Ebook: Coping with Complexity: Model Reduction and Data Analysis

This volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 – September 4, 2009. The book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.

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This volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 – September 4, 2009. The book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.

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This volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 – September 4, 2009. The book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.
Content:
Front Matter....Pages i-xii
Averaging of Fast-Slow Systems....Pages 1-7
The Use of Global Sensitivity Methods for the Analysis, Evaluation and Improvement of Complex Modelling Systems....Pages 9-36
Optimisation and Linear Control of Large Scale Nonlinear Systems: A Review and a Suite of Model Reduction-Based Techniques....Pages 37-61
Universal Algorithms, Mathematics of Semirings and Parallel Computations....Pages 63-89
Scaling Invariant Interpolation for Singularly Perturbed Vector Fields (SPVF)....Pages 91-111
Think Globally, Move Locally: Coarse Graining of Effective Free Energy Surfaces....Pages 113-131
Extracting Functional Dependence from Sparse Data Using Dimensionality Reduction: Application to Potential Energy Surface Construction....Pages 133-149
A Multilevel Algorithm to Compute Steady States of Lattice Boltzmann Models....Pages 151-167
Time Step Expansions and the Invariant Manifold Approach to Lattice Boltzmann Models....Pages 169-205
The Shock Wave Problem Revisited: The Navier–Stokes Equations and Brenner’s Two Velocity Hydrodynamics....Pages 207-229
Adaptive Simplification of Complex Systems: A Review of the Relaxation-Redistribution Approach....Pages 231-240
Geometric Criteria for Model Reduction in Chemical Kinetics via Optimization of Trajectories....Pages 241-252
Computing Realizations of Reaction Kinetic Networks with Given Properties....Pages 253-267
A Drift-Filtered Approach to Diffusion Estimation for Multiscale Processes....Pages 269-286
Model Reduction of a Higher-Order KdV Equation for Shallow Water Waves....Pages 287-298
Coarse Collective Dynamics of Animal Groups....Pages 299-309
Self-Simplification in Darwin’s Systems....Pages 311-344
Back Matter....Pages 345-348

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This volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 – September 4, 2009. The book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.
Content:
Front Matter....Pages i-xii
Averaging of Fast-Slow Systems....Pages 1-7
The Use of Global Sensitivity Methods for the Analysis, Evaluation and Improvement of Complex Modelling Systems....Pages 9-36
Optimisation and Linear Control of Large Scale Nonlinear Systems: A Review and a Suite of Model Reduction-Based Techniques....Pages 37-61
Universal Algorithms, Mathematics of Semirings and Parallel Computations....Pages 63-89
Scaling Invariant Interpolation for Singularly Perturbed Vector Fields (SPVF)....Pages 91-111
Think Globally, Move Locally: Coarse Graining of Effective Free Energy Surfaces....Pages 113-131
Extracting Functional Dependence from Sparse Data Using Dimensionality Reduction: Application to Potential Energy Surface Construction....Pages 133-149
A Multilevel Algorithm to Compute Steady States of Lattice Boltzmann Models....Pages 151-167
Time Step Expansions and the Invariant Manifold Approach to Lattice Boltzmann Models....Pages 169-205
The Shock Wave Problem Revisited: The Navier–Stokes Equations and Brenner’s Two Velocity Hydrodynamics....Pages 207-229
Adaptive Simplification of Complex Systems: A Review of the Relaxation-Redistribution Approach....Pages 231-240
Geometric Criteria for Model Reduction in Chemical Kinetics via Optimization of Trajectories....Pages 241-252
Computing Realizations of Reaction Kinetic Networks with Given Properties....Pages 253-267
A Drift-Filtered Approach to Diffusion Estimation for Multiscale Processes....Pages 269-286
Model Reduction of a Higher-Order KdV Equation for Shallow Water Waves....Pages 287-298
Coarse Collective Dynamics of Animal Groups....Pages 299-309
Self-Simplification in Darwin’s Systems....Pages 311-344
Back Matter....Pages 345-348
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