Curve-fitting parameters

We have found an alternative to the power law, Eq. (2.14), which describes experimental data as well as the latter. In the Eyring approach, however, the curve-fitting parameters have a fundamental significance in terms of a model for the flow process at the molecular level. 

A majority of the models incorporate what are essentially curve fitting parameters or functions. Some (C11, K12) are more pertinent to the pressed, briquetted, or tableted beds of particles rather than to granulated ensembles of particles, even though the distinction between the two kinds of pellets is necessarily somewhat arbitrary. 

Kurbatov plots (jj ) have often been employed to determine the net metal ion/proton exchange, x> from adsorption data. Although Kurbatov constants are convenient curve-fitting parameters, they are insensitive to the variation of x with pH and adsorption density and should be dispensed with for use in adsorbate partitioning calculations, particularly when high adsorption densities are expected ( 9 ). 

Table 5.1 Values of curve fitting parameters in new PSD function for typical three...

The six curve-fitting parameters in Equations (23) and (24) (Q, fii, ai, Cu, ixii, and crn) can be determined through use of a nonlinear regression method that minimizes a weighted residual sum of squares (RSS),... 

For TGDDM/DDS the values 1 = 2 and m + n = 2 enabled a good fit for DSC data for up to 70% conversion, after which diffusion control of the reaction rate became dominant. The difficulty with this type of approach is that for each different resin it is necessary to determine not only new pseudo-rate constants but also new values for the exponents (Lee et al, 1992, Mijovic and Wang, 1986). This supports the view that the exponents are more akin to curve-fitting parameters rather than being a true reflection of the underlying reaction mechanisms involved. 

Table B-5 Curve fit parameters for the enthalpies used for absorbers... 

On in Equation (8-19) acts as a curve-fitting parameter. Since it describes the width of the distribution, and, thus, the deviation from the mean value, it is also called the standard deviation. The deviation of an value from the mean... 

In these equations, m and n are two empirical curve-fitting parameters and are known as the fluid consistency coefficient and the flow behaviour index respectively. For a shear-thinning fluid, the index may have any value between 0 and 1. The smaller the value of n, the greater is the degree of shear-thinning. For a shear-thickening fluid, the index n will be greater than unity. When n = 1, equations (1.12) and (1.13) reduce to equation (1.1) which describes Newtonian fluid behaviour. 

Curve-fitting parameters are used in semiempirical and generalized equations to predict experimental results. The most common model was developed by Halpin and Tsai, and it has been modified for aligned discontinuous fiber composites to produce such results as the following for the longitudinal modulus ... 

An important extension of these results was provided by Nielsen (31), who incorporated the geometric constraint that the dispersed (or "included") phase could have a volume fraction no greater than max> this markedly improved the quantitative ability of the models to fit data. For this reason, we have chosen here to use the Nielsen formulation and add max curve-fitting parameter. A detailed description and rationalization for the model is given in the Appendix. 

Detailed spectra were processed with CasaXPS software (V2.3.12, Casa Software Ltd., UK). An iterated Shirley-Sherwood background subtraction was applied before peak fitting using a linear-least-squares algorithm. Minor charging was observed and corrected by referencing the aliphatic carbon to 285.0 eV. Details on the curve-fitting parameters, whieh have been measured on reference compounds, have been pubUshed elsewhere [10, 11],... 

The bubble point equation can be used to back calculate/estimate interfacial temperature. Using the effective pore diameter for a 325 x 2300 screen from Chapter 4, the methane surface tension curve fitting parameters, and the experimental bubble point data using the three different pressurant gases from the current chapter, one can estimate the interfacial temperature ... 

FIGURE 5.9 Points experiment (Dobson et al. 2012). Lines Equation 5.60 with r]Q given by Equation 5.74. The experimental conditions and oxygen diffusion coefficients are listed in Table 5.5. Common for all the curves, fitting parameters are collected in Table 5.4. 

Fig. 5 Inter metal lie layer thickness vs. time at 215 °C (419 °F) reflov, from Schaefer et al. (Ref 22) and Kang et al. (Ref 31). For Schaefer s data, in one case, the solder did not contain Cu at time zero, and in the other case, the solder is saturated with Cu at time zero. The plots are produced from the curve-fitted parameters in Ref 22.

Eguation f5.141 also gives the solution of finding the curve-fitted parameters p and P. ... 

To account for the first difference, one has to switch the sign of x in the exponential term for the second difference, a curve-fitted parameter called a is thrown in the model and for the third difference, because both the yyj value and its location are different, then two additional parameters are thrown in the model (i.e., parameters b and c). 

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