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Computational models are developed to create grain structures using mathematical algorithms based on the chaos theory such as cellular automaton,geometrical models,fractals,and stochastic methods.Because of the chaotic nature of grain structures,some of the most popular routines are based on the Monte Carlo method,statistical distributions,and random walk methods,which can be easily programmed and included in nested loops.Nevertheless,grain structures are not well defined as the results of computational errors and numerical inconsistencies on mathematical methods.Due to the finite definition of numbers or the numerical restrictions during the simulation of solidification,damaged images appear on the screen.These images must be repaired to obtain a good measurement of grain geometrical properties.Some mathematical algorithms were developed to repair,measure,and characterize grain structures obtained from cellular automata in the present work.An appropriate measurement of grain size and the corrected identification of interfaces and length are very important topics in materials science because they are the representation and validation of mathematical models with real samples.As a result,the developed algorithms are tested and proved to be appropriate and efficient to eliminate the errors and characterize the grain structures.
Computational models are developed to create grain structures using mathematical algorithms based on the chaos theory such as cellular automaton, geometrical models, fractals, and stochastic methods. Abstract of the chaotic nature of grain structures, some of the most popular routines are based on the Monte Carlo method, statistical distributions, and random walk methods, which can be easy programmed and included in nested loops. Nevertheless, grain structures are not well defined as the results of computational errors and numerical inconsistencies on mathematical methods. Due to the finite definition of numbers or the numerical restrictions during the simulation of solidification, damaged images appear on the screen. The images must be repaired to obtain a good measurement of grain geometrical properties. Some mathematical algorithms were developed to repair, measure, and characterize grain structures obtained from cellular automata in the present work. An appropriate measurement of grain size and the corrected identification of interfaces and length are very important topics in materials science because they are the representation and validation of mathematical models with real samples. As a result, the developed algorithms are tested and proved to be appropriate and efficient to eliminate the errors and characterize the grain structures.