Morphological Phase Transition Measured by "Surface Kinetic Dimension" of Growing Random Patterns

Surface kinetic was defined as a quantity to measure the logarithmic derivative of the surface with respect to the volume of growing patterns. This quantity for the growing pattern based on the hot tip model was found to show two kinks when the tip priority factor was increased. They were found to correspond to a microscopic roughening transition and a macroscopic morphological transition from a compact to a dendritic growth pattern, respectively. The result of the simulation based on the triangular pixel was also reported. A possible mechanism of the transition was discussed. It was pointed out that the surface kinetic dimension plays the role of a potential in the growing pattern dynamics.