Modeling multiscale

Quantum mechanics Moleci r dynamics Monte Carlo 

Brownian dynamics Dissipative particle dynamics Lattice Boltzmann Time-dependent Ginzburg-Landau Dynamical density functional theory 

Mori-Tanaka model Kalpin-Tsai model Lattice-spring model Finite element method Equivalent continuum approach Seif-similar approach 

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Multiscale modeling is an approach to minimize system-dependent empirical correlations for drag, particle-particle, and particle-fluid interactions [19]. This approach is visualized in Eigure 15.6. A detailed model is developed on the smallest scale. Direct numerical simulation (DNS) is done on a system containing a few hundred particles. This system is sufficient for developing models for particle-particle and particle-fluid interactions. Here, the grid is much smaller... 

Multiscale modeling of process operations. The description of process variables at different scales of abstraction implies that one could create models at several scales of time in such a way that these models communicate with each other and thus are inherently consistent with each other. The development of multiscale models is extremely important and constitutes the pivotal issue that must be resolved before the long-sought integration of operational tasks (e.g., planning, scheduling, control) can be placed on a firm foundation. 

Multiscale process identification and control. Most of the insightful analytical results in systems identification and control have been derived in the frequency domain. The design and implementation, though, of identification and control algorithms occurs in the time domain, where little of the analytical results in truly operational. The time-frequency decomposition of process models would seem to offer a natural bridge, which would allow the use of analytical results in the time-domain deployment of multiscale, model-based estimation and control. 

Feig M, Karanicolas J, Brooks CL, III (2004) MMTSB tool set Enhanced sampling and multiscale modeling methods for applications in structure biology. J Mol Graph Model 22 377—395. 

Weinan, E. Vanden-Eijnden, E., in Multiscale Modelling and Simulation, LNCSE 39, 2004 (chapter Metastability, conformation dynamics, and transition pathways in complex systems)... 

Figure 55. Physical model for multiscale modelling of particle-fluid system.

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