{"paper":{"title":"Growth Inside a Corner: The Limiting Interface Shape","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Jason Olejarz, K. Mallick, P. L. Krapivsky, S. Redner","submitted_at":"2011-09-06T18:07:38Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1253","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}