COMPARISON OF APPROACHES TO STIFFNESS


A practical method of predicting the molecular behavior within the flow system involves the RTD. A common experiment to test nonuniformities is the stimulus response experiment. A typical stimulus is a step-change in the concentration of some tracer material. The step-response is an instantaneous jump of a concentration to some new value, which is then maintained for an indefinite period. The tracer should be detectable and must not change or decompose as it passes through the mixer. Studies have shown that the flow characteristics of static mixers approach those of an ideal plug flow system. Figures 8-41 and 8-42, respectively, indicate the exit residence time distributions of the Kenics static mixer in comparison with other flow systems.  [c.748]

Another approach to the production of high melting terephthalate-based copolyamides is first to make a low molecular weight prepolymer and then sohd-phase the material to higher molecular weight this process is similar in principle to that used in the manufacture of nylon-4,6. A variation of this process is used by Mitsui to produce its nylon-6,T/6,6 product, a copolymer of nylon-6,T and nylon-6,6 via a two-step process. First, an oligomer of the copolymer is made in an autoclave and spray-dried. The particles are then fed into an extmder, where the final copolymer is produced. A third approach, used by Du Pont, is to add a second diamine, 2-methylpentamethylenediamine (trade name Dytek A) rather than a second diacid to reduce the melting point (194,195). This nylon-6,T/D,T copolymer is produced via an all-melt phase process in an autoclave. Although the resulting polymer has a high melt point, the process avoids the added cost of special process equipment and handling. Table 11 presents information on most of the high temperature resins that have been introduced into the marketplace nylon-6,6 and nylon-4,6 are included for comparison.  [c.238]

The issue of which approach to Ewald sums is most efficient for a given system size has been plagued by controversy. Probably the best comparison is that by Pollock and Glosli [46]. They implement optimized versions of Ewald summation, EMA and P3M. They conclude that for system sizes of any conceivable interest, the P3M algorithm is most efficient. Interestingly, they also show that P3M can be used to efficiently calculate energies and forces for finite boundary conditions, using a box containing the cluster and a clever filter function in reciprocal space. The particle-mesh-based algorithms are excellent at energy conservation, which is an additional advantage. On the other hand, the EMA may scale better in highly parallel implementations because of the high communication needs of the EET. In addition, since the expensive part of the EMA is due to long-range interactions, the EMA may be more appropriate for multiple time step implementations [41]. The algorithms for P3M and the force-interpolated PME are essentially identical, differing only in the form of the modification to the reciprocal space weighting factors exp[—7t-m-/p-L-]/m-. The sampling density for the P3M turns out to be a shifted B-spline, so the weighting factors are very similar. Thus for the same grid density and order of interpolation, the computational costs of the P3M and force-interpolated PME are the same. In the case that contributions to the Ewald sum from high frequency reciprocal vectors m outside the K X K X K array can be neglected, the expressions for P3M and force-interpolated PME become equivalent, and the accuracy and efficiency are thus equivalent [45]. Under all reasonable simulation parameters it was found that the errors due to neglect of high frequency reciprocal vectors were small compared to remaining errors, so the above two algorithms are equivalent for practical purposes. Eor typical simulation parameters (9 A cutoff, RMS force error lO ) the smooth PME is more efficient than either P3M or force-interpolated PME, because its accuracy is only marginally less than  [c.111]


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Mechanics of composite materials  -> COMPARISON OF APPROACHES TO STIFFNESS

Machanics of composite materials  -> COMPARISON OF APPROACHES TO STIFFNESS