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

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

Mortell, Michael P.; Seymour, Brian R.
Date: 2019-04-05
Copyright: © 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.
Related: https://doi.org/10.1051/mmnp/2019005
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
Published Version: 10.1051/mmnp/2019005

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.

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