{"paper":{"title":"Exact solution of a model of a vesicle attached to a wall subject to mechanical deformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","math.CO"],"primary_cat":"cond-mat.stat-mech","authors_text":"Aleksander L. Owczarek, Thomas Prellberg","submitted_at":"2011-11-14T19:00:44Z","abstract_excerpt":"Area-weighted Dyck-paths are a two-dimensional model for vesicles attached to a wall. We model the mechanical response of a vesicle to a pulling force by extending this model.\n  We obtain an exact solution using two different approaches, leading to a q-deformation of an algebraic functional equation, and a q-deformation of a linear functional equation with a catalytic variable, respectively. While the non-deformed linear functional equation is solved by substitution of special values of the catalytic variable (the so-called \"kernel method\"), the q-deformed case is solved by iterative substitut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3323","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":""},"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"}