Ebook: Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena
- Tags: Mathematical and Computational Physics, Complexity, Physics and Applied Physics in Engineering, Systems Theory Control, Math. Applications in Chemistry
- Year: 2006
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. Specific areas of study include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, nonlinear dynamics, nonlinear control, nonlinear estimation, and particulate systems from various branches of engineering. The generic nature and the power of the pertinent conceptual, analytical and computational frameworks helps eliminate some of the traditional language barriers, which often unnecessarily impede scientific progress and the interaction of researchers between disciplines such as physics, chemistry, biology, applied mathematics and engineering. All contributions are authored by experts, whose specialities span a wide range of fields within science and engineering.
Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. Specific areas of study include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, nonlinear dynamics, nonlinear control, nonlinear estimation, and particulate systems from various branches of engineering. The generic nature and the power of the pertinent conceptual, analytical and computational frameworks helps eliminate some of the traditional language barriers, which often unnecessarily impede scientific progress and the interaction of researchers between disciplines such as physics, chemistry, biology, applied mathematics and engineering. All contributions are authored by experts, whose specialities span a wide range of fields within science and engineering.
Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. Specific areas of study include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, nonlinear dynamics, nonlinear control, nonlinear estimation, and particulate systems from various branches of engineering. The generic nature and the power of the pertinent conceptual, analytical and computational frameworks helps eliminate some of the traditional language barriers, which often unnecessarily impede scientific progress and the interaction of researchers between disciplines such as physics, chemistry, biology, applied mathematics and engineering. All contributions are authored by experts, whose specialities span a wide range of fields within science and engineering.
Content:
Front Matter....Pages I-XI
Front Matter....Pages 1-1
A New Model Reduction Method for Nonlinear Dynamical Systems Using Singular PDE Theory....Pages 3-15
A Versatile Algorithm for Computing Invariant Manifolds....Pages 17-37
Covering an Invariant Manifold with Fat Trajectories....Pages 39-54
“Ghost” ILDM-Manifolds and Their Identification....Pages 55-79
Dynamic Decomposition of ODE Systems: Application to Modelling of Diesel Fuel Sprays....Pages 81-97
Model Reduction of Multiple Time Scale Processes in Non-standard Singularly Perturbed Form....Pages 99-113
Front Matter....Pages 115-115
Basic Types of Coarse-Graining....Pages 117-176
Renormalization Group Methods for Coarse-Graining of Evolution Equations....Pages 177-206
A Stochastic Process Behind Boltzmann’s Kinetic Equation and Issues of Coarse Graining....Pages 207-224
Finite Difference Patch Dynamics for Advection Homogenization Problems....Pages 225-246
Coarse-Graining the Cyclic Lotka-Volterra Model: SSA and Local Maximum Likelihood Estimation....Pages 247-267
Relations Between Information Theory, Robustness and Statistical Mechanics of Stochastic Uncertain Systems via Large Deviation Theory....Pages 269-292
Front Matter....Pages 293-293
Exactly Reduced Chemical Master Equations....Pages 295-315
Model Reduction in Kinetic Theory....Pages 317-341
Novel Trajectory Based Concepts for Model and Complexity Reduction in (Bio)Chemical Kinetics....Pages 343-364
Dynamics of the Plasma Sheath....Pages 365-371
Front Matter....Pages 373-373
Construction of Stochastic PDEs and Predictive Control of Surface Roughness in Thin Film Deposition....Pages 375-402
Lattice Boltzmann Method and Kinetic Theory....Pages 403-422
Numerical and Analytical Spatial Coupling of a Lattice Boltzmann Model and a Partial Differential Equation....Pages 423-441
Modelling and Control Considerations for Particle Populations in Particulate Processes Within a Multi-Scale Framework....Pages 443-464
Front Matter....Pages 373-373
Diagnostic Goal-Driven Reduction of Multiscale Process Models....Pages 465-487
Understanding Macroscopic Heat/Mass Transfer Using Meso- and Macro-Scale Simulations....Pages 489-513
An Efficient Optimization Approach for Computationally Expensive Timesteppers Using Tabulation....Pages 515-533
A Reduced Input/Output Dynamic Optimisation Method for Macroscopic and Microscopic Systems....Pages 535-560
Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. Specific areas of study include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, nonlinear dynamics, nonlinear control, nonlinear estimation, and particulate systems from various branches of engineering. The generic nature and the power of the pertinent conceptual, analytical and computational frameworks helps eliminate some of the traditional language barriers, which often unnecessarily impede scientific progress and the interaction of researchers between disciplines such as physics, chemistry, biology, applied mathematics and engineering. All contributions are authored by experts, whose specialities span a wide range of fields within science and engineering.
Content:
Front Matter....Pages I-XI
Front Matter....Pages 1-1
A New Model Reduction Method for Nonlinear Dynamical Systems Using Singular PDE Theory....Pages 3-15
A Versatile Algorithm for Computing Invariant Manifolds....Pages 17-37
Covering an Invariant Manifold with Fat Trajectories....Pages 39-54
“Ghost” ILDM-Manifolds and Their Identification....Pages 55-79
Dynamic Decomposition of ODE Systems: Application to Modelling of Diesel Fuel Sprays....Pages 81-97
Model Reduction of Multiple Time Scale Processes in Non-standard Singularly Perturbed Form....Pages 99-113
Front Matter....Pages 115-115
Basic Types of Coarse-Graining....Pages 117-176
Renormalization Group Methods for Coarse-Graining of Evolution Equations....Pages 177-206
A Stochastic Process Behind Boltzmann’s Kinetic Equation and Issues of Coarse Graining....Pages 207-224
Finite Difference Patch Dynamics for Advection Homogenization Problems....Pages 225-246
Coarse-Graining the Cyclic Lotka-Volterra Model: SSA and Local Maximum Likelihood Estimation....Pages 247-267
Relations Between Information Theory, Robustness and Statistical Mechanics of Stochastic Uncertain Systems via Large Deviation Theory....Pages 269-292
Front Matter....Pages 293-293
Exactly Reduced Chemical Master Equations....Pages 295-315
Model Reduction in Kinetic Theory....Pages 317-341
Novel Trajectory Based Concepts for Model and Complexity Reduction in (Bio)Chemical Kinetics....Pages 343-364
Dynamics of the Plasma Sheath....Pages 365-371
Front Matter....Pages 373-373
Construction of Stochastic PDEs and Predictive Control of Surface Roughness in Thin Film Deposition....Pages 375-402
Lattice Boltzmann Method and Kinetic Theory....Pages 403-422
Numerical and Analytical Spatial Coupling of a Lattice Boltzmann Model and a Partial Differential Equation....Pages 423-441
Modelling and Control Considerations for Particle Populations in Particulate Processes Within a Multi-Scale Framework....Pages 443-464
Front Matter....Pages 373-373
Diagnostic Goal-Driven Reduction of Multiscale Process Models....Pages 465-487
Understanding Macroscopic Heat/Mass Transfer Using Meso- and Macro-Scale Simulations....Pages 489-513
An Efficient Optimization Approach for Computationally Expensive Timesteppers Using Tabulation....Pages 515-533
A Reduced Input/Output Dynamic Optimisation Method for Macroscopic and Microscopic Systems....Pages 535-560
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