{"paper":{"title":"Self-similarity, Aboav-Weaire's and Lewis' laws in weighted planar stochastic lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"F. R. Dayeen, M. K. Hassan","submitted_at":"2014-09-28T16:12:18Z","abstract_excerpt":"In this article, we show that the block size distribution function in the weighted planar stochastic lattice (WPSL), which is a multifractal and whose dual is a scale-free network, exhibits dynamic scaling. We verify it numerically using the idea of data-collapse. As the WPSL is a space-filling cellular structure, we thought it was worth checking if the Lewis and the Aboav-Weaire laws are obeyed in the WPSL. To this end, we find that the mean area $<A>_k$ of blocks with $k$ neighbours grow linearly up to $k=8$, and hence the Lewis law is obeyed. However, beyond $k>8$ we find that $<A>_k$ grows"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7928","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"}