{"paper":{"title":"A cluster of many small holes with negative imaginary surface impedances may generate a negative refraction index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ahmed Alsaedi, Bashir Ahmed, Durga Prasad Challa, Mokhtar Kirane, Mourad Sini","submitted_at":"2015-06-26T14:39:00Z","abstract_excerpt":"We deal with the scattering of an acoustic medium modeled by an index of refraction $n$ varying in a bounded region $\\Omega$ of $\\mathbb{R}^3$ and equal to unity outside $\\Omega$. This region is perforated with an extremely large number of small holes $D_m$'s of maximum radius $a$, $a<<1$, modeled by surface impedance functions. Precisely, we are in the regime described by the number of holes of the order $M:=O(a^{\\beta-2})$, the minimum distance between the holes is $d\\sim a^t$ and the surface impedance functions of the form $\\lambda_m \\sim \\lambda_{m,0} a^{-\\beta}$ with $\\beta >0$ and $\\lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08096","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"}