Nonlinear physics : from the pendulum to turbulence and chaos
著者
書誌事項
Nonlinear physics : from the pendulum to turbulence and chaos
（Contemporary concepts in physics, v. 4）
Harwood Academic Publishers, c1988
- : pbk
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注記
Bibliography: p. 653-665
Includes index
内容説明・目次
内容説明
This book gathers together the basic ideas of nonlinear theory necessary for all branches of physics, including mechanics of continuous media, optics, radiophysics, solid state physics, as well as plasma physics. It covers all aspects of the field in detail, and is intended for physicists at all levels, from undergraduate students upwards. Accompanying this book are two sets of software. The first comprises six 5 1/4 inch IBM compatible floppy diskettes, on which eight scenarios of dynamic computer graphics are recorded; the second is an ATRS program for research workers.
目次
- Part 1 Particles: the elements of dynamics - phase space, systems with one degree of freedom, an example - the nonlinear pendulum, two more examples of nonlinear oscillations, Poincare's integral invariants, multidimensional integrable systems, mappings, some remarks in conclusion
- approximate methods - perturbation theory, the averaging method, adiabatic invariants, charged particles in a magnetic field, linear analogues of adiabatic invariance
- special methods - nonlinear resonance, the Kolmogorov-Arnold-Moser (KAM), structural properties of phase trajectories, simple bifurcations
- ergodic theory and chaos - ergodicity and mixing, K-systems, examples, recurrences and periodic orbits
- chaos in detail - a universal mapping for nonlinear oscillations, overlapping of resonances, formation of a stochastic layer, destruction of the integrals of motion, stochastic attractors, examples of stochastic attractors, general notes on the onset of chaos
- elements of kinetics - the Fokker-Planck-Kolmogorov equation, kinetics in dissipative mappings, stochastic acceleraton and "heating" of particles
- fractal properties of chaos - fractals, fractals and chaos. Part 2 Waves: nonlinear stationary waves - steepening of waves, stationary waves, examples of stationary waves, collision-free shock waves
- Hamiltonian description of waves - variational principles, resonance interaction of waves, nonlinear wave resonances, interaction of nonlinear waves
- chaos in wave fields - weakly nonlinear fields, the fermi-pasta-ulam (FPU) problem, turbulence of a weekly nonlinear field, stochastic instability of a nonlinear wave
- strong turbulence - Lorenz model, convective cells, features of the onset of turbulence, Langmuir turbulence, soliton turbulence
- exactly integrable wave equations - integration of the KdV equation, integrable equations. Part 3 Examples: motion of particles in wave fields - regular and stochastic dynamics of particles, motion in a magnetic field and the field of a wave packet, the paradox of the disappearance of Landau damping, stochastic web
- billiards - mixing billiards, nonlinear-ray dynamics
- nonlinear optics - nonlinear geometrical optics, nonlinear co-operative phenomena
- structural properties of one dimensional chains - atom chains, spin chains, excitation in chains of molecules
- perturbations in Kepler's problem - nonlinear dynamics in a coulomb field, excitation and ionization of a hydrogen atom, diffusion of the eccentricity of orbits in the gravitational field of planets, diffusion of comets from the oort cloud. Part 4 Numerical simulation: nonlinear physics in colour - general notes on the pictures
- diskettes
- the ATRS program.
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