Standard Model parameter values

This turbulence model is similar to the standard k-s model, but with altered model parameter values and the effect of swirl on turbulence is included in the RNG mode intending to enhance the accuracy of swirling flow simulations. 

TABLE 9.2 Summary of Model Parameter Values for the Standard Case. ... 

Here, we apply our model to answer questions that are critical for understanding EET in S. oneidensis. Furthermore, by varying the model parameter values from the standard-case parameter values listed in Table 9.2, we compare and contrast features of another model EAB, G. sulfurreducens, with those of S. oneidensis. We chose the standard case from commonly observed experimental or theoretically accepted parameter values, as described in Section 9.4. Throughout this chapter, white-filled circles in figures represent the results at the given locations for the standard case, provided in Table 9.2. 

Figure 5 A sensitivity analysis for the Barber-Cushinan model for the uptake of P by maize in Raub soil. The. sensitivity was analysed by halving and doubling each parameter value in turn while keeping all other parameters at their standard values. (From Ref. 103.)...

The only drawback in using this method is that any numerical errors introduced in the estimation of the time derivatives of the state variables have a direct effect on the estimated parameter values. Furthermore, by this approach we can not readily calculate confidence intervals for the unknown parameters. This method is the standard procedure used by the General Algebraic Modeling System (GAMS) for the estimation of parameters in ODE models when all state variables are observed. 

The ability of the sequential design to discriminate among the rival models should be examined as a function of the standard error in the measurements (oe). For this reason, artificial data were generated by integrating the governing ODEs for Model 1 with "true" parameter values kt=0.31, k2=0.18, k3=0.55 and k4=0.03 and by adding noise to the noise free data. The error terms are taken from independent normal distributions with zero mean and constant standard deviation (oE). 

Figures 18.13, through 18.17 show the experimental data and the calculations based on model I for the low temperature oxidation at 50, 75, 100, 125 and 150TZ of a North Bodo oil sands bitumen with a 5% oxygen gas. As seen, there is generally good agreement between the experimental data and the results obtained by the simple three pseudo-component model at all temperatures except the run at 125 TT. The only drawback of the model is that it cannot calculate the HO/LO split. The estimated parameter values for model I and N are shown in Table 18.2. The observed large standard deviations in the parameter estimates is rather typical for Arrhenius type expressions.

Model Parameter Parameter Values Standard Deviation (%)... 

In the work described earlier, the applicability of the Weibull model was further tested by assessing the precision of estimation [expressed by the CV defined as the standard error of estimates divided by the estimated value] and the relative accuracy of estimation of the model parameters (based on the difference of the estimates from the actual value, divided by the actual value). Regarding the precision of estimates, for data with SD = 2 the maximum CV value for Wo, b, and c was 13%, 52%, and 16%, respectively, whereas the corresponding numbers for data with SD = 4 were 33%, 151%, and 34%, respectively. As expected, the precision of the estimates decreases as the SD of the data increases, with the poorest precision for the b estimates and the best for the Wo estimates. Additionally, the maximum CV values were associated with low c values (c = 0.5). 

Discrete values of the HKF model parameters for various organic aqueous species are listed in table 8.22. Table 8.23 lists standard partial molal thermodynamic properties and HKF model parameters for aqueous metal complexes of monovalent organic acid ligands, after Shock and Koretsky (1995). 

Jacquez and Perry [37] developed the program ID ENT to investigate the identification of model parameters. In most cases, problems of identification can be detected by inspection of the standard errors of the model parameters (the standard error of a model parameter is a measure of the credibility of the parameter value, which is provided by the most fitting programs). A high standard error (for example, more than 50% of the parameter value) indicates that the parameter value cannot be assessed from the data, most likely due to an identification problem. In that case, the parameter value itself is meaningless, and thus the parameter set should be discarded (see Section 13.2.8.5). 

The conversion between the two sets of equations is shown in Table 4-1. The PSpice model parameter names are close to the standard names used to represent MOSFET operation in many textbooks. One difference is that the PSpice model parameter Kp is twice the value of K. Thus, in our model we should set KP= 40 pA/V2. All other model parameters will be the same. 

Table 4.1. Ore model parameters for both standard and modified Ore approaches (Fmin, / max, F °d and F °d), and the experimental fractions F for the noble gases and a variety of molecules. Note that when Eex < EPS, the minimum predictions have been set to zero see equation (4.38). See Charlton (1985a) for the origin of the measurements. In general, the fractions for the molecular gases have been found to be both density and temperature dependent. The value quoted here is for low densities and is thus expected to be the Ore contribution to the overall positronium fraction in these gases at higher densities...

The selection of the appropriate population pharmacokinetic base model was guided by the following criteria a significant reduction in the objective function value (p < 0.01,6.64 points) as assessed by the Likelihood Ratio Test the Akaike Information Criterion (AIC) a decrease in the residual error a decrease in the standard error of the model parameters randomness of the distribution of individual weighted residuals versus the predicted concentration and versus time post start of cetuximab administration randomness of the distribution of the observed concentration versus individual predicted concentration values around the line of identity in a respective plot. 

Determination of pure component parameters. In order to use the EOS to model real substances one needs to obtain pure component below its critical point, a technique suggested by Joffe et al. (18) was used. This involves the matching of chemical potentials of each component in the liquid and the vapour phases at the vapour pressure of the substance. Also, the actual and predicted saturated liquid densities were matched. The set of equations so obtained was solved by the use of a standard Newton s method to yield the pure component parameters. Values of exl and v for ethanol and water at several temperatures are shown in Table 1. In this calculation vH and z were set to 9.75 x 10"6 m3 mole"1 and 10, respectively (1 ). The capability of the lattice EOS to fit pure component VLE was found to be quite insensitive to variations in z (6[Pg.90]

The evolution Eq. 13 of the order parameter has a similar form to the time-dependent Landau equation [17], which is fundamental in nonequihbrium phase transitions. The asymptotic value of the order parameter 4>i,oo is determined as the zero of the velocity 4>i- The main difference from the standard model of phase transitions lies in the time dependence in the coefficients Ait) and B(t) induced by that of the achiral concentration ait) and the total chiral concentration qft). Because the concentrations a and q are nonnegative, A(t) cannot exceed Bit) Ait) < Bit). 

If supersymmetry would be an explicit symmetry of nature, superpartners would have the same mass as their corresponding Standard Model particle. However, no Standard Model particle has a superpartner of the same mass. It is therefore assumed that supersymmetry, much as the weak symmetry, is broken. Superpartners can then be much heavier than their normal counterparts, explaining why they have not been detected so far. However, the mechanism of supersymmetry breaking is not completely understood, and in practice it is implemented in the model by a set of supersymmetry-breaking parameters that govern the values of the superpartners masses (the superpartners couplings are fixed by supersymmetry). 

Figure 12.6a shows the temporal variation of the proximal tubular pressure Pt as obtained from the single-nephron model for a = 12 and T = 16 s. All other parameters attain their standard values as listed in Table 12.1. Under these conditions the system operates slightly beyond the Hopf bifurcation point, and the depicted pressure variations represent the steady-state limit cycle oscillations reached after the initial transient has died out For physiologically realistic parameter values the model reproduces the observed self-sustained oscillations with characteristic periods of 30-40 s. The amplitudes in the pressure variation also correspond to experimentally observed values. Figure 12.6b shows the phase plot Here, we have displayed the normalized arteriolar radius r against the proximal intratubular pressure. Again, the amplitude in the variations of r appears reasonable. The motion... 

The solid line is given by the initial slope aN and the dashed-dot line is the Vmax, both predicted with the simplified model (see [27]) for the standard parameter values (see Table 14.2) and an average efflux e = 0.2. (d) Vmax as a function of the substrate length. It increases for substrate shorter than 10 aa and decreases for longer substrates. The initial substrate concentration is Ni(0) = 6000. 

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