Beschreibung
Inhaltsverzeichnis
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.
Autorenporträt
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.
