Invariant Manifolds for Physical and Chemical Kinetics

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.

Alexander N. Gorban: Full Professor in Modeling & SimulationPhD 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 projectsConstructive 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

From the reviews of the first edition:

"The book presents an overwhelmingly rich display of deep ideas in the theory and applications of invariant manifolds for the dynamical systems appearing in physical and chemical kinetics, as well as in biology. An example of a gem of a result and exposition is provided by the stunningly beautiful treatment of systems with inheritance in Chapter 14, combining mathematical rigor with a wide display of concrete applications. The book should become an all time classic."

Mikhail Shubin, Matthews Distinguished University Professor Northeastern University, Boston, USA

"This book is a treasure trove filled with a variety of ideas on the reduced description of kinetics. The authors not only summarize their pioneering work --- at the heart of which is the "invariant manifold method" --- but also put it nicely into perspective and add new material (e.g., "invariant grids", "films") to compose a well-balanced picture of physical and chemical kinetics. The elegant idea of "films" consisting of macroscopically definable nonequilibrium states offers new opportunities for a deeper understanding of irreversibility. 25 years of experience in the field are condensed into deep physical insight, powerful mathematical techniques, and a wealth of illustrating examples and useful references."

Hans Christian Öttinger, Professor of Polymer Physics, ETH Zürich

"... a very remarkable, and much needed, introduction to this fascinating subject, along with a systematic treatment of advanced topics which the authors themselves have largely contributed to develop."

Sauro Succi, Research Director, Istituto Applicazioni Calcolo

 

"The great strength and unique feature of the book is the amazing wealth of practical and concrete examples which truly show 'ideas in action'! Systems as diverse as hydrodynamic turbulence, chemical reactions, polymerflows, and even quantum