Identification of a spatio-temporal model of crystal growth based on boundary curvature

A new method of identifying the spatio-temporal transition rule of crystal growth is introduced based on the connection between growth kinetics and dentritic morphology. Using a modified three-point-method, curvatures of the considered crystal branch are calculated and curvature direction is used to measure growth velocity. A polynomial model is then produced based on a curvature-velocity relationship to represent the spatio-temporal growth process. A very simple simulation example is used initially to clearly explain the methodology. The results of identifying a model from a real crystal growth experiment show that the proposed method can produce a good representation of crystal growth.