Model Reduction And Coarse-graining Approaches for Multiscale Phenomena

by Gorban, Alexander N.; Kazantzis, Nikolaos K.; Kevrekidis, Ioannis George; Ottinger, Hans Christian

• ISBN13: 9783540358855
• ISBN10: 3540358854
• Format: Hardcover
• Copyright: 2006-09-15
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Computation of Invariant Manifolds
A New Model Reduction Method for Nonlinear Dynamical Systems Using Singular PDE Theory	p. 3
A Versatile Algorithm for Computing Invariant Manifolds	p. 17
Covering an Invariant Manifold with Fat Trajectories	p. 39
"Ghost" ILDM-Manifolds and Their Identification	p. 55
Dynamic Decomposition of ODE Systems: Application to Modelling of Diesel Fuel Sprays	p. 81
Model Reduction of Multiple Time Scale Processes in Non-standard Singularly Perturbed Form	p. 99
Coarse-Graining and Ideas of Statistical Physics Basic Types of Coarse-Graining	p. 117
Renormalization Group Methods for Coarse-Graining of Evolution Equations	p. 177
XA Stochastic Process Behind Boltzmann's Kinetic Equation and Issues of Coarse Graining	p. 207
Finite Difference Patch Dynamics for Advection Homogenization Problems	p. 225
Coarse-Graining the Cyclic Lotka-Volterra Model: SSA and Local Maximum Likelihood Estimation	p. 247
Relations Between Information Theory, Robustness and Statistical Mechanics of Stochastic Uncertain Systems via Large Deviation Theory	p. 269
Kinetics and Model Reduction Exactly Reduced Chemical Master Equations	p. 295
Model Reduction in Kinetic Theory	p. 317
Novel Trajectory Based Concepts for Model and Complexity Reduction in (Bio)Chemical Kinetics	p. 343
Dynamics of the Plasma Sheath	p. 365
Mesoscale and Multiscale Modeling Construction of Stochastic PDEs and Predictive Control of Surface Roughness in Thin Film Deposition	p. 375
Lattice Boltzmann Method and Kinetic Theory	p. 403
Numerical and Analytical Spatial Coupling of a Lattice Boltzmann Model and a Partial Differential Equation	p. 423
Contents	p. xi
Modelling and Control Considerations for Particle Populations in Particulate Processes Within a Multi-Scale Framework	p. 443
Diagnostic Goal-Driven Reduction of Multiscale Process Models	p. 465
Understanding Macroscopic Heat/Mass Transfer Using Meso- and Macro-Scale Simulations	p. 489
An Efficient Optimization Approach for Computationally Expensive Timesteppers Using Tabulation	p. 515
A Reduced Input/Output Dynamic Optimisation Method for Macroscopic and Microscopic Systems	p. 535
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