{"paper":{"title":"Scattering of electromagnetic waves by small impedance particles of an arbitrary shape","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Alexander G. Ramm","submitted_at":"2015-03-02T17:51:46Z","abstract_excerpt":"An explicit formula is derived for the electromagnetic (EM) field scattered by one small impedance particle $D$ of an arbitrary shape. If $a$ is the characteristic size of the particle, $\\lambda$ is the wavelength, $a<<\\lambda$ and $\\zeta$ is the boundary impedance of $D$, $[N,[E,N]]=\\zeta [N,H]$ on $S$, where $S$ is the surface of the particle, $N$ is the unit outer normal to $S$, and $E$, $H$ is the EM field, then the scattered field is $E_{sc}=[\\nabla g(x,x_1), Q]$. Here $g(x,y)=\\frac{e^{ik|x-y|}}{4\\pi |x-y|}$, $k$ is the wave number, $x_1\\in D$ is an arbitrary point, and $Q=-\\frac{\\zeta |S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00639","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"}