Nonlinear physical systems : spectral analysis, stability and bifurcations
 Language
 English.
 Publication
 London : ISTE ; Hoboken, N.J. : Wiley, 2014.
 Physical description
 xvii, 429 pages : ill. ; 25 cm.
 Series
 Mechanical engineering and solid mechanics series.
Access
Available online

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QA372 .N656 2014

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QA372 .N656 2014
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Contributors
 Contributor
 Kirillov, Oleg N., 1972 author.
 Pelinovsky, Dmitry, author.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Preface xiii Chapter 1. Surprising Instabilities of Simple Elastic Structures1 Davide BIGONI, Diego MISSERONI, Giovanni NOSELLI and DanieleZACCARIA Chapter 2. WKB Solutions Near an Unstable Equilibrium andApplications 15 JeanFrancois BONY, Setsuro FUJIIE, Thierry RAMOND andMaher ZERZERI Chapter 3. The Sign Exchange Bifurcation in a Family of LinearHamiltonian Systems 41 Richard CUSHMAN, Johnathan M. ROBBINS and Dimitrii SADOVSKII Chapter 4. Dissipation Effect on Local and Global FluidElasticInstabilities 67 Olivier DOARE Chapter 5. Tunneling, Librations and Normal Forms in a QuantumDouble Well with a Magnetic Field 85 Sergey Y. DOBROKHOTOV and Anatoly Y. ANIKIN Chapter 6. Stability of Dipole Gap Solitons in TwoDimensionalLattice Potentials 111 Nir DROR and Boris A. MALOMED Chapter 7. Representation of Wave Energy of a Rotating Flow inTerms of the Dispersion Relation 139 Yasuhide FUKUMOTO, Makoto HIROTA and Youichi MIE Chapter 8. Determining the Stability Domain of PerturbedFourDimensional Systems in 1:1 Resonance 155 Igor HOVEIJN and Oleg N. KIRILLOV Chapter 9. Index Theorems for Polynomial Pencils 177 Richard KOLLAR and Radomir BOSAK Chapter 10. Investigating Stability and Finding New Solutions inConservative Fluid Flows Through Bifurcation Approaches 203 Paolo LUZZATTOFEGIZ and Charles H.K. WILLIAMSON Chapter 11. Evolution Equations for Finite Amplitude Waves inParallel Shear Flows 223 Sherwin A. MASLOWE Chapter 12. Continuum Hamiltonian Hopf Bifurcation I 247 Philip J. MORRISON and George I. HAGSTROM Chapter 13. Continuum Hamiltonian Hopf Bifurcation II 283 George I. HAGSTROM and Philip J. MORRISON Chapter 14. Energy Stability Analysis for a Hybrid FluidKineticPlasma Model 311 Philip J. MORRISON, Emanuele TASSI and Cesare TRONCI Chapter 15. Accurate Estimates for the Exponential Decay ofSemigroups with NonSelfAdjoint Generators 331 Francis NIER Chapter 16. Stability Optimization for Polynomials and Matrices351 Michael L. OVERTON Chapter 17. Spectral Stability of Nonlinear Waves in KdVTypeEvolution Equations 377 Dmitry E. PELINOVSKY Chapter 18. Unfreezing Casimir Invariants: SingularPerturbations Giving Rise to Forbidden Instabilities 401 List of Authors 421 Index 425.
 (source: Nielsen Book Data)
 Publisher's Summary
 Bringing together 18 chapters written by leading experts indynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents stateoftheartapproaches to a wide spectrum of new and challenging stabilityproblems. Nonlinear Physical Systems: Spectral Analysis, Stability andBifurcations focuses on problems of spectral analysis, stabilityand bifurcations arising in the nonlinear partial differentialequations of modern physics. Bifurcations and stability of solitarywaves, geometrical optics stability analysis in hydro andmagnetohydrodynamics, and dissipationinduced instabilities aretreated with the use of the theory of Krein and Pontryagin space, index theory, the theory of multiparameter eigenvalue problems andmodern asymptotic and perturbative approaches. Each chapter contains mechanical and physical examples, and thecombination of advanced material and more tutorial elements makesthis book attractive for both experts and nonspecialists keen toexpand their knowledge on modern methods and trends in stabilitytheory. Contents 1. Surprising Instabilities of Simple Elastic Structures, DavideBigoni, Diego Misseroni, Giovanni Noselli and DanieleZaccaria. 2. WKB Solutions Near an Unstable Equilibrium and Applications, JeanFrancois Bony, Setsuro Fujiie, Thierry Ramond andMaher Zerzeri, partially supported by French ANR projectNOSEVOL. 3. The Sign Exchange Bifurcation in a Family of Linear HamiltonianSystems, Richard Cushman, Johnathan Robbins and DimitriiSadovskii. 4. Dissipation Effect on Local and Global FluidElasticInstabilities, Olivier Doare. 5. Tunneling, Librations and Normal Forms in a Quantum Double Wellwith a Magnetic Field, Sergey Yu. Dobrokhotov and Anatoly Yu.Anikin. 6. Stability of Dipole Gap Solitons in TwoDimensional LatticePotentials, Nir Dror and Boris A. Malomed. 7. Representation of Wave Energy of a Rotating Flow in Terms of theDispersion Relation, Yasuhide Fukumoto, Makoto Hirota and YouichiMie. 8. Determining the Stability Domain of Perturbed FourDimensionalSystems in 1:1 Resonance, Igor Hoveijn and Oleg N. Kirillov. 9. Index Theorems for Polynomial Pencils, Richard Kollar andRadomir Bosak. 10. Investigating Stability and Finding New Solutions inConservative Fluid Flows Through Bifurcation Approaches, PaoloLuzzattoFegiz and Charles H.K. Williamson. 11. Evolution Equations for Finite Amplitude Waves in ParallelShear Flows, Sherwin A. Maslowe. 12. Continuum Hamiltonian Hopf Bifurcation I, Philip J. Morrisonand George I. Hagstrom. 13. Continuum Hamiltonian Hopf Bifurcation II, George I. Hagstromand Philip J. Morrison. 14. Energy Stability Analysis for a Hybrid FluidKinetic PlasmaModel, Philip J. Morrison, Emanuele Tassi and Cesare Tronci. 15. Accurate Estimates for the Exponential Decay of Semigroups withNonSelfAdjoint Generators, Francis Nier. 16. Stability Optimization for Polynomials and Matrices, Michael L.Overton. 17. Spectral Stability of Nonlinear Waves in KdVType EvolutionEquations, Dmitry E. Pelinovsky. 18. Unfreezing Casimir Invariants: Singular Perturbations GivingRise to Forbidden Instabilities, Zensho Yoshida and Philip J.Morrison. About the Authors Oleg N. Kirillov has been a Research Fellow at theMagnetoHydrodynamics Division of the HelmholtzZentrumDresdenRossendorf in Germany since 2011. His research interestsinclude nonconservative stability problems of structural mechanicsand physics, perturbation theory of nonselfadjoint boundaryeigenvalue problems, magnetohydrodynamics, frictioninducedoscillations, dissipationinduced instabilities and nonHermitianproblems of optics and microwave physics. Since 2013 he has servedas an Associate Editor for the journal Frontiers in MathematicalPhysics. Dmitry E. Pelinovsky has been Professor at McMaster University inCanada since 2000. His research profile includes work withnonlinear partial differential equations, discrete dynamicalsystems, spectral theory, integrable systems, and numericalanalysis. He served as the guest editor of the special issue of thejournals Chaos in 2005 and Applicable Analysis in 2010. He is anAssociate Editor of the journal Communications in Nonlinear Scienceand Numerical Simulations. This book is devoted to the problems of spectral analysis, stability and bifurcations arising from the nonlinear partialdifferential equations of modern physics. Leading experts indynamical systems, operator theory, partial differential equations, and solid and fluid mechanics present stateoftheart approachesto a wide spectrum of new challenging stability problems.Bifurcations and stability of solitary waves, geometrical opticsstability analysis in hydro and magnetohydrodynamics anddissipationinduced instabilities will be treated with the use ofthe theory of Krein and Pontryagin space, index theory, the theoryof multiparameter eigenvalue problems and modern asymptotic andperturbative approaches. All chapters contain mechanical andphysical examples and combine both tutorial and advanced sections, making them attractive both to experts in the field andnonspecialists interested in knowing more about modern methods andtrends in stability theory.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2014
 Responsibility
 edited by Oleg N. Kirillov, Dmitry E. Pelinovsky.
 Series
 Mechanical engineering and solid mechanics series
 ISBN
 9781848214200 (hbk.)
 1848214200 (hbk.)