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Nonlinear Resonance Analysis : Theory, Computation, Applications - Elena Kartashova

Nonlinear Resonance Analysis

Theory, Computation, Applications

Hardcover

Published: 1st November 2010
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Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory. Colour versions of a selection of the figures are available at www.cambridge.org/9780521763608.

'... brings significant rewards ... equipping the receptive reader to address a number of open questions.' Contemporary Physics

Prefacep. ix
Glossaryp. xiv
Expositionp. 1
An easy startp. 1
Two classifications of PDEsp. 11
Hamiltonian formalismp. 19
Kinematics: Wavenumbersp. 30
An easy startp. 30
Irrational dispersion function, analytical resultsp. 32
q-class decompositionp. 45
Rational dispersion functionp. 57
General form of dispersion functionp. 60
Kinematics: Resonance clustersp. 64
An easy startp. 64
Topological structure vs dynamical systemp. 66
Three-wave resonancesp. 69
Four-wave resonancesp. 76
NR-diagramsp. 82
What is beyond kinematics?p. 88
Dynamicsp. 90
An easy startp. 90
Decay instabilityp. 93
A triadp. 96
Clusters of triadsp. 106
A quartetp. 116
Explosive instabilityp. 117
NR-reduced numerical modelsp. 122
What is beyond dynamics?p. 127
Mechanical playthingsp. 130
Linear pendulump. 130
Elastic pendulump. 138
Wave turbulent regimesp. 144
An easy startp. 144
Quasi-resonances vs approximate interactionsp. 147
Model of laminated turbulencep. 150
Energy cascades: dynamic vs kineticp. 158
Rotational capillary wavesp. 161
Discrete regimes in various wave systemsp. 170
Open problemsp. 176
Epiloguep. 182
Appendix Softwarep. 185
Referencesp. 209
Indexp. 221
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780521763608
ISBN-10: 0521763606
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 240
Published: 1st November 2010
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 25.3 x 17.7  x 1.4
Weight (kg): 0.62