Screen LibraryChaos and structures in nonlinear plasmas /
The book is a collection of research and review articles in several areas of modern mathematics and mathematical physics published in the span of three decades. The ICM Kyoto talk "Mathematics as Metaphor" summarises the author's view on mathematics as an outgrowth of natural language...
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| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore : |
| Publication Dates: | 1996. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/3078#t=toc |
| Summary: |
The book is a collection of research and review articles in several areas of modern mathematics and mathematical physics published in the span of three decades. The ICM Kyoto talk "Mathematics as Metaphor" summarises the author's view on mathematics as an outgrowth of natural language. |
| Carrier Form: | 1 online resource (xiii,340pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 319-333) and index. |
| ISBN: | 9789812830241 |
| Index Number: | QC718 |
| CLC: | O53 |
| Contents: | 1. Nonlinear oscillations. 1.1. Harmonic generation in small amplitude oscillations. 1.2. Amplitude dispersion from secular terms. 1.3. Parametric instabilities. 1.4. Example 1.1 Parametric excitation of the pendulum. 1.5. Example 1.2 Stability of the ponderomotive potential. 1.6. Example 1.3 Oscillations of a charged particle in two longitudinal waves -- 2. Hamiltonian dynamics. 2.1. Measure-preserving flows and the Hamiltonian. 2.2. Poincare surface of section. 2.3. Fixed points and invariant curves. 2.4. KAM theory. 2.5. KAM torii, the golden mean and leaky barriers. 2.6. KAM theory in laboratory plasmas. 2.7. Visualization of the magnetic flux surfaces by electron beam mapping. 2.8. Magnetic islands and the unstable-chaotic trajectories of field lines in tokamaks. 2.9. Measure of the resonant rational surfaces. 2.10. Example 2.1 How a swing behaves. 2.11. Invariant tori and the KAM theorem -- 3. Stochasticity theory and applications in plasmas. 3.1. Trajectories in straight, nonuniform magnetic fields. 3.2. Adiabatic invariants. 3.3. Onset of chaos from a transverse electric field. 3.4. Onset of chaos from a normal magnetic field component. 3.5. E x B motion in two low-frequency waves and the diffusion approximation. 3.6. Renormalized E x B diffusion coefficients. 3.7. E x B motion in a sheared magnetic shear. 3.8. Hamilton's equations of motion in non-canonical coordinates -- 4. Phase space structures in Hamiltonian systems. 4.1. The standard map. 4.2. Maps for the motion of a charged particle in an infinite spectrum of longitudinal waves. 4.3. Fixed points, accelerator orbits and the tangent map. 4.4. Stochastic motion and the diffusion coefficient. 4.5. Regular motion in the relativistic standard map. 4.6. Symmetries of the relativistic standard map. 4.7. Stability of the periodic orbits. 4.8. Poincare-Birkhoff multifurcation for the period-4 orbit. 4.9. Concluding remarks on the standard and relativistic maps. 4.10. Example 4.1 Fermi acceleration -- 5. Solitons in plasmas. 5.1. Nonlinear coherent modes in Vlasov plasmas. 5.2. Amplitude modulation of nearly monochromatic waves and the modulational instability. 5.3. Modulational instability and nonlinear Landau damping. 5.4. Reductive perturbation analysis of nonlinear wave propagation. 5.5. Birth of the soliton. 5.6. The inverse scattering transformation method. 5.7. Gelfand-Levitan equation for the scattering potential. 5.8. Inverse scattering transform (IST) for the NLS equation. 5.9. Generalization of the integrability conditions. 5.10. Alfven soliton. 5.11. One-dimensional soliton gas models. 5.12. Example 5.1 - Elastic collisions of two solitons. 5.13. Example 5.2 - 3 x 3 matrix formalism of the inverse scattering transformation -- 6. Vortex structures in hydrodynamic and Vlasov systems. 6.1. The drift wave-Rossby wave analogy. 6.2. The drift wave mechanism and vortex. 6.3. Solitary dipolar vortex solutions. 6.4. Drift wave-ion acoustic wave equations. 6.5. Experimental features and computer simulations of the dipole vortices. 6.6. Intermittent transport from vortex collisions. 6.7. Interaction energies and kurtosis in distributions of vortices and waves. 6.8. Fluctuation spectrum from a gas of dipole vortices. 6.9. Monopolar vortices produced by sheared flows. 6.10. Discussion and conclusions -- 7. Statistical properties and correlation functions for drift waves. 7.1. Introductory remarks. 7.2. Nonlinear drift wave equation. 7.3. Renormalized, markovianized spectral equations. 7.4. Local, isotropic approximation. 7.5. Low-order wave coupling. |