{"paper":{"title":"Dynamical Scaling Behavior of the Swift-Hohenberg Equation Following a Quench to the Modulated State","license":"","headline":"","cross_cats":["cond-mat.soft","nlin.PS"],"primary_cat":"patt-sol","authors_text":"IL, Nigel Goldenfeld (University of Illinois, Qing Hou, Shin-ichi Sasa, Urbana, USA)","submitted_at":"1998-08-03T05:03:32Z","abstract_excerpt":"We study the kinetics of phase transitions in a Rayleigh-Benard system after onset of convection using 2D Swift-Hohenberg equation. An initially uniform state evolves to one whose ground state is spatially periodic. We confirmed previous results which showed that dynamical scaling occurs at medium quench ($\\epsilon = 0.25$) with scaling exponents 1/5 and 1/4 under zero noise and finite noise respectively. We find logarithmic scaling behavior for a deep quench ($\\epsilon = 0.75$) at zero noise. A simple method is devised to measure the proxy of domain wall length. We find that the energy and do"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"patt-sol/9808001","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"}