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.

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 .

Comparisons between two economically valuable forest species (Eucalyptus grandis and Pinus taeda) in relation to seed behaviour under controlled deterioration

The objectives of this work were to analyze seed behaviour under controlled deterioration and estimate viability equations for forest species Eucalyptus grandis and Pinus taeda. Desired moisture content levels were achieved from initial values after either rehydration over water or drying over silica gel, both at 25 ºC. Seed sub samples with 8 moisture contents each for E. grandis (1.2 to 18.1%, initial value of 11.3%) and P. taeda (1.5 to 19.5%, initial value of 12.9%) were sealed in laminate aluminium-foil packets and stored in incubators maintained at 40, 50 and 65 ºC. The seeds from these species exhibited true orthodox and sub-orthodox storage behaviour, respectively, however E. grandis showed higher seed storability, probably due to a different seed chemical composition. Lowest moisture content limits estimated for application of the viability equations at 65 ºC were 4.9 and 4.1 mc for E. grandis and P. taeda, on equilibrium with ±20% RH. The viability equation estimated quantified the response of seed longevity to storage environment well with K E = 9.661 and 8.838; C W = 6.467 and 5.981; C H = 0.03498 and 0.10340; C Q = 0.0002330 and 0.0005476, for E. grandis and P. taeda, respectively.

On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.

In-house ELISA method to analyze anti-Trypanosoma cruzi IgG reactivity for differential diagnosis and evaluation of Chagas disease morbidity

INTRODUCTION: The goal was to develop an in-house serological method with high specificity and sensitivity for diagnosis and monitoring of Chagas disease morbidity. METHODS: With this purpose, the reactivities of anti-T. cruzi IgG and subclasses were tested in successive serum dilutions of patients from Berilo municipality, Jequitinhonha Valley, Minas Gerais, Brazil. The performance of the in-house ELISA was also evaluated in samples from other relevant infectious diseases, including HIV, hepatitis C (HCV), syphilis (SYP), visceral leishmaniasis (VL), and American tegumentary leishmaniasis (ATL), and noninfected controls (NI). Further analysis was performed to evaluate the applicability of this in-house methodology for monitoring Chagas disease morbidity into three groups of patients: indeterminate (IND), cardiac (CARD), and digestive/mixed (DIG/Mix), based on their clinical status. RESULTS: The analysis of total IgG reactivity at serum dilution 1:40 was an excellent approach to Chagas disease diagnosis (100% sensitivity and specificity). The analysis of IgG subclasses showed cross-reactivity, mainly with NI, VL, and ATL, at all selected serum dilutions. Based on the data analysis, the IND group displayed higher IgG3 levels and the DIG/Mix group presented higher levels of total IgG as compared with the IND and CARD groups. CONCLUSIONS: These findings demonstrated that methodology presents promising applicability in the analysis of anti-T. cruzi IgG reactivity for the differential diagnosis and evaluation of Chagas disease morbidity.

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.

Prediction of cottonseed longevity

The objective of this work was to determine the viability equation constants for cottonseed and to detect the occurrence and depletion of hardseededness. Three seedlots of Brazilian cultivars IAC-19 and IAC-20 were tested, using 12 moisture content levels, ranging from 2.2 to 21.7% and three storage temperatures, 40, 50 and 65ºC. Seed moisture content level was reached from the initial value (around 8.8%) either by rehydration, in a closed container, or by drying in desiccators containing silica gel, both at 20ºC. Twelve seed subsamples for each moisture content/temperature treatment were sealed in laminated aluminium-foil packets and stored in incubators at those temperatures, until complete survival curves were obtained. Seed equilibrium relative humidity was recorded. Hardseededness was detected at moisture content levels below 6% and its releasing was achieved either naturally, during storage period, or artificially through seed coat removal. The viability equation quantified the response of seed longevity to storage environment well with K E = 9.240, C W = 5.190, C H = 0.03965 and C Q = 0.000426. The lower limit estimated for application of this equation at 65ºC was 3.6% moisture content.