Model reduction and coarse-graining approaches for multiscale phenomena
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Bibliographic Information
Model reduction and coarse-graining approaches for multiscale phenomena
（Springer complexity）
Springer, c2006
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Includes bibliographical references
Description and Table of Contents
Description
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. All contributions are 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.- A Versatile Algorithm for Computing Invariant Manifolds.- Covering an Invariant Manifold with Fat Trajectories.- "Ghost" ILDM-Manifolds and Their Identification.- Dynamic Decomposition of ODE Systems: Application to Modelling of Diesel Fuel Sprays.- Model Reduction of Multiple Time Scale Processes in Non-standard Singularly Perturbed Form.- Coarse-Graining and Ideas of Statistical Physics.- Basic Types of Coarse-Graining.- Renormalization Group Methods for Coarse-Graining of Evolution Equations.- A Stochastic Process Behind Boltzmann's Kinetic Equation and Issues of Coarse Graining.- Finite Difference Patch Dynamics for Advection Homogenization Problems.- Coarse-Graining the Cyclic Lotka-Volterra Model: SSA and Local Maximum Likelihood Estimation.- Relations Between Information Theory, Robustness and Statistical Mechanics of Stochastic Uncertain Systems via Large Deviation Theory.- Kinetics and Model Reduction.- Exactly Reduced Chemical Master Equations.- Model Reduction in Kinetic Theory.- Novel Trajectory Based Concepts for Model and Complexity Reduction in (Bio)Chemical Kinetics.- Dynamics of the Plasma Sheath.- Mesoscale and Multiscale Modeling.- Construction of Stochastic PDEs and Predictive Control of Surface Roughness in Thin Film Deposition.- Lattice Boltzmann Method and Kinetic Theory.- Numerical and Analytical Spatial Coupling of a Lattice Boltzmann Model and a Partial Differential Equation.- Modelling and Control Considerations for Particle Populations in Particulate Processes Within a Multi-Scale Framework.- Diagnostic Goal-Driven Reduction of Multiscale Process Models.- Understanding Macroscopic Heat/Mass Transfer Using Meso- and Macro-Scale Simulations.- An Efficient Optimization Approach for Computationally Expensive Timesteppers Using Tabulation.- A Reduced Input/Output Dynamic Optimisation Method for Macroscopic and Microscopic Systems.
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