{"paper":{"title":"Characterization of the equivalent acoustic scattering for a cluster of an extremely large number of small holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Andrea Mantile, Durga Prasad Challa, Mourad Sini","submitted_at":"2017-11-14T09:03:09Z","abstract_excerpt":"We deal with the time-harmonic acoustic waves scattered by a large number of small holes, of maximal radius $a, a<<1$, arbitrary (i.e. not necessarily periodically) distributed in a bounded part of a homogeneous background.\n  We show that as their number $M$ grows following the law $M:=M(a):=O(a^{-s}), \\; a<<1$, the collection of these holes has one of the following behaviors:\n  1. if $s<1$, then the scattered fields tend to vanish as $a$ tends to zero, i.e. the cluster is a soft one.\n  2. if $s=1$, then the cluster behaves as an equivalent medium modeled by a refraction index, supported in a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05003","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"}