The evolution of resonance: a multiscale approach to the effect of nonlinearity, frequency dispersion and geometry

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dc.contributor.author Mortell, Michael P.
dc.contributor.author Seymour, Brian R.
dc.date.accessioned 2019-04-30T10:43:26Z
dc.date.available 2019-04-30T10:43:26Z
dc.date.issued 2019-04-05
dc.identifier.citation Mortell, M. P. and Seymour, B. R. (2019) 'The evolution of resonance: a multiscale approach to the effect of nonlinearity, frequency dispersion and geometry', Mathematical Modelling of Natural Phenomena, 14(4), 403 (20pp). doi: 10.1051/mmnp/2019005 en
dc.identifier.volume 14 en
dc.identifier.issued 4 en
dc.identifier.startpage 1 en
dc.identifier.endpage 20 en
dc.identifier.issn 0973-5348
dc.identifier.uri http://hdl.handle.net/10468/7823
dc.identifier.doi 10.1051/mmnp/2019005 en
dc.description.abstract Nonlinear resonant oscillations in continuous media contain two natural time scales: the travel time in the medium and the ‘slow’ time defined by the small nonlinearity. A multiscale approach is used to describe the evolution to a periodic state. We focus on three basic experiments that define nonlinear resonant oscillations in continuous media: a gas in both a straight tube and a tube of variable cross-section, and shallow water in a tank. The outcomes of these experiments are described and the mathematical techniques that show the evolution to the final periodic states are given in some detail. en
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher EDP Sciences en
dc.relation.uri https://doi.org/10.1051/mmnp/2019005
dc.rights © 2019, EDP Sciences. Copyright of Mathematical Modelling of Natural Phenomena is the property of EDP Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. en
dc.subject Nonlinear wave en
dc.subject Resonance en
dc.subject Evolution en
dc.title The evolution of resonance: a multiscale approach to the effect of nonlinearity, frequency dispersion and geometry en
dc.type Article (peer-reviewed) en
dc.internal.authorcontactother Michael Mortell, School Of Mathematical Sciences, University College Cork, Cork, Ireland. +353-21-490-3000 Email: m.mortell@ucc.ie en
dc.internal.availability Full text available en
dc.date.updated 2019-04-30T10:35:29Z
dc.description.version Published Version en
dc.internal.rssid 483476272
dc.description.status Peer reviewed en
dc.identifier.journaltitle Mathematical Modelling of Natural Phenomena en
dc.internal.copyrightchecked Yes
dc.internal.licenseacceptance Yes en
dc.internal.IRISemailaddress m.mortell@ucc.ie en
dc.identifier.articleid 403 en
dc.identifier.eissn 1760-6101


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