Nonlinear physical systems : spectral analysis, stability and bifurcations /

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Bibliographic Details
Corporate Author:	Ebooks Corporation
Format:	Electronic eBook
Language:	English
Published:	London : Hoboken, NJ : ISTE ; Wiley, 2014.
Series:	Mechanical engineering and solid mechanics series.
Subjects:	Differential equations, Partial. Differential equations, Nonlinear. Dynamics. Nonlinear systems.
Online Access:	Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)

Table of Contents:

Machine generated contents note: ch. 1 Surprising Instabilities of Simple Elastic Structures / Daniele Zaccaria
1.1. Introduction
1.2. Buckling in tension
1.3. effect of constraint's curvature
1.4. Ziegler pendulum made unstable by Coulomb friction
1.5. Conclusions
1.6. Acknowledgments
1.7. Bibliography
ch. 2 WKB Solutions Near an Unstable Equilibrium and Applications / Maher Zerzeri
2.1. Introduction
2.2. Connection of microlocal solutions near a hyperbolic fixed point
2.2.1. model in one dimension
2.2.2. Classical mechanics
2.2.3. Review of semi-classical microlocal analysis
2.2.4. microlocal Cauchy problem - uniqueness
2.2.5. microlocal Cauchy problem - transition operator
2.3. Applications to semi-classical resonances
2.3.1. Spectral projection and Schrodinger group
2.3.2. Resonance-free zone for homoclinic trajectories
2.4. Acknowledgment
2.5. Bibliography
ch. 3 Sign Exchange Bifurcation in a Family of Linear Hamiltonian Systems / Dimitrii Sadovskii
3.1. Statement of problem
3.2. Bifurcation values of γ
3.3. Versal normal forms near the bifurcation values
3.3.1. Normal forms
3.3.2. Linear Hamiltonian Hopf bifurcation γ±
3.3.3. Switch twist bifurcation at γ+
3.3.4. Sign exchange bifurcation
3.4. Infinitesimally symplectic normal form
3.4.1. Normal form of Xγ at γ±
3.4.2. Normal form of Xγ at γ±
3.5. Global issues
3.5.1. Invariant Lagrange planes
3.5.2. Symplectic signs
3.6. Bibliography
ch. 4 Dissipation Effect on Local and Global Fluid-Elastic Instabilities / Olivier Doare
4.1. Introduction
4.2. Local and global stability analyses
4.2.1. Local analysis
4.2.2. Global analysis
4.3. fluid-conveying pipe: a model problem
4.4. Effect of damping on the local and global stability of the fluid-conveying pipe
4.4.1. Local stability
4.4.2. Global stability
4.5. Application to energy harvesting
4.6. Conclusion
4.7. Bibliography
ch. 5 Tunneling, Librations and Normal Forms in a Quantum Double Well with a Magnetic Field / Anatoly Y. Anikin
5.1. Introduction
5.2. 1D Landau-Lifshitz splitting formula and its analog for the ground states
5.3. splitting formula in multi-dimensional case
5.4. Normal forms and complex Lagrangian manifolds
5.4.1. Normal form in the classically allowed and forbidden regions
5.4.2. Complex continuation of integrals
5.4.3. Almost invariant complex Lagrangian manifolds
5.5. Constructing the asymptotics for the eigenfunctions in tunnel problems
5.5.1. Complex WKB-method
5.5.2. WKB-methods with real and pure imaginary phases
5.5.3. Variational methods
5.6. Splitting of the eigenvalues in the presence of magnetic field
5.7. Proof of main theorem (a sketch)
5.7.1. Lifshitz-Herring formula
5.7.2. Instanton splitting formula
5.7.3. Asymptotic behavior of the libration action
5.7.4. Reduction to the 1D splitting problem
5.7.5. Asymptotic behavior of the Floquet exponents
5.7.6. Finishing the proof
5.8. Conclusion
5.9. Acknowledgments
5.10. Bibliography
ch. 6 Stability of Dipole Gap Solitons in Two-Dimensional Lattice Potentials / Boris A. Malomed
6.1. Introduction
6.2. model
6.3. Solitons in the first bandgap: the SF nonlinearity
6.3.1. Solution families
6.3.2. Stability of solitons in the first finite bandgap
6.3.3. Bound states of solitons in the first bandgap
6.4. Stability GSs in the second bandgap
6.5. Conclusions
6.6. Bibliography
ch. 7 Representation of Wave Energy of a Rotating Flow in Terms of the Dispersion Relation / Youichi Mie
7.1. Introduction
7.2. Lagrangian approach to wave energy
7.3. Kelvin waves
7.4. Wave energy in terms of the dispersion relation
7.5. Conclusion
7.6. Bibliography
ch. 8 Determining the Stability Domain of Perturbed Four-Dimensional Systems in 1:1 Resonance / Oleg N. Kirillov
8.1. Introduction
8.1.1. Physical motivation
8.1.2. Setting
8.1.3. Main question and examples
8.2. Methods
8.2.1. Centralizer unfolding
8.2.2. Stability domain
8.2.3. Mapping into the centralizer unfolding
8.3. Examples
8.3.1. Modulation instability
8.3.2. Non-conservative gyroscopic system
8.4. Conclusions
8.5. Bibliography
ch. 9 Index Theorems for Polynomial Pencils / Radomir Bosak
9.1. Introduction
9.2. Krein signature
9.3. Index theorems for linear pencils and linearized Hamiltonians
9.4. Graphical interpretation of index theorems
9.4.1. Algebraic calculation of Z and Z
9.5. Conclusions
9.6. Acknowledgments
9.7. Bibliography
ch. 10 Investigating Stability and Finding New Solutions in Conservative Fluid Flows Through Bifurcation Approaches / Charles H.K. Williamson
10.1. Introduction
10.2. Counting positive-energy modes from IVI diagrams
10.3. approximate prediction for the onset of resonance in 2D vortices
10.4. example: three corotating vortices
10.4.1. Building a family of solutions from vorticity-preserving rearrangements
10.4.2. Computing signatures for one member of the family
10.4.3. velocity-impulse diagram
10.4.4. Uncovering bifurcations by introducing imperfections
10.4.5. Counting positive-energy modes from turning points in impulse
10.4.6. Recovering the underlying bifurcation structure
10.4.7. approximate prediction for resonance
10.5. Comparison with exact eigenvalues and discussion
10.6. Conclusions
10.7. Bibliography
ch. 11 Evolution Equations for Finite Amplitude Waves in Parallel Shear Flows / Sherwin A. Maslowe
11.1. Introduction
11.2. Wave packets
11.2.1. Conservative systems
11.2.2. Applications to hydrodynamic stability
11.2.3. Ginzburg-Landau equation
11.3. Critical layer theory
11.3.1. Asymptotic theory of the Orr-Sommerfeld equation
11.3.2. Nonlinear critical layers
11.3.3. wave packet critical layer
11.4. Nonlinear instabilities governed by integro-differential equations
11.4.1. zonal wave packet critical layer
11.5. Concluding remarks
11.6. Bibliography
ch. 12 Continuum Hamiltonian Hopf Bifurcation I / George I. Hagstrom
12.1. Introduction
12.2. Discrete Hamiltonian bifurcations
12.2.1. class of 1 + 1 Hamiltonian multifluid theories
12.2.2. Examples
12.2.3. Comparison and commentary
12.3. Continuum Hamiltonian bifurcations
12.3.1. class of 2 + 1 Hamiltonian mean field theories
12.3.2. Example of the CHH bifurcation
12.4. Summary and conclusions
12.5. Acknowledgments
12.6. Bibliography
ch. 13 Continuum Hamiltonian Hopf Bifurcation II / Philip J. Morrison
13.1. Introduction
13.2. Mathematical aspects of the continuum Hamiltonian Hopf bifurcation
13.2.1. Structural stability
13.2.2. Normal forms and signature
13.3. Application to Vlasov-Poisson
13.3.1. Structural stability in the space Cn (R) [∩]L1 (R)
13.3.2. Structural stability in W1'1
13.3.3. Dynamical accessibility and structural stability
13.4. Canonical infinite-dimensional case
13.4.1. Negative energy oscillator coupled to a heat bath
13.5. Commentary: degeneracy and nonlinearity
13.6. Summary and conclusions
13.7. Acknowledgments
13.8. Bibliography
ch. 14 Energy Stability Analysis for a Hybrid Fluid-Kinetic Plasma Model / Cesare Tronci
14.1. Introduction
14.2. Stability and the energy-Casimir method
14.3. Planar Hamiltonian hybrid model
14.3.1. Planar hybrid model equations of motion
14.3.2. Hamiltonian structure
14.3.3. Casimir invariants
14.4. Energy-Casimir stability analysis
14.4.1. Equilibrium variational principle
14.4.2. Stability conditions
14.5. Conclusions
14.6. Acknowledgments
14.7. Appendix A: derivation of hybrid Hamiltonian structure
14.8. Appendix B: Casimir verification
14.9. Bibliography
ch. 15 Accurate Estimates for the Exponential Decay of Semigroups with Non-Self-Adjoint Generators / Francis Nier
15.1. Introduction
15.2. Relevant quantities for sectorial operators
15.3. Natural examples
15.3.1. example related to linearized equations of fluid mechanics
15.3.2. Kramers-Fokker-Planck operators
15.4. Artificial examples
15.4.1. Adiabatic evolution of quantum resonances in the one-dimensional case
15.4.2. Optimizing the sampling of equilibrium distributions
15.5. Conclusion
15.6. Bibliography
ch. 16 Stability Optimization for Polynomials and Matrices / Michael L. Overton
16.1. Optimization of roots of polynomials
16.1.1. Root optimization over a polynomial family with a single affine constraint
16.1.2. root radius
16.1.3. root abscissa
16.1.4. Examples
16.1.5. Polynomial root optimization with several affine constraints
16.1.6. Variational analysis of the root radius and abscissa
16.1.7. Computing the root radius and abscissa
16.2. Optimization of eigenvalues of matrices
16.2.1. Static output feedback
16.2.2. Numerical methods for non-smooth optimization
16.2.3. Numerical results for some SOF problems
16.2.4. Diaconis-Holmes-Neal Markov chain
16.2.5. Active derogatory eigenvalues
16.3. Concluding remarks
16.4. Acknowledgments
16.5. Bibliography
Contents note continued: ch. 17 Spectral Stability of Nonlinear Waves in KdV-Type Evolution Equations / Dmitry E. Pelinovsky
17.1. Introduction
17.2. Historical remarks and examples
17.3. Proof of theorem 17.1
17.4. Generalization of theorem 17.1 for a periodic nonlinear wave
17.5. Conclusion
17.6. Bibliography
ch. 18 Unfreezing Casimir Invariants: Singular Perturbations Giving Rise to Forbidden Instabilities / Philip J. Morrison
18.1. Introduction
18.2. Preliminaries: noncanonical Hamiltonian systems and Casimir invariants
18.3. Foliation by adiabatic invariants
18.4. Canonization atop Casimir leaves
18.4.1. Extension of the phase space and canonization
18.4.2. "Minimum" canonization invoking Casimir invariants
18.5. Application to tearing-mode theory
18.5.1. Helicity and Beltrami equilibria
18.5.2. Tearing-mode instability
18.6. Conclusion
18.7. Acknowledgments
18.8. Bibliography.

Nonlinear physical systems : spectral analysis, stability and bifurcations /

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