{"paper":{"title":"The missing ingredient in effective-medium theories: Standard deviations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Akhlesh Lakhtakia, Craig F. Bohren, Xuerong Xiao","submitted_at":"2012-08-02T15:49:34Z","abstract_excerpt":"Effective-medium theories for electromagnetic constitutive parameters of particulate composite materials are theories of averages. Standard deviations are absent because of the lack of rigorous theories. But ensemble averages and standard deviations can be calculated from a rigorous theory of reflection by planar multilayers. Average reflectivities at all angles of incidence and two orthogonal polarization states for a multilayer composed of two kinds of electrically thin layers agree well with reflectivities for a single layer with the same overall thickness and a volume-weighted average of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0521","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"}