Showing papers on "Dynamic Monte Carlo method published in 1970"

Soft‐Sphere Equation of State

Abstract: The pressure and entropy for soft‐sphere particles interacting with an inverse twelfth‐power potential are determined using the Monte Carlo method. The solid‐phase entropy is calculated in two ways: by integrating the single‐occupancy equation of state from the low density limit to solid densities, and by using solid‐phase Monte Carlo pressures to evaluate the anharmonic corrections to the lattice‐dynamics high‐density limit. The two methods agree, and the entropy is used to locate the melting transition. The computed results are compared with the predictions of the virial series, lattice dynamics, perturbation theories, and cell models. For the fluid phase, perturbation theory is very accurate up to two‐thirds of the freezing density. For the solid phase, a correlated cell model predicts pressures very close to the Monte Carlo results.

Direct Simulation and the Boltzmann Equation

Abstract: The direct simulation Monte Carlo method for the numerical solution of problems in rarefied gas dynamics is described and discussed. It is shown that the procedures adopted in this method can be directly related to the Boltzmann equation and that the two are entirely consistent. It is concluded that the results obtained from the method constitute a solution of the Boltzmann equation.

Monte Carlo Study of the Thermodynamics of Electrolyte Solutions

Abstract: Monte Carlo techniques have been used to study the primitive model of an ionic solution. The parameters chosen correspond to a simple 1:1 electrolyte dissolved in water at 25°C. Data are derived for the pair distribution functions, excess internal energy and heat capacity, osmotic coefficient, and mean activity coefficient, in the range 0.01–2M. The results are compared with a nonlinear form of the Debye–Huckel theory and with integral equation results in the Percus–Yevick and hypernetted chain approximations. The last appears to be excellent up to 1M.

Random Packings and the Structure of Simple Liquids. II. The Molecular Geometry of Simple Liquids

Abstract: Machine calculations by Monte Carlo methods enable us to simulate real liquids in real space, and to reproduce the thermodynamic properties of a real liquid assembly. On the basis of the geometrical descriptions of part I, the structures of these simulated arrays are compared with the random packing. The results demonstrate the essential validity of Bernal's concept of the liquid state; moreover, by artificially hardening the interaction potential, we can throw light upon the structural differences between real and idealized systems.

Test of the Monte Carlo Method: Fast Simulation of a Small Ising Lattice

Abstract: A very fast stochastic procedure is used to generate samples of configurations of a 4 × 4 periodic Ising lattice in zero field. Running on the IBM 7094, we require only 15 μsec to process each site (cf. Yang who required 300 μsec on the 7090) and hence we generate 4000 completely new configurations each second. Our main results are based on samples of 106 configurations at each of 10 temperatures; we also took samples of 107 configurations at three temperatures. The 4 × 4 lattice can be solved exactly without much difficulty. Hence our data give information about the Monte Carlo method itself, especially its rate of convergence. We define the statistical inefficiency (SI) in a variable as the limiting ratio of the observed variance of its long‐term averages to their expected (Gaussian) variance. (Thus, if the SI is 3, then averages of the variable taken over Monte Carlo runs of three million configurations will be as accurate as averages over one million configurations drawn randomly from the true ensemble. The SI accounts for correlations between configurations closely following one another in the Monte Carlo run.) We find that for this lattice the SI in energy never exceeds 12, and that its maximum occurs slightly above the temperature which is critical for the infinite lattice. We confirm earlier statements that the influence of the initial configuration is lost very quickly, except when two phases coexist.

Computer Simulation of Vapor Deposition on Two-Dimensional Lattices

Abstract: Vapor deposition simulation programs have been developed using Monte Carlo methods to determine the molecular dynamics of condensation, evaporation, and migration on the lattice. The simulation methods employed in the programs are developed in detail. The principle application will be to systems that permit a comparison with Honig's work, although the simulation methods are easily applied to a variety of other problems. The results of the simulations demonstrate that Honig's treatment is quite accurate and is a substantial improvement over previous treatments. This agreement also serves to build confidence in the use of Monte Carlo methods in simulating molecular dynamics for vapor deposition studies.

NpT‐Ensemble Monte Carlo Calculations for the Hard‐Disk Fluid

Abstract: The NpT‐ensemble Monte Carlo method previously described, in which the hard‐disk interaction is represented by a soft pseudopotential in a reduced configuration space with a fixed periodic enclosure, is used to calculate the equation of state and radial distribution function in the high‐density fluid phase. The equation of state agrees within statistical error with the (3, 3) Pade approximant to the six‐term virial expansion and, for large enough systems, with Salsburg's analysis of the N dependence. The results also agree with recent Monte Carlo calculations by Chae, Ree, and Ree using the NVT ensemble. Some qualitative results for systems of 48 and 90 disks which lend further support to the now‐accepted presence of a solid–fluid phase transition are also presented.

Monte carlo simulation of horizontal pneumatic conveying based on the rough wall model

Abstract: On the basis of wall roughness, a simple model is presented to explain the irregular bouncing phenomena of particles in pneumatic conveying. By introducing a random factor to the model, a pneumatic transport process was simulated by Monte Carlo method. The model could fairly well account for the concentration and velocity distribution and the rate of revolution of particles. Even very small degree of roughness was found to have a great influence upon the behaviour of particles.

Monte carlo method for geometrical perturbation and its application to the pulsed fast reactor.

Abstract: The Monte Carlo method is applied to calculate the reactivity change due to a moving reflector block in the pulsed fast reactor system. This reactivity change is an important quantity in the determination of the power pulse width. In the important region of small displacements about the maximum reactivity point, the reactivity change is so small that the ordinary Monte Carlo methods, using the importance sampling, Russian roulette, or splitting techniques, require prohibitively long calculation times. To avoid this difficulty, a new Monte Carlo method, which directly calculates the geometry coefficient of reactivity due to a geometry perturbation, is developed by adopting the method used in the calculation for the Doppler coefficient by Olhoeft. The formulation of the new method is discussed. The GEMCM code for this geometry perturbation, which is made by modifying the 05R code, is described. Finally, an analysis of the critical experiment for the pulsed fast reactor is carried out using this method and t...

Determination of the free volume and the entropy by a Monte Carlo method

Abstract: The configurational integral can in principle, though not in practice, be determined from the ratio of accepted to rejected moves ( ) in the Monte Carlo method of Metropolis et al, if the moves consist of simultaneous random displacements of N particles uniformly distributed over the sample volume v In the usual Monte Carlo process only one particle at a time is displaced within a small volume If this volume is suitably chosen (VD), the acceptance ratio ( ) determines the mean free volume per particle (Vf = vD ) Evidence is presented supporting the appioximate validity of the relationship = '' which permits the evaluation of the configurational integral The entropies calculated in this way for a system of 108 Lennard— Jones particles with parameters corresponding to argon, are in good agreement with the experimental values for solid and liquid argon The results indicate that the full amount of the communal entropy appears on fusion In the well-known Monte Carlo (MC) method of Metropolis et a!' certain many-dimensional integrals containing the Boltzmann factor as weighting function are evaluated by means of the following procedure: configurations of a system of N particles are generated by small random displacements of single particles; if r is the configuration after moves and the next trial move leads to r, then this move is rejected (by setting r' = r') if and only if the difference between the potential energies — 1i(r) LP > 0 and exp (— A/kT) (1)

Pseudo-random numbers for comparative Monte Carlo calculations

Abstract: To compare the results of two slightly different situations in a given problem solved by the Monte Carlo method it is convenient to use the same random numbers in both cases. To facilitate the reproducibility of the random numbers used a method based on two pseudo-random number generators may be adopted. In this paper the method is discussed with reference to multiplicative congruential generators, the influence of the initial value on a random sequence obtained by a given multiplier being examined first.

Reactive scattering with activation energy: An empirical model

Abstract: A simple model is suggested for the empirical description of reactions with activation energy by taking account of orientational requirements for reaction in a hard-sphere model. Reaction probabilities, cross sections and a rate constant are deduced and found to be consistent with extensive Monte Carlo data for the H + H2 reaction. The form of agreement is much improved over the model due to R. D. Present, especially for collisions at larger impact parameters.

Andymg3: the basic program of a series of monte carlo programs for time- dependent transport of particles and photons.

Abstract: ANDYMG3 is the basic program of a aeries of Monte Carlo programs designed to solve applied problems in timedependent particle and photon transport for general geometries. Particle or photon type and energy are identified ty multlenersy-proup number. Cross sections are read in SJJ format viMi scattering pattern components up to Pj. Particle splitting and termination routines permit negative weights. Particle and photon emission can be delayed. A library of reaction i:ross sections is provided so that practically useful results are computed after execution of the Monte Carlo. 1'he AHDYMG3 program, in FORTRAK-IV for the CDC-66OO and UNIVAC-1108 computers, requires. 0,5-2 msec per collision (CDC-66OO) and a field length less than 60gK for most problems.

A regression method for the Monte Carlo evaluation of multidimensional integrals

Abstract: An investigation is made of some Monte Carlo estimators particularly suited to the application of regression analysis. Sets of estimators are presented which integrate exactly multivariate polynomials of prescribed degree. Application to a number of test integrals shows that economical and accurate results can be obtained as well as reliable error estimates. A comparison is made with some other methods.

Coupled sampling with the monte carlo method in neutron transport calculations.

Abstract: A scheme is devised which combines in a coupled manner the sampling from the transport equation and the adjoint transport equation to improve the sampling for a functional such as the space- and ve...

The Three-dimensional Structure of Macromolecules. I. The Conformation of Ethylene Polymers by the Monte Carlo Method

Abstract: The Monte Carlo method is employed on a high-speed digital computer in order to generate non-intersecting random chains simulating polymer molecules. For this purpose the GT-model of polyethylene is used. Suitable potential functions are used to calculate the energy and the probability of each chain conformation thus generated. The nonbonded-interaction energy is calculated by the Lennard-Jones “6–12” potential function. The average dimensions are then calculated by using this energy. It is suggested that the hydrogen atoms contribute largely to the statistical properties of the ethylene polymers.

Multiple scattering analysis by diffusion and Monte Carlo methods

Abstract: An account is given of the development, and verification by experiment, of a Monte Carlo method for obtaining the flux of radiation around a point source in an atmosphere of scattering particles, having an absorbing boundary. It is shown that the method gives satisfactory solutions in regions close to the boundary, where an earlier diffusion method became inaccurate. The two methods have complementary features which make it profitable for them to be used in conjunction, each in the domain in which it is most accurate and convenient.