{"paper":{"title":"Scattering of electromagnetic waves by many thin cylinders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math.MP"],"primary_cat":"math-ph","authors_text":"Alexander G. Ramm","submitted_at":"2011-04-17T12:08:48Z","abstract_excerpt":"Electromagnetic wave scattering by many parallel infinite cylinders is studied asymptotically as $a\\to 0$. Here $a$ is the radius of the cylinders. It is assumed that the points $\\hat{x}_m$ are distributed so that $\\mathcal{N}(\\Delta)=\\frac{1}{a}\\int_{\\Delta}N(x)dx[1+o(1)], $ where $\\mathcal{N}(\\Delta)$ is the number of points $\\hat{x}_m=(x_{m1},x_{m2})$ in an arbitrary open subset of the plane $xoy$, the axes of the cylinders are passing through points $\\hat{x}_m$, these axes are parallel to the z-axis. The function $N(x)\\geq 0$ is a given continuous function. An equation for the self-consist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3309","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"}