Solitons in Molecular Systems / Edition 2

by Davydov

Overview

Approach your problems from the It isn't that they can't see the end and begin with the answers. solution. It is that they can't Then one day, perhaps you will see the problem. find the final question. G.K. Chesterton. The Scandal of 'The Hermit Clad in Crane Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro­ gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electric engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "complete integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. The draw upon widely different sections of mathematics.

Product Details

ISBN-13:	9780792310297
Publisher:	Springer Netherlands
Publication date:	11/30/1990
Series:	Mathematics and its Applications , #61
Edition description:	2nd ed. 1991
Pages:	413
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

1. Collective Excitations in Quasi-Periodical Molecular Structures.- 1. Crisis in Bioenergetics.- 2. Alpha-Helical Structure of Proteins.- 3. Collective Excitations in a Single Chain of Peptide Groups.- 4. Excitons in Molecular a Chain.- 5. Solitons in Molecular a Chain.- 6. Solitons in Real—-Helical Molecules.- 2. Some Phenomena with Participation of Molecular Solitons.- 7. Solitons and Molecular Mechanism for Muscle Contraction.- 8. Solitons and the Molecular Mechanism of the Effect of Radiation on Cells.- 9. A Possible Mechanism for General Anesthesia.- 10. Intracellular Dynamics and Solitons.- 3. Excitation of Solitons in One-Dimensional Systems.- 11. Time-Dependent Evolution of Initial Excitation.- 12. Initial Excitation in the Form of a Hyperbolic Secant.- 13. Initial Excitation in the Form of a Rectangular Impulse.- 4. Dynamical Properties of Solitons.- 14. Free Solitons.- 15. Soliton Motion with Friction.- 16. Soliton Motion Affected by External Inhomogeneous Fields.- 5. Solitons in Molecular Systems with Nonlinear Intermolecular Interactions.- 17. The Equation of Soliton Motion for General Intermolecular Interaction.- 18. Cubic Anharmonicity.- 19. Quartic Anharmonicity.- 20. Repulsive Core Potential.- 6. Super-Sound Acoustic Solitons.- 21. Solitons in Toda Nonlinear Lattices.- 22. Acoustic Solitons in Molecular Chain with Cubic Anharmonicity.- 23. Acoustic Solitons in Molecular Chain with Quartic Anharmonicity.- 24. The Capture of an Excess Electron by Supersound Acoustic Solitons.- 25. Supersound Solitons in Nonlinear Quasi-One-Dimensional Molecular Structures.- 7 The Theory of Electron Transfer by Solitons.- 26. The Donor-Acceptor Model of Electron Transfer by Protein Molecules.- 27. The Interaction of an Electron with Nondipole Optical Phonons.- 8Space-Periodic Excitations in Nonlinear Systems.- 28. Mobile Periodical Excitations in One-Dimensional Systems.- 29. Elementary Data on Jacobian Elliptic Functions.- 30. Periodic Solutions of the Nonlinear Schrödinger Equation. Cnoidal Waves.- 31. Periodic Solutions for Some Quasiparticles in a Quasi-One-Dimensional Molecular Chain.- 32. Autolocalized Periodic Thickening of Particles Described by a Complex Field with Inertialess Self-Interaction.- 9 The Quantum Theory of Quasiparticle Motion in a Molecular Chain Taking into Account Thermal Vibrations.- 33. Equations for the Stationary States of a Quasiparticle in a One-Dimensional Chain within a Thermostat.- 34. Nonlocalized Stationary States of a Quasiparticle.- 35. Smooth Autolocalized State-Single Soliton.- 36. Solutions Describing the Movement of Periodically Arranged Quasiparticles.- 37. Strong Quasiparticle Autolocalization.- 38. Radiation Excitation of Optical Solitons in Crystalline Acetanilide.- 10 The Nonlinear Sine-Gordon Equation.- 39. Canonic Form of the Sine-Gordon Equation.- 40. Single-Phase Solutions of the Sine-Gordon Equation.- 41. The Solution of the Sine-Gordon Equation by the Method of Separation of Variables.- 42. Josephson Tunnelling Effect in Superconductors.- 43. The Dynamics of Dislocations in Crystals.- 44. Bloch Wave Motion.- 45. The Propagation of Ultrashort Optical Pulses.- 11 Conformational Excitations in One-Dimensional Molecular Systems.- 46. Quasi-One-Dimensional Systems Undergoing Structural Phase Transitions.- 12 Solitons and Proton Motion in Hydrogen-Bonded Molecular Structures.- 47. A Model of Proton Conductivity: Basic Equations.- 48. Proton Motion Neglecting the Interaction between Sublattices.- 49. Proton Motion Taking into Account the Interaction between SublatticeDisplacements.- 50. The Motion of Orientational Defects in Chains of Water Molecules.- 51. The Migration of Protons in Near-Surface Layers of Water.- 13 Three-Dimensional Solitons (Polarons) in Ionic Crystals.- 52. The Landau and Pekar Concepts of Autolocalization of the Electron in Ionic Crystal.- 53. Generalized Theory of Polarons.- 14 The Generation of Solitons and Bisolitons.- 54. The Generation of a Soliton at the Boundary of a Soft Molecular Chain.- 15 Nonlinear Bisolitonic Mechanism of High-Tc Superconductivity.- 55. Discovery of High-Tc Superconductors and their Basic Properties.- 56. The Basis of the Bisoliton Model of High-Tc Superconductivity.