Invariant Manifolds for Physical and Chemical Kinetics
Gorban, Alexander N.
Invariant Manifolds for Physical and Chemical Kinetics [electronic resource] / by Alexander N. Gorban, Ilya V. Karlin. - XVIII, 496 p. online resource. - Lecture Notes in Physics, 660 0075-8450 ; . - Lecture Notes in Physics, 660 .
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.
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.
9783540315315
10.1007/b98103 doi
Mathematical physics.
Quantum theory.
Thermodynamics.
Chemistry, Physical organic.
Mathematical Methods in Physics.
Quantum Physics.
Quantum Information Technology, Spintronics.
Thermodynamics.
Physical Chemistry.
Complex Systems.
QC5.53
530.15
Invariant Manifolds for Physical and Chemical Kinetics [electronic resource] / by Alexander N. Gorban, Ilya V. Karlin. - XVIII, 496 p. online resource. - Lecture Notes in Physics, 660 0075-8450 ; . - Lecture Notes in Physics, 660 .
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.
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.
9783540315315
10.1007/b98103 doi
Mathematical physics.
Quantum theory.
Thermodynamics.
Chemistry, Physical organic.
Mathematical Methods in Physics.
Quantum Physics.
Quantum Information Technology, Spintronics.
Thermodynamics.
Physical Chemistry.
Complex Systems.
QC5.53
530.15