Model reduction and coarse-graining approaches for multiscale phenomena

✍ Scribed by Alexander N. Gorban, Nikolas Kazantzis, I. G. Kevrekidis, Hans Christian Öttinger, Konstantinos Theodoropoulos

• Publisher: Springer
• Year: 2006
• Tongue: English
• Leaves: 554
• Series: Springer complexity
• Edition: 1
• Category: Library

✦ Synopsis

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

Contents......Page 9
Part I: Computation of Invariant Manifolds......Page 12
A New Model Reduction Method for Nonlinear Dynamical Systems Using Singular PDE Theory......Page 13
A Versatile Algorithm for Computing Invariant Manifolds......Page 26
Covering an Invariant Manifold with Fat Trajectories......Page 47
"Ghost" ILDM-Manifolds and Their Identification......Page 63
Dynamic Decomposition of ODE Systems: Application to Modelling of Diesel Fuel Sprays......Page 88
Model Reduction of Multiple Time Scale Processes in Non-standard Singularly Perturbed Form......Page 105
Part II: Coarse-Graining and Ideas of Statistical Physics......Page 120
Basic Types of Coarse-Graining......Page 121
Renormalization Group Methods for Coarse-Graining of Evolution Equations......Page 181
A Stochastic Process Behind Boltzmann's Kinetic Equation and Issues of Coarse Graining......Page 211
Finite Difference Patch Dynamics for Advection Homogenization Problems......Page 229
Coarse-Graining the Cyclic Lotka-Volterra Model: SSA and Local Maximum Likelihood Estimation......Page 251
Relations Between Information Theory, Robustness and Statistical Mechanics of Stochastic Uncertain Systems via Large Deviation Theory......Page 272
Part III: Kinetics and Model Reduction......Page 296
Exactly Reduced Chemical Master Equations......Page 297
Model Reduction in Kinetic Theory......Page 318
Novel Trajectory Based Concepts for Model and Complexity Reduction in (Bio)Chemical Kinetics......Page 343
Dynamics of the Plasma Sheath......Page 365
Part IV: Mesoscale and Multiscale Modeling......Page 372
Construction of Stochastic PDEs and Predictive Control of Surface Roughness in Thin Film Deposition......Page 373
Lattice Boltzmann Method and Kinetic Theory......Page 401
Numerical and Analytical Spatial Coupling of a Lattice Boltzmann Model and a Partial Differential Equation......Page 421
Modelling and Control Considerations for Particle Populations in Particulate Processes Within a Multi-Scale Framework......Page 440
Diagnostic Goal-Driven Reduction of Multiscale Process Models......Page 462
Understanding Macroscopic Heat/Mass Transfer Using Meso- and Macro-Scale Simulations......Page 485
An Efficient Optimization Approach for Computationally Expensive Timesteppers Using Tabulation......Page 510
A Reduced Input/Output Dynamic Optimisation Method for Macroscopic and Microscopic Systems......Page 529