Simulated decay

Figure 10. Simulated decay curves from the kinetic analysis of the TCPO-H2O2-DPA chemiluminescence. Arbitrary units (a.u.) used on both axes. (Reproduced from Ref. 24. Copyright 1986 American Chemical Society.)...

Hughes, T. J. R., L. Mazzei, A. A. Oberai, and A. A. Wray (2001b). The multiscale formulation of large eddy simulation Decay of homogeneous isotropic turbulence. 

The quality of fits to simulated decays wasjudged by the usual criteria the reduced chi-square, x2 and visual inspection of the residual, r, and weighted residuals, rWj, plots. 56,57lXri is given by... 

Since the decay follows an exponential function, the similarity between the simulated decay curve slopes and the theoretical, infinite dilution ideal is even more apparent when the plots are compared in log space, as shown in Fig. 3.14B. 

Fig. 6.11. Temporally and spatially resolved CARS signal from a l- lm polystyrene sphere embedded in water at a Raman shift centered at 3054 cm 1 where aromatic C-H stretching vibrations reside. A Measured and simulated decay curves when focused on the bead and into bulk water. B RFID images and the lateral intensity profiles along the lines indicated by the arrows at time 0 and r 370 fs, demonstrating the complete removal of nonresonant background contributions from both the object and the solvent to the image contrast at r w 370fs (Adapted from [64])...

FIGURE 3.20. Simulated decay curves for devices stressed at 1 mA/cm2 and 150 /zA/cm2. Evolution of —0.3-eV trap states is represented with a conversion. 

Iy(t) can be calculated. Since we are interested in comparing simulated decays with observed ones, all the simulated decays presented were convoluted with a temporal response function characteristic of that of our experimental apparatus.42 In addition, all simulations pertain to the anthracene molecule. Thus, all rotational constants used, (B + C) and A - + C), were near 0.415... 

Other simulations To aid direct comparison with experimental data, simulations have been performed43 using the experimentally derived 4x4 and 3x3 Hamiltonian matrices [Eqs. (3.35) and (3.34)] that describe the coupling of S, anthracene levels at vib = 1420 and 1380 cm-1, respectively. Figure 39 shows simulated decays as a function of temperature for the 6-type bands of the vib = 1420 cm-1 system. The 6-type band was treated because good time-resolved data for it are relatively easy to obtain and because its decay is dominated by a single beat component at 1.0 GHz (- 1 phase). The rotational constants used in the calculation are given in the caption to Fig. 39. (Sets of... 

Figure 38. Simulated decays as a function of rotational temperature for the a-type and b-type decays of a coupled two-level system. The lowest rotational states of the two zero-order levels were taken to be spaced by 2.24 GHz (the b> state being at higher energy) and the coupling matrix element was taken to be 1 GHz. The rotational constants used, i(B + C) and A - (B + Q, were 0.4119 and 1.7396 GHz for the a> state and 0.4116 and 1.7385 GHz for the b> state. For other details see the text.

Figure 48. Comparison of experimental and simulated fluorescence polarization anisotropies for the S, + 789 cm 1 excitation of jet-cooled r-stilbene. The anisotropies include convolution effects associated with the finite excitation pulse width. The upper trace was calculated using the theoretical results of Ref. 49. The lower trace was obtained from experiment. The inset shows a simulated decay for this excitation band. 

Figure 9. Transient fluorescence decay profile of 4.76 X 10 7 mol/g DP A on Cab-O-Sil, with Gaussian model simulated decay profiles at 18 °C and various pressures of oxygen ( ex = 337 nm and Xob = 430 nm).

A new numerical solver RF-RTM for the reactive transport in fractured porous media was investigated. The simulator RF-RTM is a three-dimensional model, that can consider several nonequilibrium kinetic type models. This paper illustrates the accuracy with the finite element model for simulating decay reactions in fractured porous media. The presented results show the capability of RF-RTM to simulate transport of one or more species. The finite element model RF-RTM was verified for several situations when sorption occurs imder equilibrium conditions such as in Example 1 and 5, or in case of matrix diffusion such as in Example 4. Validation of the nonequilibrium model was shown in Example 3. The nonequilibrium model is verified only for homogenous media. Numerical modelling of the decay chain reactions in fractured porous media with a nonequilibrimn sorption model is treated for the first time. Especially the different penetrations of decay chain components in a fiacture-matrix system was illustrated through a series of simulations (see Example 6). Further research is needed to quantify the effect of nonlinear sorption in the migration of the contaminants with sequentially deca3ong processes in fractured porous media. 

Rate constants were obtained by numerically simulating decay traces, using the complete reaction mechanism and including all reactive and absorbing species. Thus, in most cases, the primary rate constant was obtained instead of the observed rate constant (which include secondary loss processes). 

A set of decays recorded at constant temperature and pressure and various concentrations of hydrocarbon, R, and scavenger, S, is evaluated as a whole by fitting to them simulated decays calculated according to the 2nd order differential equation ... 

Errors in the short time dynamics of a stochastic simulation can be addressed by comparison to MD simulations, which are expected to be more realistic. This comparison has been performed for ethylene glycol in water by Widmalm and Pastor [51], Xiang et aL compared GLE and BD simulations of nonane [16]. Each of these investigations indicates that the initial drop in the correlation function occurs more rapidly in the more sophisticated simulation. After this initial drop, correlation functions calculated from the various simulations decay at about the same rate. 

It is seen that, after 12 fs, the wave packet splits into two parts, moving to the left and to the right, respectively. The part on the left-hand side represents the molecules that isomerize to the ethylene complex. These parts are absorbed by a complex absorbing potential (CAP) that simulates decay of the complex, and they disappear for t > 80 fs. The part that moves along the right-hand side of the barrier runs into the local minimum of the P-agostic structure. It evolves further to the TS2 barrier, where it is reflected at 144 fs. Subsequently, the wave packet returns to the TSl barrier, where a part of it overcomes the barrier and is thus... 

A comparison of simulated decays for lattices with 100 and 500 sites under steady state initial conditions with experimental decay profiles of P2VN is shown in Fig. 11. It is evident that the quality features of iDp(f) are consistent with experimental data in the sense that (1) there is a strong L dependence, (2) decays are nonexponential, and (3) first order processes do not dominate the kinetics. Only when first order kinetics dominate is loF t) exponential with a decay time (Tdf) one-half the phosphorescence lifetime (Tp). Unfortunately a direct comparison of lifetime data is difficult since polymer phosphorescence usually arises from shallow traps, e.g. in PIVN Tdf = 0 msec whereas Tp = 1.9 sec (1). 

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