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Solitons in Molecular Systems : Mathematics and Its Applications - A. S. Davydov

Solitons in Molecular Systems

Mathematics and Its Applications

By: A. S. Davydov, E.S. Kryachko (Translator)

Hardcover Published: 30th November 1990
ISBN: 9780792310297
Number Of Pages: 413

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'Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematicsis a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics seIVe as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One seIVice topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

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.- 26.1. Pairing of Two Excess Electrons in a One-Dimensional Molecular Chain.- 27. The Interaction of an Electron with Nondipole Optical Phonons.- 8 Space-Periodic Excitations in Nonlinear Systems.- 28. Mobile Periodical Excitations in One-Dimensional Systems.- 28.1. First Type of Periodic Excitations.- 28.2. Second Type of Periodic Excitations.- 29. Elementary Data on Jacobian Elliptic Functions.- 30. Periodic Solutions of the Nonlinear Schrodinger Equation. Cnoidal Waves.- 30.1. Cnoidal Waves of the First Kind.- 30.2. Cnoidal Waves of the Second Kind.- 30.3. Solutions of the Nonlinear Schrodinger Equation with a Negative Nonlinearity Parameter.- 31. Periodic Solutions for Some Quasiparticles in a Quasi-One-Dimensional Molecular Chain.- 31.1. Superconductivity of Organic Crystals.- 32. Autolocalized Periodic Thickening of Particles Described by a Complex Field with Inertialess Self-Interaction.- 32.1. First Type of Autolocalized Solutions: Attractive Forces.- 32.2. Second Type of Autolocalized Solutions: Attractive Forces.- 32.3. Repulsive Forces.- 32.4. Autolocalized Excitations in Closed Molecular Chains.- 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.- 37.1. Chains with Narrow Energy Bands.- 37.2. Chains with Broad Energetic Bands.- 38. Radiation Excitation of Optical Solitons in Crystalline Acetanilide.- 38.1. Optical Solitons in Crystalline Acetanilide.- 38.2. Absorption of Radiation Resulting from the Creation of Optical Solitons.- 38.3. Acoustic Solitons in an ACN Crystal.- 10 The Nonlinear Sine-Gordon Equation.- 39. Canonic Form of the Sine-Gordon Equation.- 40. Single-Phase Solutions of the Sine-Gordon Equation.- 40.1. Magnetic-Type Wave Solutions.- 40.2. Electric-Type Wave Solutions.- 41. The Solution of the Sine-Gordon Equation by the Method of Separation of Variables.- 41.1. Single-Phase Solutions.- 41.2. Double-Phase Solutions.- 41.3. Standing Waves.- 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.- 46.1. Order-Disorder Transitions.- 46.2. Displacive 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 Sublattice Displacements.- 50. The Motion of Orientational Defects in Chains of Water Molecules.- 50.1. The Motion of Orientational Defects in an Electric Field.- 50.2. The Interaction of Orientational Bjerrum Defects.- 51. The Migration of Protons in Near-Surface Layers of Water.- 51.1. Proton Pumps in Cellular Membranes.- 51.2. The Role of Structuralized Water in Cartilage Tissues.- 13 Three-Dimensional Solitons (Polarons) in Ionic Crystals.- 52. The Landau and Pekar Concepts of Autolocalization of the Electron in Ionic Crystal.- 52.1. Adiabatic Theory of Pekar's Polaron.- 53. Generalized Theory of Polarons.- 53.1. The Direct Variational Principle.- 53.2. Energy and Wave Function of a Slow Polaron.- 14 The Generation of Solitons and Bisolitons.- 54. The Generation of a Soliton at the Boundary of a Soft Molecular Chain.- 54.1. The Dependence of Wave Functions. Soliton Generation.- 54.2. Bisoliton Generation.- 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.- 56.1. Isolated Bisolitons in a Quasi-One-Dimensional Chain.- 56.2. Bose Condensation of Bisolitons.- 56.3. Stability of the Bisoliton Condensate and Critical Superconducting Currents.- 56.4. Small and Medium Quasiparticle Densities in a Chain.- 56.5. The Generation of Bisolitons at the Boundary of a Metal with Superconductors.- 56.6. Direct Measurements of Energy Gap in Superconductors.

ISBN: 9780792310297
ISBN-10: 0792310292
Series: Mathematics and Its Applications
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 413
Published: 30th November 1990
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 2.39
Weight (kg): 0.77
Edition Number: 2
Edition Type: Revised

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