Both the Monte Carlo and the molecular dynamics methods (see Section III-2B) have been used to obtain theoretical density-versus-depth profiles for a hypothetical liquid-vapor interface. Rice and co-workers (see Refs. 72 and 121) have found that density along the normal to the surface tends to be a [Pg.79]

Bunker D L 1964 Monte Carlo calculations. IV. Further studies of unimolecular dissociation J. Chem. [Pg.1038]

Bunker D L 1962 Monte Carlo calculation of triatomic dissociation rates. I. N2O and O3 J. Chem. Rhys. 37 393-403 [Pg.1038]

Figure 6.11 Schematic of Monte Carlo simulation 6.2.5 The parametric method |

Jorgenson W L and Ravimohan C 1985 Monte Carlo simulation of the differences in free energy of hydration J. Chem. Phys. 83 3050 [Pg.555]

Berne B J 1985 Molecular dynamics and Monte Carlo simulations of rare events Multiple Timescales ed J V Brackbill and B I Cohen (New York Academic Press) [Pg.896]

Bunker D L and Davidson B S 1972 Photolytic cage effect. Monte Carlo experiments J. Am. Chem. Soc. 94 1843 [Pg.869]

Alavi A 1996 Path integrals and ab initio molecular dynamics Monte Carlo and Molecular Dynamics of Condensed Matter Systems ed K Binder and G Ciccotti (Bologna SIF) [Pg.556]

Figure 6.10 Probability distributions for two variables input for Monte Carlo |

Valleau J P and Cohen L K 1980 Primitive model electrolytes. I. Grand canonical Monte Carlo computations J. Chem. Phys. 72 5932 [Pg.554]

Figure A2.3.12 The osmotic coefficient of a 1-1 RPM electrolyte compared with the Monte Carlo results of |

The alternative simulation approaches are based on molecular dynamics calculations. This is conceptually simpler that the Monte Carlo method the equations of motion are solved for a system of A molecules, and periodic boundary conditions are again imposed. This method pennits both the equilibrium and transport properties of the system to be evaluated, essentially by numerically solvmg the equations of motion [Pg.564]

Figure A2.3.13 The excess energy of 1-1, 2-1, 3-1 and 2-2 RPM electrolytes in water at 25°C. The frill and dashed curves are from the HNC and MS approximations, respectively. The Monte Carlo results of Card and Valleau [63] for the 1-3 and 2-2 charge types are also shown. |

Keywords deterministic methods, STOllP, GllP, reserves, ultimate recovery, net oil sands, area-depth and area-thickness methods, gross rock volume, expectation curves, probability of excedence curves, uncertainty, probability of success, annual reporting requirements, Monte-Carlo simulation, parametric method [Pg.153]

In Fig. III-7 we show a molecular dynamics computation for the density profile and pressure difference P - p across the interface of an argonlike system [66] (see also Refs. 67, 68 and citations therein). Similar calculations have been made of 5 in Eq. III-20 [69, 70]. Monte Carlo calculations of the density profile of the vapor-liquid interface of magnesium how stratification penetrating about three atomic diameters into the liquid [71]. Experimental measurement of the transverse structure of the vapor-liquid interface of mercury and gallium showed structures that were indistinguishable from that of the bulk fluids [72, 73]. [Pg.63]

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. [Pg.839]

Progress in the theoretical description of reaction rates in solution of course correlates strongly with that in other theoretical disciplines, in particular those which have profited most from the enonnous advances in computing power such as quantum chemistry and equilibrium as well as non-equilibrium statistical mechanics of liquid solutions where Monte Carlo and molecular dynamics simulations in many cases have taken on the traditional role of experunents, as they allow the detailed investigation of the influence of intra- and intemiolecular potential parameters on the microscopic dynamics not accessible to measurements in the laboratory. No attempt, however, will be made here to address these areas in more than a cursory way, and the interested reader is referred to the corresponding chapters of the encyclopedia. [Pg.832]

The solutions to this approximation are obtained numerically. Fast Fourier transfonn methods and a refomuilation of the FINC (and other integral equation approximations) in tenns of the screened Coulomb potential by Allnatt [M are especially useful in the numerical solution. Figure A2.3.12 compares the osmotic coefficient of a 1-1 RPM electrolyte at 25°C with each of the available Monte Carlo calculations of Card and Valleau [ ]. [Pg.495]

From the probability distributions for each of the variables on the right hand side, the values of K, p, o can be calculated. Assuming that the variables are independent, they can now be combined using the above rules to calculate K, p, o for ultimate recovery. Assuming the distribution for UR is Log-Normal, the value of UR for any confidence level can be calculated. This whole process can be performed on paper, or quickly written on a spreadsheet. The results are often within 10% of those generated by Monte Carlo simulation. [Pg.169]

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