Experimental and simulated

A systematic comparison of two sets of data requires a numerical evaluation of their likeliness. TOF-SARS and SARIS produce one- and two-dhnensional data plots, respectively. Comparison of sunulated and experimental data is accomplished by calculating a one- or two-dimensional reliability (R) factor [33], respectively, based on the R-factors developed for FEED [34]. The R-factor between tire experimental and simulated data is minimized by means of a multiparameter simplex method [33]. 

Quantitative analyses ean be aehieved by using the seattering and reeoiling imaging eode (SARIC) simulation and minimization of the R-faetor [33] (seetion B 1.23.4.4) between the experimental and simulated images as a... 

Figure Bl.23.16. Plots of the two-dimensional fJ-faetors as a fiinotion of the deviation d) of the first-seeond interlayer spaeing from the bulk value. The experimental and simulated images along the (ill) and (I I2) azimuths of figure Bl.23,15 were used in the eomparison.

Fig.4.53. Experimental and simulated PM (polarization modulated) IRRAS spectra of single monolayers of (A) PEG and (B) K(LK)7 at the air-water interface. The surface pressure was 20 mN m [4.281],...

Although the experimental and simulation time scales differ, the CFD simulation (Figure 8.29(a),(c),(e)) for the zeroth moment (Mq) indicates that once the particles reach the observable size, they will appear approximately in the experimentally observed regions (Figure 8.29 (b),(d),(f)). Predicted velocity vectors are superimposed on supersaturation profiles in Figure 8.30. 

A breakthrough curve with the nonretained compound was carried out to estimate the axial dispersion in the SMB column. A Peclet number of Pe = 000 was found by comparing experimental and simulated results from a model which includes axial dispersion in the interparticle fluid phase, accumulation in both interparticle and intraparticle fluid phases, and assuming that the average pore concentration is equal to the bulk fluid concentration this assumption is justified by the fact that the ratio of time constant for pore diffusion and space time in the column is of the order of 10. ... 

Several options are now available to the user in the main menu of the program. Probabilities can be calculated using an iterative method. Brown s modified version of the Levenberg-Marquardt algorithm (14-16). by substi futing values for P1-P4 in Equation 1 to calculate the peak integral which are then used in Equation 2 to simulate spectra until a good match between experimental and simulated data is achieved. 

Figure 4 shows zoomed regions of the experimental and simulated spectra. The methine region was simulated separately using the same optimized probability but with a linewidth of 8.0 Hz. At this point the user may wish to use the spectral manipulation options (overlay, subtraction, etc.), repeat the calculation, or do further simulations. 

A portion of the database for this polymer is shown in Figure 6. Literature reports that this polymer follows second-order Markov statistics ( 21 ). And, in fact, probabilities that produced simulated spectra comparable to the experimental spectrum could not be obtained with Bernoullian or first-order Markov models. Figure 7 shows the experimental and simulated spectra for these ten pentads using the second-order Markov probabilities Pil/i=0.60, Piv/i=0.35, Pvi/i=0.40, and Pvv/i=0.55 and a linewidth of 14.8 Hz. 

Diffusivities. Our results for the dlffuslvltles of both systems are summarized In Table I. The pore average transverse dlffuslvlty for the bulk fluid at equilibrium agrees very well with experimental and simulation values for the dlffuslvlty of Argon at the same density and temperature (18.12.5). 

As a result of the difference between the experimental and simulation results fiiture development will focus on inclusion in the model of a PAC product inhibition term with a thresh-hold concentration value of approx 180 mM. 

Figure 6. Simulated cyclic voltammogram for the oxidation of ascorbic acid without Inclusion of ec catalysis by the surface qulnone functionalities. Filled circles represent the simulated data and an experimental curve Is shown with a line for comparison. A scan rate of 100 mV s was assumed for experimental and simulated data.

Typical concentration-time profiles during the 1-hexyne hydrogenation over 0.4wt.% Pd/ACF catalyst are presented in Figure 7 showing the experimental and simulated curves (Langmuir-Hinshelwood mechanism). Pd/ ACF materials with the same particle size but different Pd loading (0.4, 0.6, 1.2wt.%) show identical initial activity of 0.140 0.004 kmolHj/kgp(j/s. This indicates the absence of diffusion limitations. Selectivity to 1-hexene is 97.1 +0.4% up to 80% conversion, and 95.9 + 0.4% at 90% conversion. 

As a large part of the experimental and simulation results given in this chaptei were obtained with or specifically calculated for the UHV multichamber deposi... 

All programs use input and output files (experimental and simulated spectra) consisting of 1024 amplitude values in a single column in ASCII format. If you have experimental files in a different format, then you must first modify them. A program is included to change from n to 1024 points. 

Cation distribution in zeolitic structures is one of the key aspects to the understanding of the adsorption mechanisms and selectivities. Many experimental and simulation methods have been used to try to localise the cations. The present work confronts the different analytical methods and gives general distribution trends in accordance with results from the literature. 

Basile, A.G. Chiappetta, S. Tosti, and V. Violante, Experimental and simulation of both Pd and Pd/Ag for a water gas shift membrane reactor, Sep. Purif. Technol., 25,549-571, 2001. 

Experimental and simulated burning cloud snapshot for Coyote trial 3 (1 m height, 103 s). (From Rigas, F. and Sklavounos, S., Chem. Eng. Sci., 61,1444, 2006. With permission from Elsevier.)... 

Fig. 12 C -detected C CSA patterns of the SHPrP109 i22 fibril sample. The upper and lower traces correspond to the experimental and simulated spectra, respectively. Simulations correspond to the evolution of a one-spin system under the ROCSA sequence. The only variables are the chemical shift anisotropy and the asymmetry parameter. A Gaussian window function of 400 Hz was applied to the simulated spectmm before the Fourier transformation. (Figure and caption adapted from [164], Copyright (2007), with permission from Elsevier)...

Fig. 6 (a) SQ and (b) DQ rotor-synchronized 2H MAS NMR spectra of sodium tetrathionate dihydrate-d4 (solid lines). The dashed line in (a) represents the exact numerical simulation of the SQ spectrum for random molecular motion with the rate constant k given in the figure, (c) The corresponding experimental and simulated static 2H quadrupolar-echo spectra, (d) Simulated SQ (solid line) and DQ (dashed line) linewidths as functions of k. (Reproduced with permission from [88])... 

Fig. 19. (A) Simulated bleaching of a hypothetical dye using Eq. (24) at different concentrations of Feni-TAML catalyst (in M) with the rate constants ki (in s-1) and ku (in M-1s-1). The numerical values are indicated on the graph. (B) Normalized experimental and simulated bleaching of Safranine O (4.3 x 10-5M) by H202 (0.012 M) catalyzed by la at pH 11 and 25°C. Experimental data are shown as a and. The simulations, shown as solid lines, were made as in (A). From Ref. (52).

Figure 1. Experimental and simulated normalized rates of polymerization for HEMA initiated by DMPA.

Comparison of the Experimental and Simulation Results. The preceding discussion has shown that both the experimental anthracene fluorescence profiles and the simulated anthracene concentration profiles decrease in a manner which closely follows an exponential decay. Therefore, the most convenient way to compare the simulation results to the experimental data is to define an effective overall photosensitization rate constant, kx or k2, as described above. Adoption of this lumped-parameter effective kinetic constant allows us to conveniently and efficiently compare the experimental data to the simulation results by contrasting the rate constant obtained from the steady-state fluorescence decay with the value obtained from the simulated decrease in the anthracene concentration. 

The experimental and simulation results presented here indicate that the system viscosity has an important effect on the overall rate of the photosensitization of diary liodonium salts by anthracene. These studies reveal that as the viscosity of the solvent is increased from 1 to 1000 cP, the overall rate of the photosensitization reaction decreases by an order of magnitude. This decrease in reaction rate is qualitatively explained using the Smoluchowski-Stokes-Einstein model for the rate constants of the bimolecular, diffusion-controlled elementary reactions in the numerical solution of the kinetic photophysical equations. A more quantitative fit between the experimental data and the simulation results was obtained by scaling the bimolecular rate constants by rj"07 rather than the rf1 as suggested by the Smoluchowski-Stokes-Einstein analysis. These simulation results provide a semi-empirical correlation which may be used to estimate the effective photosensitization rate constant for viscosities ranging from 1 to 1000 cP. 

In this section a short description of a comparison between experimental and simulation results for heat transfer is illustrated (Nijemeisland and Dixon, 2001). The experimental set-up used was a single packed tube with a heated wall as shown in Fig. 8. The packed bed consisted of 44 one-inch diameter spheres. The column (single tube) in which they were packed had an inner diameter of two inches. The column consisted of two main parts. The bottom part was an unheated 6-inch packed nylon tube as a calming section, and the top part of the column was an 18-inch steam-heated section maintained at a constant wall temperature. The 44-sphere packed bed fills the entire calming section and part of the heated section leaving room above the packing for the thermocouple cross (Fig. 8) for measuring gas temperatures above the bed. 

After this computer experiment, a great number of papers followed. Some of them attempted to simulate with the ab-initio data the properties of the ion in solution at room temperature [76,77], others [78] attempted to determine, via Monte Carlo simulations, the free energy, enthalpy and entropy for the reaction (24). The discrepancy between experimental and simulated data was rationalized in terms of the inadequacy of a two-body potential to represent correctly the n-body system. In addition, the radial distribution function for the Li+(H20)6 cluster showed [78] only one maximum, pointing out that the six water molecules are in the first hydration shell of the ion. The Monte Carlo simulation [77] for the system Li+(H20)2oo predicted five water molecules in the first hydration shell. A subsequent MD simulation [79] of a system composed of one Li+ ion and 343 water molecules at T=298 K, with periodic boundary conditions, yielded... 

There has been extensive effort in recent years to use coordinated experimental and simulation studies of polymer melts to better understand the connection between polymer motion and conformational dynamics. Although no experimental method directly measures conformational dynamics, several experimental probes of molecular motion are spatially local or are sensitive to local motions in polymers. Coordinated simulation and experimental studies of local motion in polymers have been conducted for dielectric relaxation,152-158 dynamic neutron scattering,157,159-164 and NMR spin-lattice relaxation.17,152,165-168 A particularly important outcome of these studies is the improved understanding of the relationship between the probed motions of the polymer chains and the underlying conformational dynamics that leads to observed motions. In the following discussion, we will focus on the... 

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