By Guy B. Marin
Content material: hide -- Advances in Chemical Engineering -- Contents -- individuals -- Preface -- A evaluation of Multiscale research: Examples from structures Biology, fabrics Engineering, and different Fluid-Surface Interacting platforms -- advent -- Deterministic, Continuum types -- Hierarchy of versions -- fixing Deterministic, Continuum Differential Equation versions: strategies and standing -- evaluate of Discrete, Particle versions -- Hierarchy of Stochastic versions for Well-mixed, Chemically Reacting platforms -- fixing grasp Equations Stochastically: Monte Carlo tools -- class of Multiscale Simulation techniques -- Hybrid Multiscale Simulation -- Onion-type Hybrid Multiscale Simulations and Algorithms -- software of Onion-type Hybrid Multiscale Simulation to development of fabrics -- functions of Onion-type Hybrid Multiscale Simulation to different components -- Multigrid-type Hybrid Multiscale Simulations -- An instance of Multigrid-type Hybrid Multiscale Simulation for progress 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 disbursed (Lattice) KMC Simulation -- Multiscale, Stochastic Modeling of organic Networks -- Spatially Well-mixed structures -- Spatially disbursed platforms -- structures projects -- Sensitivity and Identifiability Analyses -- Parameter Estimation from Experimental info 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 thoughts -- creation -- ideas of MR Measurements -- Spatially Unresolved and Spatially Resolved Experiments -- Nuclear Spin leisure instances -- shipping -- Temperature -- The K-space Raster -- speedy facts Acquisition -- fresh advancements in MR as a device in Chemical Engineering learn -- ''Ultra-fast'' Imaging of speed Fields -- a number of photographs 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 circulation in Fixed-Bed Reactors -- Measuring Chemical Composition and Mass move in Fixed-Bed Reactors: In Situ stories of Reactions -- Two-Phase stream in Fixed-Bed Reactors -- Hydrodynamic Transitions in Fixed-Bed Reactors -- destiny clients -- Acknowledgments -- Modeling of shipping and Transformation methods in Porous and Multiphase our bodies -- advent -- method -- illustration of Multiphase Media -- constitution Acquisition -- Morphological Characterization -- electronic Reconstruction of Multiphase Media -- Calculation of powerful houses -- Effective-scale delivery types -- variations -- Skeletonization -- part Transitions
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Extra resources for Advances in Chemical Engineering: Multiscale Analysis
To overcome the disparity of length scales, an adaptive mesh reﬁnement strategy has been used with four levels that enable linking macroscopic scales to the nanometer, as shown schematically in Fig. 9b (note that these multiple grids differ from the schematic of Fig. 6 to better ﬁt the problem at hand). One question is: Where and when does one decide to reﬁne the mesh? This is actually done probabilistically. Since 28 DIONISIOS G. VLACHOS nucleation has a higher probability of occurrence wherever concentrations are high, the mesh is reﬁned when and where the probability for nucleation is above a certain low threshold.
However, materials simulations have revealed that this approach causes problems in some cases. Coarse graining of MD to large scales (Rudd and Broughton, 1998), or combination of FEM reﬁning and MD coarse graining are other options that may in fact be superior (for a review see Rudd and Broughton (2000)). The issues of proper coupling in the overlapping subdomain, along with additional challenges of hybrid simulations, are discussed in detail in section F. D. MULTIGRID-TYPE HYBRID MULTISCALE SIMULATIONS The above problems exhibit phenomena with well-separated length scales, where the coupling between the continuum and discrete models happens at an interface (the overlapping or handshaking regime).
SPATIOTEMPORAL ACCELERATION OF DISTRIBUTED (LATTICE) KMC SIMULATION Integration of spatial and temporal acceleration methods discussed above to create a stochastic simulation toolkit that can reach large length and time scales is entirely possible. , 2005). While combination of time-acceleration methods with lattice KMC is possible, most time acceleration methods affect noise adversely. Therefore, it appears that integration of the t-leap method (or a derivative of it) with a spatially distributed (lattice) KMC simulation is the most promising approach for many applications.