Disequilibrium and Self-Organisation

✍ Scribed by Karl-Erik Eriksson (auth.), C. W. Kilmister (eds.)

• Publisher: Springer Netherlands
• Year: 1986
• Tongue: English
• Leaves: 307
• Series: Mathematics and Its Applications 30
• Edition: 1
• Category: Library

✦ Synopsis

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chif1ese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized 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 programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

✦ Table of Contents

Front Matter....Pages i-ix
Self-Organization and Information Theory....Pages 1-10
The Mathematics Needed for Self-Organisation....Pages 11-17
Entropy and Order....Pages 19-21
Pattern Formation for a One Dimensional Evolution Equation Based on Thom’s River Basin Model.....Pages 23-46
On the Modelling of Vehicular Traffic Flow....Pages 47-63
Alternative Exploitation of Dissipation Inequality Demonstrated for Hyperbolic Heat Conduction....Pages 65-74
A New Approach to Thermodynamics of Irreversible Processes by Means of Lagrange-Formalism....Pages 75-92
A Boundary-Layer Theory for the Dynamics and Thermodynamics of Phase-Interfaces....Pages 93-127
Large Scale Magnetic Fields in Fluids — An Example of a Dissipative Structure....Pages 129-140
Facing Some Problems with Entropy....Pages 141-153
On the Spontaneous Emission from Two-Level Atoms in a Damped Cavity....Pages 155-163
Polynucleotides — A Class of Self-Organizing Biomolecules....Pages 165-168
Stages of Emerging Life — Five Principles of Early Organization....Pages 169-183
The Physical Matrix for Self-Organisation....Pages 185-195
Spontaneously Broken Symmetries and Dissipative Structures....Pages 197-205
On the Coherence of Ultraweak Photonemission from Living Tissues....Pages 207-230
Evolution: Natural Selection or Self-Organization?....Pages 231-242
Thermodynamics and Complex Systems....Pages 243-253
The Transition from Town to City: Metropolitan Behaviour in the 19th Century....Pages 255-284
Creation, Organisation and Preservation of Dissipative Structures....Pages 285-305
Back Matter....Pages 307-309

✦ Subjects

Statistical Physics, Dynamical Systems and Complexity;Mathematical Modeling and Industrial Mathematics;Coding and Information Theory