Simulator, Figure

From the binding energies calculated for the different cluster compositions, we determined abundance mass spectra for heated CggLi clusters from a simple Monte Carlo simulation. Figure 11 shows the simulated mass spectra resulting from these calculations, including the Li and Cgo isotope distributions. The peaks at A = 12 and at x = 6 + n (where n is the cluster charge) observed in the experiment (Fig. 9) are well reproduced. For more details, see ref. [12]. 

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. 

Dynamic information such as reorientational correlation functions and diffusion constants for the ions can readily be obtained. Collective properties such as viscosity can also be calculated in principle, but it is difficult to obtain accurate results in reasonable simulation times. Single-particle properties such as diffusion constants can be determined more easily from simulations. Figure 4.3-4 shows the mean square displacements of cations and anions in dimethylimidazolium chloride at 400 K. The rapid rise at short times is due to rattling of the ions in the cages of neighbors. The amplitude of this motion is about 0.5 A. After a few picoseconds the mean square displacement in all three directions is a linear function of time and the slope of this portion of the curve gives the diffusion constant. These diffusion constants are about a factor of 10 lower than those in normal molecular liquids at room temperature. 

This power law decay is captured in MPC dynamics simulations of the reacting system. The rate coefficient kf t) can be computed from — dnA t)/dt)/nA t), which can be determined directly from the simulation. Figure 18 plots kf t) versus t and confirms the power law decay arising from diffusive dynamics [17]. Comparison with the theoretical estimate shows that the diffusion equation approach with the radiation boundary condition provides a good approximation to the simulation results. 

The 3D density contour maps for the Na+ ion distribution determined over the last 250 ns of simulation (Figure 14-8) show that the overall highest probability Na+ occupation sites were concentrated in the active site for both the reactant and activated precursor. This suggests that the HHR folds to form a strong local electronegative pocket that is able to attract and bind Mg2+ if present in solution, or recruit a high local concentrations of Na+ ions in the absence of Mg2+. 

The temperature experiment can be expected to show only the effects of the temperature dependence of the equilibrium constants in the carbonate system. Other possible consequences of changing temperature are not included in the simulation. Figure 6-7 shows little response by the calcium... 

Fig. 25.4. Oxygen and carbon stable isotopic compositions of calcite ( ) and dolomite ( ) cements from Lyons sandstone (Levandowski et al., 1973), and isotopic trends (bold arrows) predicted for dolomite cements produced by the mixing reaction shown in Figure 25.3, assuming differing CO2 fugacities (25, 50, and 100) for the Fountain brine. Fine arrows, for comparison, show isotopic trends predicted in calculations which assume (improperly) that fluid and minerals maintain isotopic equilibrium over the course of the simulation. Figure after Lee and Bethke (1996).

Figure 4 (Plate 3). Typical snapshot of a start configuration in MD simulation. Figure 1 (Plate 1) resulted from the equilibration of this initial guess. From [102]. Reproduced by permission of the American Institute of Physics. Copyright (2003)...

The interpretation of the Langmuir experiments with the carbosilane den-drimers is supported by the results of molecular dynamics simulation. Figure 14 shows snapshots of a dumbbell-like conformation of carbosilane dendximers observed during lateral compression of a dendrimer monolayer on a polar sub-... 

Using the data of Table 4.5, the other two configurations are also simulated. Figure 4.22 depicts the comparison between the J-V curves, and Figure 4.23 the relative power densities. 

The Duffing Equation 14.4 seems to be a model in order to describe the nonlinear behavior of the resonant system. A better agreement between experimentally recorded and calculated phase portraits can be obtained by consideration of nonlinear effects of higher order in the dielectric properties and of nonlinear losses (e.g. [6], [7]). In order to construct the effective thermodynamic potential near the structural phase transition the phase portraits were recorded at different temperatures above and below the phase transition. The coefficients in the Duffing Equation 14.4 were derived by the fitted computer simulation. Figure 14.6 shows the effective thermodynamic potential of a TGS-crystal with the transition from a one minimum potential to a double-well potential. So the tools of the nonlinear dynamics provide a new approach to the study of structural phase transitions. 

Click Run button to initiate the dynamic simulation (Figure 14.6). 

We show results for several test cases. In one, R0 = 0.1 cm and tq — 1 x 10-1 sec. The simple model predicts that 3.3 x 101 ergs is the minimum ignition energy and these results agree well with the simulation (Figures 6 and 7). Both models predict... 

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