{"paper":{"title":"Strongly nonlocal dislocation dynamics in crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Enrico Valdinoci, Serena Dipierro","submitted_at":"2013-11-14T15:52:57Z","abstract_excerpt":"We consider the equation $$v_t=L_s v-W'(v)+\\sigma_\\epsilon(t,x) \\quad {\\mbox{ in }} (0,+\\infty)\\times\\R,$$ where $L_s$ is an integro-differential operator of order $2s$, with $s\\in(0,1)$, $W$ is a periodic potential, and $\\sigma_\\epsilon$ is a small external stress. The solution $v$ represents the atomic dislocation in the Peierls--Nabarro model for crystals, and we specifically consider the case $s\\in(0,1/2)$, which takes into account a strongly nonlocal elastic term.\n  We study the evolution of such dislocation function for macroscopic space and time scales, namely we introduce the function "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3549","kind":"arxiv","version":1},"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"}