Multi-scale modelling methods

Molecular and multi-scale modelling methods of polymer device degradation... 

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... 

Li, J., Tung, Y., and Kwauk, M. Method of energy minimization in multi-scale modelling of particle-fluid two-phase flow, m Circulating Fluidized Bed Technology II (Basu, P., and Large, J. F., eds.), p. 75. Pergamon Press (1988). 

Li, J. Multi-scale modeling and method of energy minimization for particle-fluid two-phase flow," Ph. D. Thesis, Institute of Chemical Metallurgy, Academia Sinica, Beijing (1987). 

Quantum mechanics is the bedrock upon which multi-scale models are built. For decades, it has been a source of parameters for force-field models, which are vastly less computationally expensive and hence able to reach much longer length and time scales. It is also being increasingly used in concert with force-field methods through mixed quantum mechanics/molecular mechanics... 

Figure 13.2 Multi-scale modelling hierarchy [35], showing the approximate regimes of time and length scales over which atomistic modelling techniques (quantum and molecular mechanics) can usefully be applied and how these link with process methods via mesoscale modelling.

Multi-scale modeling provides a hierarchical computational approach to describe macroscopic catalytic processes. In this approach, atomistic methods (first principle quantum chemistry calculations and classical molecular dynamics) are used which reveal microscopic insight into the meehanisms and molecular-scale dynamics of reactions at electrode surfaces (for e.g. see [15,... 

Luo, et al. [80] have used multi-scale homogenization (MH) and FEM for wavy and straight SWCNTs, they have compare their results with Mori-Tanaka, Cox, and Halpin-Tsai, Fu, et al. [81] and Lauke [82], Trespass, et al. [83] used 3D elastic beam for C-C bond, 3D space frame for CNT, and progressive fracture model for prediction of elastic modulus, they used rule of mixture for compression of their results. Their assumption was embedded a single SWCNT in polymer with perfect bonding. The multi-scale modeling, MC, FEM, and using equivalent continuirm method was used by Spanos and Kontsos [84] and compared with Zhu, et al. [85] and Paiva, et al. [86] results. 

Ghosh, S. (2010) Micromechanical Analysis and Multi-scale Modeling Using the Voronoi Cell Finite Element Methods, CRC Press, Boca Raton, Florida. 

This stimulated advances in the development of the finite-element method in combination with a multi-scale homogenization procedure. In general, the multi-scale modelling of structure-property relationships of textile reinforced composites can be summarized in the diagram in Fig. 1.13 as follows ... 

Intensive studies in the area of dendritic macromolecules, which include applied research and are generally interdisciplinary, have created a need for a more systematic approach to dendritic architectures development that employs a multi-scale modeling and simulation approach. A possible way is to determine the atomic-scale characteristics of dendritic molecules using computer simulation and computational approaches. Computer simulation, as a powerful and modem tool for solving scientific problems, can be performed for dendritic architectures without synthesizing them. Computer simulation not only used to reproduce experiment to elucidate the invisible microscopic details and further explain experiments, but also can be used as a useful predictive tool. Currently, Monte Carlo, Brownian dynamics and molecular dynamics are the most widely used simulation methods for molecular systems [5]. 

In the following, the key issues and related models at different scales in PEMFCs are outlined in Section 3.2. In Section 3.3, the multi-scale strategies across neighboring scales are summarized and compared. The typical applications based on coarse-grained molecular dynamics (CG-MD) method areal so exhibited to discuss the multi-scale modeling techniques in PEMFC. However, there are still some major challenges and limitations in these modeling and simulations, as summarized in Section 3.4. 

---