Observation and simulations

The velocity autocorrelation function has been measured by Fedele and Kim [515]. A charged Brownian particle of radius 0.11 0.01 jam 

The effect of density on the velocity autocorrelation function was studied by Verlet and Levesque [519]. In Fig. 52, two velocity autocorrelation functions are shown which correspond to two densities of the Lennard—Jones spheres used in the numerical study (see also Gubbins 1520]. Rdsibois and De Leener [490] have made the following observations on these results. 

Velocity autocorrelation function for spheres interacting through Leonard— Jones (12—6) potentials, after Verlet and Levesque [519]. The reduced variables are, 7 = t(mro/48e0) 2, n = nrf, and T = fe jT/e , in which m is the particle mass and e0 and are the potential energy and separation at the energy minimum, (a) n = 

In more complex molecular systems, increased coupling between the translational motion and both rotational and vibrational modes occurs. It is difficult to separate these effects completely. Nevertheless, the velocity autocorrelation functions of the Lennard—Jones spheres [519] (Fig. 52) and the numerical simulation of the carbon tetrachloride (Fig. 39) are quite similar [452a]. 

Some information about the molecular structure and relaxation of the solvent cage has been deduced from neutron scattering experiments [521]. The local solvent density can be observed and the equation of 

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Fig. 42.9. Observed and simulated histograms of the waiting time (days) in a municipal drinking water laboratory for 3 units and the total laboratory...

Output errors can be especially insidious since the natural tendency of most model users is to accept the observed data values as the "truth" upon which the adequacy and ability of the model will be judged. Model users should develop a healthy, informed scepticism of the observed data, especially when major, unexplained differences between observed and simulated values exist. The FAT workshop described earlier concluded that rt is clearly inappropriate to allocate all differences between predicted and observed values as model errors measurement errors in field data collection programs can be substantial and must be considered. 

Fig. 13 Monthly observed and simulated streamflows on station Q071 (Ega en Estella, ID 090) during the calibration (1962-1983) and validation period (1984-1990). Observed values are represented by black dots and a continuous black line, whereas simulated values are represented by blue squares with a dotted blue line. Vertical red lines separate the warming-up, calibration and validation periods, respectively...

Delaygue et al. (2000) have modeled the present day 0 distribution in the Atlantic and Pacific Ocean and its relationship with salinity (see Fig. 3.19). A good agreement is found between observed and simulated 5 0-values using an oceanic circulation model. As shown in Fig. 3.19 the Atlantic Ocean is enriched by more than 0.5%c relative to the Pacific Ocean, but both ocean basins show the same general patterns with high 0-values in the subtropics and lower values at high latitudes. 

Figure 11 Observed (—) and simulated (—) ESR spectra of permethyloligosilane radical cations at 77 K in y-irradiated freon matrices. The simulations were carried out under the assumption that an unpaired electron is delocalized over the entire Si-Si chain.

Fig. 11. Evaluation of kinetic parameters for the DOC model—CO and HC oxidation. Comparison of experimentally observed and simulated outlet concentrations in the course of the oxidation light-off for simple mixtures (a) CO, reaction Rl (b) Ci0H22, reactions R4 and R7 (cf. Table II). Lab experiments with isothermal monolith sample using synthetic gas mixtures (14% 02, 6% C02, 6% H20, N2 balance). Rate of temperature increase /min, SV = 30,000 h 1 (Kryl et al., 2005). Reprinted with permission from Ind. Eng. Chem. Res. 44, 9524, 2005 American Chemical Society.

Fig. 22. Experimentally observed and simulated light-off curves for fresh NSRC. (a) CO oxidation, influence of lean (excess of 02) and rich (excess of CO) conditions. Composition of inlet gas (mol. fractions)—lean mixture 0.25% CO, 7% 02 rich mixture 0.25% CO, 0.05% 02. (b) C3H6 oxidation, influence of inhibition by NO. Composition of inlet gas (mol. fractions) 200 ppm C3H6, 0.25% CO, 7% 02 and 0 or 150 ppm NO. (c) Water gas shift—production of hydrogen, composition of inlet gas (mol. fractions) 4.2% CO, 0.0% 02. All gas mixtures 10% H20, 10% C02 and balance N2. Temperature ramp 3K/min (Koci et al., 2007b).

Fig. 23. Experimentally observed and simulated oxygen storage and reduction fresh NSRC. Composition of inlet gas (mol. fractions)—lean mixture 7% 02, 0% H2 rich mixture 1.4% H2, 0% 02 both mixtures 10% H20, 10% C02, balance N2 (Koci et al., 2007b).

In addition to ab initio quantum simulations of the experimental femtosecond and picosecond pump-probe spectra, traditional continuous-wave (CW) spectra could also be simulated using the time-dependent approach to absorption spectroscopy [13]. The results show that femtosecond/picosecond versus CW spectroscopy is complementary in the present case, the radial and angular pseudorotation and the symmetric stretch are observed, and simulated with preferential sensitivity using CW picosecond, and femtosecond spectroscopy, respectively. 

Figure 1. Binding geometry of CHC1, adsorbed Figure 2. Observed and simulated heats of...

TROPOSPHERIC AEROSOL FORMATION PROCESSES, OBSERVATIONS AND SIMULATIONS... 

Comparison of the observed specimen intensity transform with that calculated for a model of the structure of the specimen provides a powerful test of the correctness of the model. In the present contribution we describe some preliminary attempts to simulate fiber diffraction patterns. When the observed and simulated intensity transforms are displayed visually they provide a useful guide to the progress of a structure refinement as well... 

FIGURE 49. /-resolved 29 Si NMR spectrum of a mixture of compounds shown in the inset and the observed and simulated traces along the FI axis. Reprinted with permission from Reference 121. Copyright 1993 American Chemical Society... 

Figure 15-19. Observed and simulated CARS spectra of (a) the S, DPA and (b) S2 DPA. Dots show observed data obtained (a) 40-60ps and (b) -5 to 5ps after photoexcitations, respectively. Solid lines show simulated spectra and denotes cyclohexane signals. (Reprinted with permission from Ref. [39].)...

The second, and more ambitious, objective is to find at least the general form of the potential function for a particular reaction, by successively adjusting V, until the observed and simulated results coincide. In essence, this is the same approach as that which is adopted to interpret elastic scattering measurements in terms of the central potential acting between two atoms (Section I.A.l), but the problem is now considerably more complex. 

Fig. 5.4. Spectral profiles of Da line [12]. (a) 8cm and (b) 0.5 cm away from the outer divertor plates. The viewing chords are shown in the upper figure. The thick and thin lines indicate the observed and simulated profiles, respectively. Compositions for the simulated 7r-component line are also shown. The kinetic energy of the D atoms corresponding to the wavelength shift is indicated above figure (a). The electron temperature and density were, respectively, 90 eV and 0.5 x 1019m 3 at the outer separatrix strike point. The toroidal magnetic field at the outer separatrix strike point was 4.15 T...

Because the Pt3 triangle of the triplatinum cluster is an isosceles triangle— that is, two kinds of Pt exist in the cluster core— the cluster shows a comphcated Pt NMR spectrum similar to that of the uns3un-metric Pt4 cluster (Section II,D). The spectrum consists of a summation of the spectra of five isotopomers (A, A2, B, AB, and A2B) and involves two main singlets with an intensity ratio of 3 1 and an AB pattern in addition to weak signals. Figure 33 shows the observed and simulated... 

Figures 3a and 3b show, respectively, observed and simulated spectra for the pseudorotating trimer at T = 4.2 K. Absorption linewidths for the "bar spectrum" were derived from Equation (10),...

Figure 9. Comparison of observed and simulated rate for four CO2 partial pressures at 25° C in the free drift experiments of Erga and Terjesen (15). The variation in rate as a function of Pco is closely predicted by the rate model of Plummer et at. (1).

There is no clear cage effect in the dissociation process inside the impact-heated cluster. This is contrary to experimental observations and simulations of photodissociation of molecules in clusters. This is not unexpected. For caging the dissociation products, the surrounding medium has to slow them down and to confine them so that they can recombine. No such strong cage effects are seen in our simulations. Once the halogen molecule has dissociated, the two atoms recede with hardly any noticeable hindrance. We consider that at least two factors, both unique to... 

Some general properties for stochastic errors have been established for impedance measurements through experimental observation and simulations. The results described here correspond to additive time-domain errors. The comparison between simulations and experimental results obtained via Fourier analysis supports the suggestion that the nature of experimental time-domain errors is likely to be additive rather than proportional ... 

S Nonequivalent homonuclear spins. If two homonuclear spins that are not equivalent are coupled, then when other interactions are present the MAS lineshape will depend on the MAS rate (Wu and Wasylishen 1993). In the case of N in cis-azobenzene dioxide large changes in the lineshape were observed and simulations showed that the lineshape was dependent on the relative orientation of two chemical shift tensors and their orientation with respect to the intemuclear vector. 

Figure 4.6. Observed and simulated spectra of the synthetic aluminosilicate mineral pink ultramarine, including fitted peaks, showing resolution of all possible Si(nAl) units. From Klinowski et al. (1987), by permission of MacMillan Magazines Ltd.

Figure 5.5. Observed and simulated MAS NMR spectra of Al2Si05 polymorphs. A. Andalusite (top) and simulation (bottom) according to the following parameters xq = 5.9...

Figure 6.1. A. O static echo and MAS spectra of albite glass. Note the singularities in the static spectrum which allow the contributions from the Si-O-Si and Si-O-Al groups to be separated. Asterisks denote spinning side bands. From Dirken et al. (1997) by permission of the copyright owner. B. Observed and simulated O MAS NMR spectra of a crystalline titanodiphenylsiloxane at three magnetic fields. Asterisks denote spinning side bands. C. Observed and simulated O 14.1 T static NMR spectrum of the same titanodiphenylsiloxane. From Gervais et al. (2000) by permission of the copyright owner.

Figure 6.2. Observed and simulated O MAS NMR spectra of an amorphous Ti02-Si02 material at three magnetic fields, showing resolution of the various structural sites. Asterisks denote spinning side bands. From Gervais et al. (2001) by permission of the copyright owner.

From van Eck and Smith (1998). C. Observed and simulated H- 0 CP echo NMR spectrum of Mg(OH)x(OCH3)2-x without using proton decoupling during acquisition. From van Eck and Smith (1998). All figures used by permission of the copyright owners. 

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