{"paper":{"title":"Fractal Dimensions of the Hydrodynamic Modes of Diffusion","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"J. R. Dorfman, P. Gaspard, T. Gilbert","submitted_at":"2000-07-10T15:32:31Z","abstract_excerpt":"We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the hydrodynamic modes of diffusion form fractal curves in the complex plane, with a Hausdorff dimension larger than one. In the limit of vanishing wavenumber, we derive a simple expression of the diffusion coefficient in terms of this Hausdorff dimension and the positive Lyapunov exponent of the chaotic model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0007008","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"}