Modeling multi-scale

Crampin EJ, Smith NP, Hunter PJ. Multi-scale modelling and the lUPS physiome project. J Mol Histol 2004 35 707-14. 

Multi-scale modeling problems in heterogeneously catalyzed a-olefin polymerization... 

Hester SD, Belmonte JM, Gens JS, Clendenon SG, Glazier JA (2011) A multi-cell, multi-scale model of vertebrate segmentation and somite formation. PLoS Comput Biol 7( 10 ) e 1002155. doi 10.1371/journal.pcbi. 1002155... 

Li, J., Multi-Scale Modeling and Method of Energy Minimization for Particle-Fluid Two Phase Flow, Ph.D. thesis (in Chinese), Institute of Chemical Metallurgy, Chinese Academy of Sciences, Beijing (1987). 

During the past few decades, various theoretical models have been developed to explain the physical properties and to find key parameters for the prediction of the system behaviors. Recent technological trends focus toward integration of subsystem models in various scales, which entails examining the nanophysical properties, subsystem size, and scale-specified numerical analysis methods on system level performance. Multi-scale modeling components including quantum mechanical (i.e., density functional theory (DFT) and ab initio simulation), atom-istic/molecular (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational... 

This section deals with multi-scale models for the PEFC and consists of three subsections, 4.1,4.2, and 4.3, that relate to molecular-level models, bridging models between scales and device/process level models, respectively. The objectives of these subsections are to survey the development and application of these models. 

Figure 25 Multi-scale modeling of HDI (a) ab initio (atomic), (b) MC/MD (molecular), (c) coarse-graining procedure (molecular/meso-scale), (d) diffusion characteristics and surface topography, and (e) LBM (meso-scale) and integration HDI (system design).

As emphasized in the previous section, it is critical for the multi-scale integration to develop mathematically simple (with few parameters) yet physically realistic models with nanoscopic information. For the description of the multi-scale framework of HDI, we provide a bot-tom-up approach as given below to sketch multi-scale modeling as described in Figures 24 and 25 (Jhon et al., 2011). 

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