{"paper":{"title":"Weakly nonlinear analysis of Turing pattern dynamics on curved surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["nlin.CD","physics.bio-ph"],"primary_cat":"nlin.PS","authors_text":"Ryosuke Nishide, Shuji Ishihara","submitted_at":"2024-03-19T05:07:54Z","abstract_excerpt":"Pattern dynamics on curved surfaces are ubiquitous. Although the effect of surface topography on pattern dynamics has gained much interest, there is a limited understanding of the roles of surface geometry and topology in pattern dynamics. Recently, we reported that a static pattern on a flat plane can become a propagating pattern on a curved surface [Nishide and Ishihara, Phys. Rev. Lett. 2022]. By examining reaction-diffusion equations on axisymmetric surfaces, certain conditions for the onset of pattern propagation were determined. However, this analysis was limited by the assumption that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.12444","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.12444/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}