dc.contributor.author De la Hoz, F. dc.contributor.author Vega, L. dc.date.accessioned 2018-07-06T12:00:31Z dc.date.available 2018-07-06T12:00:31Z dc.date.issued 2018-06-28 dc.identifier.issn 0938-8974 dc.identifier.uri http://hdl.handle.net/20.500.11824/823 dc.description.abstract In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular M-corner polygon as initial datum can be explained at infinitesimal times as the superposition of M one-corner initial data. This fact is mainly sustained with the calculation of the speed of the center of mass; in particular, we show that several conjectures made at the numerical level are in agreement with the theoretical expectations. Moreover, due to the spatial periodicity, the evolution of VFE at later times can be understood as the nonlinear interaction of infinitely many filaments, one for each corner; and this interaction turns out to be some kind of nonlinear Talbot effect. We also give very strong numerical evidence of the transfer of energy and linear momentum for the M-corner case; and the numerical experiments carried out provide new arguments that support the multifractal character of the trajectory defined by one of the corners of the initial polygon. en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Intermittency en_US dc.subject Multifractality en_US dc.subject Talbot Effect en_US dc.subject Transfer of Energy en_US dc.subject Turbulence en_US dc.subject Vortex filament equation en_US dc.title On the Relationship between the One-Corner Problem and the $M-$Corner Problem for the Vortex Filament Equation en_US dc.type info:eu-repo/semantics/article en_US dc.identifier.doi 10.1007/s00332-018-9477-7 dc.relation.publisherversion https://link.springer.com/article/10.1007%2Fs00332-018-9477-7 en_US dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/669689 en_US dc.relation.projectID ES/1PE/SEV-2013-0323 en_US dc.relation.projectID EUS/BERC/BERC.2014-2017 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/publishedVersion en_US dc.journal.title Journal of Nonlinear Science en_US
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