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arXiv · 1109.1253

Growth Inside a Corner: The Limiting Interface Shape

Jason Olejarz·P. L. Krapivsky·S. Redner·K. Mallick
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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.

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Jason Olejarz, P. L. Krapivsky, S. Redner, K. Mallick. 2012-02-27. Growth Inside a Corner: The Limiting Interface Shape. https://doi.org/10.1103/physrevlett.108.016102

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