{"paper":{"title":"Current Flow in Random Resistor Networks: The Role of Percolation in Weak and Strong Disorder","license":"","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cond-mat.dis-nn","authors_text":"Eduardo L\\'opez, H. Eugene Stanley, Lidia A. Braunstein, Sergey V. Buldyrev, Shlomo Havlin, Zhenhua Wu","submitted_at":"2004-11-02T17:43:21Z","abstract_excerpt":"We study the current flow paths between two edges in a random resistor network on a $L\\times L$ square lattice. Each resistor has resistance $e^{ax}$, where $x$ is a uniformly-distributed random variable and $a$ controls the broadness of the distribution. We find (a) the scaled variable $u\\equiv L/a^\\nu$, where $\\nu$ is the percolation connectedness exponent, fully determines the distribution of the current path length $\\ell$ for all values of $u$. For $u\\gg 1$, the behavior corresponds to the weak disorder limit and $\\ell$ scales as $\\ell\\sim L$, while for $u\\ll 1$, the behavior corresponds t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0411062","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"}