Dinâmica não-linear e reagente limitante: um exemplo de bifurcação transcrítica

The nonlinear analysis of a general mixed second order reaction was performed, aiming to explore some basic tools concerning the mathematics of nonlinear differential equations. Concepts of stability around fixed points based on linear stability analysis are introduced, together with phase plane and integral curves. The main focus is the chemical relationship between changes of limiting reagent and transcritical bifurcation, and the investigation underlying the conclusion.

On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Algorithm to determine the intersection curves between bezier surfaces by the solution of multivariable polynomial system and the differential marching method

The determination of the intersection curve between Bézier Surfaces may be seen as the composition of two separated problems: determining initial points and tracing the intersection curve from these points. The Bézier Surface is represented by a parametric function (polynomial with two variables) that maps a point in the tridimensional space from the bidimensional parametric space. In this article, it is proposed an algorithm to determine the initial points of the intersection curve of Bézier Surfaces, based on the solution of polynomial systems with the Projected Polyhedral Method, followed by a method for tracing the intersection curves (Marching Method with differential equations). In order to allow the use of the Projected Polyhedral Method, the equations of the system must be represented in terms of the Bernstein basis, and towards this goal it is proposed a robust and reliable algorithm to exactly transform a multivariable polynomial in terms of power basis to a polynomial written in terms of Bernstein basis .

Dynamics of the control of Aedes (Stegomyia) aegypti Linnaeus (Diptera, Culicidae) by Bacillus thuringiensis var israelensis, related with temperature, density and concentration of insecticide

The dynamics of the control of Aedes (Stegomyia) aegypti Linnaeus, (Diptera, Culicidae) by Bacillus thuringiensis var israelensis has been related with the temperature, density and concentration of the insecticide. A mathematical model for biological control of Aedes aegypti with Bacillus thuringiensis var israelensis (Bti) was constructed by using data from the literature regarding the biology of the vector. The life cycle was described by differential equations. Lethal concentrations (LC50 and LC95) of Bti were determined in the laboratory under different experimental conditions. Temperature, colony, larvae density and bioinsecticide concentration presented marked differences in the analysis of the whole set of variables; although when analyzed individually, only the temperature and concentration showed changes. The simulations indicated an inverse relationship between temperature and mosquito population, nonetheless, faster growth of populations is reached at higher temperatures. As conclusion, the model suggests the use of integrated control strategies for immature and adult mosquitoes in order to achieve a reduction of Aedes aegypti.

Simulação do equilíbrio: o método de Monte Carlo

We make several simulations using the Monte Carlo method in order to obtain the chemical equilibrium for several first-order reactions and one second-order reaction. We study several direct, reverse and consecutive reactions. These simulations show the fluctuations and relaxation time and help to understand the solution of the corresponding differential equations of chemical kinetics. This work was done in an undergraduate physical chemistry course at UNIFIEO.

Integração numérica de leis de velocidade diferenciais com o uso do SCILAB

In this work, we applied the free open source SCILAB software for the numerical integration of differential rate law equations to obtain the concentration profiles of chemical species involved in the kinetics of some complex reactions. An automated method was applied to construct the system of ordinary differential equations (ODE) from the postulated chemical models. The solutions of the ODEs were obtained numerically by standard SCILAB functions. We successfully simulated even complex chemical systems such as pH oscillators. This communication opens up the possibility of using SCILAB in simulations and modeling by our chemistry undergraduate students.

Reference values for lung function tests: I. Static volumes

Static lung volume (LV) measurements have a number of clinical and research applications; however, no previous studies have provided reference values for such tests using a healthy sample of the adult Brazilian population. With this as our main purpose, we prospectively evaluated 100 non-smoking subjects (50 males and 50 females), 20 to 80 years old, randomly selected from more than 8,000 individuals. Gender-specific linear prediction equations were developed by multiple regression analysis with total lung capacity (TLC), functional residual capacity (FRC), residual volume (RV), RV/TLC ratio and inspiratory capacity (IC) as dependent variables, and with age, height, weight, lean body mass and indexes of physical fitness as independent ones. Simpler demographic and anthropometric variables were as useful as more complex measurements in predicting LV values, independent of gender and age (R2 values ranging from 0.49 to 0.78, P<0.001). Interestingly, prediction equations from North American and European studies overestimated the LV at low volumes and underestimated them at high volumes (P<0.05). Our results, therefore, provide a more appropriate frame of reference to evaluate the normalcy of static lung volume values in Brazilian males and females aged 20 to 80 years.

Reference values for lung function tests: II. Maximal respiratory pressures and voluntary ventilation

The strength of the respiratory muscles can be evaluated from static measurements (maximal inspiratory and expiratory pressures, MIP and MEP) or inferred from dynamic maneuvers (maximal voluntary ventilation, MVV). Although these data could be suitable for a number of clinical and research applications, no previous studies have provided reference values for such tests using a healthy, randomly selected sample of the adult Brazilian population. With this main purpose, we prospectively evaluated 100 non-smoking subjects (50 males and 50 females), 20 to 80 years old, selected from more than 8,000 individuals. Gender-specific linear prediction equations for MIP, MEP and MVV were developed by multiple regression analysis: age and, secondarily, anthropometric measurements explained up to 56% of the variability of the dependent variables. The most cited previous studies using either Caucasian or non-Caucasian samples systematically underestimated the observed values of MIP (P<0.05). Interestingly, the self-reported level of regular physical activity and maximum aerobic power correlates strongly with both respiratory and peripheral muscular strength (knee extensor peak torque) (P<0.01). Our results, therefore, provide a new frame of reference to evaluate the normalcy of some useful indexes of respiratory muscle strength in Brazilian males and females aged 20 to 80.

Reference values for lung function tests: III. Carbon monoxide diffusing capacity (transfer factor)

Carbon monoxide diffusing capacity (DLCO) or transfer factor (TLCO) is a particularly useful test of the appropriateness of gas exchange across the lung alveolocapillary membrane. With the purpose of establishing predictive equations for DLCO using a non-smoking sample of the adult Brazilian population, we prospectively evaluated 100 subjects (50 males and 50 females aged 20 to 80 years), randomly selected from more than 8,000 individuals. Gender-specific linear prediction equations were developed by multiple regression analysis with single breath (SB) absolute and volume-corrected (VA) DLCO values as dependent variables. In the prediction equations, age (years) and height (cm) had opposite effects on DLCOSB (ml min-1 mmHg-1), independent of gender (-0.13 (age) + 0.32 (height) - 13.07 in males and -0.075 (age) + 0.18 (height) + 0.20 in females). On the other hand, height had a positive effect on DLCOSB but a negative one on DLCOSB/VA (P<0.01). We found that the predictive values from the most cited studies using predominantly Caucasian samples were significantly different from the actually measured values (P<0.05). Furthermore, oxygen uptake at maximal exercise (VO2max) correlated highly to DLCOSB (R = 0.71, P<0.001); this variable, however, did not maintain an independent role to explain the VO2max variability in the multiple regression analysis (P>0.05). Our results therefore provide an original frame of reference for either DLCOSB or DLCOSB/VA in Brazilian males and females aged 20 to 80 years, obtained from the standardized single-breath technique.

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.

Mathematical modeling of microbial growth in milk

A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth.