By Guy B. Marin
Content material: conceal -- Advances in Chemical Engineering -- Contents -- members -- Preface -- A overview of Multiscale research: Examples from structures Biology, fabrics Engineering, and different Fluid-Surface Interacting platforms -- advent -- Deterministic, Continuum versions -- Hierarchy of types -- fixing Deterministic, Continuum Differential Equation versions: strategies and standing -- review of Discrete, Particle versions -- Hierarchy of Stochastic types for Well-mixed, Chemically Reacting platforms -- fixing grasp Equations Stochastically: Monte Carlo tools -- category of Multiscale Simulation techniques -- Hybrid Multiscale Simulation -- Onion-type Hybrid Multiscale Simulations and Algorithms -- software of Onion-type Hybrid Multiscale Simulation to progress of fabrics -- functions of Onion-type Hybrid Multiscale Simulation to different parts -- Multigrid-type Hybrid Multiscale Simulations -- An instance of Multigrid-type Hybrid Multiscale Simulation for progress lower than huge size Scale Gradients -- demanding situations in Hybrid Multiscale Simulations -- Coarse Graining of Stochastic types -- Temporal Upscaling of KMC Simulation in Well-mixed platforms -- Spatial Upscaling of disbursed (Lattice) KMC Simulation -- Spatiotemporal Acceleration of disbursed (Lattice) KMC Simulation -- Multiscale, Stochastic Modeling of organic Networks -- Spatially Well-mixed structures -- Spatially dispensed platforms -- platforms projects -- Sensitivity and Identifiability Analyses -- Parameter Estimation from Experimental information and Finer Scale versions -- version aid and keep watch over -- Bifurcation -- Outlook -- Acknowledgments -- Quantifying Physics and Chemistry at a number of Length-scales utilizing Magnetic Resonance options -- creation -- rules of MR Measurements -- Spatially Unresolved and Spatially Resolved Experiments -- Nuclear Spin leisure occasions -- delivery -- Temperature -- The K-space Raster -- quick information Acquisition -- fresh advancements in MR as a device in Chemical Engineering examine -- ''Ultra-fast'' Imaging of pace Fields -- a number of photos From a unmarried Excitation -- Imaging Rotating structures -- ''Ultra-fast'' Diffusion dimension -- Gas-phase MR -- response Engineering: From Catalyst to Reactor -- MR Spectroscopy of Catalysts -- Micro-imaging and Molecular Diffusion stories of shaped Catalyst Pellets -- Single-Phase circulate in Fixed-Bed Reactors -- Measuring Chemical Composition and Mass move in Fixed-Bed Reactors: In Situ experiences of Reactions -- Two-Phase movement in Fixed-Bed Reactors -- Hydrodynamic Transitions in Fixed-Bed Reactors -- destiny clients -- Acknowledgments -- Modeling of delivery and Transformation approaches in Porous and Multiphase our bodies -- creation -- method -- illustration of Multiphase Media -- constitution Acquisition -- Morphological Characterization -- electronic Reconstruction of Multiphase Media -- Calculation of potent homes -- Effective-scale delivery types -- adjustments -- Skeletonization -- part Transitions
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Additional info for Advances in Chemical Engineering: Multiscale Analysis
2004). Such instabilities may occur when the time step of the KMC becomes too large to violate the numerical stability criterion of the continuum model, or when rare events happen that create huge variations in the boundary condition or in the source/sink term of the continuum model. This numerical instability is a result of the small size of the KMC simulation box (a problem stemming from our inability to deal with realistically large length scales). Consequently, the KMC response is considerably noisier than what one would have for realistic length scales.
Recently, the mathematical foundations for spatial CG-KMC have been introduced for grand canonical and canonical ensemble simulations of Ising-type systems in Katsoulakis et al. (2003a, b) and Katsoulakis and Vlachos (2003). This work deserves a review of its own. However, in order to put it in context with the other multiscale developments, some exciting developments are briefly summarized. The essence of the method is the creation of a lattice of coarse cells, each consisting of several microscopic cells.
SPATIAL UPSCALING OF DISTRIBUTED (LATTICE) KMC SIMULATION The problem of coarse graining in space is also very important but has received less attention. The overall idea of coarse graining degrees of freedom to move up in scales comes originally from renormalization group theory. An interesting idea revolves around coarse graining of the Hamiltonian using wavelets. , 2005a, b). Coarse graining of the Hamiltonian was also presented by Ishikawa and Ogawa (2002), but it can be shown that the proposed expression does not obey detailed balance.