Nonlinear Physical Systems

Spectral Analysis, Stability and Bifurcations

Nonfiction, Science & Nature, Mathematics
Cover of the book Nonlinear Physical Systems by Oleg N. Kirillov, Dmitry E. Pelinovsky, Wiley
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Oleg N. Kirillov, Dmitry E. Pelinovsky ISBN: 9781118577547
Publisher: Wiley Publication: December 11, 2013
Imprint: Wiley-ISTE Language: English
Author: Oleg N. Kirillov, Dmitry E. Pelinovsky
ISBN: 9781118577547
Publisher: Wiley
Publication: December 11, 2013
Imprint: Wiley-ISTE
Language: English

Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.
Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynamics, and dissipation-induced instabilities are treated with the use of the theory of Krein and Pontryagin space, index theory, the theory of multi-parameter eigenvalue problems and modern asymptotic and perturbative approaches.
Each chapter contains mechanical and physical examples, and the combination of advanced material and more tutorial elements makes this book attractive for both experts and non-specialists keen to expand their knowledge on modern methods and trends in stability theory.

Contents

  1. Surprising Instabilities of Simple Elastic Structures, Davide Bigoni, Diego Misseroni, Giovanni Noselli and Daniele Zaccaria.
  2. WKB Solutions Near an Unstable Equilibrium and Applications, Jean-François Bony, Setsuro Fujiié, Thierry Ramond and Maher Zerzeri, partially supported by French ANR project NOSEVOL.
  3. The Sign Exchange Bifurcation in a Family of Linear Hamiltonian Systems, Richard Cushman, Johnathan Robbins and Dimitrii Sadovskii.
  4. Dissipation Effect on Local and Global Fluid-Elastic Instabilities, Olivier Doaré.
  5. Tunneling, Librations and Normal Forms in a Quantum Double Well with a Magnetic Field, Sergey Yu. Dobrokhotov and Anatoly Yu. Anikin.
  6. Stability of Dipole Gap Solitons in Two-Dimensional Lattice Potentials, Nir Dror and Boris A. Malomed.
  7. Representation of Wave Energy of a Rotating Flow in Terms of the Dispersion Relation, Yasuhide Fukumoto, Makoto Hirota and Youichi Mie.
  8. Determining the Stability Domain of Perturbed Four-Dimensional Systems in 1:1 Resonance, Igor Hoveijn and Oleg N. Kirillov.
  9. Index Theorems for Polynomial Pencils, Richard Kollár and Radomír Bosák.
  10. Investigating Stability and Finding New Solutions in Conservative Fluid Flows Through Bifurcation Approaches, Paolo Luzzatto-Fegiz and Charles H.K. Williamson.
  11. Evolution Equations for Finite Amplitude Waves in Parallel Shear Flows, Sherwin A. Maslowe.
  12. Continuum Hamiltonian Hopf Bifurcation I, Philip J. Morrison and George I. Hagstrom.
  13. Continuum Hamiltonian Hopf Bifurcation II, George I. Hagstrom and Philip J. Morrison.
  14. Energy Stability Analysis for a Hybrid Fluid-Kinetic Plasma Model, Philip J. Morrison, Emanuele Tassi and Cesare Tronci.
  15. Accurate Estimates for the Exponential Decay of Semigroups with Non-Self-Adjoint Generators, Francis Nier.
  16. Stability Optimization for Polynomials and Matrices, Michael L. Overton.
  17. Spectral Stability of Nonlinear Waves in KdV-Type Evolution Equations, Dmitry E. Pelinovsky.
  18. Unfreezing Casimir Invariants: Singular Perturbations Giving Rise to Forbidden Instabilities, Zensho Yoshida and Philip J. Morrison.

About the Authors

Oleg N. Kirillov has been a Research Fellow at the Magneto-Hydrodynamics Division of the Helmholtz-Zentrum Dresden-Rossendorf in Germany since 2011. His research interests include non-conservative stability problems of structural mechanics and physics, perturbation theory of non-self-adjoint boundary eigenvalue problems, magnetohydrodynamics, friction-induced oscillations, dissipation-induced instabilities and non-Hermitian problems of optics and microwave physics. Since 2013 he has served as an Associate Editor fo

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.
Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynamics, and dissipation-induced instabilities are treated with the use of the theory of Krein and Pontryagin space, index theory, the theory of multi-parameter eigenvalue problems and modern asymptotic and perturbative approaches.
Each chapter contains mechanical and physical examples, and the combination of advanced material and more tutorial elements makes this book attractive for both experts and non-specialists keen to expand their knowledge on modern methods and trends in stability theory.

Contents

  1. Surprising Instabilities of Simple Elastic Structures, Davide Bigoni, Diego Misseroni, Giovanni Noselli and Daniele Zaccaria.
  2. WKB Solutions Near an Unstable Equilibrium and Applications, Jean-François Bony, Setsuro Fujiié, Thierry Ramond and Maher Zerzeri, partially supported by French ANR project NOSEVOL.
  3. The Sign Exchange Bifurcation in a Family of Linear Hamiltonian Systems, Richard Cushman, Johnathan Robbins and Dimitrii Sadovskii.
  4. Dissipation Effect on Local and Global Fluid-Elastic Instabilities, Olivier Doaré.
  5. Tunneling, Librations and Normal Forms in a Quantum Double Well with a Magnetic Field, Sergey Yu. Dobrokhotov and Anatoly Yu. Anikin.
  6. Stability of Dipole Gap Solitons in Two-Dimensional Lattice Potentials, Nir Dror and Boris A. Malomed.
  7. Representation of Wave Energy of a Rotating Flow in Terms of the Dispersion Relation, Yasuhide Fukumoto, Makoto Hirota and Youichi Mie.
  8. Determining the Stability Domain of Perturbed Four-Dimensional Systems in 1:1 Resonance, Igor Hoveijn and Oleg N. Kirillov.
  9. Index Theorems for Polynomial Pencils, Richard Kollár and Radomír Bosák.
  10. Investigating Stability and Finding New Solutions in Conservative Fluid Flows Through Bifurcation Approaches, Paolo Luzzatto-Fegiz and Charles H.K. Williamson.
  11. Evolution Equations for Finite Amplitude Waves in Parallel Shear Flows, Sherwin A. Maslowe.
  12. Continuum Hamiltonian Hopf Bifurcation I, Philip J. Morrison and George I. Hagstrom.
  13. Continuum Hamiltonian Hopf Bifurcation II, George I. Hagstrom and Philip J. Morrison.
  14. Energy Stability Analysis for a Hybrid Fluid-Kinetic Plasma Model, Philip J. Morrison, Emanuele Tassi and Cesare Tronci.
  15. Accurate Estimates for the Exponential Decay of Semigroups with Non-Self-Adjoint Generators, Francis Nier.
  16. Stability Optimization for Polynomials and Matrices, Michael L. Overton.
  17. Spectral Stability of Nonlinear Waves in KdV-Type Evolution Equations, Dmitry E. Pelinovsky.
  18. Unfreezing Casimir Invariants: Singular Perturbations Giving Rise to Forbidden Instabilities, Zensho Yoshida and Philip J. Morrison.

About the Authors

Oleg N. Kirillov has been a Research Fellow at the Magneto-Hydrodynamics Division of the Helmholtz-Zentrum Dresden-Rossendorf in Germany since 2011. His research interests include non-conservative stability problems of structural mechanics and physics, perturbation theory of non-self-adjoint boundary eigenvalue problems, magnetohydrodynamics, friction-induced oscillations, dissipation-induced instabilities and non-Hermitian problems of optics and microwave physics. Since 2013 he has served as an Associate Editor fo

More books from Wiley

Cover of the book Effective Group Coaching by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book Adult Learning by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book The Plugged-In Manager by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book Strategies to the Prediction, Mitigation and Management of Product Obsolescence by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book Physico-chemical Aspects of Textile Coloration by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book Understanding Diabetes by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book Celestial Dynamics by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book Practical High-Performance Liquid Chromatography by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book The New Form 990 by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book How to Work With and Lead People Not Like You by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book Dividends and Dividend Policy by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book Signal and Image Processing for Biometrics by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book Translational Research and Discovery in Gastroenterology by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book Powerful Exhibit Marketing by Oleg N. Kirillov, Dmitry E. Pelinovsky
Cover of the book Satellite Communications Payload and System by Oleg N. Kirillov, Dmitry E. Pelinovsky
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy