{"paper":{"title":"Theoretical bounds for the exponent in the empirical power-law advance-time curve for surface flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"physics.flu-dyn","authors_text":"Allen G. Hunt, Behzad Ghanbarian, Hamed Ebrahimian, M. Th. van Genuchten","submitted_at":"2018-01-28T05:27:28Z","abstract_excerpt":"A fundamental and widely applied concept used to study surface flow processes is the advance-time curve characterized by an empirical power law with an exponent r and a numerical prefactor p (i.e., x = p*t^r). In the literature, different values of r have been reported for various situations and types of surface irrigation. Invoking concepts from percolation theory, we related the exponent r to the backbone fractal dimension Db, whose value depends on two factors: dimensionality of the system (e.g., two or three dimensions) and percolation class (e.g., random or invasion percolation with/witho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09182","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"}