{"paper":{"title":"From homogenization to averaging in cellular flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexei Novikov, Gautam Iyer, Lenya Ryzhik, Tomasz Komorowski","submitted_at":"2011-07-30T15:03:06Z","abstract_excerpt":"We consider an elliptic eigenvalue problem with a fast cellular flow of amplitude $A$, in a two-dimensional domain with $L^2$ cells. For fixed $A$, and $L \\to \\infty$, the problem homogenizes, and has been well studied. Also well studied is the limit when $L$ is fixed, and $A \\to \\infty$. In this case the solution equilibrates along stream lines.\n  In this paper, we show that if \\textit{both} $A \\to \\infty$ and $L \\to \\infty$, then a transition between the homogenization and averaging regimes occurs at $A \\approx L^4$. When $A\\gg L^4$, the principal Dirichlet eigenvalue is approximately consta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0074","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"}