Hybrid journal (It can contain Open Access articles) ISSN (Print) 2040-3607 - ISSN (Online) 2040-3615 Published by Inderscience Publishers[449 journals]

Authors:Samuel A. Surulere, Micheal Y. Shatalov, Andrew C. Mkolesia, Julius O. Ehigie Pages: 239 - 254 Abstract: Many well-known semiempirical potential energy functions have been used to construct potential energy curves from the physical or chemical properties of atoms. In this study, we identify the Lennard-Jones and Biswas-Hamann potential parameters and use these to calculate and reconstruct potential energy curves using experimental datasets of gold atom. Two different approaches are studied in detail. The Lennard-Jones potential yielded complex conjugate eigenvalues for both approaches. Numerical estimates proved the considered approaches gives better approximations as constructed and reconstructed potential energy curves were almost graphically indistinguishable. Keywords: potential parameters; objective functions; potential energy curves; PECs; objective least squares function; ObLSf Citation: International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 10, No. 3 (2020) pp. 239 - 254 PubDate: 2020-07-21T23:20:50-05:00 DOI: 10.1504/IJMMNO.2020.108612 Issue No:Vol. 10, No. 3 (2020)

Authors:Larysa Ivanivna Korotka, Dmitriy Gegegemonovich Zelentsov Pages: 255 - 269 Abstract: In the work on solving problems of optimal design, structures working in aggressive external environments, a modified method is proposed, which is based on the flexible tolerance method. The proposed method allows to control the accuracy of solving systems of differential equations when calculating the constraint functions of an optimisation problem. Based on the information about the degree of closeness of the point of the solution space to the local extremum point, which is received by the neural network controller, its parameters change. For this purpose, various matrices of neural network synapses, trained for different precisions of calculating the functions of constraints, are used. This strategy is used to modify the flexible tolerance method, based on the use of a neural network controller. As a criterion of the flexible tolerance, the error of calculating the constraint functions is used. It is shown that the use of a neural network regulator of the accuracy of calculating the restriction functions in the modified flexible tolerance method allows to significantly increase its efficiency while simultaneously obtaining a solution to the problem with a given accuracy and compensating the computational costs connected with using the α-level generalisation principle. Keywords: neural network regulator; flexible tolerance; optimal design; fuzzy variables Citation: International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 10, No. 3 (2020) pp. 255 - 269 PubDate: 2020-07-21T23:20:50-05:00 DOI: 10.1504/IJMMNO.2020.108613 Issue No:Vol. 10, No. 3 (2020)

Authors:Allaoua Boudjedour, Mohamed Dalah Pages: 270 - 286 Abstract: We consider a quasistatic contact modelled with the regularised friction law for electro-elastic and the foundation is assumed to be electrically conductive. This regularisation is obtained by replacing the function <i>j</i>(.) by the function <i>j<SUB align="right">ρ</i>(.), where <i>ρ</i> is a strictly positive parameter. The classical formulation for the antiplane problem is formulated as a time dependent of corresponding variational formulation and is solved by the Banach fixed-point theorem and classical results for variational inequalities. We provide a weak formulation of the contact problem in the form variational system in which the unknowns are the displacement and the stress fields, then we establish the existence of a unique weak solution to the model. Finally, we have given a convergence criterion of the solution as the parameter of regularisation <i>ρ</i> converges to zero. Keywords: quasistatic contact; electro-elastic material; antiplane; regularised friction law; weak solution; variational formulation Citation: International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 10, No. 3 (2020) pp. 270 - 286 PubDate: 2020-07-21T23:20:50-05:00 DOI: 10.1504/IJMMNO.2020.108616 Issue No:Vol. 10, No. 3 (2020)

Authors:Ahmed Tchvagha Zeine, Emmanuel Pagnacco, Rachid Ellaia Pages: 287 - 306 Abstract: In this paper, a new multi-objective immune algorithm (MOIAs) called BIAMO is proposed for tackling continuous multi-objective optimisation problems. It uses the updated archive to sort the non-dominated solutions of the Pareto front as well as the mutation and crossover operators of the backtracking search algorithm (BSA). Experimental results are produced for various benchmark problems and for a variety of engineering design problems. They show that, compared to the recent multi-objective optimisation evolutionary algorithms, the proposed algorithm improves not only the convergence capacity but also preserves the diversity of the population. In this paper, thirteen benchmark and engineering design problems are presented and the obtained results were compared with other well-known optimisers. The obtained results demonstrate that the proposed algorithm requires less number of function evaluations and in most cases gives better results compared to others considered algorithms. Keywords: multi-objective optimisation; evolutionary algorithms; backtracking search; hybrid recombination; hybrid mutation Citation: International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 10, No. 3 (2020) pp. 287 - 306 PubDate: 2020-07-21T23:20:50-05:00 DOI: 10.1504/IJMMNO.2020.108619 Issue No:Vol. 10, No. 3 (2020)

Authors:Preety Kalra, Shreya Tangri Pages: 307 - 329 Abstract: The rapidly elevating contamination of water bodies is one of the present-day critical problems occurring worldwide. It is a well-determined fact that the direct discharge of household wastes, industrial effluents, chemicals, acids and other pollutants into water bodies along with eutrophication are degrading the water quality. Washing-off of land pollutants in water bodies coupled with acid rain further increase the toxicity and acidity of water. These phenomena are leading to decrease of dissolved oxygen in water which is endangering the growth and survival of populations residing in water. To investigate the stress of increasing toxicity and acidity of water bodies like ponds, lakes and rivers on the aquatic population due to decrease in dissolved oxygen, a nonlinear mathematical model is proposed. The model is analysed and the stability conditions are derived in terms of the parameters. To substantiate the analytical results, numerical simulations are carried out using MATLAB. Keywords: aquatic population; toxicity; acidity; dissolved oxygen; model; stability; pollutants; carbon; sensitivity Citation: International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 10, No. 3 (2020) pp. 307 - 329 PubDate: 2020-07-21T23:20:50-05:00 DOI: 10.1504/IJMMNO.2020.108621 Issue No:Vol. 10, No. 3 (2020)