Logarithmic diagrams ratio

The number of cycles at which a certain mean strain is reached during the dynamic experiment can be plotted In a semi-logarithmic diagram versus the stress ratio R. By using linear regression analyses, the number of cycles for the case = 1,1. e., the time at which this mean strain is reached under static load, can be extrapolated. Time f and number of cycles Ai are correlated by the frequency / ... 

Figure 5.233 shows the correlation between static and dynamic behavior at 6 N/mm. The diagram shows the number of cycles at equal strain versus load ratio. Linear regression in a semi-logarithmic diagram leads to a good extrapolation of the dynamic experimental data for creep deformation (R= 1). 

Figure 1.93. /02-pH diagram with the stability fields of aqueous species in Na-K-H-S-Se-0 system for the conditions SS = 10 mol/kg H2O, ESe = 10 mol/kg H2O, ionic strength = 1, and temperature = 150°C. Dashed lines are the ratio ho-a i- /a i- in logarithmic units. Stability fields for native sulfur and native selenium and the boundaries between predominance regions of oxidized and reduced selenium species are omitted for clarity (Shikazono, 1978b). 

Figure 7.5 Schematic diagram of Land and McCann s prototype (a). Logarithmic receptors are spaced equidistant along a path. The output of two adjacent receptors A and B is added at point C. Because the first term is added with a negative voltage, the ratio of reflectances between A and B is computed at C. At point E the existing sequential product D is added to the result from C. The black square denotes that the sequential product is set to zero if it becomes larger than zero. The reflectances are read out at point F. A circuit for two adjacent receptors A and B is shown in (b). A light bulb (F) is used to visualize the reflectances (Reproduced from Land EH and McCann JJ 1971 Lightness and retinex theory. Journal of the Optical Society of America, 61(1), 1-11 by permission from The Optical Society of America).

Two graphical methods described here, a master variable (pC-pH) diagram and a distribution ratio diagram, are extremely useful aids for visualizing and solving acid-base problems. They help to determine the pH at which an extraction should be performed. Both involve the choice of a master variable, a variable important to the solution of the problem at hand. The obvious choice for a master variable in acid-base problems is [H+] [equations (2.9)—(2.12)], or pH when expressed as the negative logarithm of [H+]. 

Figure 1.1 Partial pressure diagram of ethanol, C2H5OH, in logarithmic scale. The small deviation of the curve partial pressure p versus temperature T from linearity demonstrates that p(T) is not exactly exponential. The ethanol concentration scale c as a volume ratio refers to an ambient pressure of 1.013 105 Pa.

Figure 5 A display of prominent exotic (presolar) noble-gas compositions (from Anders and Zinner, 1993). In the left two panels, for each isotope on the abscissa the ordinate is the ratio (to °Xe) in the HL component (left panel) or the G (formerly termed Xe-S) component (center panel), divided by the equivalent ratio in solar xenon (i.e., solar xenon would plot with all isotopes at unity on the ordinate). The HL component shows the defining characteristics of enriched heavy and light isotopes. For the G-component, the pattern is that expected for s-process (slow neutron capture) nucleosynthesis. The right panel is a three-isotope diagram analogous to Figure 4, except that both scales are logarithmic. It shows experimental limits for the R-component (formerly Ne-E(L)) and the G-component (formerly...

Fig. 11.1 Two-dimensional bifurcation diagram calculated by continuation from the Citri-Epstein mechanism for the chlorite-iodide system. Plot of 2D space of constraints is chosen to be the ratio of input concentrations, [CIO ]o/[I ]o> versus the logarithm of the reciprocal resideuce time, logfco-Notation SSI, SS2, region of steady states with high [1 ] and low [I ], respectively Osc, region of periodic oscillations Exc, region of excitahihty snl, sn2, curves of saddle-node bifurcations of steady states hp, curve of Hopf bifiucatious sup, ciuve of saddle-node bifurcations of periodic orbits swt, swallow tail (a small area of tristability) C, cusp point TB, Takens-Bogdanov point (terminus of hp on snl). (From [5].)...

Figure 5. Softening points for the birch xylan at various temperatures shown in a diagram of the logarithm of the loading frequency versus moisture ratio, convertedfrom Figure 3 using the isotherms in Figure 4. The 95% confidence interval for the moisture ratio determinations of the softening points was 0.35%. The lines are based on a linear regression of the data for each...

As was derived in chapter 9, the amplitude ratio for a dead-time process is 1.0 and the phase shift -0)6. The amplitude ratio for the process becomes then AR (second-order process) x AR(dead-time process). The phase shift of the process becomes then (second-order process) + dead-time process). Figure 32.3 shows the Bode diagram in which the logarithm of the amplitude ratio and the phase shift are plotted against the frequency O). For the amplitude ratio two asymptotes emerge, one for low frequencies a>- ) (static behaviour) en one for high frequencies 0)- °° (high-frequency behaviour). The values can easily be calculated from ... 

A first sort of diagram consists of drawing the fraction a of the metal present (the ratio of the concentration of the considered species and the sum of concentrations of all the species containing the metallic ion) as a function of the free ligand concentration or of its decimal co-logarithm. Hence, in the case of eadmium eomplexes (investigated above), the different fraetions a are... 

Bode plot A type of frequency response diagram used for analysing the frequency response of a system to a disturbance signal. It is the plot of the logarithm of the amplitude ratio with the logarithm of the phase angle measurements. 

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