Showing papers on "Dynamic Monte Carlo method published in 1974"
TL;DR: In this paper, the free energy of a Lennard-Jones fluid in the liquid-vapour coexistence region was estimated by relating it to that of the inverse-twelve (soft sphere) fluid, which itself shows no condensation.
1,179 citations
TL;DR: The theoretical skill of Monte Carlo approximations to the stochastic dynamic forecasting technique proposed by Epstein is examined by means of an extension of earlier atmospheric predictability studies that used the test-field model of two-dimensional turbulence as mentioned in this paper.
Abstract: The theoretical skill of Monte Carlo approximations to the stochastic dynamic forecasting technique proposed by Epstein is examined by means of an extension of earlier atmospheric predictability studies that used the test-field model of two-dimensional turbulence. The fundamental statistical hydrodynamical concept of an ensemble of phase paths evolving in a dynamical phase space is reviewed and used to define the statistical properties of a finite Monte Carlo sample. The application of a linear regression step to arrive at a final best estimate of the state of the atmosphere is also discussed. The resulting forecasts approach the climatological mean at forecast times so late that all skill has been lost. For an ideal case with an observing resolution, hopefully achievable in the 1980s with satellite-based sensors, it is found that the. Monte Carlo procedure leads to the greatest improvement in mean-square vector wind forecast skill in the 6- to 10-day range. For another case corresponding roughly...
755 citations
TL;DR: In this article, the chemical potential of hard-sphere fluids over the reduced density range 0·1⩽ σ 3 ρ ⩽ 0·8 was derived by means of Monte Carlo sampling.
Abstract: The ‘potential distribution’ expressions derived by Widom for the pressure and chemical potential of a fluid are developed for the special case of a hard-sphere fluid. The exact equations produced are closely related to those used in Scaled Particle Theory. They have been used to determine the chemical potential of hard-sphere fluids over the reduced density range 0·1 ⩽ σ 3 ρ ⩽ 0·8 by means of Monte Carlo sampling. The chemical potential so obtained is in excellent agreement with that found by integrating over pressure as a function of volume. It is found, however, that the chemical potential is considerably more dependent on the sample size than the pressure. The Monte Carlo results for the nearest-particle distribution around random points in the fluid are compared with the predictions of Scaled Particle Theory. The agreement is close, particularly at low densities. Two simple methods of Monte Carlo sampling of the grand canonical ensemble—an exact method and a more convenient, though inexact, modificat...
310 citations
TL;DR: In this paper, the Hartree-Fock potential for water-water interactions was used to assess the effect of neglecting the correlation energy correction, and a number of semi-empirical corrections based on the London, Kirkwood, and Wigner formulas were used.
Abstract: The two‐body Hartree‐Fock potential for water‐water interactions previously used to describe small water clusters and used in Monte Carlo studies of liquid water has been used to assess the effect of neglecting the correlation energy correction. A number of semiempirical corrections based on the London, Kirkwood, and Wigner formulas were used. They have an energy spread such that they encompass the expected magnitude of the exact correlation energy correction. Short range correlation interactions were included using a modification of the functional of density proposed by Wigner and the corresponding long range interactions were given by a term proportional to r−6 with coefficients due to both London and Kirkwood. After adding the corrections to the Hartree‐Fock potential the various potentials were compared by generating a number of potential energy surfaces. Following this the water‐water potentials were used in a Monte Carlo simulation of liquid water to calculate thermodynamic and structural data. Afte...
87 citations
TL;DR: In this paper, the energy, specific heat, and radial density distribution of physical clusters containing 8, 27, and 64 water molecules have been calculated for 263.2 and 298.0°K using the Monte Carlo method.
Abstract: The energy, specific heat, and radial density distribution of physical clusters containing 8, 27, and 64 water molecules have been calculated for 263.2 and 298.0°K using the Monte Carlo method. A pairwise water‐water potential is used which has been constructed from Hartree‐Fock calculations and corrected for correlation energy effects. For the larger clusters, a radial dipole ordering of the water molecules in the core of the clusters is found, the effect being more pronounced at the lower temperature. The results of these numerical experiments are compared with results obtained for bulk water and for clusters of 8 water molecules at zero temperature using the same water‐water potential.
78 citations
TL;DR: In this paper, Monte Carlo computations for fluids of hard spheres with embedded point dipoles, at two densities and for a range of dipole moments, were performed for mean spherical and Onsager models and those of thermodynamic perturbation theory.
Abstract: The paper reports Monte Carlo computations for fluids of hard spheres with embedded point dipoles, at two densities and for a range of dipole moments. The results are compared with the predictions of the mean spherical and Onsager models and those of thermodynamic perturbation theory; the last appears to be most successful.
78 citations
TL;DR: In this paper, the properties of the restricted primitive model (RPM) were analyzed for 24 (V.T )-points in the fluid region by means of the Monte Carlo method.
77 citations
TL;DR: In this paper, Monte Carlo techniques have been used to obtain pair functions and some thermodynamic functions for a two-dimensional system of particles interacting with a Lennard-Jones 12-6 potential.
Abstract: Monte Carlo techniques have been used to obtain pair functions and some thermodynamic functions for a two-dimensional system of particles interacting with a Lennard-Jones 12-6 potential. The results extend from the solid phase to the gas, and are at temperatures both above and below the liquid-gas critical point.
69 citations
TL;DR: In this article, Monte Carlo calculations were carried out for a two-dimensional Ising model of a binary alloy with nearest-neighbor attractive interactions between like atoms, and the pair correlation observed had the form of an exponentially damped cosine function with parameters varying as the one-sixth power of the time.
Abstract: Monte Carlo calculations were carried out for a two-dimensional Ising model of a binary alloy with nearest-neighbor attractive interactions between like atoms. The pair correlation observed had the form of an exponentially damped cosine function with parameters varying as the one-sixth power of the time.
61 citations
TL;DR: In this paper, the Monte Carlo method was used to evaluate the reaction field strength and the Kirkwood structure factor in a fluid of hard cores with central embedded point dipoles, and the long ranged interactions were computed by a crystallographic method.
54 citations
IBM1
TL;DR: In this paper, the authors investigated the Fisher's droplet model in three dimensions using the Monte Carlo simulation technique and found that considerable deviation from the phenomenological model is found for clusters consisting of less than l ≈ 100 particles.
TL;DR: In this paper, the Monte Carlo method is used to study the Ising and Heisenberg models and various boundary conditions are used to elucidate various aspects of phase transitions. But the results are limited to the case of a single spin-flip kinetic Ising model.
Abstract: Ising and Heisenberg models are studied by the Monte Carlo method. Several hundred up to 60 000 spins located at two- and three-dimensional lattices are treated and various boundary conditions used to elucidate various aspects of phase transitions. Using free boundaries the finite size scaling theory is tested and surface properties are derived, while the periodic boundary condition or the effective field-like ‘self-consistent’ boundary condition are used to derive bulk critical properties. Since Monte Carlo averages can be interpreted as time averages of a stochastic model, ‘critical slowing down of convergence’ occurs. The critical dynamics is investigated in the case of the single spin-flip kinetic Ising model. Also non-equilibrium relaxation processes are treated, e.g. switching on small negative fields the magnetization reversal and nucleation processes are studied. The metastable states found can be understood in terms of a scaling theory and the droplet model. Using a spin exchange model t...
TL;DR: In this paper, the mutual interaction between steps of a step train on a crystal surface in contact with a vapour phase has been investigated and the data obtained by Monte Carlo computer simulation experiments have been compared with recent numerical results, based on a description of these phenomena by Burton, Cabrera and Frank, including the Schwoebel effect.
TL;DR: In this article, expressions for the distribution of ion energy among thermal, drift and random field components are given in terms of the ion drift velocity and the field derivative of ion mobility, without restrictions on the ion-neutron mass ratio or force law.
Abstract: Expressions for the distribution of ion energy among thermal, drift and random field components are given in terms of the ion drift velocity and the field derivative of the ion mobility. Comparison with available Monte Carlo calculations indicates that the expressions are accurate to high field strengths, without restrictions on the ion-neutron mass ratio or force law.
TL;DR: In this article, the excluded volume expansion factor of a flexible chain is calculated with a smooth density model providing for a distribution of both sizes and shapes of the segment cloud, and an approximate empirical function is constructed to describe the distribution of ellipsoidal dimensions.
Abstract: The excluded‐volume expansion factor of a flexible chain is calculated with a smooth‐density model providing for a distribution of both sizes and shapes of the segment cloud. From the known average moments of the inertial tensor found previously by Monte Carlo methods, an approximate empirical function is constructed to describe the distribution of ellipsoidal dimensions. With a suitably related pseudopotential representing the excluded‐volume forces, an expansion factor αs2 for the mean square radius is obtained which requires very little scale adjustment to match first‐order perturbation theory and which also gives a good representation at higher values of the interaction parameter. The empirical function approach is supplemented with a Monte Carlo study to remove bias inherent in the choice of the functional form. Because of the small increase in asymmetry with increasing excluded volume, the direct effect of shape variation on the expansion factor is less important than that of size variation. A calcu...
TL;DR: In this article, Monte Carlo rate constants and lifetime distributions for H−C≡C-H, H-C−C−H, Cl−C ≥ C−Cl−Cl, and Cl-C ≤ C−C −Cl were determined by classical trajectories.
Abstract: Monte Carlo rate constants and lifetime distributions for H–C≡C–H, H–C≡C–Cl, and Cl–C≡C–Cl at 200 kcal/mole were determined by classical trajectories. The Monte Carlo rate constants agree to within 30% of the RRKM prediction. Energy randomization is faster in Cl–C≡C–Cl than in H–C≡C–H and H–C≡C–Cl. An analysis of nonrandom lifetime distributions indicates that energy randomization is complete by 10−12 sec. for each of the molecules. Comparisons are made between our results and other unimolecular studies.
TL;DR: In this paper, the authors describe a computer simulation experiment which reproduces, upon an idealized (100) cubic crystalline surface, the atomic processes occurring in condensation, evaporation, and surface diffusion.
Abstract: This paper describes a computer simulation experiment which reproduces, upon an idealized (100) cubic crystalline surface, the atomic processes occurring in condensation, evaporation, and surface diffusion. Nucleation of two‐dimensional clusters was observed. The equilibrium distribution of cluster sizes and the critical cluster size were measured for various parameter values and compared to predictions of the Walton‐Rhodin atomistic nucleation theory. Very good agreement between the simulation and theoretical values was obtained. The nucleation rate was also measured for one particular set of parameter values and found to agree satisfactorily with the atomistic theory prediction. Consequently, we conclude that the Monte Carlo method is suitable for the simulation of the phenomena of heterogeneous nucleation. Suggestions are offered for the refinement and extension of the simulation model for future simulation experiments to help answer the unresolved questions of heterogeneous nucleation theory.
TL;DR: In this paper, the variation of diffusion coefficient with departure from stoichiometry in pyrrhonist was investigated using a modified Monte Carlo method, and four different site-exclusion models were chosen to describe the interaction between vacancies.
Abstract: Using a modified Monte Carlo method, the authors have investigated the variation of diffusion coefficient with departure from stoichiometry in pyrrhonist. Fe-S. Four different site-exclusion models were chosen to describe the interaction between vacancies. Comparison of the calculated results with available tracer diffusion data suggest that below the Neel temperature (1) vacancy-vacancy interaction extends to fifth nearest neighbours, and (2) the direct jump between sites in adjacent basal planes is the most favoured diffusion path.
TL;DR: In this article, Monte Carlo data have been generated for a simple model fluid consisting of hard spheres with an attractive triangular well potential, and the ranges spanned by the temperature and density are as follo...
Abstract: Monte Carlo data have been generated for a simple model fluid consisting of hard spheres with an attractive triangular well potential. The ranges spanned by the temperature and density are as follo...
TL;DR: In this article, a modified Poisson Boltzmann equation for symmetrical electrolytes is considered, which includes estimates for both the fluctuation potential and the volume term, and the equation is solved using a previously developed quasilinearization procedure for 1 : 1 and 2 : 2 electrolytes.
Abstract: A modified Poisson-Boltzmann equation for symmetrical electrolytes is considered which includes estimates for both the fluctuation potential and the volume term. The equation is solved using a previously developed quasilinearization procedure for 1 : 1 and 2 : 2 electrolytes and the results compared with the Monte Carlo computations. In the 1 : 1 case good agreement is found with the Monte Carlo calculations, the results being on a par with the HNC calculations. In the 2 : 2 case satisfactory qualitative agreement is found with the preliminary findings of the Monte Carlo calculations.
TL;DR: In this article, a simulation of a one-dimensional binary alloy system is presented, where fluctuations can be observed on an atomic time scale, and it is shown that thermal fluctuations may play an important role in coarsening in real alloys.
Abstract: Recently Cahn's generalized diffusion equation theory of spinodal decomposition in binary alloys has been modified to include the effects of thermal fluctuations. This paper reports studies of a one-dimensional binary alloy system in which fluctuations can be observed on an atomic time scale. The system, a computer-simulated linear chain binary alloy which evolves from an initially random atomic arrangement through interchange of unlike nearest neighbors via the Monte Carlo technique, rapidly develops grains of two different concentrations and then slowly experiences coarsening. A numerical solution of the diffusion equation successfully predicts the development of grain structure, but only predicts coarsening to the extent present as fluctuations in the initial atomic arrangement. The simulated alloy coarsens further than the prediction of the diffusion equation because of thermal fluctuations which develop naturally during its evolution. This suggests that thermal fluctuations may play an important role in coarsening in real alloys.
TL;DR: The letter reports the results of a preliminary feasibility study of an efficient method of statistical analysis for linear nonreciprocal circuits.
Abstract: The letter reports the results of a preliminary feasibility study of an efficient method of statistical analysis for linear nonreciprocal circuits.
TL;DR: In this paper, a Monte Carlo method was used for the determination of the areas under chromatographic curves (peaks) based on the application of the Monte Carlo procedure, and its advantage lies in its successful application to irregular curves.
Abstract: A rapid method is described for the determination of the areas under chromatographic curves (peaks) The method is based on the application of the Monte Carlo procedure, and its advantage lies in its successful application to irregular curves
30 Apr 1974
TL;DR: In this paper, three main Monte Carlo methods have been used to solve the full Boltzmann equation of kinetic theory, namely (1) test particle method of J K Haviland, (2) simulation method of G A Bird and (3) integral evaluation method of A Nordsieck and B L Hicks.
Abstract: : The present review contains a description with comments of the three main Monte Carlo methods which have been used to date in solution of the full Boltzmann equation of kinetic theory - namely (1) test particle method of J K Haviland (2) simulation method of G A Bird and, (3) integral evaluation method of A Nordsieck and B L Hicks A chapter containing the necessary formulas for kinetic theory and one on probability theory is included at the beginning The author's first hand experience with the simulation method has made possible the inclusion of some new material in chapter 4
TL;DR: In this paper, a method is given for assessing the precision of Monte Carlo simulations of probability distributions, and the method is simple, virtually cost free and gives estimates of precision not currently being used.
Abstract: In this note a method is given for assessing the precision of Monte Carlo simulations of probability distributions. The method is simple, virtually cost free and gives estimates of precision not currently being used.
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TL;DR: In this paper, the spin-pair correlation functions of the classical Heisenberg ferromagnet with simple cubic lattice have been calculated in the paramagnetic and ferromagnetic temperature range using the self-consistent Monte Carlo method.
Abstract: The spin-pair correlation functions of the classical Heisenberg ferromagnet with simple cubic lattice have been calculated in the paramagnetic and ferromagnetic temperature range using the self-consistent Monte Carlo method.