Growth rate, true values

The crystal growth rate has been found in many eases to be extremely rapid, more rapid than can be accounted for on the diffusion hypothesis thus Tammann (foe. cit.) found for benzophe-none a maximum crystallisation velocity of 2 4 mm. per minute (Walton and Judd, J. Phys. Ohem. xvni, 722,1914). Much higher values, e.g. 6840 mm. per minute for water and 60,000 mm. per minute for phosphorus (Gernez, O.R, xcv. 1278, 1882) have been recorded. In some cases the rate was found independent of the speed of rotation of the stirrer and occasionally the reaction velocity followed a bimolecular law instead of the simple unimolecular expression which holds true for solution. 

A limitation of the methods described so far is that they have assumed a constant overall yield coefficient and do not allow the endogenous respiration coefficient kd (or alternatively the maintenance coefficient, m) to be evaluated. Equation 5.54 shows that the overall yield, as measured when monitoring a batch reactor, is affected by the growth rate and has the greatest impact when the growth rate is low. Consequently, it is desirable to be able to estimate the values of kd or m, so that the yield coefficient reflects the true growth yield. An equivalent method would be one where the specific rates of formation of biomass and consumption of substrate were determined independently, again without the assumption of a constant overall yield-coefficient. 

The specific growth rate can be calculated from cellular concentration data if the cell viability is sufficiently high. When the cell death rate is significant, the value obtained from Equation 4 is in fact an apparent specific rate, since the measured values in the laboratory are determined as a balance between growth and death. The apparent rate is related to the true specific growth rate by the following equation ... 

Disturbance will grow with time when the real part of the complex frequency Is positive. This Is true at all capillary numbers for wavenumbers less than I/Cq. The growth rate reaches Its maximum positive value when x Is equal to 1//2. The maximum growth rate Is then... 

As discussed above, these rate equations make no allowance for the restrictions on growth of the nuclei. It is necessary to relate the unrestricted fractional decomposition, nr, to the true value, nr. A general but complicated solution to the problem has been provided [1,8]. For the simpler case of three-dimensional growth of randomly-distributed nuclei on large crystals, Avrami [21] has shown that nr and... 

The load imbalance resulting from a dynamic distribution of tasks is very difficult to model because the times required for the individual computational tasks are not known in advance. Provided that the number of tasks is much larger than the number of processes, however, it is reasonable to assume that the dynamic task distribution will enable an essentially even distribution of the load. For this to remain true as the number of processes increases, the number of tasks, umn, must increase proportionally to p. Although this is the same growth rate as obtained for a static work distribution, the actual value for umn needed for high efficiency for a given process count is much smaller for the dynamic distribution, and the assumption of perfect load balance is therefore adequate for our purposes. 

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