Monte Carlo simulation results

FIG. 1 Total local density p(z) for bulk density p = 0.821 and e /k T = 4.25. The solid line is for PYl theory, the dashed line is for HNCl approximation and the points denote the Monte Carlo simulation results. (Reprinted from S. Sokolowski, D. Henderson, A. Trokhymchuk, O. Pizio. Density profiles of associating fluid near a hard wall PY/EMSA and HNC/EMSA singlet theory, Physica A, 220, 22-32. (1995), with permission from Elsevier Science.)... 

Thus we have found that the screening should be more efficient than in the Debye-Hiickel theory. The Debye length l//c is shorter by the factor 1 — jl due to the hard sphere holes cut in the Coulomb integrals which reduce the repulsion associated with counterion accumulation. A comparison with Monte Carlo simulation results [20] bears out this view of the ion size effect [19]. 

Bayesian methods are very amenable to applying diverse types of information. An example provided during the workshop involved Monte Carlo predictions of pesticide disappearance from a water body based on laboratory-derived rate constants. Field data for a particular time after application was used to adjust or update the priors of the Monte Carlo simulation results for that day. The field data and laboratory data were included in the analysis to produce a posterior estimate of predicted concentrations through time. Bayesian methods also allow subjective weight of evidence and objective evidence to be combined in producing an informed statement of risk. 

Fig. 15 Monte Carlo simulation results for emulsion polymerization that involves polymer transfer reactions, under the conditions Cm=5xl0" =5x10" and Cfp=5xl0" without radical desorption...

The effects of the adsorption mechanism, the pore geometry and the energetic heterogeneity of the pore walls on the determination of the micropore size distribution of activated carbons from adsorption isotherms are evaluated by means of Monte Carlo simulation. Results are applied to the characterization of two series of activated carbons with different burn-off degrees. 

In Figure 5.27 a curve calculated from Equation 5.216 is compared with the predictions of other studies. The dotted line is calculated by means of the Henderson theory. The theoretical curve calculated by Kjellander and Sarmatf for ( ) = 0.357 and h>2 by using the anisotropic Percus-Yevick approximation is shown by the dashed line the crosses represent grand canonical Monte Carlo simulation results due to Karlstrom. We proceed now with separate descriptions of solvation, depletion, and colloid structural forces. 

Thus, if we know the dielectric constant of the fluid, then Eq. (3.3.15) could be used to improve the results obtained from the SSOZ-MSA approximation, for example. This has been done for dipolar hard dumbbell fluid by Lee and Rasaiah using Monte Carlo simulation results for the dielectric constant (Morriss ), and by Rossky, Pettitt and Stell. However, this approach does not seem to have any value as a predictive tool. Moreover, in the case of some interaction site models, notably hard linear triatomics, the site-site direct correlation function is not a short-range function but in fact increases with increasing r. This notwithstanding, the Cummings-Stell analysis remains an important contribution to our understanding of the SSOZ equation. 

Figure 2 Comparison of the effective diffusivities Dee s) derived from the models and from Monte Carlo simulation results (o). Simulation conditions c = 3.2510 , K — 20, D = 1. Solid lines represent (a) the fractal layer model, obtained by solving eqs. (8)-(ll) in the Laplace domain (b) the two-timescale model, eq. (6). Fitting parameters (a) Dfo = 0.95, Lf = 7 (b) = 0.013, Df = 0.9.

In this paper, we present an exact calculation of the statistical mechanics of a lattice model of hydrocarbon adsorption in the quasi one-dimensional pores of zeolites, based on a matrix method that utilises the Constant Pressure partition. The model is tested on benzene adsorption, where it reproduces experimentally observed steps in isotherms. The model has been extended also to linear alkanes where it reproduces very accurately experimental adsorption isotherms as well as Monte-Carlo simulation results of ethane. 

Dynamic Properties of Polymer Melts above the Glass Transition Monte Carlo Simulation Results... 

Monte Carlo simulation results for the non-equilibrium and equilibrium d3oiamics of a glassy polymer melt are presented. When the melt is rapidly quenched into the supercooled state, it freezes on the time scale of the simulation in a non-equilibrium structure that ages physically in a fashion similar to experiments during subsequent relaxation. At moderately low temperatures these non-equilibrium effects can be removed completely. The structural relaxation of the resulting equilibrated supercooled melt is strongly stretched on all (polymeric) length scales and provides evidence for the time-temperature superposition property. 

Pedersen and coworkers [74, 80, 81, 86] have modified Eq. 78 based on Monte Carlo simulation results from chains exhibiting excluded volume effects. Written in terms of a micelle constituted of a A-B block copolymer, this can be written independently of morphology (spherical, ellipsoidal, or cylindrical) ... 

Figure 6. Monte Carlo simulation results of annual oil spill.

Fig. 4.9 Dynamic Monte Carlo simulation results of single-chain collapse transition, (a) The curves of mean square radius of gyration /(N—l) vs. B/kT for varying chain lengths N as labeled. (0.032, 0.26) is the theta point, (b) Radial distributions of local-average concentrations < q > of chain units in 512-mer at various temperatures (Hu 1998) (Reprinted with permission)...

FIGURE 21.4. Histogram of Monte Carlo simulation results. 

We have presented continuum NPT Monte Carlo simulation results for alkane and polymer systems composed of chains up to 78 units long, using a realistic... 

This paper is organized as follows. First, section 2 provides an overview of the steps of the TOPAZ safety risk assessment cycle and for which step Monte Carlo simulation is of direct use. Next, section 3 provides an overview of how to develop a Monte Carlo simulation model of a given operation. In order to keep the explanation concrete, a particular example is introduced first. Subsequently section 4 provides an overview of key issues that have to be taken into account when using a Monte Carlo simulation supported safety risk assessment. Section S presents Monte Carlo simulation results for the particular example identified in section 3. Finally, conclusions are drawn in section 6. 

In Fig. 4.10 we compare the free volume fraction a calculated from (4.6), in the good solvency limit with Ss/R in (4.7) from (4.33), with Monte Carlo simulation results of Fortini et al. [51] for q = 1.05 along the binodal gas-liquid curve. Except for some deviation at large colloid volume fractions the agreement is excellent. 

We compare gas-liquid coexistence curves from GFVT in the good solvent limit with Monte Carlo simulation results of Bolhuis et al. [52] in Fig. 4.11 for q = 0.67 and 1.05. It is clear GFVT is capable of predicting the location of flie phase boundaries reasonably well. 

Fig. 5.3 Phase diagram of big + small hard spheres in the < 2 representation for q = a-ijax = 0.1. Data points are redrawn Monte Carlo simulation results [10] guided by a dotted curve. The curves are the FVT predictions...

The results for the coexisting concentrations, which now depend on L/D, are given in Fig. 6.2 (see also [21]). In this figure we also present Monte Carlo simulation results [4] as well as the Onsager limit result L/D oo). Clearly, the... 

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