of nonlinear difusion and convection-difusion problems, formulated as transient one-dimensional partial diferential equations with potential dependent equation coefficients. The Generalized Integral Transform Technique (GITT) is first implemented for the hybrid numerical-analytical solution of such classes of problems, through the symbolic integral transformation and elimination of the space variable, followed by the utilization of the built-in Mathematica function NDSolve for handling the resulting transformed ODE system. This approach ofers an error-controlled final numerical solution, through the simultaneous control of local errors in this reliable ODE's solver and of the proposed eigenfunction expansion truncation order. For covalidation purposes, the same built-in function NDSolve is employed in the direct solution of these partial diferential equations, as made possible by the algorithms implemented in Mathematica (versions 3.0 and up), based on application of the method of lines. Various numerical experiments are performed and relative merits of each approach are critically pointed out.

Flows of Bingham Materials Through Ideal Porous Media: an Experimental and Theoretical Study

The flow of Bingham liquids through porous media has been studied. Experiments have been performed to determine the flow rate / pressure drop relationship for the flow of a grease of Binghamian rheological behavior through an array of rods of circular cross section. The yield stress and plastic viscosity of the grease have been determined with the aid of a controlled stress rotational rheometer. To investigate a wider range of the flow parameters, the mass and momentum conservation equations have been solved numerically, in conjunction with the generalized Newtonian constitutive law and the bi-viscosity model. The finite volume method has been employed to obtain the numerical solution. These numerical results also yielded a flow rate / pressure drop relationship, which is in very good agreement with the experimental results. A capillaric theory has been developed to determine an analytical relationship between the flow rate and pressure drop for flows of Bingham liquids through porous media. It is shown that the predictions of this theory are in good agreement with the experimental and numerical results.

Limited-sampling strategy models for estimating the pharmacokinetic parameters of 4-methylaminoantipyrine, an active metabolite of dipyrone

Bioanalytical data from a bioequivalence study were used to develop limited-sampling strategy (LSS) models for estimating the area under the plasma concentration versus time curve (AUC) and the peak plasma concentration (Cmax) of 4-methylaminoantipyrine (MAA), an active metabolite of dipyrone. Twelve healthy adult male volunteers received single 600 mg oral doses of dipyrone in two formulations at a 7-day interval in a randomized, crossover protocol. Plasma concentrations of MAA (N = 336), measured by HPLC, were used to develop LSS models. Linear regression analysis and a "jack-knife" validation procedure revealed that the AUC0-¥ and the Cmax of MAA can be accurately predicted (R²>0.95, bias <1.5%, precision between 3.1 and 8.3%) by LSS models based on two sampling times. Validation tests indicate that the most informative 2-point LSS models developed for one formulation provide good estimates (R²>0.85) of the AUC0-¥ or Cmax for the other formulation. LSS models based on three sampling points (1.5, 4 and 24 h), but using different coefficients for AUC0-¥ and Cmax, predicted the individual values of both parameters for the enrolled volunteers (R²>0.88, bias = -0.65 and -0.37%, precision = 4.3 and 7.4%) as well as for plasma concentration data sets generated by simulation (R²>0.88, bias = -1.9 and 8.5%, precision = 5.2 and 8.7%). Bioequivalence assessment of the dipyrone formulations based on the 90% confidence interval of log-transformed AUC0-¥ and Cmax provided similar results when either the best-estimated or the LSS-derived metrics were used.

A simple model for circadian timing by mammals

Circadian timing is structured in such a way as to receive information from the external and internal environments, and its function is the timing organization of the physiological and behavioral processes in a circadian pattern. In mammals, the circadian timing system consists of a group of structures, which includes the suprachiasmatic nucleus (SCN), the intergeniculate leaflet and the pineal gland. Neuron groups working as a biological pacemaker are found in the SCN, forming a biological master clock. We present here a simple model for the circadian timing system of mammals, which is able to reproduce two fundamental characteristics of biological rhythms: the endogenous generation of pulses and synchronization with the light-dark cycle. In this model, the biological pacemaker of the SCN was modeled as a set of 1000 homogeneously distributed coupled oscillators with long-range coupling forming a spherical lattice. The characteristics of the oscillator set were defined taking into account the Kuramoto's oscillator dynamics, but we used a new method for estimating the equilibrium order parameter. Simultaneous activities of the excitatory and inhibitory synapses on the elements of the circadian timing circuit at each instant were modeled by specific equations for synaptic events. All simulation programs were written in Fortran 77, compiled and run on PC DOS computers. Our model exhibited responses in agreement with physiological patterns. The values of output frequency of the oscillator system (maximal value of 3.9 Hz) were of the order of magnitude of the firing frequencies recorded in suprachiasmatic neurons of rodents in vivo and in vitro (from 1.8 to 5.4 Hz).

Attentional bias modulation by reappraisal in patients with generalized anxiety disorder: an event-related potential study

Affective states influence subsequent attention allocation. We evaluated emotional negativity bias modulation by reappraisal in patients with generalized anxiety disorder (GAD) relative to normal controls. Event-related potential (ERP) recordings were obtained, and changes in P200 and P300 amplitudes in response to negative or neutral words were noted after decreasing negative emotion or establishing a neutral condition. We found that in GAD patients only, the mean P200 amplitude after negative word presentation was much higher than after the presentation of neutral words. In normal controls, after downregulation of negative emotion, the mean P300 amplitude in response to negative words was much lower than after neutral words, and this was significant in both the left and right regions. In GAD patients, the negative bias remained prominent and was not affected by reappraisal at the early stage. Reappraisal was observed to have a lateralized effect at the late stage.

Estimating the average length of hospitalization due to pneumonia: a fuzzy approach

Exposure to air pollutants is associated with hospitalizations due to pneumonia in children. We hypothesized the length of hospitalization due to pneumonia may be dependent on air pollutant concentrations. Therefore, we built a computational model using fuzzy logic tools to predict the mean time of hospitalization due to pneumonia in children living in São José dos Campos, SP, Brazil. The model was built with four inputs related to pollutant concentrations and effective temperature, and the output was related to the mean length of hospitalization. Each input had two membership functions and the output had four membership functions, generating 16 rules. The model was validated against real data, and a receiver operating characteristic (ROC) curve was constructed to evaluate model performance. The values predicted by the model were significantly correlated with real data. Sulfur dioxide and particulate matter significantly predicted the mean length of hospitalization in lags 0, 1, and 2. This model can contribute to the care provided to children with pneumonia.

Air blast freezing of fruit pulp models in commercial boxes: influence of preferential channels in the bed on freezing times estimating

The freezing times of fruit pulp models packed and conditioned in multi-layered boxes were evaluated under conditions similar to those employed commercially. Estimating the freezing time is a difficult practice due to the presence of significant voids in the boxes, whose influence may be analyzed by means of various methods. In this study, a procedure for estimating freezing time by using the models described in the literature was compared with experimental measurements by collecting time/temperature data. The following results show that the airflow through packages is a significant parameter for freezing time estimation. When the presence of preferential channels was considered, the predicted freezing time in the models could be 10% lower than the experimental values, depending on the method. The isotherms traced as a function of the location of the samples inside the boxes showed the displacement of the thermal center in relation to the geometric center of the product.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.

Estimating microalgae Synechococcus nidulans daily biomass concentration using neuro-fuzzy network

In this study, a neuro-fuzzy estimator was developed for the estimation of biomass concentration of the microalgae Synechococcus nidulans from initial batch concentrations, aiming to predict daily productivity. Nine replica experiments were performed. The growth was monitored daily through the culture medium optic density and kept constant up to the end of the exponential phase. The network training followed a full 3³ factorial design, in which the factors were the number of days in the entry vector (3,5 and 7 days), number of clusters (10, 30 and 50 clusters) and internal weight softening parameter (Sigma) (0.30, 0.45 and 0.60). These factors were confronted with the sum of the quadratic error in the validations. The validations had 24 (A) and 18 (B) days of culture growth. The validations demonstrated that in long-term experiments (Validation A) the use of a few clusters and high Sigma is necessary. However, in short-term experiments (Validation B), Sigma did not influence the result. The optimum point occurred within 3 days in the entry vector, 10 clusters and 0.60 Sigma and the mean determination coefficient was 0.95. The neuro-fuzzy estimator proved a credible alternative to predict the microalgae growth.