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Growth inside a corner: the limiting interface shape
Jason Olejarz1, P L Krapivsky, S Redner
1Center for Polymer Studies, and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Abstract:
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.
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