Hierarchical simulation strategy

Maroudas and co-workers have described a hierarchical scheme for atomistic simulations involving the use of electronic structure calculations to develop and test semiempirical potentials that are in turn used for MD simulations. These results can sometimes be used to develop elementary step transition probabilities for use in dynamic Monte Carlo schemes. With Monte Carlo techniques, the well-known length and time scale limitations of MD can be greatly extended. This hierarchical approach appears to have great promise for the development of simulation strategies that will allow studies of a wide range of practical surface and thin-film chemical and physical processes. 

De Mori et al. have taken a different approach to take advantage of MC simulations. They used a coarse-grained Hamiltonian to presample phase space in an approximate manner. This is followed by MD simulations starting from representative structures from the most dominantly populated clusters within the MC ensemble. Such a hierarchical strategy was employed to study the folding of a small protein [144] and the oligomer formation of short, amyloidogenic peptides [145]. 

Partitioning is most appropriate when one is only interested in the subsets or clusters, while hierarchical decomposition is most applicable when one seeks to show similarity relationships between clusters. Section 2.1 formalizes the combinatorics of the partitional strategy and Section 2.2 does the same for hierarchical methods. The formulations we derive here provide the basis for the application of the simulated annealing algorithm to the underl5dng optimization problem as we show in Section 3. 

Pseudo-2D models can be especially valuable when a hierarchical strategy is employed, wherein CFD simulations are employed to obtain the transverse transport correlations that are then used in pseudo-2D models [26]. Results using this strategy for non-adiabatic microbumers are presented in subsequent sections. We use Fluent 6.2 [27] to solve a 2D eDiptic model for the combined flow, transport and reaction problem. To ensure accuracy of the Nu and Sh values computed, a non-uniform grid is chosen such that the smallest cell is 1 pm wide in the transverse direction in the fluid phase near the reactor wall. Simulations are performed for various operating conditions and Nu and Sh are computed using Equations (10.2) and (10.3). 

The overall strategy for the hierarchical procedure is as follows. First, the six pretreatment methods are compared in terms of energy requirements. Then, the implementation of a direct recycle integration strategy is analyzed. The pretreatment options are then combined with conversion configurations and analyzed via process simulation. Next, a separation step based on conventional distillation is implemented. Finally, reactor fixed costs are estimated for some options to complete the analysis. Figure 2.2 summarizes the overall methodology. 

---