Discussion on Criterion of Determination of the Kinetic Parameters of the Linear Heating Reactions

Generally, the linear correlation coefficient is one of the most significant criteria to appraise the kinetic parameters computed from different reaction models. Actually, the optimal kinetic triplet should meet the following two requirements: first, it can be used to reproduce the original kinetic process; second, it can be applied to predict the other kinetic process. The aim of this paper is to attempt to prove that the common criteria are insufficient for meeting the above two purposes simultaneously. In this paper, the explicit Euler method and Taylor expansion are presented to numerically predict the kinetic process of linear heating reactions. The mean square error is introduced to assess the prediction results. The kinetic processes of hematite reduced to iron at different heating rates (8, 10 and 18 K/min) are utilized for validation and evaluation. The predicted results of the reduction of Fe2O3 → Fe3O4 indicated that the inferior linear correlation coefficient did provide better kinetic predicted curves. In conclusion, to satisfy the above two requirements of reproduction and prediction, the correlation coefficient is an insufficient criterion. In order to overcome this drawback, two kinds of numerical prediction methods are introduced, and the mean square error of the prediction is suggested as a superior criterion for evaluation.

Development of impact attenuator analysis tools in crash scenario using Euler method and finite element analysis

The problem considered in this work is the development of simulation method for simulating car crash which utilizes simple car—impact attenuator model developed in MATLAB. Usually, car crash simulation is done using full finite element simulation which could take hours or days depending on the model size. The purpose of proposed method is to achieve quick results on the car crash simulation. Past works which utilizes simple car—impact attenuator model to simulate car crash use continuous time model and the impact attenuator parameter is obtained from the experimental results. Different from the related works, this work uses discrete time model, and the impact attenuator parameter is obtained from finite element simulation. Therefore, the proposed simulation method is not only achieving quick simulation results but also minimizing the cost and time in obtaining the impact attenuator parameter. The proposed method is suitable for parametric study of impact attenuator.

Nonlinear modeling and transition corridor calculation of a tiltrotor without cyclic pitch

In order to solve the problem of rotor airflow interference to the wing of tiltrotor UAV, the lift and drag in the slipstream area and the free flow area were calculated respectively according to the hydrodynamics theory and CFD simulation. The longitudinal nonlinear dynamics model of tiltrotor UAV is established by Newton-Euler method. In order to solve the problem that the lift and thrust are difficult to balance the body gravity in the transition flight mode, a method for calculating the transition corridor of a tiltrotor UAV without cyclic pitch is proposed. The boundary of the transition corridor is restricted by the Angle of attack of the wing and the thrust of the rotor. Considering the requirements of UAV cruise speed, flight safety and minimum energy consumption, the optimal transition curve is selected. The result show that the designed transition curve can ensure that the lift and the rotor thrust can balance the gravity completely and the Angle of attack is in a reasonable range, and the rotor force has enough margin of safety.

Chaotic System Design Based on Recurrent Artificial Neural Network for the Simulation of EEG Time Series

Electroencephalogram (EEG) signals captured from brain activities demonstrate chaotic features, and can be simulated by nonlinear dynamic time series outputs of chaotic systems. This article presents the research work of chaotic system generator design based on artificial neural network (ANN), for studying the chaotic features of human brain dynamics. The ANN training performances of Nonlinear Auto-Regressive (NAR) model are evaluated for the generation and prediction of chaotic system time series outputs, based on varying the ANN architecture and the precision of the generated training data. The NAR model is trained in open loop form with 1,000 training samples generated using Lorenz system equations and the forward Euler method. The close loop NAR model is used for the generation and prediction of Lorenz chaotic time series outputs. The training results show that better training performance can be achieved by increasing the number of feedback delays and the number of hidden neurons, at the cost of increasing the computational load.

SIR model for propagation of COVID-19 in the Paraíba's State (Brazil)

This work aims to apply the SIR-type compartmental model (Susceptible - Infected - Removed) in the evolution of Covid-19 in Paraíba's State and Campina Grande City. For that, the parameters of the model were considered to be variable during time evolution, within an appropriate range. The system of differential equations was solved numerically using the Euler method. The parameters were obtained by adjusting the model to the infected data provided by the Paraíba Health Department. According to the results obtained, the model describes the infected population well. There was a reduction in the effective reproduction number in Paraíba and the town of Campina Grande. It is noteworthy that understanding the dynamics of infection transmission and evaluating the effectiveness of control measures is crucial to assess the potential for sustained transmission to occur in new areas. The model can also be applied to describe epidemic dynamics in other regions and countries.

Lumped-Circuits Model of Lossless Transmission Lines and Its Numerical Characteristics

Aiming at the lumped-circuits model of the lossless transmission line in the digital simulation, the article discusses and analyzes the unit step response generation of the lumped-circuits model by comparing the numerical simulation results of the implicit trapezoidal method, the implicit Euler method, and a multi-step formula. The root cause of numerical oscillations pointed out that using the L-stable numerical algorithm to indirectly simulate the dynamic response of the lumped-circuits model is a numerical method that does not truly reflect the original model, but it can directly reflect the true dynamic response of the lossless transmission line. In this study, a method for determining the chained number in the digital simulation of a lumped-circuits model is given. The simulation results prove the effectiveness of the method.

Parameter-Uniform Numerical Scheme for Singularly Perturbed Delay Parabolic Reaction Diffusion Equations with Integral Boundary Condition

Numerical computation for the class of singularly perturbed delay parabolic reaction diffusion equations with integral boundary condition has been considered. A parameter-uniform numerical method is constructed via the nonstandard finite difference method for the spatial direction, and the backward Euler method for the resulting system of initial value problems in temporal direction is used. The integral boundary condition is treated using numerical integration techniques. Maximum absolute errors and the rate of convergence for different values of perturbation parameter ε and mesh sizes are tabulated for two model examples. The proposed method is shown to be parameter-uniformly convergent.

Euler method can outperform more complex ODE solvers in the numerical implementation of the Izhikevich artificial Spiking Neuron Model given the allocated FLOPS

The Izhikevich artificial spiking neuron model is among the most employed models in neuromorphic engineering and computational neuroscience, due to the affordable computational effort to discretize it and its biological plausibility. It has been adopted also for applications with limited computational resources in embedded systems. It is important therefore to realize a compromise between error and computational expense to solve numerically the model's equations. Here we investigate the effects of discretization and we study the solver that realizes the best compromise between accuracy and computational cost, given an available amount of Floating Point Operations per Second (FLOPS). We considered three frequently used fixed step Ordinary Differential Equations (ODE) solvers in computational neuroscience: Euler method, the Runge-Kutta 2 method and the Runge-Kutta 4 method. To quantify the error produced by the solvers, we used the Victor Purpura spike train Distance from an ideal solution of the ODE. Counterintuitively, we found that simple methods such as Euler and Runge Kutta 2 can outperform more complex ones (i.e. Runge Kutta 4) in the numerical solution of the Izhikevich model if the same FLOPS are allocated in the comparison. Moreover, we quantified the neuron rest time (with input under threshold resulting in no output spikes) necessary for the numerical solution to converge to the ideal solution and therefore to cancel the error accumulated during the spike train; in this analysis we found that the required rest time is independent from the firing rate and the spike train duration. Our results can generalize in a straightforward manner to other spiking neuron models and provide a systematic analysis of fixed step neural ODE solvers towards a trade-off between accuracy in the discretization and computational cost.

Nonstandard Finite Difference Schemes for an SIR Epidemic Model

This paper aims to present two nonstandard finite difference (NFSD) methods to solve an SIR epidemic model. The proposed methods have important properties such as positivity and boundedness and they also preserve conservation law. Numerical comparisons confirm that the accuracy of our method is better than that of other existing standard methods such as the second-order Runge–Kutta (RK2) method, the Euler method and some ready-made MATLAB codes.