{"paper":{"title":"The Neumann sieve problem and dimensional reduction: a multiscale approach","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Caterina Ida Zeppieri, Jean-Francois Babadjian, Nadia Ansini","submitted_at":"2006-05-30T20:51:10Z","abstract_excerpt":"We perform a multiscale analysis for the elastic energy of a $n$-dimensional bilayer thin film of thickness $2\\delta$ whose layers are connected through an $\\epsilon$-periodically distributed contact zone. Describing the contact zone as a union of $(n-1)$-dimensional balls of radius $r\\ll \\epsilon$ (the holes of the sieve) and assuming that $\\delta \\ll \\epsilon$, we show that the asymptotic memory of the sieve (as $\\epsilon \\to 0$) is witnessed by the presence of an extra interfacial energy term. Moreover we find three different limit behaviors (or regimes) depending on the mutual vanishing ra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605769","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"}