{"paper":{"title":"The point-interaction approximation for the fields generated by contrasted bubbles at arbitrary fixed frequencies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anupam Pal Choudhury, Durga Prasad Challa, Habib Ammari, Mourad Sini","submitted_at":"2018-01-24T11:03:51Z","abstract_excerpt":"We deal with the linearized model of the acoustic wave propagation generated by small bubbles in the harmonic regime. We estimate the waves generated by a cluster of $M$ small bubbles, distributed in a bounded domain $\\Omega$, with relative densities having contrasts of the order $a^{\\beta}, \\beta>0, $ where $a$ models their relative maximum diameter, $a\\ll 1$. We provide useful and natural conditions on the number $M$, the minimum distance and the contrasts parameter $\\beta$ of the small bubbles under which the point interaction approximation (called also the Foldy-Lax approximation) is valid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07921","kind":"arxiv","version":3},"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"}