Invariant Manifolds for Physical and Chemical Kinetics

Alexander N. Gorban, Ilya V. Karlin (auth.)3540226842, 9783540226840

By bringing together various ideas and methods for extracting the slow manifolds the authors show that it is possible to establish a more macroscopic description in nonequilibrium systems. The book treats slowness as stability. A unifying geometrical viewpoint of the thermodynamics of slow and fast motion enables the development of reduction techniques, both analytical and numerical. Examples considered in the book range from the Boltzmann kinetic equation and hydrodynamics to the Fokker-Planck equations of polymer dynamics and models of chemical kinetics describing oxidation reactions. Special chapters are devoted to model reduction in classical statistical dynamics, natural selection, and exact solutions for slow hydrodynamic manifolds. The book will be a major reference source for both theoretical and applied model reduction. Intended primarily as a postgraduate-level text in nonequilibrium kinetics and model reduction, it will also be valuable to PhD students and researchers in applied mathematics, physics and various fields of engineering.

Table of contents :
Introduction….Pages 1-19
The Source of Examples….Pages 21-63
Invariance Equation in Differential Form….Pages 65-67
Film Extension of the Dynamics: Slowness as Stability….Pages 69-78
Entropy, Quasiequilibrium, and Projectors Field….Pages 79-138
Newton Method with Incomplete Linearization….Pages 139-178
Quasi-Chemical Representation….Pages 179-187
Hydrodynamics From Grad’s Equations: What Can We Learn From Exact Solutions?….Pages 189-246
Relaxation Methods….Pages 247-277
Method of Invariant Grids….Pages 279-298
Method of Natural Projector….Pages 299-323
Geometry of Irreversibility: The Film of Nonequilibrium States….Pages 325-366
Slow Invariant Manifolds for Open Systems….Pages 367-417
Dimension of Attractors Estimation….Pages 419-456
Accuracy Estimation and Post-Processing in Invariant Manifolds Construction….Pages 457-466
Conclusion….Pages 467-468
References….Pages 469-489
Mathematical Notation and Some Terminology….Pages 491-492