Simulation studies, sampling distribution

Computationally, polydispersity is best handled within a grand canonical (GCE) or semi-grand canonical ensemble in which the density distribution p(a) is controlled by a conjugate chemical potential distribution p(cr). Use of such an ensemble is attractive because it allows p(a) to fluctuate as a whole, thereby sampling many different realizations of the disorder and hence reducing finite-size effects. Within such a framework, the case of variable polydispersity is considerably easier to tackle than fixed polydispersity The phase behavior is simply obtained as a function of the width of the prescribed p(cr) distribution. Perhaps for this reason, most simulation studies of phase behavior in polydisperse systems have focused on the variable case [90, 101-103]. 

Ounis et al. ° performed a series of Lagrangian simulation studies for dispersion and deposition of particles emitted from a point source in the viscons snblayer of a turbulent near-wall flow. Figures 23 to 25 show time variation of particle trajectory statistics for different diameters, for the case that the point source is at a distance of 0.5 wall units away from the wall. In these simulations, it is assumed that when particles touch the wan they will stick to it. At every time step, the particle ordinates are statistically analyzed, and the mean, standard deviation, and the sample minimum and maximum were evaluated. The points at which the minimum curve touches the wall identify Ihe locations of a deposited particle. Figure 23 shows that O.OS-pm particles have a narrow distribution, and in the duration of 40 wall units, none of... 

A two-stage Monte-Carlo simulation study was performed for generating Sp(dM) values. In the first part, the Cp values were estimated following the procedure of Birgoren [19] for specified values of a and p, a sample of n values are generated from a Weibull distribution with parameters m = 1 and (To= 1 then min dp / o-p) is calculated for the three methods and... 

Recently, many experiments have been performed on the structure and dynamics of liquids in porous glasses [175-190]. These studies are difficult to interpret because of the inhomogeneity of the sample. Simulations of water in a cylindrical cavity inside a block of hydrophilic Vycor glass have recently been performed [24,191,192] to facilitate the analysis of experimental results. Water molecules interact with Vycor atoms, using an empirical potential model which consists of (12-6) Lennard-Jones and Coulomb interactions. All atoms in the Vycor block are immobile. For details see Ref. 191. We have simulated samples at room temperature, which are filled with water to between 19 and 96 percent of the maximum possible amount. Because of the hydrophilicity of the glass, water molecules cover the surface already in nearly empty pores no molecules are found in the pore center in this case, although the density distribution is rather wide. When the amount of water increases, the center of the pore fills. Only in the case of 96 percent filling, a continuous aqueous phase without a cavity in the center of the pore is observed. 

---