Constraint-based simulation methods

A three-dimensional simulation method was used to simulate this extrusion process and others presented in this book. For this method, an FDM technique was used to solve the momentum equations Eqs. 7.43 to 7.45. The channel geometry used for this method was essentially identical to that of the unwound channel. That is, the width of the channel at the screw root was smaller than that at the barrel wall as forced by geometric constraints provided by Fig. 7.1. The Lagrangian reference frame transformation was used for all calculations, and thermal effects were included. The thermal effects were based on screw rotation. This three-dimensional simulation method was previously proven to predict accurately the simulation of pressures, temperatures, and rates for extruders of different diameters, screw designs, and resin types. 

An SMB process is identified by using the subspace identification method. The input/output data-based prediction model is used to obtain the prediction model. The identified model exhibits an excellent prediction performance. The input/output data-based predictive controller based on the identified model is designed and applied to MIMO control problems for the SMB process under the presence of the input and output constraints. The simulation results demonstrate that the controller proposed in diis study shows an excellent control performance not only for the disturbance rejection but also for the setpoint tracking. 

Constraints provide a very direct means to add information to a simulation— simply requiring all generated structures to satisfy certain additional conditions. This approach has been used extensively to generate three-dimensional structures from NMR spectra [52], which provide data in the form of interatomic distances. In principle, if one had enough distance constraints, the problem would be overdetermined and could be solved mathematically with no further information required. It has been shown, however, that the use of knowledge-based simulations based on homologous structures or fragment libraries from the PDB provides more accurate models than constraint-based methods alone [20,53]. 

Some of the coarse-grained parameters, i e and can be easily measured by experiments or in simulations. The other two parameters, %N and the suppression of density fluctuations, XqN, are thermodynamic characteristics, which are not directly related to the structure (i.e., they cannot be simply expressed as a function of the molecular coordinates). If density fluctuations of the polymeric liquid are small on the length scale of interest (e.g., width of an interface between domains), then the value of the compressibility has only a minor relevance and decreasing it even further will not significantly affect the behavior of the system. Thus, field-theoretic calculations often take the idealized limit of strict incompressibility. In particle-based simulations, however, one often softens the constraint in order to facilitate the motion of the interaction centers and, thereby, reduces the viscosity of the polymer liquid. The Flory-Huggins parameter, in turn, is a crucial coarse-grained parameter and different methods have been devised to extract it from experiments or simulations [16, 20-25]. We shall briefly discuss this important issue in Section 5.2.3, and further refer the reader to the literature, where computer simulations have been quantitatively compared with mean field predictions and where the role of fluctuations on the coarse-grained parameters is discussed [16, 22]. 

The purification of value-added pharmaceuticals in the past required multiple chromatographic steps for batch purification processes. The design and optimization of these processes were often cumbersome and the operations were fundamentally complex. Individual batch processes requires optimization between chromatographic efficiency and enantioselectivity, which results in major economic ramifications. An additional problem was the extremely short time for development of the purification process. Commercial constraints demand that the time interval between non-optimized laboratory bench purification and the first process-scale production for clinical trials are kept to a minimum. Therefore, rapid process design and optimization methods based on computer aided simulation of an SMB process will assist at this stage. 

Hahn [47] developed a hybrid simulation based on BD and Monte Carlo methods. Incorporation of the statistical techniques of Monte Carlo methods relaxes the constraint that time steps must be sufficiently short such that external force fields can be considered constant, and the BD improves upon the Monte Carlo methods by allowing dynamic information to be collected. Hahn applied the model to the investigation of theoretical deposition by simulating a... 

Thus, if we restrict ourselves to those simulations that have a clear quantum-chemical component, in the simplest case one is basing the procedure on perturbation theory, with a model in which the protein is represented by a collection of point particles (i.e., the atoms), with some distance constraints in an attempt to account for the existence of bonds, using an energy minimization method with appropriate computational techniques, the final... 

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