{"paper":{"title":"Growth Exponent in the Domany-Kinzel Cellular Automaton","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"A.P.F. Atman, J.G. Moreira","submitted_at":"2001-09-24T21:59:06Z","abstract_excerpt":"In a roughening process, the growth exponent $\\beta$ describes how the roughness $w$ grows with the time $t$: $w\\sim t^{\\beta}$. We determine the exponent $\\beta$ of a growth process generated by the spatiotemporal patterns of the one dimensional Domany-Kinzel cellular automaton. The values obtained for $\\beta$ shows a cusp at the frozen/active transition which permits determination of the transition line. The $\\beta$ value at the transition depends on the scheme used: symmetric ($\\beta \\sim 0.83$) or non-symmetric ($\\beta \\sim 0.61$). Using damage spreading ideas, we also determine the active"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0109443","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"}