Peyresq lectures on nonlinear phenomena [Volume 1] / editors, Robin Kaiser, James Montaldi.

Format:

Book

Contributor:

Kaiser, R. (Robin)

Montaldi, J. (James)

Language:

English

Subjects (All):

Nonlinear theories.

Mathematical physics.

Physical Description:

1 online resource (296 p.)

Other Title:

Nonlinear phenomena

Place of Publication:

Singapore ; New York : World Scientific Publishing, c2000.

Language Note:

English

Summary:

Nonlinear science has a very broad scope and the aim of this volume of lectures is to introduce different aspects of this vast domain to research students whose studies are necessarily concentrated on only one. The lectures given at summer schools in France between 1997 and 1999, describe analytical, geometrical and experimental approaches to subjects as diverse as turbulence, elasticity, physiology, classical mechanics, quantum chaos, water waves and the laser cooling of atoms.

Contents:

CONTENTS; Preface; Addresses of Contributors; ELASTICITY AND GEOMETRY; 1 Introduction; 2 Differential geometry of 2D manifolds; 2.1 Developable surfaces; 2.2 Geometry of the Poincari half-plane; 3 Thin plate elasticity; 3.1 Euler-Lagrange functional; 3.2 Scaling of the FvK equations; 3.3 Geometry and the FvK equations; 3.4 Thin shells: an example; 4 Buckling in thin film delamination; 4.1 The straight sided blister; 4.2 Telephone cord delamination; References; QUANTUM CHAOS; 1 What is Quantum Chaos?; 1.1 Classical Chaos; 1.2 Quantum dynamics; 1.3 Semiclassical dynamics

1.4 Physical situations of interest1.5 A simple example: the hydrogen atom in a magnetic field; 2 Time scales - Energy scales; 3 Statistical Properties of Energy Levels - Random Matrix Theory; 3.1 Level Dynamics; 3.2 Statistical analysis of the spectral fluctuations; 3.3 Regular Regime; 3.4 Chaotic Regime - Random Matrix Theory; 3.5 Random Matrix Theory - Continued; 4 Semiclassical Approximation; 4.1 Regular Systems - EBK/WKB Quantization; 4.2 Semiclassical Propagator; 4.3 Green's function; 4.4 Trace Formula; 4.5 Convergence Properties of the Trace Formula; 4.6 An Example : the Helium Atom

5 ConclusionReferences; THE WATER-WAVE PROBLEM AS A SPATIAL DYNAMICAL SYSTEM; 1 Introduction; 2 Formulation as a reversible dynamical system; 2.1 Case of one layer with surface tension at the free surface; 2.2 Case of two layers without surface tension; 3 The linearized Problem; 4 Basic codimension one reversible normal forms; 4.1 Case (i); 4.2 Case (ii); 4.3 Case (Hi); 4.4 Case (iv); 5 Typical results for finite depth problems; 6 Infinite depth case; 6.1 Spectrum of the linearized problem; 6.2 Normal forms in infinite dimensions; 6.3 Typical results; References

COLD ATOMS AND MULTIPLE SCATTERING1 Classical model of Doppler cooling; 1.1 Internal motion: elastically bound electron; 1.2 Radiation forces acting on the atom: ""Classical approach""; 1.3 Resonant radiation pressure; 1.4 Dipole force; 1.5 Doppler cooling; 2 Interferences in multiple scattering; 2.1 Scattering cross section of single atoms; 2.2 Multiple scattering samples in atomic physics; 2.3 Dwell time; 2.4 Coherent backscattering of light; 2.5 Strong localization of light in atoms?; 3 Conclusion; References; AN INTRODUCTION TO ZAKHAROV THEORY OF WEAK TURBULENCE; 1 Introduction

2 Hamiltonian formalism for water waves2.1 Fundamental equations; 2.2 Hamilton's equations of motion; 2.3 The pertubative expansion; 3 The normal form of the Hamiltonian; 3.1 H.o=sum ofharmonic oscillators; 3.2 Nonlinear terms: three wave interactions; 3.3 Nonlinear terms: four wave interactions; 3.4 Dimensional analysis and scaling laws; 3.5 Miscellaneous remarks; 4 Kinetic equations; 4.1 Derivation of the kinetic equations; 4.2 Conservation laws; 5 Stationary spectra of weak turbulence; 5.1 Dimensional estimates; 5.2 Zakharov transformation; 5.3 Examples and final remarks; Acknowledgments

References

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9789812792778

9812792775

OCLC:

827944978