Log normal plot

Fig. 1.15 A log-normal plot. Note the irregular shape, arising from the smallness of the sample. (Courtesy, DallaValle )...

FIG. 20-16 Log -normal plot of residence-time distrihiition in Phelps Dodge mill. 

FIG. 28 Log-normal plot of relaxation time t2 vs bias for three different chain lengths (given as a parameter) and a series of medium densities [21]. 

In this application of the log-normal plot, note that the "n chanical" separation of "fines" has created anew particle distribution with 62 = 2 p. Even the value of 02 differs from that of the major particle distribution. In the "fines" fraction, it appears that the largest pcirticle does not exceed about 5 p. Needless to say, lamps prepared from this phosphor were inferior in brightness. Armed with this information, one could then recommend that the method of "fines" removal be changed. 

Procedures for curve fitting by polynomials are widely available. Bell shaped curves usually are fitted better and with fewer constants by ratios of polynomials. Problem P5.02.02 compares a Gamma fit with those of other equations, of which a log normal plot is the best. In figuring chemical conversion, fit of the data at low values of Ett) need not be highly accurate since those regions do not affect the overall result very much. 

Another factor that is of great importance for the observed sulfur isotope variations of natural sulfides is whether sulfate reduction takes place in an open or closed system. An open system has an infinite reservoir of sulfate in which continuous removal from the source produces no detectable loss of material. Typical examples are the Black Sea and local oceanic deeps. In such cases, H2S is extremely depleted in " S while consumption and change in " S remain negligible for the sulfate. In a closed system, the preferential loss of the lighter isotope from the reservoir has a feedback on the isotopic composition of the unreacted source material. The changes in the " S-content of residual sulfate and of the H2S are modeled in Fig. 2.21, which shows that 5 S-values of the residual sulfate steadily increase with sulfate consumption (a linear relationship on the log-normal plot). The curve for the derivative H2S is parallel to the sulfate curve at a distance which depends on the magnitude of... 

FIGURE 2.13 Mixing two size distributions, bimodal nonintersecting distributions (a) linearized log-normal plot, (b) relative % versus size. Taken from Figures 4.14 and 4.15 in Allen [1]. 

The broadness of the distribution is given by the parameter j, obtained from the slope (tan 0) of the log-normal plot where tan d = 7A/2. The polydispersity ratio (Af /Afp = exp(7 /2) no and x are constants in the distribution function not determinable from the log-normal line. (Special cases of the general distribution function have also been employed, e.g., the Lansing and Kraemer relationship where x = 0 [304] and the Wesslau relationship [305], where x = —1). Fractionation data can also be adequately represented by other exponential distributions such as that of Tung [306] W(n) dn = abn exp(—an ) dn. (W(n) = 1 — exp(—an )). Fig. 14a(c). 

In this application showing how the log-normal plot can be utilized, we can readily see that the "mechanicaT separation of "fines" has created a new particle distribution with d 2 = 2 p. Even the Aralue of differs from... 

If poins are aligned on a line (in fact 3 line) then the line is drawn through the points that were aheady placed on the log-normal plot ... 

Reading the value of a on the special axis from the right side of the log-normal plot. 

Determining median lifetimes t, for each of the three stress levels, respective the times corresponding to a failure percentage of 50%, while reading these three values on the time axis from the log-normal plot previously drawn-up, presented in Fig. 2. The value reading for median lifetime (IEEE 1977) are f i = 1, 12-10 h,tm2 = 7 - 10 h,tm3 = 1,1 10 h ... 

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