Logarithmic scales

Figure Bl.15.3. Typical magnitudes of interactions of electron and nuclear spins in the solid state (logarithmic scale).

Fig. 4. The average end-to-end-distance of butane as a function of timestep (note logarithmic scale) for both single-timestep and triple-timestep Verlet schemes. The timestep used to define the data point for the latter is the outermost timestep At (the interval of updating the nonbonded forces), with the two smaller values used as Atj2 and At/A (for updating the dihedral-angle terms and the bond-length and angle terms, respectively).

Figure 4.8 Fraction of amorphous polyethylene as a function of time for crystallizations conducted at indicated temperatures (a) linear time scale and (b) logarithmic scale. Arrows in (b) indicate shifting curves measured at 126 and 130 to 128°C as described in Example 4.4. [Reprinted with permission from R. H. Doremus, B. W. Roberts, and D. Turnbull (Eds.) Growth and Perfection of Crystals, Wiley, New York, 1958.]...

The superpositioning of experimental and theoretical curves to evaluate a characteristic time is reminiscent of the time-tefnperature superpositioning described in Sec. 4.10. This parallel is even more apparent if the theoretical curve is drawn on a logarithmic scale, in which case the distance by which the curve has to be shifted measures log r. Note that the limiting values of the ordinate in Fig. 6.6 correspond to the limits described in Eqs. (6.46) and (6.47). Because this method effectively averages over both the buildup and the decay phases of radical concentration, it affords an experimentally less demanding method for the determination of r than alternative methods which utilize either the buildup or the decay portions of the non-stationary-state free-radical concentration. 

Fig. 20. Primary x-ray line and Bremsstrahlung background excited by bombardment with 15 keV electrons, (a) Linear scale plot, (b) Logarithmic scale...

Fig. 13. Characteristics of a 50-)J.m long DFB laser, (a) Light-current properties, (b) spectral intensity plotted on a logarithmic scale to better illustrate...

Fig. 2. Histograms of the data from Table 1, plotted on (a) a linear and (b) a logarithmic scale.

Fig. 1. Vapor pressure of ordinary water, where represents linear and (--) logarithmic scale. To convert MPa to psi, multiply by 145.

Fig. 1. Logarithmic scale of the electrical conductivities of materials categorized by magnitude and carrier type, ie, ionic and electronic, conductors. The various categories and applications ate given. The wide conductivity range for the different valence/defect states of Ti oxide is highlighted. MHD is...

FIG. 20-2 Particle -size distribution curve plotted using a logarithmic scale for tbe abscissa,... 

Figures 12 and 13 illustrate two of the more commonly used methods for displaying societal risk results (1) an F-N curve and (2) a risk profile. The F-N curve plots the cumulative frequencies of events causing N or more impacts, with the number of impacts (N) shown on the horizontal axis. With the F-N curve you can easily see the expected frequency of accidents that could harm greater than a specified number of people. F-N curve plots are almost always presented on logarithmic scales because of...

For low-cycle fatigue of un-cracked components where (imax or iCT inl am above o-y, Basquin s Law no longer holds, as Fig. 15.2 shows. But a linear plot is obtained if the plastic strain range defined in Fig. 15.3, is plotted, on logarithmic scales, against the cycles to failure, Nf (Fig. 15.4). TTiis result is known as the Coffin-Manson Law ... 

Unfortunately there are very little reliable data on the frequency of wall perforation caused by corrosion in most cases comprehensive data about wall thickness, pipe coating, type of soil, etc. are lacking. The incidence of wall perforation is usually plotted on a logarithmic scale against the service life of the pipeline (see Fig. 22-3). Cases are also known where a linear plot gives a straight line. Curve 1 in... 

On Figure 6.1.1, the four consecutive reaction steps are indicated on a vertical scale with the forward reaction above the corresponding reverse reaction. The lengths of the horizontal lines give the value of the rate of reaction in mol/m s on a logarithmic scale. In steady-state the net rates of all four steps must be equal. This is given on the left side with 4 mol/m s rate difference, which is 11 mm long. The forward rate of the first step is 4.35 molW s and the reverse of the first reaction is only 0.35 mol/m s, a small fraction of the forward rate. 

For a sequenee of reaetion steps two more eoneepts will be used in kinetics, besides the previous rules for single reaetions. One is the steady-state approximation and the seeond is the rate limiting step eoneept. These two are in strict sense incompatible, yet assumption of both causes little error. Both were explained on Figure 6.1.1 Boudart (1968) credits Kenzi Tamaru with the graphical representation of reaction sequences. Here this will be used quantitatively on a logarithmic scale. 

As a starting point it is useful to plot the relationship between shear stress and shear rate as shown in Fig. 5.1 since this is similar to the stress-strain characteristics for a solid. However, in practice it is often more convenient to rearrange the variables and plot viscosity against strain rate as shown in Fig. 5.2. Logarithmic scales are common so that several decades of stress and viscosity can be included. Fig. 5.2 also illustrates the effect of temperature on the viscosity of polymer melts. 

Did we predict the number of atoms required to complete additional layers around the metal-coated C(jo correctly Figure 6 shows a spectrum of Qo covered with the largest amount of Ca experimentally possible (note the logarithmic scale). Aside from the edges of A = 32 and a = 104 which we have already discussed, there are additional clear edges at a = 236 and A = 448 (completion of a third layer was also observed at QoSr23g). Note that these values are identical to the ones just predicted above for the completion of the third and fourth layer of metal atoms. We, therefore, feel confident that the alkaline earth metals studied do, in fact, form the distinct layers around a central C50 molecule with the structures depicted in Fig. 5. 

Logarithmic scales are frequently used in presenting risk results but most of the public do not understand logarithmic scales. 

A weighting scale, dBA The unit of sound intensity expressed as a logarithmic scale, related to a reference level of 10 W m"-. The A weighting scale is the most commonly used scale, as it reduces the response of sound meters to very high and low frequencies and emphasize those within the range audible by the human ear. 

Decontamination factor A logarithmic scale used to measure the collection efficiency of a particulate collection device. 

The agreement between the criterion and experiment is even better than that at first glance because Figures 2-37, 2-38, and 2-40 are plotted at a logarithmic scale. The maximum stress and strain criteria are incorrect by 100% at 30 l... 

At pH 7, [H ] = [OH ] that is, there is no excess acidity or basicity. The point of neutrality is at pH 7, and solutions having a pH of 7 are said to be at neutral pH. The pH values of various fluids of biological origin or relevance are given in Table 2.3. Because the pH scale is a logarithmic scale, two solutions whose pH values differ by one pH unit have a 10-fold difference in [H ]. For example, grapefruit juice at pH 3.2 contains more than 12 times as much H as orange juice at pH 4.3. 

Figure 1.1 Cosmic abundances of the elements as a function of atomic number Z. Abundances are expressed as numbers of atoms per 10 atoms of Si and are plotted on a logarithmic scale. (From A. G. W. Cameron, Space Sci. Rev. 15, 121-46 (1973), with some updating.)...

Logarithmic Scale of Locomotives in Service—Class 1 Railroads. 

The common types oi vacuum-producing equipment used in commercial processes are indicated on this chart, together with the approximate operating range of each one. The central logarithmic scale shows absolute pressures in... 

Figure 4-327. plots for a U.S. Gulf Coast well in shales (a) linear scale (b) logarithmic scale. (Courtesy SPE [101].,)... 

FIGURE 3.12 Dependence of constitutive receptor activity as ordinates (expressed as a percent of the maximal response to a full agonist for each receptor) versus magnitude of receptor expression (expressed as the amount of human cDNA used for transient transfection, logarithmic scale) in Xenopus laevis melanophores. Data shown for human chemokine CCR5 receptors (open circles), chemokine CXCR receptors (filled triangles), neuropeptide Y type 1 receptors (filled diamonds), neuropeptide Y type 2 receptors (open squares), and neuropeptide Y type 4 receptors (open inverted triangles). Data recalculated and redrawn from [27],... 

FIGURE 4.13 Effect of the allosteric modulator 5-(N-ethyl-N-isopropyl)-amyloride (EPA) on the kinetics dissociation of [3H] yohimbine from c/j-adrenoceptors, (a) Receptor occupancy of [3H] yohimbine with time in the absence (filled circles) and presence (open circles) of EPA 0.03 mM, 0.1 mM (filled triangles), 0.3 mM (open squares), 1 mM (filled squares), and 3 mM (open triangles), (b) Regression of observed rate constant for offset of concentration of [3H] yohimbine in the presence of various concentrations of EPA on concentrations of EPA (abscissae in mM on a logarithmic scale). Data redrawn from [13]. 

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