Distribution standard deviation

The Burchell model s prediction of the tensile failure probability distribution for grade H-451 graphite, from the "SIFTING" code, is shown in Fig. 23. The predicted distribution (elosed cireles in Fig. 23) is a good representation of the experimental distribution (open cireles in Fig. 23)[19], especially at the mean strength (50% failure probability). Moreover, the predicted standard deviation of 1.1 MPa con ares favorably with the experimental distribution standard deviation of 1.6 MPa, indicating the predicted normal distribution has approximately the correct shape. 

Clifford et ah (1987a,b) considered acid spurs (primary radicals H and OH) and computed the evolution of radical and molecular products by the master equation (ME) and IRT methods. Reasonable values were assumed for initial yields, diffusion constants, and rate constants, and a distribution of spur size was included. To be consistent with experimental yields at 100 ns, however, they found it necessary that the spur radius be small—for example, the radius of H distribution (standard deviation in a gaussian distribution) for a spur of one dissociation was only in the 0.4—0.75 nm range. Since in acid spurs H atoms inherit the distribution of eh, this is considered too low. This preliminary finding has later been revised in favor of spurs of much greater radius. 

We find that the synthesis as reported by Bleier and Cannon [7], but changing the salt concentration, is capable of reproducibly making 100 250 nm (average diameter) zirconia colloids with a narrow distribution (standard deviation always smaller than 50... 

The baseline structural deficiency Y = 20 represents the maximum of a tight distribution (standard deviation a = 2.25) of T-values for the structural deficiency of soluble proteins with no disulfide bridges. This baseline T-value implies that soluble proteins are not perfectly packed and maintain at least 20% of unburied backbone hydrogen bonds. Since such structural deficiencies locally promote backbone hydration, they belong to an intermediate region between order and disorder and hence represent markers of structural flexibility. Thus, because of its universality, the Y = 20 constant may be interpreted as the baseline flexibility needed for protein function. 

To determine the number of samples required to achieve an experimental standard deviation (S) equal to or less than the Poisson distribution standard deviation (a), a 1 cc/sec gas flow rate and four minute samples were used. The particles were generated with a PUS, Inc. particle generator model PG-100, providing a particle count of 2000 partlcles/ft or greater. 

Arithmetic mean for normai distributions, geometric mean for iog-normal distributions, and the mode for trianguiar distributions. Standard deviation for normai distributions, geometric standard deviation for Iog-normai distributions, and minimum and maximum for trianguiar and uniform distributions. 

Simulations on the effect of step free energy on grain growth behaviour have also been made. Figure 15.11 shows the result of a Monte Carlo simulation made by Cho. For the simulation, Cho assumed that the grain network was a set of grains with a Gaussian size distribution (standard deviation of 0.1) located on vertices of a two-dimensional square lattice. Deterministic rate equations, Eq. (15.15) for v/> and Eq. (15.29) for v j, were... 

Mean locates center of distribution. Standard deviation measures width of distribution. 

A significant modification to the simple mixing of solutions is the slow and controlled release of one of the reactants. For example, Ohtaki et al. prepared CdS nanoparticles in nonaqueous solvents, where one of the reactants (S ) was made available slowly and uniformly via the controlled hydrolysis of P2S5 (114). The CdS particles were, on average, 6 nm in diameter, had a size distribution standard deviation of 1.2 nm, and formed stable suspensions under the protection of polymers (Figure 14). A similar strategy was used by Meisel and coworkers (115) and, more recently, by Yin et al. (116) in the preparation of CdS nanoparticles, where the slow release of S was achieved through the use of pulse radiolysis. 

Ni particles produced. The expansion was at a constant pressure of about 3000 psia through a fused-silica capillary nozzle with an inner diameter of 77 jtm. These Ni nanoparticles had an average particle size of 5.8 nm and a size distribution standard deviation of 0.54 nm, according to the TEM image (Figure 32). The particles were largely amorphous, exhibiting an extfemely diffuse x-ray... 

The average particle size in diameter (Z>, nm) and the size distribution standard deviation (a, nm) were determined via TEM analyses. 

The Ag nanoparticles prepared via RESOLV with the microemulsion having a Wo value of 12 had an average particle size of 10.4 nm and a size distribution standard deviation of 3.8 nm (263). 

Pore radius corresponding to the maximum of the log-normal pore size distribution, standard deviation in the pore radius. 

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