Shumylyak L. Continuous cellular automata modeling of alloy crystallization processes

This thesis describes development and implementation of scientific principles of mathematical modeling of first ordered phase transformations processes by using continuous asynchronous cellular automata method. The purpose of this study is to increase efficiency of crystal growth process by modeling its dynamics based on the development of asynchronous cellular automaton models of diffusion and thermal phenomena with first-order phase transitions. Simulation of the process of alloys directed crystallization was performed taking into account segregation and dependence of the phase transition temperature on the material. This can, under certain conditions, lead to concentrated overcooling and uneven geometry of crystallisation front. A quantitative model of the processes of diffusion and heat conductivity through continuous cellular automata is obtained. This model, unlike previous ones, provides a solution to the problem of heat conductivity at any point in time.A comparison of already known theoretical and experimental data and the results of numerical solutions for certain problems of thermal conductivity to the corresponding results of computational experiments carried out using the method of asynchronous cellular automata has been made. A comprehensive testing of the constructed model was conducted to confirm the adequacy of its application. Methodology for conducting a technological process to obtain multicomponent alloys by the method of zone melting was improved by application of the searching algorithm of optimal growing conditions. The software product is developed that runs cellular automata model of thermal conductivity and is intended to increase the efficiency of thermoelectric material quality through computational experiments. The results of the work have been introduced into “Interm” Ltd, “ValSoft" Ltd and to the educational process of the Department of Semiconductor Physics and Nanostructures of Yuriy Fedkovych Chernivtsi National University.