Analysis of finite element method for one-dimensional time-dependent Schrödinger equation on unbounded domain

This paper addresses the theoretical analysis of a fully discrete scheme for the one-dimensional time-dependent Schrödinger equation on unbounded domain. We first reduce the original problem into an initial-boundary value problem in a bounded domain by introducing a transparent boundary condition, then fully discretize this reduced problem by applying Crank–Nicolson scheme in time and linear or quadratic finite element approximation in space. By a rigorous analysis, this scheme has been proved to be unconditionally stable and convergent, its convergence order has also be obtained. Finally, two numerical examples are performed to show the accuracy of the scheme.     

Laminar flamelet modeling of a turbulent CH4/H2/N2 jet diffusion flame using artificial neural networks

The laminar flamelet concept is used in the prediction of mean reactive scalars in a non-premixed turbulent CH₄/H₂/N₂ flame. First, a databank for temperature and species concentrations is developed from the solutions of counter-flow diffusion flames. The effects of flow field on flamelets are considered by using mixture fraction and scalar dissipation rate. Turbulence-chemistry interactions are taken into account by integrating different quantities based on a presumed probability density function (PDF), to calculate the Favre-averaged values of scalars. Flamelet library is then generated. To interpolate in the generated library, one artificial neural network (ANN) is trained where the mean and variance of mixture fraction and the scalar dissipation rate are used as inputs, and species mean mass fractions and temperature are selected as outputs. The weights and biases of this ANN are implemented in a CFD flow solver code, to estimate mean values of the scalars. Results reveal that ANN yields good predictions and the computational time has decreased as compared to numerical integration for the estimation of mean thermo-chemical variables in the CFD code. Predicted thermo-chemical quantities are close to those from experimental measurements but some discrepancies exist, which are mainly due to the assumption of non-unity Lewis number in the calculations.     

First principles versus artificial neural network modelling of a solar desalination system with experimental validation

ABSTRACT

The present study mainly focuses on enhancing the performance of solar still unit using solar energy through cylindrical parabolic collector and solar panels. A 300 W solar panel is used to heat saline water by thermal elements outside the solar still unit. Solar panels are cooled during the hot hours of the day; thus, reducing their temperature may lead to an increase in solar panel efficiency followed by an increase in the efficiency of the solar still unit. The maximum amount of freshwater used in the experiment was 2.132 kg/day. The experiments were modelled using ANNs. Based on neural network simulation results, there is a significant correlation between experimental data and neural network modelling. This paper compares experimental data with data obtained from mathematical modelling and ANNs. As a conclusion, the artificial neural network prediction has been more accurate than the simplified first principles model presented.     

THE APPROXIMATIONS OF THE EXACT BOUNDARY CONDITION AT AN ARTIFICIAL BOUNDARY FOR LINEARIZED INCOMPRESSIBLE VISCOUS FLOWS

1.IntroductionManyproblemsarisinginfluidmechanicsaregiveninanunboundeddomain,suchasfluidflowaroundobstacles.Whencomputingthenumericalsolutionsoftheseproblems,oneoftenintroducesartificialboundariesandsetsupaxtificialboundaryconditionsonthem.Thentheoriginal…     

Analysis of natural convection from a column of cold horizontal cylinders using Artificial Neural Network

Artificial Neural Networks (ANNs) offer an alternative way to tackle complex problems. They can learn from the examples and once trained can perform predictions and generalizations at high speed. They are particularly useful in behavior or system identification. According to the above advantages of ANN in the present paper ANN is used to predict natural convection heat transfer and fluid flow from a column of cold horizontal circular cylinders having uniform surface temperature. Governing equations are solved in a few specified cases by finite volume method to generate the database for training the ANN in the range of Rayleigh numbers of 10⁵–10⁸ and a range of cylinder spacing of 0.5, 1.0, and 1.5 diameters, thereafter a Multi-Layer Perceptron (MLP) network is used to capture the behavior of flow and temperature fields and then generalized this behavior to predict the flow and temperature fields for any other Rayleigh numbers. Different training algorithms are used and it is found that the resilient back-propagation algorithm is the best algorithm regarding the faster training procedure. To validate the accuracy of the trained network, comparison is performed among the ANN and available CFD results. It is observed that ANN can be used more efficiently to determine cold plume and thermal field in lesser computational time. Based on the generalized results from the ANN new correlations are developed to estimate natural convection from a column of cold horizontal cylinders with respect to a single horizontal cylinder.     

Neural network prediction of load from the morphology of trabecular bone

Bone adaptation models are often solved in the forward direction, meaning that the response of bone to a given set of loads is determined by running a bone tissue adaptation model. The model is generally solved using a numerical technique such as the finite element model. Conversely, one may be interested in the loads that have resulted in a given state of bone. This is the inverse of the former problem. Even though the inverse problem has several applications, it has not received as much attention as the forward problem, partly because solving the inverse problem is more difficult. A nonlinear system identification technique is needed for solving the inverse problem. In this study, we use artificial neural networks for prediction of tissue adaptation loads from a given density distribution of trabecular bone. It is shown that the proposed method can successfully identify the loading parameters from the density distribution of the tissue. Two important challenges for all load prediction algorithms are the non-uniqueness of the solution of the inverse problem and the inaccuracies in the measurement of the morphology of the tissue. Both challenges are studied, and it is shown that the load prediction technique proposed in this paper can overcome both.     

Robust neural modeling for the cross-sectional analysis of accounting information

The performance of robust artificial neural network models in learning bivariate relationships between accounting magnitudes is assessed in this paper. Predictive performances of a number of modeling paradigms (namely, linear models, log-linear structures, classical ratios and artificial neural networks) are compared with regard to the problem of modeling a number of the most outstanding accounting ratio relations. We conduct a large scale analysis, carried out on a representative Spanish data base.     

Application of a heuristic search technique for the improvement of spray zones cooling conditions in continuously cast steel billets

The process of casting occupies an important place in the metallurgical industry, and the entire world of the metal user. In the past, the ingot casting–rolling (slabbing, blooming, or billeting) process was commonly used. The continuous casting process has largely replaced this earlier method because of the inherent advantages of energy savings, enhanced productivity, higher yield and reduced costs. However, continuous casting process is not without of its problems. Considerable effort has been made by many researches to establish adequate design, operation and maintenance of continuous casting machine to ensure metallurgical quality of the final product. One of the most severe defects in continuous casting products is concerned with the cracks provoked by improper design of the spray cooling system. The aim of this work is to develop a two dimensional heat transfer model based on the finite difference method in order to calculate the strand temperatures and the solid shell profile along the machine. An Artificial Intelligence heuristic search procedure interacts with the numerical model to determine the improved cooling conditions for the sprays zones of a real continuous caster for the production of quality billets.     

Improving weighted information criterion by using optimization

Although artificial neural networks (ANN) have been widely used in forecasting time series, the determination of the best model is still a problem that has been studied a lot. Various approaches available in the literature have been proposed in order to select the best model for forecasting in ANN in recent years. One of these approaches is to use a model selection strategy based on the weighted information criterion (WIC). WIC is calculated by summing weighted different selection criteria which measure the forecasting accuracy of an ANN model in different ways. In the calculation of WIC, the weights of different selection criteria are determined heuristically. In this study, these weights are calculated by using optimization in order to obtain a more consistent criterion. Four real time series are analyzed in order to show the efficiency of the improved WIC. When the weights are determined based on the optimization, it is obviously seen that the improved WIC produces better results.     

Limitations of learning in automata-based systems

In this article, we aim to analyze the limitations of learning in automata-based systems by introducing the L⁺$L^{+}$ algorithm to replicate quasi-perfect learning, i.e., a situation in which the learner can get the correct answer to any of his queries. This extreme assumption allows the generalization of any limitations of the learning algorithm to less sophisticated learning systems. We analyze the conditions under which the L⁺$L^{+}$ infers the correct automaton and when it fails to do so. In the context of the repeated prisoners’ dilemma, we exemplify how the L⁺$L^{+}$ may fail to learn the correct automaton. We prove that a sufficient condition for the L⁺$L^{+}$ algorithm to learn the correct automaton is to use a large number of look-ahead steps. Finally, we show empirically, in the product differentiation problem, that the computational time of the L⁺$L^{+}$ algorithm is polynomial on the number of states but exponential on the number of agents.