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dc.contributor.authorDe la Hoz, F.
dc.contributor.authorKumar, S.
dc.contributor.authorVega, L. 
dc.date.accessioned2020-02-19T15:29:18Z
dc.date.available2020-02-19T15:29:18Z
dc.date.issued2019-09-03
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1078
dc.description.abstractIn this paper, we consider the evolution of the Vortex Filament equa- tion (VFE): Xt = Xs ∧ Xss, taking M-sided regular polygons with nonzero torsion as initial data. Us- ing algebraic techniques, backed by numerical simulations, we show that the solutions are polygons at rational times, as in the zero-torsion case. However, unlike in that case, the evolution is not periodic in time; more- over, the multifractal trajectory of the point X(0,t) is not planar, and appears to be a helix for large times. These new solutions of VFE can be used to illustrate numerically that the smooth solutions of VFE given by helices and straight lines share the same instability as the one already established for circles. This is accomplished by showing the existence of variants of the so-called Rie- mann’s non-differentiable function that are as close to smooth curves as desired, when measured in the right topology. This topology is motivated by some recent results on the well-posedness of VFE, which prove that the selfsimilar solutions of VFE have finite renormalized energy.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectMULTIFRACTALITYen_US
dc.subjectTALBOT EFFECTen_US
dc.subjectTURBULENCEen_US
dc.subjectVORTEX FILAMENT EQUATIONen_US
dc.titleOn the Evolution of the Vortex Filament Equation for regular M-polygons with nonzero torsionen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/669689en_US
dc.relation.projectIDES/1PE/SEV-2017-0718en_US
dc.relation.projectIDEUS/BERC/BERC.2018-2021en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/submittedVersionen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España