{"paper":{"title":"On the justification of the Foldy-Lax approximation for the acoustic scattering by small rigid bodies of arbitrary shapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Durga Prasad Challa, Mourad Sini","submitted_at":"2013-08-14T10:11:50Z","abstract_excerpt":"We are concerned with the acoustic scattering problem by many small rigid obstacles of arbitrary shapes.\n  We give a sufficient condition on the number $M$ and the diameter $a$ of the obstacles as well as the minimum distance $d$ between them under which the Foldy-Lax approximation is valid.\n  Precisely, if we use single layer potentials for the representation of the scattered fields, as it is done sometimes in the literature, then this condition is $(M-1)\\frac{a}{d^2} <c$, with an appropriate constant $c$, while if we use double layer potentials then a weaker condition of the form $\\sqrt{M-1}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3228","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"}