{"paper":{"title":"Torsional rigidity for cylinders with a Brownian fracture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"F. den Hollander, M. van den Berg","submitted_at":"2017-11-27T17:16:29Z","abstract_excerpt":"We obtain bounds for the expected loss of torsional rigidity of a cylinder $\\Omega_L=(-L/2,L/2) \\times \\Omega\\subset \\R^3$ of length $L$ due to a Brownian fracture that starts at a random point in $\\Omega_L,$ and runs until the first time it exits $\\Omega_L$. These bounds are expressed in terms of the geometry of the cross-section $\\Omega \\subset \\R^2$. It is shown that if $\\Omega$ is a disc with radius $R$, then in the limit as $L \\rightarrow \\infty$ the expected loss of torsional rigidity equals $cR^5$ for some $c\\in (0,\\infty)$. We derive bounds for $c$ in terms of the expected Newtonian ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09838","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"}