By Guy B. Marin
Content material: conceal -- Advances in Chemical Engineering -- Contents -- participants -- Preface -- A evaluate of Multiscale research: Examples from structures Biology, fabrics Engineering, and different Fluid-Surface Interacting platforms -- creation -- Deterministic, Continuum versions -- Hierarchy of types -- fixing Deterministic, Continuum Differential Equation types: ideas and standing -- review of Discrete, Particle types -- Hierarchy of Stochastic versions for Well-mixed, Chemically Reacting structures -- fixing grasp Equations Stochastically: Monte Carlo tools -- class of Multiscale Simulation methods -- Hybrid Multiscale Simulation -- Onion-type Hybrid Multiscale Simulations and Algorithms -- program of Onion-type Hybrid Multiscale Simulation to development of fabrics -- purposes of Onion-type Hybrid Multiscale Simulation to different parts -- 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 types -- Temporal Upscaling of KMC Simulation in Well-mixed platforms -- Spatial Upscaling of allotted (Lattice) KMC Simulation -- Spatiotemporal Acceleration of allotted (Lattice) KMC Simulation -- Multiscale, Stochastic Modeling of organic Networks -- Spatially Well-mixed platforms -- Spatially allotted platforms -- structures projects -- Sensitivity and Identifiability Analyses -- Parameter Estimation from Experimental info and Finer Scale versions -- version relief and regulate -- Bifurcation -- Outlook -- Acknowledgments -- Quantifying Physics and Chemistry at a number of Length-scales utilizing Magnetic Resonance strategies -- creation -- rules of MR Measurements -- Spatially Unresolved and Spatially Resolved Experiments -- Nuclear Spin rest occasions -- shipping -- Temperature -- The K-space Raster -- quick facts Acquisition -- fresh advancements in MR as a device in Chemical Engineering study -- ''Ultra-fast'' Imaging of speed 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 experiences of shaped Catalyst Pellets -- Single-Phase circulation in Fixed-Bed Reactors -- Measuring Chemical Composition and Mass move in Fixed-Bed Reactors: In Situ reviews of Reactions -- Two-Phase move in Fixed-Bed Reactors -- Hydrodynamic Transitions in Fixed-Bed Reactors -- destiny customers -- Acknowledgments -- Modeling of shipping and Transformation procedures in Porous and Multiphase our bodies -- advent -- method -- illustration of Multiphase Media -- constitution Acquisition -- Morphological Characterization -- electronic Reconstruction of Multiphase Media -- Calculation of potent homes -- Effective-scale delivery versions -- changes -- Skeletonization -- section Transitions
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Additional info for Advances in Chemical Engineering: Multiscale Analysis
An example of coupled deterministic/stochastic ODEs was recently introduced by Zak et al. (2003) for a relatively large regulatory genetic network (118 reactions, 44 species, 97 parameters). In this case, species in large concentrations (proteins and transcription factor dimers) were treated as continuum variables and integrated with the implicit Euler method, whereas species in relatively low concentrations (promoters and transcripts) were treated as discrete variables and their corresponding material balances were solved using the KMC method.
In addition, appropriate boundary conditions for the microscopic grid model need to be developed to increase the accuracy and robustness of the hybrid scheme. Furthermore, the inverse problem of mapping coarse-grid information into a microscopic grid is ill posed. Thus, it is 32 DIONISIOS G. VLACHOS not currently clear what the best way of reconstructing the information on the ﬁne grid is. Future work will elucidate these issues. VI. Coarse Graining of Stochastic Models Hybrid multiscale simulation is currently by far the main multiscale computational toolkit under development.
The method was termed heterogeneous multiscale method and is conceptually in the same spirit as the work of Tammaro et al. (1995). , 2003) to deal with these problems. , 1999). Multigrid ideas to resolve small-scale information and pass it into largescale models for climate predictions have also been discussed by Majda and coworkers (Majda and Khouider, 2002). E. AN EXAMPLE OF MULTIGRID-TYPE HYBRID MULTISCALE SIMULATION GROWTH UNDER LARGE LENGTH SCALE GRADIENTS FOR An example of the aforementioned multigrid-type hybrid multiscale simulation from crystal growth for simulating nucleation and growth in large length scale systems is provided following Gummalla et al.
Advances in Chemical Engineering: Multiscale Analysis by Guy B. Marin