Growth inside a corner: the limiting interface shape.
We investigate the growth of a crystal that is built by depositing cubes inside a corner. The interface of this crystal approaches a deterministic growing limiting shape in the long-time limit. Building on known results for the corresponding two-dimensional system and accounting for basic three-dimensional symmetries, we conjecture a governing equation for the evolution of the interface profile. We solve this equation analytically and find excellent agreement with simulations of the growth process. We also present a generalization to arbitrary spatial dimension.
Center for Polymer Studies, and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Jason
J
Olejarz
P L
PL
Krapivsky
S
S
Redner
K
K
Mallick