Beta parameter notes

To test the foregoing dimensionless relationship, two powders (Avicel Pl 1101, a ductile, viscoelastic material, and Emcompress, a brittle material, blended with 0.5% magnesium steaiate) were compressed on the PressterTw, a single-station mechanical replicator of rotary tablet presses. In the first set of experiments, a 16-station Manesty Betapress (a research-scale press) was simulated at two speeds, 60 and 100 rpm. In the second set, a 36-station Fette P2090 (a medium-scale production press) was simulated at two speeds, 55.8 and 70 rpm. It should be noted that 100 rpm of the Beta-press corresponds to 55.8 rpm of the Fette 2090 in terms of the linear speed of the turret. Basic parameters for the two tablet presses arc presented in Table 3. 

Note that, while the spread parameter crj is the same for all terms in the summation, the conditional parameter 0-2,0, can depend on a. Also, the functional form used for 6 1 need not be the same as that used for ( -g- 1 could use beta EQMOM, while 2 uses Gaussian EQMOM). Although the form in Eq. (3.134) is not as general as that in Eq. (3.124), we shall see that it leads to a direct method for moment inversion that is very similar to the one used in the CQMOM. The bivariate moments found from Eq. (3.134) have the form... 

In this section, we present results found with the scalar-conditioned velocity algorithm introduced in the previous section using the NDF representation in Eq. (8.108). All of these calculations have been done with beta EQMOM using n = 2 nodes for the first quadrature and M = 50 nodes for the second. The initial NDF, where f e [0,1] is the particle volume, has one of two forms. In the first case, referred to as small spread, the NDF is represented by two beta functions, one near = 1/3 and one near f = 2/3, with a small spread parameter cr. The initial moments for this case are shown in Figure 8.28. As can be observed from this figure, the moments are nonzero only within the spatial domain x (-0.8, -0.2). Some statistics computed from the initial NDF are given in Figure 8.29. Note that the initial conditional velocity u(0,x,f) = 1 is independent of the particle size, and the mean and standard deviation of the volume do not depend on x. 

The first term of Equation 13.8 accounts for the transportation costs. Note that the unitary transportation cost parameter (trc(i, j, t)) is now defined for every time period t. The second and third terms determine the capital investment from the capacity expansions. We assume that the capital investment is a linear function of the capacity expansions, where alpha(i, t) and beta(i, t) are the fixed and variable capital investment parameters, respectively. For simplicity, we have not considered the temporal value of money, but note that this could be easily accounted for in the model by introducing the interest rate. 

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