{"paper":{"title":"On the Kinetics of Multi-dimensional Fragmentation","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat","authors_text":"M. K. Hassan, P. Singh","submitted_at":"1996-07-04T11:10:25Z","abstract_excerpt":"We present two classes of exact solutions to a geometric model which describes the kinetics of fragmentation of $d$-dimensional hypercuboid-shaped objects. The first class of exact solutions is described by a fragmentation rate $a({x_1},...,{x_d}) = 1$ and daughter distribution function $b({x_1},..,{x_d} | {{x_{1}^{\\p}}},...,{{x_{d}^{\\p}}})= {{(\\a_1 + 2)x_1^{\\a_1}}\\over{x_1^{\\p(\\a_1+1)}}}...{{(\\a_d+2)x_d^{\\a_d}}\\over {x_d^{\\p(\\a_d+1)}}}$. The second class of exact solutions is described by a fragmentation rate $ a({x_1},...,{x_d}) = {{{x_1}^{\\a_1}}...{{x_d}^{\\a_d}}/{2^d}}$ and a daughter distr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9607027","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cond-mat/9607027/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}