Methane combustion kinetic rate constants determination: an ill-posed inverse problem analysis

Methane combustion was studied by the Westbrook and Dryer model. This well-established simplified mechanism is very useful in combustion science, for computational effort can be notably reduced. In the inversion procedure to be studied, rate constants are obtained from [CO] concentration data. However, when inherent experimental errors in chemical concentrations are considered, an ill-conditioned inverse problem must be solved for which appropriate mathematical algorithms are needed. A recurrent neural network was chosen due to its numerical stability and robustness. The proposed methodology was compared against Simplex and Levenberg-Marquardt, the most used methods for optimization problems.

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.

Comparison of the Polar S810i monitor and the ECG for the analysis of heart rate variability in the time and frequency domains

The aim of the present study was to compare heart rate variability (HRV) at rest and during exercise using a temporal series obtained with the Polar S810i monitor and a signal from a LYNX® signal conditioner (BIO EMG 1000 model) with a channel configured for the acquisition of ECG signals. Fifteen healthy subjects aged 20.9 ± 1.4 years were analyzed. The subjects remained at rest for 20 min and performed exercise for another 20 min with the workload selected to achieve 60% of submaximal heart rate. RR series were obtained for each individual with a Polar S810i instrument and with an ECG analyzed with a biological signal conditioner. The HRV indices (rMSSD, pNN50, LFnu, HFnu, and LF/HF) were calculated after signal processing and analysis. The unpaired Student t-test and intraclass correlation coefficient were used for data analysis. No statistically significant differences were observed when comparing the values analyzed by means of the two devices for HRV at rest and during exercise. The intraclass correlation coefficient demonstrated satisfactory correlation between the values obtained by the devices at rest (pNN50 = 0.994; rMSSD = 0.995; LFnu = 0.978; HFnu = 0.978; LF/HF = 0.982) and during exercise (pNN50 = 0.869; rMSSD = 0.929; LFnu = 0.973; HFnu = 0.973; LF/HF = 0.942). The calculation of HRV values by means of temporal series obtained from the Polar S810i instrument appears to be as reliable as those obtained by processing the ECG signal captured with a signal conditioner.