Showing papers on "Dynamic Monte Carlo method published in 1976"

Study of the structure of molecular complexes. XIII. Monte Carlo simulation of liquid water with a configuration interaction pair potential

Abstract: A water–water interaction potential obtained from configuration interaction calculations has been used to simulate liquid water, at 25 °C, by a Monte Carlo technique. The resulting radial distribution functions and x‐ray and neutron scattering intensities are compared with experiment and found to be in satisfactory agreement. Some thermodynamic properties are also computed and discussed. The overall agreement seems to indicate that many‐body effects contribute little in determining the structure of liquid water, although they seem to be important for an accurate simulation of internal energy and related quantities.

Monte Carlo principles and applications.

Abstract: A discussion of random number generation is given, and the connection between Monte Carlo methods and random numbers is indicated. Outlines of two well established Monte Carlo sampling techniques are given together with examples illustrating their use. The general techniques for improving the efficiency of Monte Carlo calculations are discussed. Monte Carlo literature pertinent to medical physics is reviewed.

Renormalization Group by Monte Carlo Methods

Abstract: I discuss the basic ideas in applying the Monte Carlo methods to the renormalization-group study of static and dynamic critical phenomena within the framework of a kinetic Ising model. Simple calculations demonstrating these ideas are presented.

A Monte Carlo study of ion–water clusters

Abstract: The procedures developed in this paper have been employed to calculate theoretical free energies of formation of ion–water clusters for comparison with experiment. Gibbs free energies were calculated for the gas phase reaction, ion(H2O)N−1+H2O(vapor)=ion(H2O)N, for the Li+, Na+, K+, Cl−, and F− ions and for N=1–6. The standard state for all calculations was taken as 298 °K and 1 atm. The Monte Carlo method was used to evaluate the appropriate classical expressions of statistical mechanics by employing the intermolecular potential functions recently developed from ab initio Hartree–Fock calculations. Enthalpies, entropies, and structural information were also calculated. Agreement with experiment is sufficiently good to demonstrate the feasibility of this approach.

A Monte Carlo approach to the direct simulation of electron penetration in solids

Abstract: A new Monte Carlo approach to the direct simulation of scattering process of a penetrating electron in matter has been attempted. The theoretical stopping powers for elementary excitation processes (conduction-electron, plasmon and L-shell electron excitations) were used instead of Bethe's stopping power equation to describe the energy loss process in the electron penetration. The result obtained for aluminium describes the energy as well as the angular distribution of the transmitted electrons satisfactorily. This approach has also been applied to copper as a preliminary example. The theory describes qualitatively the energy and angular distributions of the transmitted electrons fairly well, but there is some discrepancy between theory and experiment in the energy distribution.

A new Monte Carlo method for calculating surface tension

Abstract: A new Monte Carlo method for calculating the surface tension of a liquid is described. The method is based on a direct evaluation of the free energy required to create a surface, unlike earlier Monte Carlo calculations which evaluated the surface stress. It is applied to the 6:12 fluid in conditions close to the triple point for argon. The calculated surface tension agrees within statistical uncertainty with previous Monte Carlo estimates, but the statistical uncertainty of the present method is much lower. Agreement with experimental data for argon is not good, as should be expected; estimates of the effects of using a correct pair potential and particularly of including three‐body interactions indicate that they would lead to good agreement.

Monte carlo estimates of the distributions of the random polygons determined by random lines in a plane

Abstract: The results of a Monte Carlo study of the random polygons determined by homogeneous and isotropic random limes in the plane (the standard passion line process) are presented. The study involved the generation and mensuration by computer of nearly 200,000 polygons

Grand ensemble Monte-Carlo studies of physical adsorption

Abstract: A grand canonical ensemble, Monte Carlo method has been used to simulate 12-6 argon-like molecules in the potential field of a plane, uniform homogeneous solid. The adsorbent field was assumed to be entirely due to dispersion forces, and parameters corresponding to graphite were used. Thermodynamic equations appropriate for a multicomponent adsorption system in the grand ensemble are discussed. The methods for realization of the various parameters in a single component system are presented. Results have been obtained for temperatures of 80 and 120 K and mainly for coverages above a statistical monolayer. Isotherms, isosteric heats and other thermodynamic properties are presented and where possible compared with nearby experimental data.

Molecular Dynamics and Monte Carlo Calculations in Statistical Mechanics

Abstract: Monte Carlo and molecular dynamics calculations on statistical mechanical systems is reviewed giving some of the more significant recent developments. It is noted that the term molecular dynamics refers to the time-averaging technique for hard-core and square-well interactions and for continuous force-law interactions. Ergodic questions, methodology, quantum mechanical, Lorentz, and one-dimensional, hard-core, and square and triangular-well systems, short-range soft potentials, and other systems are included. 268 references. (JFP)

Monte Carlo high-field transport in degenerate GaAs

Abstract: An extension of the traditional Monte Carlo transport calculation is presented which takes into account the Pauli exclusion principle This method is applied here to the determination of the electron distribution function in degenerate GaAs at 77K: the results are in satisfactory agreement with available experimental data

Random differential equations as models of ecosystems: Monte Carlo simulation approach

Abstract: The behavior of a simple aquatic ecosystem with algae, bacteria, Daphnia , detritus, and usable dissolved organic carbon as its components was studied using random differential equation models. The randomness in the system has been introduced through initial conditions, input variables, and parameters. The computer simulation results show that the deterministic solution and the stochastic mean are different. Also, there was some degree of increased “stability” in the stochastic system. A large number of numerical solutions generated by the Monte Carlo procedure give a range of biomass values which is very similar to the range of values obtained from field measurements. These models enable us to make predictions in terms of means and associated variances and thus are more useful than deterministic models for applied problems in ecology and resource management.

Hard dumbells: Monte Carlo pressures and virial coefficients

Abstract: The equation of state was determined by Monte Carlo simulation for 108 dumb-bells subject to periodic boundary conditions. The isotropic fluid-solid phase transition was observed. An orientational phase transition was not observed. Virial coefficients through B5 were calculated.

Grand Ensemble Monte Carlo Calculation of the Thermodynamic Properties of a Solid/Vapour Interface

Abstract: The thermodynamic properties of the krypton/graphite interface have been evaluated by the grand canonical ensemble Monte Carlo method. Submonolayer adsorption isotherms have been calculated at temperatures of 77.31, 84.11 and 90.12 K, together with particle distribution functions, surface pressures and isosteric heats of adsorption. The results are compared with experiment and discussed in relation to the existence of surface phase transitions. The Monte Carlo adsorptions were used to check the error in assuming Henry's law adsorption at low pressure.

Monte Carlo study of systems of linear oligomers in two‐dimensional spaces

Abstract: The statistical mechanical properties of systems of linear r‐mers (r=4, 5, and 6) in a square lattice space and of those in a two‐dimensional continuous space were studied by Monte Carlo simulations. In the lattice space systems, the site fractions of the 4‐mers ranged from 0.08 to 0.75, those of the 5‐mers from 0.075 to 0.800, and those of the 6‐mers from 0.12 to 0.667. In the continuous space systems, the concentrations were in more narrow ranges. In the lattice space systems, statistical quantities of finite systems were extrapolated to those of infinite systems. Pressures or osmotic pressures of the lattice space systems were close to the Huggins and the Miller–Guggenheim theoretical ones, while pressures of the continuous space systems, in dilute concentrations ranges, were better described by the Flory theory. The occurrence of each conformation of the r‐mers was random in dilute concentration ranges but not in dense ranges. The nonrandomness was much increased in the continuous space systems, especially in the case of the 4‐mers. No sign of the cooperative aligning of the r‐mers was found in the lattice space systems.

A stable estimator for linear models: 1. Theoretical development and Monte Carlo Experiments

Abstract: Instant unit hydrograph (IUH) type linear models have been widely used to simulate many hydrologic systems. Unfortunately, the classical parameter estimators used to calibrate this type of model often fail to give a reliable and meaningful solution. It has been suggested that a set of constraints that can be deduced from the physics of the hydrologic system be imposed on the IUH in order to reduce the high sensitivity of the classical estimators to errors in the available data. Therefore a mathematically correct constrained estimator has been devised, and its solution is obtained by using quadratic programing. The higher degree of efficiency of this estimator (smaller dispersion of the estimates about the true value) is shown numerically through Monte Carlo experiments.

Prediction of Statistical Error in Monte Carlo Transport Calculations

Abstract: Successive solutions to two coupled integral equations provide the expected statistical error of any Monte Carlo calculation in which the external source is specified and the score resulting from each collision has a known probability distribution. Each equation can be transformed into a differential-integro form that is adjoint to the transport equation. This result agrees with the stochastic theory of Bell for those special situations described by both theories. The coupled integral equations in the Monte Carlo theory of Coveyou et al. have other adjoint properties because they describe physically different quantities. In the presented theory, the first equation (for the expected value), but not the second (for the expected squared value), can readily be understood in terms of Selengut's general interpretation of adjoint solutions. The principal aim of this work is to provide a method for determining in advance whether or not development of a contemplated Monte Carlo program would be worthwhile. Any of the approximations commonly applied to the transport equation can be used. Some examples are worked out by diffusion theory, interpreted, and tested for accuracy.

Monte carlo technique to simulate aflatoxin testing programs for peanuts

Abstract: A computer model that accounts for sampling, subsampling, and analytical variability was developed to simulate aflatoxin testing programs. Monte Carlo solution techniques were employed to account for conditional probabilities that arise from multiple samples, subsamples, and/or analyses being used in testing programs. The aflatoxin testing program to be used on the 1974 peanut crop was evaluated by use of the described model.

Functional Expansion Technique for Monte Carlo Electron Transport Calculations

Abstract: A new method for Monte Carlo electron transport calculations has previously been outlined. Briefly, the method is as follows: the quantity of interest (e.g., x-ray photoemission angular distribution) is expanded in a complete set of orthogonal functions; the individual trajectories of the Monte Carlo sample are used to calculate the expansion coefficients; the resulting coefficients are used to evaluate a (continuous) representation of the relevant distribution. In this paper we discuss this orthogonal function expansion method at some length. A precise mathematical formulation is given to two types of expansions: expansions of the probability density of a random variable; expansions of functions defined on a stochastic process. The method as formulated is then used for several problems of practical interest. The POEM Monte Carlo electron transport code has been modified to provide expansions for the following: one- and two-dimensional x-ray photoemission angular distributions; dose enhancement profiles near high-Z/low-Z interfaces, and energy distributions for finite beams incident on an interface. A discussion is given of the applicability of the method, particularly as it relates to the specific applications. Several pathological examples are cited which indicate the discretion necessary in applying the technique. These examples serve to counterpoint the desirable properties of convergence, smoothing, and variance reduction which arise from a properly applied expansion.

Monte Carlo calculation on trans/cis-polysarcosine.

Abstract: Monte Carolo calculations were made on unperturbed trans-polysarcosine chain, non-self-intersecting trans-polysarcosine chain, and also non-self-intersecting trans/cis-polysarcosine chain by using a hard-sphere model. In the last case, an attempt was first made to introduce cis amide bond into the Monte Carlo calculation of polypeptide chain. Dipeptide energy maps for four different trans/cis dyad sequences were calculated. The allowed regions were consistent with the pairs of dihedral angles observed in cyclo-pentasarcosyl and cyclo-octasarcosyl. The mean-square end-to-end distance and higher even moments were obtained. The distribution function of the end-to-end distance was calculated from the even moments by using Nagai's equation and compared with the direct Monte Carlo data. The best agreement was obtained by cutting off the terms containing much higher order even moments than a critical order. The fractions of cis amide bond and of the four different trans/cis dyad sequences in polysarcosine were calculated. The results of calculation were compared with the 220-MHz NMR spectra of polysarcosine in three different solvents. Qualitative agreement was stained for longer chains.

Monte Carlo calculations on spatial distribution of implanted ions in silicon

Abstract: The Monte Carlo technique has been applied to simulate the trajectories of ions implanted into an amorphous target. By this method much information about the spatial distribution of ions is obtained in a straightforward way: the results show a good agreement with the experiments available in current literature.

Absolute complex formation cross sections for alkali—alkali halide collisions: a Monte Carlo trajectory study

Abstract: A classical Monte Carlo trajectory study has been performed, where the potential energy function used is an ideal dipole potential with its center displaced from the center of mass The potential shape depends on two parameters For one choice of parameters, the theoretical Roach and Child surface is well approximated at large and intermediate distances Several other choices of parameter values have also been used Complex formation cross sections and angular distributions at the centrifugal barrier have been determined, and a comparison with the theoretical quantities for a spherically symmetric potential is made The previously proposed mechanisms, assumed to explain the experimentally found low values of σ c and the quantity of Γ, have not been found to be significant A dynamical picture is used to interpret the present results It also provides an interpretation of the previous experimental results In this picture rotational energy transfer at the barrier is of great importance

Comment on the thermodynamics of a classical one-component plasma

Abstract: A variational method used recently in the theory of liquid metals and screened Coulomb systems is extended to treat the thermodynamic properties of a classical, uniform, one-component plasma. The Helmholtz free energy and corresponding thermodynamic derivatives can all be expressed in concise parametric form as functions of an equivalent hard-sphere packing function. Finally, the results are generally found to agree well with recent Monte Carlo calculations, especially at temperatures close to the observed crystallization temperature.