Identification of radius-vector functions of interface evolution for star-shaped crystal growth

This article introduces a new method based on a radius-vector function for identifying the spatio-temporal transition rule of star-shaped crystal growth directly from experimental crystal growth imaging data. From the morphology point of view, the growth is decomposed as initial conditions, uniform growth and directional growth, which is represented by a static polynomial model based on the Fourier expansion. A recursive model is also introduced to help understand the dynamic characteristics of the observed systems. The applicability of the proposed approach is demonstrated using data from a simulation and from a real crystal growth experiment.