The evolution of a particle under surface diffusion and migration

DISCUSSION

Due to the surface tension anisotropy, if b is zero, the shape will shrink as a circle, if the b is something between zero and one, the shape shrinks as a pointed shape. The Wullf construction is what determines the final shape so that surface energy is minimized. The particle first changes shape then reduces in size.

These simulations also show that even when the starting particle is not a circle, or even symmetric, the equations based on energy minimization will always simulate the same shape and shrink the particle. Comparing the different runs, run 1 and run 5 both started with the same number of nodes but very different shapes and both shrank to a circle. Then, looking at run 3 and run 6, or run 4 and run 7, the b was set to .3 and these particles shrank to a “square” and a “pentagon” respectively because of the user input of “k” or “Number of sides of final shape”. These runs shrank to these similar shapes of “square” and “pentagon” respectively even though the starting shapes were very different between the runs.