{"paper":{"title":"A new type of relaxation oscillation in a model with rate-and-state friction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"K. Uldall Kristiansen","submitted_at":"2019-03-28T19:36:28Z","abstract_excerpt":"In this paper we prove the existence of a new type of relaxation oscillation occurring in a one-block Burridge-Knopoff model with Ruina rate-and-state friction law. In the relevant parameter regime, the system is slow-fast with two slow variables and one fast. The oscillation is special for several reasons: Firstly, its singular limit is unbounded, the amplitude of the cycle growing like $\\log \\epsilon^{-1}$ as $\\epsilon\\rightarrow 0$. As a consequence of this estimate, the unboundedness of the cycle cannot be captured by a simple $\\epsilon$-dependent scaling of the variables, see e.g. \\cite{G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12232","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"}