Disequilibrium and Self-Organisation / Edition 1by C.W. Kilmister
Pub. Date: 07/31/1986
Publisher: Springer Netherlands
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 ContentsSelf-Organization and Information Theory.- The Mathematics Needed for Self-Organisation.- Entropy and Order.- Pattern Formation for a One Dimensional Evolution Equation Based on Thom’s River Basin Model.- On the Modelling of Vehicular Traffic Flow.- Alternative Exploitation of Dissipation Inequality Demonstrated for Hyperbolic Heat Conduction.- A New Approach to Thermodynamics of Irreversible Processes by Means of Lagrange-Formalism.- A Boundary-Layer Theory for the Dynamics and Thermodynamics of Phase-Interfaces.- Large Scale Magnetic Fields in Fluids An Example of a Dissipative Structure.- Facing Some Problems with Entropy.- On the Spontaneous Emission from Two-Level Atoms in a Damped Cavity.- Polynucleotides A Class of Self-Organizing Biomolecules.- Stages of Emerging Life Five Principles of Early Organization.- The Physical Matrix for Self-Organisation.- Spontaneously Broken Symmetries and Dissipative Structures.- On the Coherence of Ultraweak Photonemission from Living Tissues.- Evolution: Natural Selection or Self-Organization?.- Thermodynamics and Complex Systems.- The Transition from Town to City: Metropolitan Behaviour in the 19th Century.- Creation, Organisation and Preservation of Dissipative Structures.
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