PMID: 11308559Apr 20, 2001Paper

Scarred patterns in surface waves

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
A KudrolliJ P Gollub

Abstract

Surface wave patterns are investigated experimentally in a system geometry that has become a paradigm of quantum chaos: the stadium billiard. Linear waves in bounded geometries for which classical ray trajectories are chaotic are known to give rise to scarred patterns. Here, we utilize parametrically forced surface waves (Faraday waves), which become progressively nonlinear beyond the wave instability threshold, to investigate the subtle interplay between boundaries and nonlinearity. Only a subset (three main types) of the computed linear modes of the stadium are observed in a systematic scan. These correspond to modes in which the wave amplitudes are strongly enhanced along paths corresponding to certain periodic ray orbits. Many other modes are found to be suppressed, in general agreement with a prediction by Agam and Altshuler based on boundary dissipation and the Lyapunov exponent of the associated orbit. Spatially asymmetric or disordered (but time-independent) patterns are also found even near onset. As the driving acceleration is increased, the time-independent scarred patterns persist, but in some cases transitions between modes are noted. The onset of spatiotemporal chaos at higher forcing amplitude often involves a no...Continue Reading

References

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Citations

Jan 5, 2011·Chaos·G DelonH Caps
Jan 22, 2002·Physical Review Letters·S ResidoriS Fauve
Oct 10, 2006·Physical Review Letters·Andor Kormányos, Henning Schomerus
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Daniel A Vega, Leopoldo R Gómez
Apr 19, 2017·Physical Review. E·Chun-Ti ChangPaul H Steen
Jul 15, 2016·Physical Review. E·Nicolas PérinetSeungwon Shin
Jun 13, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Valérie DoyaChristian Miniatura
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Feb 21, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·K Damborsky, L Kaplan
Oct 17, 2020·Reports on Progress in Physics·John W M Bush, Anand Uttam Oza
Feb 1, 2008·Physical Review Letters·Claire MichelFabrice Mortessagne
Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G BáezR A Méndez-Sánchez
Oct 30, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P H TuanY F Chen
Nov 13, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yunfei TangBaowen Li
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Jan 22, 2002·Physical Review Letters·Valérie DoyaChristian Miniatura

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