Invariant Manifolds for Physical and Chemical Kinetics

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.

Major reference source for both theoretical and applied model reduction. Includes supplementary material: sn.pub/extras

Autorentext

Alexander N. Gorban: Full Professor in Modeling & Simulation
PhD in Physics & Math (Differential Equations & Math. Physics), 1980, Thesis: "Slow Relaxations and Bifurcations of Omega-Limit Sets of Dynamical Systems";
Dr Sc in Physics & Math (Biophysics), 1990, Thesis: "Extremal Principles and a priori Estimations in Biological and Formal Kinetics.
Affiliation:
Head of Nonequilibrium Systems Laboratory (1989 - present) and Deputy Director (1995 - present), Institute of Computational Modeling, Russian Academy of Sciences, Russia;
Elected Chair of Applied Mathematics, University of Leicester, UK (2004).
Part-time:
Institute of Polymers, Polymer Physics, Swiss Federal Institute of technology (ETH), Zurich, Switzerland (2003 - present); Head of Neurocomputers Chair, Krasnoyarsk State Technical University, Russia (1993 - present).
Visiting:
Clay Mathematics Institute (Cambridge, USA), 03.2000-08.2000;
Northeastern University (Boston, USA), 03.2000-05.2000;
Courant Mathematics Institute (New York, USA), 04.2000;
Institut des Hautes Etudes Scientiques (IHES, Paris, France), 10.2000-12.2000, 07.2001-08.2001,11.2002-12-2002, 09.2003;
Scientific advisor of 22 PhD thesis and 3 Dr. Sc.
Publications: 14 monographs, 4 patents, over 200 papers.
Some of current research projects
Constructive Methods of Invariant Manifolds for Kinetic Problems (1989-present);
Cluster structure of Genome (2000-present);
Molecular Individualism: Theory, computational models, applications (2003-present).

Iliya Karlin obtained the doctral degree in physics in 1992 for his thesis "Methods of invariant manifolds in physical kinetics". During 1995-1997 he was the Humbold Fellow at the University of Ulm. He was visiting professor at the University of Rome during 1997-1998. At present he is affiliated as a senior scientist at the Swiss Federal institute of Technology (ETH), and as a senior researcher at the Institute of Computational Modeling of Russian Academy of Sciences. He authors about 100 papers on kinetic theory, polymer dynamics, chemical kinetics and computational fluid dynamics. His current research projects include constructive methods of invariant manifolds, theory of polymer dynamics and turbulence modeling.

Inhalt
Introduction.- The Source of Examples.- Invariance Equation in the Differential Form.- Film Extension of the Dynamics: Slowness as Stability.- Entropy, Quasi-Equilibrium and Projector Field.- Newton Method with Incomplete Linearization.- Quasi-chemical Representation.- Hydrodynamics from Grad's Equations: Exact Solutions.- Relaxation Methods.- Method of Invariant Grids.- Method of Natural Projector.- Geometry of Irreversibility: The Film of Nonequilibrium States.- Slow Invariant Manifolds for Open Systems.- Estimation of Dimension of Attractors.- Accuracy Estimation and Post-Processing.- Conclusion.