{"paper":{"title":"Creating materials with a desired refraction coefficient: numerical experiments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP"],"primary_cat":"math.NA","authors_text":"Alexander G.Ramm, Sapto W. Indratno","submitted_at":"2010-02-18T14:33:43Z","abstract_excerpt":"A recipe for creating materials with a desired refraction coefficient is implemented numerically. The following assumptions are used: \\bee \\zeta_m=h(x_m)/a^\\kappa,\\quad d=O(a^{(2-\\kappa)/3}),\\quad M=O(1/a^{2-\\kappa}),\\quad \\kappa\\in(0,1), \\eee where $\\zeta_m$ and $x_m$ are the boundary impedance and center of the $m$-th ball, respectively, $h(x)\\in C(D)$, Im$h(x)\\leq 0$, $M$ is the number of small balls embedded in the cube $D$, $a$ is the radius of the small balls and $d$ is the distance between the neighboring balls.\n  An error estimate is given for the approximate solution of the many-body "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3533","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1002.3533/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}