{"paper":{"title":"On homogenized conductivity and fractal structure in a high contrast continuum percolation model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Shigeki Matsutani, Yoshiyuki Shimosako","submitted_at":"2013-11-26T23:10:30Z","abstract_excerpt":"In the previous article (S. Matsutani and Y. Shimosako and Y. Wang, Physica A \\bf{391} (2012) 5802-5809) we numerically investigated an electric potential problem with high contrast local conductivities ($\\gamma_0$ and $\\gamma_1$, $0<\\gamma_0 \\ll \\gamma_1$) for a two-dimensional continuum percolation model (CPM). As numerical results, we showed there that the equipotential curves exhibit the fractal structure around the threshold $p_c$ and gave an approximated curve representing a relation between the homogenized conductivity and the volume fraction $p$ over $[p_c,1]$. In this article, using t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6843","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"}