{"paper":{"title":"Analytical Approximations for the Collapse of an Empty Spherical Bubble","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Danail Obreschkow, Martin Bruderer, Mohamed Farhat","submitted_at":"2012-05-18T17:19:36Z","abstract_excerpt":"The Rayleigh equation 3/2 R'+RR\"+p/rho=0 with initial conditions R(0)=Rmax, R'(0)=0 models the collapse of an empty spherical bubble of radius R(T) in an ideal, infinite liquid with far-field pressure p and density rho. The solution for r=R/Rmax as a function of time t=T/Tcollapse, where R(Tcollapse)=0, is independent of Rmax, p, and rho. While no closed-form expression for r(t) is known we find that s(t)=(1-t^2)^(2/5) approximates r(t) with an error below 1%. A systematic development in orders of t^2 further yields the 0.001%-approximation r*(t)=s(t)[1-a Li(2.21,t^2)], where a=-0.01832099 is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4202","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"}