{"paper":{"title":"Equations for the self-consistent field in random medium","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.G.Ramm","submitted_at":"2003-01-31T20:54:40Z","abstract_excerpt":"An integral-differential equation is derived for the self-consistent (effective) field in the medium consisting of many small bodies randomly distributed in some region. Acoustic and electromagnetic fields are considered in such a medium. Each body has a characteristic dimension $a\\ll\\lambda$, where $\\lambda$ is the wavelength in the free space.\n The minimal distance $d$ between any of the two bodies satisfies the condition $d\\gg a$, but it may also satisfy the condition $d\\ll\\lambda$. Using Ramm's theory of wave scattering by small bodies of arbitrary shapes, the author derives an integral-di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0301046","kind":"arxiv","version":3},"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"}