Curve crossing model experimental data

Fig. 22. Plot of relaxed permittivity versus time for a low molecular weight DGEBA resin (EPON 825) cured isothermally with DDS at temperatures between410 K and460 K. Crosses represent experimental data the solid curve represents the model described in the text. (Reprinted from Ref. 71 > with permission of the Society of Plastics Engineers)...

Fig. 2 Coexistence curve for CO2 in the temperature-density plane (a), vapor pressure at coexistence (b), and surface tension versus temperature (c). Dashed curves are the experimental data, while solid curves describe the prediction of the simple (truncated and shifted) LJ model (5), where the critical temperature and density are adjusted to coincide with experiment to fix the two parameters Sgs and as for Fig. 1. Stars and crosses denote the results of [131] for the parameter q Tc) that controls the strength of the quadrupolar interaction being chosen as q Tc) = 0.387 or q(Tc) = 0.47, respectively (see Sect. 2.2). Plus symbols and triangles are the result of atomistic models called EPM and EPM2 [146]. Small circles near the pluses are the results for flexible monomers [146], which give essentially the same results for the thermodynamic properties as the model for rigid molecules. Big circles and squares are simulation results [156] for two ab initio potentials [146,150]. Note that the interaction parameters of the EPM2 models have similarly been rescaled to fit the critical density and temperature of the experiment as done in Fig. 1, and that no prediction for the liquid-vapor surface tension from the atomistic models is available. From Mognetti et al. [131]...

Fig. 6. Normalized cross-peak volumes of five representative spin pairs from NOESY spectra of cyclo(Pro-Gly) at different temperatures, recorded with Tm = 300 ms. Circles, crossrelaxation rates calculated from eq. (27a) using only the linear term. Dashed lines were drawn according to eqs (la) and (2a) using uiol2n = 500 MHz (actual resonance frequency) and interproton distances, r, from the model (table 1). Solid lines connect the points of one spin pair at different temperatures. Experimental temperatures indicated at the top are superimposed on the correlation time axis according to eq. (5) logTc 1/T. Reciprocal temperature axis is scaled and shifted to produce the best visual overlap of the theoretical curves and experimental data points. Inset represents the indicated region around the crossrelaxation rate maximum in the extreme-narrowing regime, magnified 14 times.

Figure 13 Charge exchange cross sections due to and (upper left panel), He (lower left panel), He (lower right panel), and He° (upper right panel) impact on water vapor. The curves are fitted to experimental data [199,211-215] by various model functions and extrapolated where data are lacking.

The QRRK rate constant in Fig. 10.7 certainly fits the experimental data well. However, this is to be expected given the origin of the parameters in the model. Specifically, the high-pressure Arrhenius parameters were obtained from fits to the experimental data. The number of oscillators was taken as an adjustable parameter, as was the collision cross section used in ks. Thus the QRRK curve in Fig. 10.7 should match the experiment in the high-pressure limit, and two parameters were varied to enable a fit to the pressure fall-off behavior. 

Initial atom coordinates for the refinement were taken from single crystal data of related SAPO-34.5 For both as-synthesised materials it was essential to incorporate a template into the model otherwise the refinement was not stable. Thermal parameters were refined isotropically and no restrictions were used. Crystal data and refinement results of both as-synthesised materials are given in Table 1 and final Rietveld plots (crosses represent experimental points, solid line is calculated curve below is the difference vertical lines mark reflection positions) are presented on Figures 2 and 3. 

FIGURE2.12 The swelling capacities of PEO gels of different cross-link densities in chloroform as a function of temperature. Symbols are experimental data. The two dashed lines are the predictions of the model for the lowest (upper curve) and the highest (lower curve) cross-hnk densities. Solid lines are calculated by slightly varying the binary parameter as shown in Table 2.8. 

Figure 11. The neutron inelastic scattering cross-section of room temperature, poly crystalline NaNa for , = 225 cm and a scattering angle of 25°K. The dots represent the experimental data, and the numbers denote the vibrational energies of the more prominent transitions. The peak at approximately channel 90 arises from elastically scattered neutrons. The lower two curves correspond to the resolution-broadened, calculated cross-sections for the atomic and molecular models discussed in the text.

Fig. 2 Elastic differential cross section for scattering of electrons by cyclopropane panel) and helium atom (right panel). Collision energies are 2.6 eV (left panel) and 10 eV (right panel). Present calculations with exact exchange interaction are displayed by red curves while the local AAFEGE exchange model is shown by green curves. The results are compared to experimental data for cyclopropane [22] and helium [23], both displayed as circles in respective panels...

Figure 18. Total cross section for X-vacancy transfer in Si " + Ti collisions. The experimental data are from Hall et The curve labeled TSAE originates from calculations using the method by Lin and Tunnell. The model calculations are obtained using the SHM matrix elements (18) and the correction function (37). The analytic results are from Eq. (41) with corrections from Eq. (37).

Figure 4.11 The shapes of local current density for the two dew points of the humidifier (two compositions of the cathode feed). Points experimental data of (Berg et ah, 2004). Squares correspond to the dew point of 0 °C, and crosses—dew point of 43 °C. Solid lines—model. Parameters for the curves are p = 1, = 10 , Eq = 12, / = 0.8 r = 0.8 for dew point 0 °C...

FIGURE 4.6 (a) Effect of the Nafion weight fraction, 7 /, in CCL with uniform composition on the fuel cell voltage, Eceih evaluated at different values of the current density, yo. Experimental data taken from Passalacqua et al. (2001) (crosses) are shown for comparison. (b) Comparison of polarization curves, calculated in the model of composition-dependent performance, with experimental data of Uchida et al. (1995a,b). 

In the melt flow curve (viscosity versus shear rate), a Newtonian plateau at very low shear rate is usually considered as the ZSV. For polymers of very low molecular weight, this ZSV can be obtained directly from the shear rheology experiment (Dealy and Wissburn 1990). However, this is really difficult to obtain for high molecular weight polymers as well for LCPs. From the experimental data presented in Fig. 4.5, it was impossible to determine the ZSV, since there was no distinct plateau detected at a lower shear rate up to 0.01 s . Therefore, a modified Cross model (4.6) was used to determine the zero shear viscosity of the LCPs. Data from low and high shear rates were combined to fit into the Cross model predictions (Fig. 4.5). The model prediction showed good agreement with experimental data. 

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