Results of numerical simulations

The steady state number of CTEs (ni) occupying the donor-acceptor interface and the number of dissociated pairs (52) as a function of the pumping intensity. The pumping intensity S is equal to the number of charge-transfer exci-tons produced at the interface during a CTE lifetime in the absence of dissociation processes. The results are from the numerical simulations of the CTE system described in the text. Reprinted with permission from Kiselev et al. (20). Copyright Elsevier (1998). 

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Baker et al. (1978a) developed a method which can predict blast pressures in the near field. This method is based on results of numerical simulations (see Section 6.3.1.1) and replaces Step 5 of the basic method (Figure 6.20). The refined method s procedure is shown in Figure 6.25. 

Figure 10. Results of numerical simulations to obtain the Strehl ratio at 2.2 pm over the field of view for a held of diameter 1 arcminute (left) and 1.5 arcminute (right) when using three natural guide stars.

Figure 3.2.1 shows flame kernels of the schlieren photograph taken by a high-speed camera. These photographs can be compared with the calculated temperature distribution in Figure 3.2.4. As can be seen, both of them bear a close resemblance. From this result, the authors firmly believe that the numerical simulation is a significant tool for grasping the mechanism of spark ignition. Of course, the experimental work should also be of importance to verify the results obtained by numerical simulations. In this work, the authors mainly introduce the results of numerical simulations that have been obtained xmtil then in their laboratory.

In Chapter 3.2, M. Kono and M. Tsue examine the mechanism of flame development from a flame kernel produced by an electric spark. They discuss results of numerical simulations performed in their laboratory in confrontation with experimental observations and confirm numerical simulation as a significant tool for elucidating the mechanism of spark ignition. 

U.S. EPA s rationale for the requirement of composite bottom liner option in the final doubleliner rule is based on the relative permeability of the two liner systems.13 The results of numerical simulations performed by U.S. EPA,10 which compared the performance of a composite bottom liner to that of a compacted soil bottom liner under various top liner leakage scenarios, showed that liquids passing through defects in the top FML enter the secondary LCRS above the bottom liners. The hydraulic conductivities of bottom liner systems greatly affect the amount of liquids detected, collected, and removed by the secondary LCRS. 

In Fig. 1.1, the parameter space for transient and stable cavitation bubbles is shown in R0 (ambient bubble radius) - pa (acoustic amplitude) plane [15]. The ambient bubble radius is defined as the bubble radius when an acoustic wave (ultrasound) is absent. The acoustic amplitude is defined as the pressure amplitude of an acoustic wave (ultrasound). Here, transient and stable cavitation bubbles are defined by their shape stability. This is the result of numerical simulations of bubble pulsations. Above the thickest line, bubbles are those of transient cavitation. Below the thickest line, bubbles are those of stable cavitation. Near the left upper side, there is a region for bubbles of high-energy stable cavitation designated by Stable (strong nf0) . In the brackets, the type of acoustic cavitation noise is indicated. The acoustic cavitation noise is defined as acoustic emissions from... 

In Fig. 1.9, the results of numerical simulations at 300 kHz and 3 bar in ultrasonic frequency and pressure amplitude, respectively are shown as a function of ambient radius [39]. In Fig. 1.9a, the temperature inside a bubble at the end of the bubble collapse is shown with the molar fraction of water vapor inside a bubble. 

In Section 4.1.4.1 results of numerical simulations were presented for the case when the basic system is operated as a fed-batch reactor. In this section, results of the numerical simulations are presented for the case when the basic system is operated in continuous reactors. The results were obtained for several reactor types. In terms of compartmental analysis (see Section 4.1.3.2) these types are determined by the number of compartments (n) considered to make up the reactor (see Figure 4.3). Three cases are presented here n = ... 

Results of Numerical Simulations for the Extended Basic System... 

In this section, results of numerical simulations are presented for the case when the extended basic system is operated in a continuous reactor. Here, the inhibitor enters the reactor as a component of the feed stream and affects the enzyme Ei (it is competitive with Si). In Figures 4.72 to 4.77 the effects of the system parameters on the concentration of B in a PFR with an external inhibitor are presented. The sets of the basic values used for the parameters involved are given in Table 4.12, set I. 

The results of numerical simulation of bluff-body stabilized premixed flames by the PPDF method are presented in section 12.2. This method was developed to conduct parametric studies before applying a more sophisticated and CPU time consuming PC JVS PDF method. The adequate boundary conditions (ABC) at open boundaries derived in section 12.3 play an essential role in the analysis. Section 12.4 deals with testing and validating the computational method and discussing the mechanism of flame stabilization and blow-off. 

In the work by Hales and co-authors [83] the prehistory distribution was observed experimentally using a semiconductor laser with optical feedback. Near the solitary threshold, the system was unstable after a period of nearly steady operation, the radiation intensity decreased then it recovered comparatively quickly, growing to regain its original value decreased again and the cycle repeated. In the experiment, the output intensity was digitized with 1 ns resolution. The pi, obtained in [83] from 1512events is shown in Fig. 9. The results were compared with the results of numerical simulation for the system (17). 

Fig. 5. The value of 5pxx/pf3o from Eqs. (1), (9) (solid line) shown as a function of [3/f3o together with the results of numerical simulations [15] presented for different values of /3o (triangles for /3o = 0.09, boxes for (3o = 0.06, circles for j3o = 0.03). Data for all numerical curves are shown for f3 < 0.3. Inset The crossover from quadratic to a linear dependence at /3/do 0.05. This crossover was not resolved in numerical simulations.

Which of these two profiles better represents the results of numerical simulations is a question that must be answered by higher resolution simulations (which seem to be pointing to an inner slope 7 that depends on the mass of the... 

The construction and operation of a continuous rotating annular chromatographic reactor are described. Experimental data for the dehydration of cyclohexane over a Pt/Al Oj catalyst are presented, and the performance of the apparatus as a combined reactor-separator is discussed. A mathematical model is developed, and the results of numerical simulation of reactor performance are presented. 

The results of numerical simulation lead to the following observations [18]. 

Figure 12. Population relaxation of linear OCS with energy E = 20,000 cm. The circles are the results of numerical simulation and the solid line represents the results of the theoretical kinetics model. The initial population is assumed to be in region II. The top panel is the population versus time in region 1, and the lower panel is the population versus time in region 11. [From M. 1. Davis, J. Chem. Phys. 83, 1016 (1985).]...

For instance, as for the recurrence phenomenon discovered in the FPU nonlinear lattices [25], whose explicit Hamiltonian will be presented in Section IV, there may exist a gap between the results of numerical simulations and the mathematical theorem, but a rigorous result certainly plays a significant role and theoretical arguments based on it can be deduced [26],... 

Now using as interpretative framework the above-described macroscopic model, we present the results of numerical simulations for slow Da < 1) and fast Da 3> 1) reaction. 

The final configuration of the tower (number and length of storeys, number of optical modules per storey, distance between the storeys) has to be optimized following the results of numerical simulations. However, the modular structure of the tower will permit the modification of these parameters to experimental... 

Fig. 3. Na spectrum of a sample of NaN02 showing the satellite-transition sidebands (left column) and the CT peak (right column). The top trace is experimental and the bottom trace is a result of numerical simulation. From both the experimental and simulated spectra the quadrupolar parameters were estimated as x = 1.1 0.03 MHz and 17 = 0.10 0.03. In the left column the CT line has been chopped off for a better view of the satellite-transition sidebands. (Reprinted with permission from Jung et al. Copyright (1999) Elsevier.)...

In order to obtain confidence in the results of numerical simulations, numerical experiments are performed. These involve solving similar problems, for which theoretical or numerical treatments or high-quality experimental data are available. Ultimately, however, simulations of the problem of interest must be verified by increasing the grid density until the solution does not change when additional grid points are added. For an unsteady solution, convergence on time-step size must also be verified. 

The dispersions (95) of the NFM (or equivalently Gaussian) and ML phase estimators found in experiments with light are shown in Fig. 13. The true phase was fixed at 0 = n/3. The number of detected quadruples 3, + /15, H(, used for the calculation of the dispersions varied from 1000 samples for the input mean number of photons N = 60 to more than 100,000 samples for N = 0.1. The error bars corresponding to these finite numbers of samples are the result of numerical simulation. The visibility during the experiments was better than 99.6%. 

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