Straight-line dependence, effect

Effect of Urethane RIM Morphology on Deviation from Second-Order, Straight-Line Dependence... 

Another example indicating the effect of RIM elastomer composition on the deviation from straight line dependence was taken from the paper of Stephen D. Lipshitz and Christopher W. Macosco (15). 

Straight lines are obtained for the various inorganic anions when the eluent concentration is varied at constant pH value and when the logarithm of the net retention volume is plotted versus the logarithm of the eluent concentration. The slope of the straight line depends on the type of eluent and analyte ion, Sy, respectively. Fig. 3-69 illustrates this effect on the eluents and solute ions investigated by Small [81]. The coelution of some anions and the reversal of the elution order under specific chromatographic conditions is remarkable. The retention behavior is described mathematically as ... 

The variation of o,.jj with trap depth is presented in Figure 12-19. The effect of traps on the mobility, reflected in an increase of acjj, becomes noticeable only above a certain critical trap depth that depends on concentration. Above that critical value, a2,.), increases approximately linearly with ,. Figure 12-20 shows complementary information concerning the effect of the trap concentration on a,. at constant trap depth. The data reproduces as a family of parallel straight lines on a (Pr/jlo)2 versus In c plot. Their intersection with the ov)jla— 1 tine indicates the critical concentration c, of traps of depth , needed to effect the mobility (see Fig. 12-21). 

Polymer growth J(c) showed nonlinear monomer concentration dependence in the presence of ATP (Carrier et al., 1984), while in the presence of ADP, the plot of J(c) versus monomer concentration for actin was a straight line, as expected for reversible polymerization. The data imply that newly incorporated subunits dissociate from the filament at a slower rate than internal ADP-subunits in other words, (a) the effect of nucleotide hydrolysis is to decrease the stability of the polymer by increasing k and (b) nucleotide hydrolysis is uncoupled from polymerization and occurs in a step that follows incorporation of a ATP-subunit in the polymer. Newly incorporated, slowly dissociating, terminal ATP-subunits form a stable cap at the ends of F-actin filaments. 

One of the apparent results of introducing couple stress is the size-dependent effect. If the problem scale approaches molecular dimension, this effect is obvious and can be characterized by the characteristic length 1. The size effect is a distinctive property while the film thickness of EHL is down to the nanometre scale, where the exponent index of the film thickness to the velocity does not remain constant, i.e., the film thickness, if plotted as a function of velocity in logarithmic scale, will not follow the straight line proposed by Ham-rock and Dowson. This bridges the gap between the lubrication theory and the experimental results. 

One must note that probability alone can only detect alikeness in special cases, thus cause-effect cannot be directly determined - only estimated. If linear regression is to be used for comparison of X and Y, one must assess whether the five assumptions for use of regression apply. As a refresher, recall that the assumptions required for the application of linear regression for comparisons of X and Y include the following (1) the errors (variations) are independent of the magnitudes of X or Y, (2) the error distributions for both X and Y are known to be normally distributed (Gaussian), (3) the mean and variance of Y depend solely upon the absolute value of X, (4) the mean of each Y distribution is a straight-line function of X, and (5) the variance of X is zero, while the variance of Y is exactly the same for all values of X. 

The latter discussion confirms the results of the potential dependence of the current in that the activation barrier for the hydrogen evolution reaction is, at least on copper and silver, not affected by the electrode potential. This behavior is, on the other hand, connected with the observation of straight lines in a Tafel plot. It would be premature to come up with a comprehensive model that would explain this behavior more experimental work is necessary to substantiate and quantify the effects for a larger variety of systems and reactions. A few aspects, however, should be pointed out. 

It is a common practice to describe mass dependent isotope fractionation processes by a single linear curve on a three-isotope-plot (Matsuhisa et al. 1978). The resulting straight lines are referred to as terrestrial mass fractionation lines and deviations from it are used as indicating nonmass-dependent isotope effects. The three-isotope-plot is based on the approximation of a power law function to linear format. To describe how far a sample plots off the mass-dependent fractionation line, a new term has been introduced A 0, A Mg, A S, etc. Several definitions of A have been introduced in the literature, which have been discussed by Assonov and Bren-ninkmeijer (2005). The simplest definition is given by ... 

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