Growth Inside a Corner: The Limiting Interface Shape

Details Growth Inside a Corner: The Limiting Interface Shape Growth Inside a Corner: The Limiting Interface Shape

2011-09-06

arxiv.org/abs/1109.1253v2

Phys. Rev. Lett. 108, 016102 (2012)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2-column revtex4 format. Revised version in response to referee comments

Scientific paper

10.1103/PhysRevLett.108.016102

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.

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