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.

Estimating Attractor Dimension on the Nonlinear Pendulum Time Series

Chaotic dynamical systems exhibit trajectories in their phase space that converges to a strange attractor. The strangeness of the chaotic attractor is associated with its dimension in which instance it is described by a noninteger dimension. This contribution presents an overview of the main definitions of dimension discussing their evaluation from time series employing the correlation and the generalized dimension. The investigation is applied to the nonlinear pendulum where signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the time series. State space reconstruction and the determination of attractor dimensions are carried out regarding periodic and chaotic signals. Results obtained from time series analyses are compared with a reference value obtained from the analysis of mathematical model, estimating noise sensitivity. This procedure allows one to identify the best techniques to be applied in the analysis of experimental data.

Simulation of Steady-State Nonlinear Heat Transfer Problems Through the Minimization of Quadratic Functionals

In this work it is presented a systematic procedure for constructing the solution of a large class of nonlinear conduction heat transfer problems through the minimization of quadratic functionals like the ones usually employed for linear descriptions. The proposed procedure gives rise to an efficient and easy way for carrying out numerical simulations of nonlinear heat transfer problems by means of finite elements. To illustrate the procedure a particular problem is simulated by means of a finite element approximation.

An Investigation into Mechanisms of Loss of Safe Basins in a 2 D.O.F. Nonlinear Oscillator

In this work we consider the transient stability of coupled motions of a 2 D.O.F. nonlinear oscillator that can represent, for example, the motions of a sea vessel under the action of trains of regular lateral waves. Instability is studied as the escape of the system from a safe potential well. The set of initial conditions in phase space that lead to acceptable motions constitutes its safe basin. We investigate the evolution of these safe basins under variation of parameters such as frequency and amplitude of waves, and an internal tuning parameter. Complex nonlinear phenomena are known to play an important role in determining the loss of safe basins as, say, wave amplitude is increased. We therefore investigate those processes, and attempt to classify them in terms of their speed relative to changes in parameter values. "Mechanism basins" are produced depicting regions of parameter space in which rapid or slow losses of safe basin are observed. We propose that a comprehensive understanding of mechanisms of loss of safe basins can be a valuable tool in assessing stability properties of these systems, and we give a conceptual view of how such information could be used.

Experimental Vibration Characteristics of a Beam with Nonlinear Support Using Receptance Coupling Analysis

This paper applies the Multi-Harmonic Nonlinear Receptance Coupling Approach (MUHANORCA) (Ferreira 1998) to evaluate the frequency response characteristics of a beam which is clamped at one end and supported at the other end by a nonlinear cubic stiffness joint. In order to apply the substructure coupling technique, the problem was characterised by coupling a clamped linear beam with a nonlinear cubic stiffness joint. The experimental results were obtained by a sinusoidal excitation with a special force control algorithm where the level of the fundamental force is kept constant and the level of the harmonics is kept zero for all the frequencies measured.

Application of the center manifold theory to the study of slewing flexible Non-ideal structures with nonlinear curvature: a case study

In this paper is Analyzed the local dynamical behavior of a slewing flexible structure considering nonlinear curvature. The dynamics of the original (nonlinear) governing equations of motion are reduced to the center manifold in the neighborhood of an equilibrium solution with the purpose of locally study the stability of the system. In this critical point, a Hopf bifurcation occurs. In this region, one can find values for the control parameter (structural damping coefficient) where the system is unstable and values where the system stability is assured (periodic motion). This local analysis of the system reduced to the center manifold assures the stable / unstable behavior of the original system around a known solution.

Early prediction of poor outcome in patients with acute asthma in the emergency room

Early identification of patients who need hospitalization or patients who should be discharged would be helpful for the management of acute asthma in the emergency room. The objective of the present study was to examine the clinical and pulmonary functional measures used during the first hour of assessment of acute asthma in the emergency room in order to predict the outcome. We evaluated 88 patients. The inclusion criteria were age between 12 and 55 years, forced expiratory volume in the first second below 50% of predicted value, and no history of chronic disease or pregnancy. After baseline evaluation, all patients were treated with 2.5 mg albuterol delivered by nebulization every 20 min in the first hour and 60 mg of intravenous methylprednisolone. Patients were reevaluated after 60 min of treatment. Sixty-five patients (73.9%) were successfully treated and discharged from the emergency room (good responders), and 23 (26.1%) were hospitalized or were treated and discharged with relapse within 10 days (poor responders). A predictive index was developed: peak expiratory flow rates after 1 h <=0% of predicted values and accessory muscle use after 1 h. The index ranged from 0 to 2. An index of 1 or higher presented a sensitivity of 74.0, a specificity of 69.0, a positive predictive value of 46.0, and a negative predictive value of 88.0. It was possible to predict outcome in the first hour of management of acute asthma in the emergency room when the index score was 0 or 2.

Prediction of exposed domains of envelope glycoprotein in Indian HIV-1 isolates and experimental confirmation of their immunogenicity in humans

We describe the impact of subtype differences on the seroreactivity of linear antigenic epitopes in envelope glycoprotein of HIV-1 isolates from different geographical locations. By computer analysis, we predicted potential antigenic sites of envelope glycoprotein (gp120 and gp4l) of this virus. For this purpose, after fetching sequences of proteins of interest from data banks, values of hydrophilicity, flexibility, accessibility, inverted hydrophobicity, and secondary structure were considered. We identified several potential antigenic epitopes in a B subtype strain of envelope glycoprotein of HIV-1 (IIIB). Solid- phase peptide synthesis methods of Merrifield and Fmoc chemistry were used for synthesizing peptides. These synthetic peptides corresponded mainly to the C2, V3 and CD4 binding sites of gp120 and some parts of the ectodomain of gp41. The reactivity of these peptides was tested by ELISA against different HIV-1-positive sera from different locations in India. For two of these predicted epitopes, the corresponding Indian consensus sequences (LAIERYLKQQLLGWG and DIIGDIRQAHCNISEDKWNET) (subtype C) were also synthesized and their reactivity was tested by ELISA. These peptides also distinguished HIV-1-positive sera of Indians with C subtype infections from sera from HIV-negative subjects.

Clinical signs of pneumonia in children: association with and prediction of diagnosis by fuzzy sets theory

The present study compares the performance of stochastic and fuzzy models for the analysis of the relationship between clinical signs and diagnosis. Data obtained for 153 children concerning diagnosis (pneumonia, other non-pneumonia diseases, absence of disease) and seven clinical signs were divided into two samples, one for analysis and other for validation. The former was used to derive relations by multi-discriminant analysis (MDA) and by fuzzy max-min compositions (fuzzy), and the latter was used to assess the predictions drawn from each type of relation. MDA and fuzzy were closely similar in terms of prediction, with correct allocation of 75.7 to 78.3% of patients in the validation sample, and displaying only a single instance of disagreement: a patient with low level of toxemia was mistaken as not diseased by MDA and correctly taken as somehow ill by fuzzy. Concerning relations, each method provided different information, each revealing different aspects of the relations between clinical signs and diagnoses. Both methods agreed on pointing X-ray, dyspnea, and auscultation as better related with pneumonia, but only fuzzy was able to detect relations of heart rate, body temperature, toxemia and respiratory rate with pneumonia. Moreover, only fuzzy was able to detect a relationship between heart rate and absence of disease, which allowed the detection of six malnourished children whose diagnoses as healthy are, indeed, disputable. The conclusion is that even though fuzzy sets theory might not improve prediction, it certainly does enhance clinical knowledge since it detects relationships not visible to stochastic models.

Fuzzy expert system in the prediction of neonatal resuscitation

In view of the importance of anticipating the occurrence of critical situations in medicine, we propose the use of a fuzzy expert system to predict the need for advanced neonatal resuscitation efforts in the delivery room. This system relates the maternal medical, obstetric and neonatal characteristics to the clinical conditions of the newborn, providing a risk measurement of need of advanced neonatal resuscitation measures. It is structured as a fuzzy composition developed on the basis of the subjective perception of danger of nine neonatologists facing 61 antenatal and intrapartum clinical situations which provide a degree of association with the risk of occurrence of perinatal asphyxia. The resulting relational matrix describes the association between clinical factors and risk of perinatal asphyxia. Analyzing the inputs of the presence or absence of all 61 clinical factors, the system returns the rate of risk of perinatal asphyxia as output. A prospectively collected series of 304 cases of perinatal care was analyzed to ascertain system performance. The fuzzy expert system presented a sensitivity of 76.5% and specificity of 94.8% in the identification of the need for advanced neonatal resuscitation measures, considering a cut-off value of 5 on a scale ranging from 0 to 10. The area under the receiver operating characteristic curve was 0.93. The identification of risk situations plays an important role in the planning of health care. These preliminary results encourage us to develop further studies and to refine this model, which is intended to implement an auxiliary system able to help health care staff to make decisions in perinatal care.

Linear and nonlinear analysis of heart rate variability in healthy subjects and after acute myocardial infarction in patients

The objectives of this study were to evaluate and compare the use of linear and nonlinear methods for analysis of heart rate variability (HRV) in healthy subjects and in patients after acute myocardial infarction (AMI). Heart rate (HR) was recorded for 15 min in the supine position in 10 patients with AMI taking β-blockers (aged 57 ± 9 years) and in 11 healthy subjects (aged 53 ± 4 years). HRV was analyzed in the time domain (RMSSD and RMSM), the frequency domain using low- and high-frequency bands in normalized units (nu; LFnu and HFnu) and the LF/HF ratio and approximate entropy (ApEn) were determined. There was a correlation (P < 0.05) of RMSSD, RMSM, LFnu, HFnu, and the LF/HF ratio index with the ApEn of the AMI group on the 2nd (r = 0.87, 0.65, 0.72, 0.72, and 0.64) and 7th day (r = 0.88, 0.70, 0.69, 0.69, and 0.87) and of the healthy group (r = 0.63, 0.71, 0.63, 0.63, and 0.74), respectively. The median HRV indexes of the AMI group on the 2nd and 7th day differed from the healthy group (P < 0.05): RMSSD = 10.37, 19.95, 24.81; RMSM = 23.47, 31.96, 43.79; LFnu = 0.79, 0.79, 0.62; HFnu = 0.20, 0.20, 0.37; LF/HF ratio = 3.87, 3.94, 1.65; ApEn = 1.01, 1.24, 1.31, respectively. There was agreement between the methods, suggesting that these have the same power to evaluate autonomic modulation of HR in both AMI patients and healthy subjects. AMI contributed to a reduction in cardiac signal irregularity, higher sympathetic modulation and lower vagal modulation.

Utility of a novel risk score for prediction of ventricular tachycardia and cardiac death in chronic Chagas disease - the SEARCH-RIO study

The SEARCH-RIO study prospectively investigated electrocardiogram (ECG)-derived variables in chronic Chagas disease (CCD) as predictors of cardiac death and new onset ventricular tachycardia (VT). Cardiac arrhythmia is a major cause of death in CCD, and electrical markers may play a significant role in risk stratification. One hundred clinically stable outpatients with CCD were enrolled in this study. They initially underwent a 12-lead resting ECG, signal-averaged ECG, and 24-h ambulatory ECG. Abnormal Q-waves, filtered QRS duration, intraventricular electrical transients (IVET), 24-h standard deviation of normal RR intervals (SDNN), and VT were assessed. Echocardiograms assessed left ventricular ejection fraction. Predictors of cardiac death and new onset VT were identified in a Cox proportional hazard model. During a mean follow-up of 95.3 months, 36 patients had adverse events: 22 new onset VT (mean±SD, 18.4±4‰/year) and 20 deaths (26.4±1.8‰/year). In multivariate analysis, only Q-wave (hazard ratio, HR=6.7; P<0.001), VT (HR=5.3; P<0.001), SDNN<100 ms (HR=4.0; P=0.006), and IVET+ (HR=3.0; P=0.04) were independent predictors of the composite endpoint of cardiac death and new onset VT. A prognostic score was developed by weighting points proportional to beta coefficients and summing-up: Q-wave=2; VT=2; SDNN<100 ms=1; IVET+=1. Receiver operating characteristic curve analysis optimized the cutoff value at >1. In 10,000 bootstraps, the C-statistic of this novel score was non-inferior to a previously validated (Rassi) score (0.89±0.03 and 0.80±0.05, respectively; test for non-inferiority: P<0.001). In CCD, surface ECG-derived variables are predictors of cardiac death and new onset VT.

HIGH PRESSURE PHASE EQUILIBRIUM: PREDICTION OF ESSENTIAL OIL SOLUBILITY

This work describes a method to predict the solubility of essential oils in supercritical carbon dioxide. The method is based on the formulation proposed in 1979 by Asselineau, Bogdanic and Vidal. The Peng-Robinson and Soave-Redlich-Kwong cubic equations of state were used with the van der Waals mixing rules with two interaction parameters. Method validation was accomplished calculating orange essential oil solubility in pressurized carbon dioxide. The solubility of orange essential oil in carbon dioxide calculated at 308.15 K for pressures of 50 to 70 bar varied from 1.7± 0.1 to 3.6± 0.1 mg/g. For same the range of conditions, experimental solubility varied from 1.7± 0.1 to 3.6± 0.1 mg/g. Predicted values were not very sensitive to initial oil composition.

Application of mathematical models for the prediction of adsorption isotherms in solid mixture for mango powder refreshment

Solid mixtures for refreshment are already totally integrated to the Brazilian consumers' daily routine, because of their quick preparation method, yield and reasonable price - quite lower if compared to 'ready-to-drink' products or products for prompt consumption, what makes them economically more accessible to low-income populations. Within such a context, the aim of this work was to evaluate the physicochemical and mineral composition, as well as the hygroscopic behavior of four different brands of solid mixture for mango refreshment. The BET, GAB, Oswim and Henderson mathematical models were built through the adjustment of experimental data to the isotherms of adsorption. Results from the physiochemical evaluation showed that the solid mixtures for refreshments are considerable sources of ascorbic acid and reductor sugar; and regarding mineral compounds, they are significant sources of calcium, sodium and potassium. It was also verified that the solid mixtures for refreshments of the four studied brands are considered highly hygroscopic.

An artificial neural network model for prediction of quality characteristics of apples during convective dehydration

In this study, the effects of hot-air drying conditions on color, water holding capacity, and total phenolic content of dried apple were investigated using artificial neural network as an intelligent modeling system. After that, a genetic algorithm was used to optimize the drying conditions. Apples were dried at different temperatures (40, 60, and 80 °C) and at three air flow-rates (0.5, 1, and 1.5 m/s). Applying the leave-one-out cross validation methodology, simulated and experimental data were in good agreement presenting an error < 2.4 %. Quality index optimal values were found at 62.9 °C and 1.0 m/s using genetic algorithm.