Simulation report

The full ab-initio molecular dynamics simulation revealed the insertion of ethylene into the Zr-C bond, leading to propyl formation. The dynamics simulations showed that this first step in ethylene polymerisation is extremely fast. Figure 2 shows the distance between the carbon atoms in ethylene and between an ethylene carbon and the methyl carbon, from which it follows that the insertion time is only about 170 fs. This observation suggests the absence of any significant barrier of activation at this stage of the polymerisation process, and for this catalyst. The absence or very small value of a barrier for insertion of ethylene into a bis-cyclopentadienyl titanocene or zirconocene has also been confirmed by static quantum simulations reported independently... 

J. M. O Coimor, T. C. Ginn, and G. V. Pase, The Evaluation and Description of a Power Plant Condenser Tube Simulator, Report No. 8-0248-956, New York University Medical Center, New York, 1977. 

A simulation report shall be supplied based on the final configuration and controls that will adequately safeguard the system. 

The vertical reactor simulations reported In this paper typically Involved 14,000 unknowns and took 25 CPU seconds per Newton Iteration on a Cray-2. The tracing of a complete family of solutions for one parameter (e.g. susceptor temperature) cost approximately 25 CPU minutes. The latter number underscores the advantage of using supercomputers to understand the structure of the solution space for physical problems which often Involve many parameters. 

All the simulations reported in this chapter relate to a disk-shaped UME, characterized by RG = 10, which is typical of the probes used in SECM experiments and for most previous theoretical treatments. 

The theory has been verified by voltammetric measurements using different hole diameters and by electrochemical simulations [13,15]. The plot of the half-wave potential versus log[(4d/7rr)-I-1] yielded a straight line with a slope of 60 mV (Fig. 3), but the experimental points deviated from the theory for small radii. Equations (3) to (5) show that the half-wave potential depends on the hole radius, the film thickness, the interface position within the hole, and the diffusion coefficient values. When d is rather large or the diffusion coefficient in the organic phase is very low, steady-state diffusion in the organic phase cannot be achieved because of the linear diffusion field within the microcylinder [Fig. 2(c)]. Although no analytical solution has been reported for non-steady-state IT across the microhole, the simulations reported in Ref. 13 showed that the diffusion field is asymmetrical, and concentration profiles are similar to those in micropipettes (see... 

The use of fire safe PVC wire coating products in a plenum, did not contribute, in virtually any of the simulations reported here, to a significant increase in the fire hazard due to the fire itself. This conclusion is valid both for the cases where the fire starts in the room and for the cases where the fire starts in the plenum. 

Subsequent to the simulations reported in Dixon et al. (2003), some runs were carried out in which the virtual stacking was used, to provide a similar length of heated tube as in the runs without heat sinks, for comparison purposes. Some results for the third segment are given in Fig. 31, which shows a horizontal plane at the vertical midpoint of the WS and a vertical plane at the horizontal midpoint of the WS, under inlet tube conditions. The level of particle activity was rcut/rv — 0.95, which was closest to the egg-shell picture. 

The filtering process removes all SGS fluctuations so that U(x, t) is considerably smoother than U(x, t). As a general rule, the bandwidth should be at least twice the smallest resolved scale in an LES calculation. However, it is not unusual to see LES simulations reported where the bandwidth is nearly equal to the grid spacing. 

These results indicate that, compared to bulk water, interfacial water exhibits unique oscillations in density with distance from the surface and preferential dipolar orientations. Both simulations report density values which are unreasonable. Part of this problem arises from attempting to fix the water density based on the average cell volume and the number of water molecules an approach which... 

The majority of simulations reported in the literature use a fixed time step, bt [48,50] however, this treatment is computationally inefficient. When the particles are well separated the probability of encounter is small. Sophisticated methods have been developed, which allow more efficient computation by incorporating variable time steps [47,49,51], In these treatments, the time step, bt, is determined by the proximity of the particles. The time step is selected by one of two methods ... 

In order to test the small x assumptions in our calculations of condensed phase vibrational transition probabilities and rates, we have performed model calculations, - for a colinear system with one molecule moving between two solvent particles. The positions ofthe solvent particles are held fixed. The center of mass position of the solute molecule is the only slow variable coordinate in the system. This allows for the comparison of surface hopping calculations based on small X approximations with calculations without these approximations. In the model calculations discussed here, and in the calculations from many particle simulations reported in Table II, the approximations made for each trajectory are that the nonadiabatic coupling is constant that the slopes of the initial and final... 

Thus (L / Dma)1/2 is the appropriate factor used to convert an ambiguous material flux to a meaningful current term. In the simulations reported next, the dimensionless current parameter is given by Z(K). If diffusion-limited conditions are obtained, the relative concentration of electroactive species in the first element is zero. Thus the form most frequently used is... 

An introduction to the modeling methods can be found in refs. [22,231. The classical MD simulations reported here were performed with the modified AMBER software/241 in which the potential energy consists of harmonic deformations of bond and angles, dihedral energies, plus non-bonded interactions represented by a sum of pair wise additive coulombic and van der Waals contributions ... 

Delmau, L. H., Haverlock, T. J., Sloop, F. V., Jr., and Moyer, B. A. Caustic-Side Solvent Extraction, Prediction of Cesium Extraction from Actual Wastes and Actual Waste Simulants, Report ORNL TM-2003/011, Oak Ridge National laboratory, Oak Ridge, TN, February 2003. 

The coordinates of all atoms were recorded every 2 fs, and were used to construct the time-dependent CC Hamiltonian including the solvent-induced site energy shifts. A typical MD simulation time was 1 ns for each trajectory. Fig. 6 shows snapshots of P4 along a 1 ns MD run with various positions of the single chromophores to each other. Compared with our earlier simulations reported in Ref. [8] the change from a methanol to an ethanol solvent reduced somewhat the conformational flexibility of P4. 

The two-diaensional pseudohoaogenous reactor aodel (Eq.l) is the basis for the standardized coaputer progran FIBSAS (9), which was used for the evaluation and simulation reported here. 

Miiller-Plathe. F., "Generating Starting Structures for Polymer Simulations . Report C ECAM. April 13-16. 1993. Orsav, France. 

Fig. 4. Predicted jamming point for small disks, as a function of the surface coverage by large disks, h, compared with the results of Monte Carlo simulations reported in [25], for y = 2.0 and 8.0.

The simulated and experimental hydronium diffusivities both increase with increasing water contents. The simulated values are lower than the experimental values, presumably, due to the fact that the simulations report only the vehicular contribution to the proton diffusivity, whereas the experiment measures the total proton diffusivity. Experimentally, Nafion has higher proton diffusivity than SSC at low water contents and lower proton diffusivity than SSC at high water contents. The vehicular diffusion coefficients of the hydronium ion measured from simulation are higher for Nafion than in SSC PFSA at all water contents. Clearly a detailed understanding of the total proton diffusivity as a function of polymer architecture requires a model capable of structural diffusion. 

The simulations reported here consisted of pressurizing an initially evacuated adsorber with four mixtures of different compositions. These simulations are very much like the traditional flash calculations of chemical engineering thermodynamics applied to an adsorption system. The first set of runs, which we refer to as set G-NVT, is equivalent to solving Eq. (4) with = 0, qf = 0, = y "AF > 0, closure condition... 

The fuel cell modelling is either a simple one where power output and efficiency are linked by an empirical curve such as the one shown in Fig. 4.5, or a combination of relationships for each component in the fuel cell system (Fig. 4.2). For the simulations reported below, the two methods gave similar... 

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