Diffusion-assisted aggregation in crystal growth

When particles gather and form a stable pattern, their kinetic energy must be dissipated into the surrounding medium. This means that the medium plays an essential role in the pattern formation. Here I present a crystal growt h theory that accommodates the dynamics of the medium, and I apply it to sn owflake pattern formation. When the kinematic viscosity of the medium is su fficiently large, macroscopic velocity waves in the medium can be produced by the gathering particles. Then, the waves work as the long-range interact ion and assist the formation of ordered patterns.