Hard sphere Monte Carlo simulation

A Hard Sphere Monte Carlo (HSMC) simulation is run for P atoms at densities appropriate to the doped and undoped glasses, with the constraint that each P atom is two-fold coordinated. This creates a PP PP chain structure that is 99% perfect to produce a perfect... 

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]. 

Sese, L. M., Path integral and effective potential Monte Carlo simulations of liquid nitrogen, hard-sphere and Lennard-Jones potentials, Mol. Phys. 1991, 74, 177-189... 

The density functional theories are also accurate for the density profiles of fused-sphere chains. Figures 4(a) and 4(b) compare the theory of Yethiraj [39] (which is a DFT with the Curtin-Ashcroft weighting function) to Monte Carlo simulations of fused-hard-sphere chains at hard walls for N = 4 and 16, respectively. For both chain lengths the theory is in quantitative agreement with the simulation results and appears to get more accurate as the chain length is increased. Similarly good results were also found by SCMC who compared... 

Figure 10. The compressibility factor for a charg and dipolar hard sphere mixture pr icted by perturbation thmiy is compared with the results of Monte Carlo simulation. Tl e elementaiy electronic charge is denoted e.

The main question is whether the hydrated ions behave as hard spheres while this seems plausible for ions much larger than the water molecules, it is probably not entirely applicable to small ions, whose hydration shells continuously change. Marcelj a calculated recently the double layer interaction8 using the anisotropic hypemetted chain method and potentials of mean force between pairs of ions in water, provided by Monte Carlo simulations. This... 

Figure 7.8 For the unit-diameter hard sphere fluid at p = 0.277, comparison of the Poisson distribution (solid curve) with primitive quasi-chemical distribution Eq. (7.27) (dashed curve). This is the dense gas thermodynamic suggested in Fig. 4.2, p. 74, and the dots are the results of Monte Carlo simulation (Gomez et al, 1999). The primitive quasi-chemical default model depletes the probability of high- and low- constellations and enhances the probability near the mode.

Figure 4. The bridging between Bose-Einstein condensation in the low-density, weak interaction region and in the high-density, strong interaction region [124, 125]. Data for Tc/r , where is the critical temperature and T is the critical temperature in an ideal Bose-Einstein gas, were calculated from quantum path integral Monte-Carlo simulations for a hard-sphere many-boson model [124, 125], The effective dimensionless interaction parameter is pa, where p is the density and CT is the hard-core sphere diameter. The two open circles (o) represent experimental data for bulk liquid He.

Figure 2.3. Computer graphics visualizations of states from a 108-particIe Monte Carlo simulation of the hard-sphere system (a) coexisting fluid state (b) coexisting solid state.

Dembo et al. [1988] developed a model based on the ideas of Evans [1985] and Bell [1978]. In this model, a piece of membrane is attached to the wall, and a pulling force is exerted on one end while the other end is held fixed. The cell membrane is modeled as a thin inextensible membrane. The model of Dembo et al. [1988] was subsequentlyextended via a probabilistic approach for the formation of bonds by Coezens-Roberts et al. [1990]. Other authors used the probabilistic approach and Monte Carlo simulation to study the adhesion process as reviewed by Zhu [ 2000]. Dembo s model has also been extended to account for the distribution of microvilli on the surface of the cell and to simulate the rolling and the adhesion of a cell on a surface under shear flow. Hammer and Apte [1992] modeled the cell as a microvilli-coated hard sphere covered with adhesive springs. The binding and breakage of bonds and the distribution of the receptors on the tips of the microvilli are computed using a probabilistic approach. 

Yoon and Ohr derived an expression for the compressibility of hard-sphere fluids in terms of the radial free space distribution function, (r), which is the probability of acceptance of a (radial) displacement, r, in a Monte Carlo simulation.Alemany et al. performed MD simulations of liquid 50 and calculated its diffusion coefficient and shear viscosity. They simulated a system of 1372 Ceo molecules interacting through Girifalco s potential. 

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