{"paper":{"title":"Boundary-layer analysis of a pile-up of walls of edge dislocations at a lock","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adriana Garroni, Lucia Scardia, Mark Peletier, Patrick van Meurs","submitted_at":"2015-02-20T09:03:46Z","abstract_excerpt":"In this paper we analyse the behaviour of a pile-up of vertically periodic walls of edge dislocations at an obstacle, represented by a locked dislocation wall. Starting from a continuum non-local energy $E_\\gamma$ modelling the interactions$-$at a typical length-scale of $1/\\gamma$$-$of the walls subjected to a constant shear stress, we derive a first-order approximation of the energy $E_\\gamma$ in powers of $1/\\gamma$ by $\\Gamma$-convergence, in the limit $\\gamma\\to\\infty$. While the zero-order term in the expansion, the $\\Gamma$-limit of $E_\\gamma$, captures the `bulk' profile of the density"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05805","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"}