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.

Cardiorespiratory adaptations induced by aerobic training in middle-aged men: the importance of a decrease in sympathetic stimulation for the contribution of dynamic exercise tachycardia

We investigated the effects of aerobic training on the efferent autonomic control of heart rate (HR) during dynamic exercise in middle-aged men, eight of whom underwent exercise training (T) while the other seven continued their sedentary (S) life style. The training was conducted over 10 months (three 1-h sessions/week on a field track at 70-85% of the peak HR). The contribution of sympathetic and parasympathetic exercise tachycardia was determined in terms of differences in the time constant effects on the HR response obtained using a discontinuous protocol (4-min tests at 25, 50, 100 and 125 watts on a cycle ergometer), and a continuous protocol (25 watts/min until exhaustion) allowed the quantification of the parameters (anaerobic threshold, VO2 AT; peak O2 uptake, VO2 peak; power peak) that reflect oxygen transport. The results obtained for the S and the T groups were: 1) a smaller resting HR in T (66 beats/min) when compared to S (84 beats/min); 2) during exercise, a small increase in the fast tachycardia (D0-10 s) related to vagal withdrawal (P<0.05, only at 25 watts) was observed in T at all powers; at middle and higher powers a significant decrease (P<0.05 at 50, 100 and 125 watts) in the slow tachycardia (D1-4 min) related to a sympathetic-dependent mechanism was observed in T; 3) the VO2 AT (S = 1.06 and T = 1.33 l/min) and VO2 peak (S = 1.97 and T = 2.47 l/min) were higher in T (P<0.05). These results demonstrate that aerobic training can induce significant physiological adaptations in middle-aged men, mainly expressed as a decrease in the sympathetic effects on heart rate associated with an increase in oxygen transport during dynamic exercise.

Endogenous vasopressin and the central control of heart rate during dynamic exercise

The present article contains a brief review on the role of vasopressinergic projections to the nucleus tractus solitarii in the genesis of reflex bradycardia and in the modulation of heart rate control during exercise. The effects of vasopressin on exercise tachycardia are discussed on the basis of both the endogenous peptide content changes and the heart rate response changes observed during running in sedentary and trained rats. Dynamic exercise caused a specific vasopressin content increase in dorsal and ventral brainstem areas. In accordance, rats pretreated with the peptide or the V1 blocker into the nucleus tractus solitarii showed a significant potentiation or a marked blunting of the exercise tachycardia, respectively, without any change in the pressure response to exercise. It is proposed that the long-descending vasopressinergic pathway to the nucleus tractus solitarii serves as one link between the two main neural controllers of circulation, i.e., the central command and feedback control mechanisms driven by the peripheral receptors. Therefore, vasopressinergic input could contribute to the adjustment of heart rate response (and cardiac output) to the circulatory demand during exercise.

Ambulatory blood pressure and Doppler echocardiographic indexes of borderline hypertensive men presenting an exaggerated blood pressure response during dynamic exercise

Borderline hypertension (BH) has been associated with an exaggerated blood pressure (BP) response during laboratory stressors. However, the incidence of target organ damage in this condition and its relation to BP hyperreactivity is an unsettled issue. Thus, we assessed the Doppler echocardiographic profile of a group of BH men (N = 36) according to office BP measurements with exaggerated BP in the cycloergometric test. A group of normotensive men (NT, N = 36) with a normal BP response during the cycloergometric test was used as control. To assess vascular function and reactivity, all subjects were submitted to the cold pressor test. Before Doppler echocardiography, the BP profile of all subjects was evaluated by 24-h ambulatory BP monitoring. All subjects from the NT group presented normal monitored levels of BP. In contrast, 19 subjects from the original BH group presented normal monitored BP levels and 17 presented elevated monitored BP levels. In the NT group all Doppler echocardiographic indexes were normal. All subjects from the original BH group presented normal left ventricular mass and geometrical pattern. However, in the subjects with elevated monitored BP levels, fractional shortening was greater, isovolumetric relaxation time longer, and early to late flow velocity ratio was reduced in relation to subjects from the original BH group with normal monitored BP levels (P<0.05). These subjects also presented an exaggerated BP response during the cold pressor test. These results support the notion of an integrated pattern of cardiac and vascular adaptation during the development of hypertension.

Spectral analysis of the electromyograph of the erector spinae muscle before and after a dynamic manual load-lifting test

The aim of the present study was to assess the spectral behavior of the erector spinae muscle during isometric contractions performed before and after a dynamic manual load-lifting test carried out by the trunk in order to determine the capacity of muscle to perform this task. Nine healthy female students participated in the experiment. Their average age, height, and body mass (± SD) were 20 ± 1 years, 1.6 ± 0.03 m, and 53 ± 4 kg, respectively. The development of muscle fatigue was assessed by spectral analysis (median frequency) and root mean square with time. The test consisted of repeated bending movements from the trunk, starting from a 45º angle of flexion, with the application of approximately 15, 25 and 50% of maximum individual load, to the stand up position. The protocol used proved to be more reliable with loads exceeding 50% of the maximum for the identification of muscle fatigue by electromyography as a function of time. Most of the volunteers showed an increase in root mean square versus time on both the right (N = 7) and the left (N = 6) side, indicating a tendency to become fatigued. With respect to the changes in median frequency of the electromyographic signal, the loads used in this study had no significant effect on either the right or the left side of the erector spinae muscle at this frequency, suggesting that a higher amount and percentage of loads would produce more substantial results in the study of isotonic contractions.

Identification of anaerobic threshold using heart rate response during dynamic exercise

The objective of the present study was to characterize the heart rate (HR) patterns of healthy males using the autoregressive integrated moving average (ARIMA) model over a power range assumed to correspond to the anaerobic threshold (AT) during discontinuous dynamic exercise tests (DDET). Nine young (22.3 ± 1.57 years) and 9 middle-aged (MA) volunteers (43.2 ± 3.53 years) performed three DDET on a cycle ergometer. Protocol I: DDET in steps with progressive power increases of 10 W; protocol II: DDET using the same power values as protocol 1, but applied randomly; protocol III: continuous dynamic exercise protocol with ventilatory and metabolic measurements (10 W/min ramp power), for the measurement of ventilatory AT. HR was recorded and stored beat-to-beat during DDET, and analyzed using the ARIMA (protocols I and II). The DDET experiments showed that the median physical exercise workloads at which AT occurred were similar for protocols I and II, i.e., AT occurred between 75 W (116 bpm) and 85 W (116 bpm) for the young group and between 60 W (96 bpm) and 75 W (107 bpm) for group MA in protocols I and II, respectively; in two MA volunteers the ventilatory AT occurred at 90 W (108 bpm) and 95 W (111 bpm). This corresponded to the same power values of the positive trend in HR responses. The change in HR response using ARIMA models at submaximal dynamic exercise powers proved to be a promising approach for detecting AT in normal volunteers.

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.

Hemodynamic mechanisms of the attenuated blood pressure response to mental stress after a single bout of maximal dynamic exercise in healthy subjects

To determine the hemodynamic mechanisms responsible for the attenuated blood pressure response to mental stress after exercise, 26 healthy sedentary individuals (age 29 ± 8 years) underwent the Stroop color-word test before and 60 min after a bout of maximal dynamic exercise on a treadmill. A subgroup (N = 11) underwent a time-control experiment without exercise. Blood pressure was continuously and noninvasively recorded by infrared finger photoplethysmography. Stroke volume was derived from pressure signals, and cardiac output and peripheral vascular resistance were calculated. Perceived mental stress scores were comparable between mental stress tests both in the exercise (P = 0.96) and control (P = 0.24) experiments. After exercise, the blood pressure response to mental stress was attenuated (pre: 10 ± 13 vs post: 6 ± 7 mmHg; P < 0.01) along with lower values of systolic blood pressure (pre: 129 ± 3 vs post: 125 ± 3 mmHg; P < 0.05), stroke volume (pre: 89.4 ± 3.5 vs post: 76.8 ± 3.8 mL; P < 0.05), and cardiac output (pre: 7.00 ± 0.30 vs post: 6.51 ± 0.36 L/min; P < 0.05). Except for heart rate, the hemodynamic responses and the mean values during the two mental stress tests in the control experiment were similar (P > 0.05). In conclusion, a single bout of maximal dynamic exercise attenuates the blood pressure response to mental stress in healthy subjects, along with lower stroke volume and cardiac output, denoting an acute modulatory action of exercise on the central hemodynamic response to mental stress.

Dynamic expression of desmin, α-SMA and TGF-β1 during hepatic fibrogenesis induced by selective bile duct ligation in young rats

We previously described a selective bile duct ligation model to elucidate the process of hepatic fibrogenesis in children with biliary atresia or intrahepatic biliary stenosis. Using this model, we identified changes in the expression of alpha smooth muscle actin (α-SMA) both in the obstructed parenchyma and in the hepatic parenchyma adjacent to the obstruction. However, the expression profiles of desmin and TGF-β1, molecules known to be involved in hepatic fibrogenesis, were unchanged when analyzed by semiquantitative polymerase chain reaction (RT-PCR). Thus, the molecular mechanisms involved in the modulation of liver fibrosis in this experimental model are not fully understood. This study aimed to evaluate the molecular changes in an experimental model of selective bile duct ligation and to compare the gene expression changes observed in RT-PCR and in real-time quantitative PCR (qRT‐PCR). Twenty-eight Wistar rats of both sexes and weaning age (21-23 days old) were used. The rats were separated into groups that were assessed 7 or 60 days after selective biliary duct ligation. The expression of desmin, α-SMA and TGF-β1 was examined in tissue from hepatic parenchyma with biliary obstruction (BO) and in hepatic parenchyma without biliary obstruction (WBO), using RT-PCR and qRT‐PCR. The results obtained in this study using these two methods were significantly different. The BO parenchyma had a more severe fibrogenic reaction, with increased α-SMA and TGF-β1 expression after 7 days. The WBO parenchyma presented a later, fibrotic response, with increased desmin expression 7 days after surgery and increased α-SMA 60 days after surgery. The qRT‐PCR technique was more sensitive to expression changes than the semiquantitative method.