Repeated Simulation

Intended Use The intended use of the model sets the sophistication required. Relational models are adequate for control within narrow bands of setpoints. Physical models are reqiiired for fault detection and design. Even when relational models are used, they are frequently developed bv repeated simulations using physical models. Further, artificial neural-network models used in analysis of plant performance including gross error detection are in their infancy. Readers are referred to the work of Himmelblau for these developments. [For example, see Terry and Himmelblau (1993) cited in the reference list.] Process simulators are in wide use and readily available to engineers. Consequently, the emphasis of this section is to develop a pre-liminaiy physical model representing the unit. 

Figure 10-7. Periodically repeated simulation unit cell containing uracil and 39 water molecules. The SOMOs of the ROKS tttt excited state are shown in dark grey/light grey and black/white...

The sole exceptions axe discussed in Sec. 3.2, where free boundary conditions perpendicular to the direction of shock propagation were assumed so that critical widths in two dimensions could be studied. Spot checks were made to ensure that increasing the size of the repeated simulation cell did not significantly affect the results obtained with periodic boundary conditions. When the model material was taken as infinite in the direction of the... 

Decisions Powerful computation allows many simulation trials to find a better solution in decision maldng. For example, an optimal material handling equipment selection can be obtained through repeated simulation runs. 

For non-ideal mixtures, particularly in azeotropic mixtures, a simple method cannot be used to design an SSC in a shortcut manner. A common approach is to use repeated simulations, for example, by estimating the side stream location and flow rate, and then attempting to converge on a solution (Rooks et al, 1996). This method, however, is time-consuming and provides few insights. To overcome these drawbacks, efforts have been... 

Figure 18.11 Optimization of a process with recycle (a) repeated simulation (feasible path approach) ...

The last point deals with the numerical process of estimation of tiie parameters, which usually involves to find the minimum of a least-squares type criterion. Whatever the optimization tectoique used for this task, calling or not the Jacobian matrix of the model, repeated simulations are needed, to compute the theoretical values corresponding to each experimental point... 

Through repeated simulations, the SCM ensures that the resulting capital tie-up and ist effects are calculated before you finally commit to the capital tie-up you will tolerate. 

Simulations generally involve a fixed number of particles (N). To model bulk systems with a finite number of particles, periodic boundary conditions are applied. The volume (V) of the periodically repeating simulation box may be kept fixed or varied. Extensions to the scheme in Eq. (2) allow coupling the system to a thermostat and/or barostat to control the temperature T and pressure P of the system [22-24]. Hence, depending on the chosen conditions, the distribution sampled during the MD simulation is representative of either the microcanonical (NVE), canonical (NVT), or isothermal-isobaric (NPT) statistical mechanics ensembles [19]. 

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