Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena

Abstract

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.