By Guy B. Marin
Content material: hide -- Advances in Chemical Engineering -- Contents -- participants -- Preface -- A assessment of Multiscale research: Examples from platforms Biology, fabrics Engineering, and different Fluid-Surface Interacting structures -- creation -- Deterministic, Continuum types -- Hierarchy of versions -- fixing Deterministic, Continuum Differential Equation versions: recommendations and standing -- assessment of Discrete, Particle types -- Hierarchy of Stochastic types for Well-mixed, Chemically Reacting structures -- fixing grasp Equations Stochastically: Monte Carlo equipment -- type 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 development below huge size Scale Gradients -- demanding situations in Hybrid Multiscale Simulations -- Coarse Graining of Stochastic versions -- Temporal Upscaling of KMC Simulation in Well-mixed structures -- Spatial Upscaling of disbursed (Lattice) KMC Simulation -- Spatiotemporal Acceleration of allotted (Lattice) KMC Simulation -- Multiscale, Stochastic Modeling of organic Networks -- Spatially Well-mixed platforms -- Spatially allotted platforms -- structures initiatives -- Sensitivity and Identifiability Analyses -- Parameter Estimation from Experimental facts and Finer Scale types -- version relief and keep an eye on -- Bifurcation -- Outlook -- Acknowledgments -- Quantifying Physics and Chemistry at a number of Length-scales utilizing Magnetic Resonance innovations -- creation -- rules of MR Measurements -- Spatially Unresolved and Spatially Resolved Experiments -- Nuclear Spin leisure occasions -- delivery -- Temperature -- The K-space Raster -- quickly facts Acquisition -- contemporary advancements in MR as a device in Chemical Engineering study -- ''Ultra-fast'' Imaging of pace Fields -- a number of photographs From a unmarried Excitation -- Imaging Rotating platforms -- ''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 reviews of Reactions -- Two-Phase circulation in Fixed-Bed Reactors -- Hydrodynamic Transitions in Fixed-Bed Reactors -- destiny clients -- Acknowledgments -- Modeling of shipping and Transformation procedures in Porous and Multiphase our bodies -- creation -- technique -- illustration of Multiphase Media -- constitution Acquisition -- Morphological Characterization -- electronic Reconstruction of Multiphase Media -- Calculation of powerful houses -- Effective-scale shipping versions -- differences -- Skeletonization -- part Transitions
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Additional resources for Advances in Chemical Engineering: Multiscale Analysis
2002a, b) and Drews et al. (2003b, 2004). One advantage of stand-alone coarse-grained models over multigrid-type hybrid simulations is that one does not have to interface multiple models; thus, one avoids the challenges mentioned in the previous section. Another is that it is possible to retain the correct noise and thus overcome either numerical instabilities or the alteration of the physics (see discussion above on challenges in hybrid simulation, and below for the effect of coarse graining on noise).
Additional problems are that large jumps in time can cause incorrect behavior even if the concentrations are non-negative, and that the magnitude of the noise is increased for substantial coarse graining in time increments. , 2005d; Tian and Burrage, 2004). While the essence of the techniques is the same, the method of Tian and Burrage (2004) appears to be limited to reaction networks whose species are not shared by multiple chemical reactions. , 2005b). , 2005d). The initial criterion proposed to ensure accuracy and avoid negative concentrations in simulations of typical length required a small change in the propensity functions.
1998). A major challenge in simulating such problems is that nucleation occurs at the nanometer scale whereas self-organization entails competition between numerous pattern blocks for reagents over microns to millimeters. These problems do not exhibit an obvious separation of length scales. From a different point of view, the stochasticity is built within the PDE as a source or sink term (if one were able to write such a PDE). Furthermore, surface diffusion is faster than the other microscopic processes by many orders of magnitude, but PE cannot be applied since the actual value of diffusion dictates the presence or absence of patterns.
Advances in Chemical Engineering: Multiscale Analysis by Guy B. Marin