By Guy B. Marin
Content material: disguise -- Advances in Chemical Engineering -- Contents -- members -- Preface -- A overview of Multiscale research: Examples from platforms Biology, fabrics Engineering, and different Fluid-Surface Interacting structures -- advent -- Deterministic, Continuum versions -- Hierarchy of types -- fixing Deterministic, Continuum Differential Equation versions: innovations and standing -- review of Discrete, Particle versions -- Hierarchy of Stochastic types for Well-mixed, Chemically Reacting platforms -- fixing grasp Equations Stochastically: Monte Carlo equipment -- class of Multiscale Simulation methods -- Hybrid Multiscale Simulation -- Onion-type Hybrid Multiscale Simulations and Algorithms -- software of Onion-type Hybrid Multiscale Simulation to development of fabrics -- purposes of Onion-type Hybrid Multiscale Simulation to different components -- 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 dispensed (Lattice) KMC Simulation -- Spatiotemporal Acceleration of disbursed (Lattice) KMC Simulation -- Multiscale, Stochastic Modeling of organic Networks -- Spatially Well-mixed structures -- Spatially allotted platforms -- structures initiatives -- Sensitivity and Identifiability Analyses -- Parameter Estimation from Experimental facts and Finer Scale types -- version relief and keep watch over -- Bifurcation -- Outlook -- Acknowledgments -- Quantifying Physics and Chemistry at a number of Length-scales utilizing Magnetic Resonance recommendations -- advent -- ideas of MR Measurements -- Spatially Unresolved and Spatially Resolved Experiments -- Nuclear Spin leisure instances -- shipping -- Temperature -- The K-space Raster -- quick facts Acquisition -- fresh advancements in MR as a device in Chemical Engineering study -- ''Ultra-fast'' Imaging of pace Fields -- a number of pictures 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 movement in Fixed-Bed Reactors -- Measuring Chemical Composition and Mass move in Fixed-Bed Reactors: In Situ reviews of Reactions -- Two-Phase circulate in Fixed-Bed Reactors -- Hydrodynamic Transitions in Fixed-Bed Reactors -- destiny customers -- Acknowledgments -- Modeling of shipping and Transformation methods in Porous and Multiphase our bodies -- creation -- method -- illustration of Multiphase Media -- constitution Acquisition -- Morphological Characterization -- electronic Reconstruction of Multiphase Media -- Calculation of powerful houses -- Effective-scale shipping types -- ameliorations -- Skeletonization -- part Transitions
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Extra resources for Advances in Chemical Engineering: Multiscale Analysis
Furthermore, this is a difﬁcult task to accomplish because constitutive equations, such as the ones written above, do not exist for most microscopic models. Matching of ﬂuxes at the interface leads at least to conservation, but further work is needed to fully understand this point. Another issue in hybrid multiscale simulation pertains to possible mass conservation caused by truncation errors. , updating the concentration, is easy. However, the reverse task of mapping continuum changes of concentrations into an integer number of molecules along with their spatial placement is also important (see Schulze (2004)) for some interesting ideas and a coupling factor that is iteratively determined to match ﬂuxes).
1998), and Monine et al. (2004). For reviews, see Raimondeau and Vlachos (2002a) on surface–ﬂuid interactions and chemical reactions, and Li et al. (2004) for chemical reactors. In the area of ﬂuids, coupling of MD near a wall with a continuum, deterministic description of the Navier–Stokes unidirectional ﬂow farther away from the wall based on overlapping subdomains of domain decomposition was presented in O’Connell and Thompson (1995). A nice description of ensuring continuity of momentum ﬂux was given and the velocity ﬁeld was made consistent across the interface by using constraint dynamics in MD.
In the area of ﬂuids, coupling of MD near a wall with a continuum, deterministic description of the Navier–Stokes unidirectional ﬂow farther away from the wall based on overlapping subdomains of domain decomposition was presented in O’Connell and Thompson (1995). A nice description of ensuring continuity of momentum ﬂux was given and the velocity ﬁeld was made consistent across the interface by using constraint dynamics in MD. See also Nie et al. (2003) for coupling of MD with a continuum model of ﬂow, and Hadjiconstantinou and Patera (1997), where MD was again coupled with a continuum description of the incompressible Navier–Stokes solved using a spectral element method and the Schwart alternating method with overlapping subdomains.