Growth Inside a Corner: The Limiting Interface Shape

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.

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

References in corpus (3)

• Slow decorrelations in KPZ growth
• Finite time corrections in KPZ growth models
• Statistics of layered zigzags: a two-dimensional generalization of TASEP

Cited by in corpus (8)

• Limiting Shapes of Ising Droplets, Ising Fingers, and Ising Solitons
• Limiting Shapes in Two-Dimensional Ising Ferromagnets
• Crystal Growth Inside an Octant
• Stochastic Dynamics of Growing Young Diagrams and Their Limit Shapes
• Conformal invariance of loop ensembles under Kardar-Parisi-Zhang dynamics
• Reply to Comment on "Growth Inside a Corner: The Limiting Interface Shape"
• Comment on "Growth Inside a Corner: The Limiting Interface Shape"
• The heat equation shrinks Ising droplets to points