Growth Inside a Corner: The Limiting Interface Shape
Statistical Mechanics
2012-03-06 v2
Abstract
We investigate the growth of a crystal that is built by depositing cubes onto the inside of a corner. The interface of this crystal evolves into a limiting shape in the long-time limit. Building on known results for the corresponding two-dimensional system and accounting for the symmetries of the three-dimensional problem, 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.
Cite
@article{arxiv.1109.1253,
title = {Growth Inside a Corner: The Limiting Interface Shape},
author = {Jason Olejarz and P. L. Krapivsky and S. Redner and K. Mallick},
journal= {arXiv preprint arXiv:1109.1253},
year = {2012}
}
Comments
4 pages, 2-column revtex4 format. Revised version in response to referee comments