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              <p>Following Hunt’s model to predict the extent of columnar and equiaxed grain structures in casting, determinisitic approaches have been developed. The main limitation of the deterministic models is yet due to the grain shape approximations. Thus the impingement of an equiaxed grain with a growing front and its further preferred development in the direction of the temperature gradient is not accounted for. This limitation is overcome by considering the development of each individual grain. This is possible using stochastic models in which the growth front of each crystal is considered. Comparison between predictions and in-situ observations of the solidification of a binary alloy in the casting configuration proposed by Hebditch and Hunt is presented. The effect of macrosegregation on the development of the structure is demonstrated. The model offers the possibility to quantify the approximation of using a model in which no consideration of the grain structure is accounted for.</p>
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