Structural stability in physics : proceedings of two International Symposia on Applications of Catastrophe Theory and Topological Concepts in Physics, Tübingen, Fed. Rep. of Germany, May 2-6 and December 11-14, 1978

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Structural stability in physics : proceedings of two International Symposia on Applications of Catastrophe Theory and Topological Concepts in Physics, Tübingen, Fed. Rep. of Germany, May 2-6 and December 11-14, 1978

editors, W. Güttinger and H. Eikemeier

（Springer series in synergetics, v. 4）

Springer-Verlag, 1979

  • : U.S.
  • : Germany
  • : pbk

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Includes bibliographical references and index

Description and Table of Contents

Volume

: Germany ISBN 9783540094630

Description

This volume is the record and product of two International Symposia on the Appli- cation of Catastrophe Theory and Topological Concepts in Physics, held in May and December 1978 at the Institute for Information Sciences, University of TUbingen. The May Symposium centered around the conferral of an honorary doctorate upon Professor Rene Thom, Paris, by the Faculty of Physics of the University of TUbingen in recognition of his discovery of universal structure principles and the new di- mension he has added to scientific knowledge by his pioneering work on structural stability and morphogenesis. Owing to the broad scope and rapid development of the field, the May Sympos,ium was followed in December by a second one on the same sub- jects. The symposia, attended by more than 50 scientists, brought together mathe- maticians, physicists, chemists and biologists to exchange ideas about the recent faSCinating impact of topological concepts on the physical sciences, and also to introduce young scientists to the field. The contributions, covering a wide spectrum, are summarized in the subsequent Introduction. The primary support of the Symposia was provided by the "Vereinigung der Freunde der Univertat TUbingen" (Association of the Benefactors of the University). We are particularly indebted to Dr. H. Doerner for his personal engagement and efficient help with the projects, both in his capacity as Secretary of the Association and as Administrative Director of the University.

Table of Contents

I General Concepts.- Towards a Revival of Natural Philosophy.- Catastrophe Theory.- Catastrophe Geometry in Physics: A Perspective.- Synergetics and a New Approach to Bifurcation Theory.- II Topological Aspects of Wave Motion.- Catastrophe and Fractal Regimes in Random Waves.- Distribution of Modes in Fractal Resonators.- Optical Caustics and Diffraction Catastrophes.- III Catastrophes in Infinite Dimensions.- Infinite Dimensions and the Fold Catastrophe.- Catastrophes and Bifurcations in Variational Problems.- Semiclassical Path Integrals in Terms of Catastrophes.- Catastrophe and Stochasticity in Semiclassical Quantum Mechanics.- IV Defects and Dislocations.- Stable Defects in Ordered Media.- Structural Stability in Evolving Flow Fields.- Wavefront Dislocations and Their Analysis Using Catastrophe Theory.- V Statistical Mechanics and Phase Transitions.- Structural Stability in Statistical Mechanics.- The 180 Rule at Triple Points: A Consideration Based on a Modified Butterfly Model.- Phase Diagrams and Catastrophes.- Information Measures and Thermodynamic Criteria of Motion.- Phase Transitions as Catastrophes: A Perspective.- VI Solitons.- Solitons in Physics: Basic Concepts.- Solitons in Mathematics.- Spin Wave Breathers in 3He B..- VII Dynamical Systems.- Catastrophic Effects in Pattern Recognition.- Cusp Bifurcation in Pituitary Thyrotropin Secretion.- Chaos.- Index of Contributors.
Volume

: pbk ISBN 9783642673658

Description

This volume is the record and product of two International Symposia on the Appli cation of Catastrophe Theory and Topological Concepts in Physics, held in May and December 1978 at the Institute for Information Sciences, University of TUbingen. The May Symposium centered around the conferral of an honorary doctorate upon Professor Rene Thom, Paris, by the Faculty of Physics of the University of TUbingen in recognition of his discovery of universal structure principles and the new di mension he has added to scientific knowledge by his pioneering work on structural stability and morphogenesis. Owing to the broad scope and rapid development of the field, the May Sympos,ium was followed in December by a second one on the same sub jects. The symposia, attended by more than 50 scientists, brought together mathe maticians, physicists, chemists and biologists to exchange ideas about the recent faSCinating impact of topological concepts on the physical sciences, and also to introduce young scientists to the field. The contributions, covering a wide spectrum, are summarized in the subsequent Introduction. The primary support of the Symposia was provided by the "Vereinigung der Freunde der Univertat TUbingen" (Association of the Benefactors of the University). We are particularly indebted to Dr. H. Doerner for his personal engagement and efficient help with the projects, both in his capacity as Secretary of the Association and as Administrative Director of the University.

Table of Contents

I General Concepts.- Towards a Revival of Natural Philosophy.- Catastrophe Theory.- Catastrophe Geometry in Physics: A Perspective.- Synergetics and a New Approach to Bifurcation Theory.- II Topological Aspects of Wave Motion.- Catastrophe and Fractal Regimes in Random Waves.- Distribution of Modes in Fractal Resonators.- Optical Caustics and Diffraction Catastrophes.- III Catastrophes in Infinite Dimensions.- Infinite Dimensions and the Fold Catastrophe.- Catastrophes and Bifurcations in Variational Problems.- Semiclassical Path Integrals in Terms of Catastrophes.- Catastrophe and Stochasticity in Semiclassical Quantum Mechanics.- IV Defects and Dislocations.- Stable Defects in Ordered Media.- Structural Stability in Evolving Flow Fields.- Wavefront Dislocations and Their Analysis Using Catastrophe Theory.- V Statistical Mechanics and Phase Transitions.- Structural Stability in Statistical Mechanics.- The 180 Degrees Rule at Triple Points: A Consideration Based on a Modified Butterfly Model.- Phase Diagrams and Catastrophes.- Information Measures and Thermodynamic Criteria of Motion.- Phase Transitions as Catastrophes: A Perspective.- VI Solitons.- Solitons in Physics: Basic Concepts.- Solitons in Mathematics.- Spin Wave Breathers in 3He B..- VII Dynamical Systems.- Catastrophic Effects in Pattern Recognition.- Cusp Bifurcation in Pituitary Thyrotropin Secretion.- Chaos.- Index of Contributors.

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