{"paper":{"title":"Uncertain Loading and Quantifying Maximum Energy Concentration within Composite Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Michael Stuebner, Paul Sinz, Robert Lipton","submitted_at":"2016-07-01T01:36:29Z","abstract_excerpt":"We introduce a systematic method for identifying the worst case load among all boundary loads of fixed energy. Here the worst case load is defined to be the one that delivers the largest fraction of input energy to a prescribed subdomain of interest. The worst case load is identified with the first eigenfunction of a suitably defined eigenvalue problem. The first eigenvalue for this problem is the maximum fraction of boundary energy that can be delivered to the subdomain. We compute worst case boundary loads and associated energy contained inside a prescribed subdomain through the numerical so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00093","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"}