Showing papers on "Dynamic Monte Carlo method published in 1972"
TL;DR: A technique of digital simulation of multivariate and/or multidimensional Gaussian random processes (homogeneous or nonhomogeneous) which can represent physical processes germane to structural engineering is presented.
534 citations
TL;DR: In this article, a Monte Carlo method for the calculation of thermodynamic properties in the isothermal-isobaric ensemble is described, and the accuracy attainable in estimates of the excess properties is discussed in terms of statistical fluctuations in various calculated quantities and the advantages and disadvantages of the method are examined in relation to calculations by the more familiar constant-volume method.
Abstract: A Monte Carlo method for the calculation of thermodynamic properties in the isothermal-isobaric ensemble is described. Application is made to the calculation of excess thermodynamic properties (enthalpy, volume and Gibbs free energy) of binary mixtures of Lennard-Jones 12–6 liquids. Comparison is made with the predictions of a number of theories of liquid mixtures; the so-called van der Waals one-fluid model and the variational theory of Mansoori and Leland are both found to give excellent results. The accuracy attainable in estimates of the excess properties is discussed in terms of statistical fluctuations in various calculated quantities and the advantages and disadvantages of the method are examined in relation to calculations by the more familiar constant-volume method.
371 citations
TL;DR: In this article, a method for estimating the free energy and entropy of an assembly of particles is described, which is done by using Metropolis Monte Carlo techniques to generate energy distributions from which we may calculate the absolute volume of configuration space corresponding to a given energy, and thus the configuration integral.
Abstract: A method is described for estimating the free energy and entropy of an assembly of particles. This is done by using Metropolis Monte Carlo techniques to generate energy distributions from which we may calculate the absolute volume of configuration space corresponding to a given energy, and thus the configuration integral. One incidentally obtains the thermodynamic quantities over a wide range of reduced temperature. It is particularly easy to apply the method to particles having hard cores, and calculations are reported for hard spheres with Coulombic forces.
238 citations
TL;DR: In this article, a Monte Carlo technique is presented which can effectively be used for nonlinear response analysis of a structure subjected to a random pressure field undergoing large deflections, where the pressure field is idealized as a multidimensional Gaussian process with mean zero and homogeneous both in time and space.
Abstract: A Monte Carlo technique is presented which can effectively be used for nonlinear response analysis of a structure subjected to a random pressure field undergoing large deflections. The pressure field is idealized as a multidimensional Gaussian process with mean zero and homogeneous both in time and space. The response analysis is performed in the time domain by numerically simulating generalized forces rather than in the frequency domain. The solution satisfies the boundary conditions and the differential equation in a Galerkin sense. Two numerical examples involving large deflections of a string and a plate are worked out. The result indicates that the present method indeed provides a powerful tool in solving nonlinear structural response problems under random excitations.
105 citations
TL;DR: The use of Monte Carlo calculations in reactor criticality and shielding problems requires cross section data sets which are properties of the individual isotopes rather than group averaged sets as mentioned in this paper, which is not a suitable approach.
Abstract: The use of Monte Carlo calculations in reactor criticality and shielding problems requires cross section data sets which are properties of the individual isotopes rather than group averaged sets. A...
99 citations
TL;DR: In this article, a Monte Carlo technique was applied to study the fundamental phenomena in the electron probe microanalyzer (EPMA) and the scanning electron microscope (SEM), which are brought about by scattering of the primary electrons in a specimen.
Abstract: A Monte Carlo technique was applied to study the fundamental phenomena in the electron probe microanalyzer (EPMA) and the scanning electron microscope (SEM), which are brought about by scattering of the primary electrons in a specimen. The calculation procedure was based on Lewis' multiple scattering theory; however, some attempts were made to improve it by introducing the substeps to each step which had been used in previous calculations. The main purpose is to investigate the applicability of this improvement through the comparison with the experimental results with respect to backscattered electrons obtained by Kanter, and next to give a theoretical explanation for the experimental results of Wells as well as to obtain more detailed information on the electron backscattering. The results show that the fidelity of the present Monte Carlo simulation for the electron backscattering is satisfactory.
88 citations
TL;DR: In this article, a scheme is proposed to sample the distance to collision without resorting to numeric integration, when the total macroscopic cross section varies in an arbitrary manner along projected particle f...
Abstract: A scheme is proposed to sample the distance to collision, without resorting to numeric integration, when the total macroscopic cross section varies in an arbitrary manner along projected particle f...
62 citations
59 citations
TL;DR: Two algorithms are provided for the above task in which the invidious 'sort' or ordering operation (ii) is completely avoided and the u(i) are directly generated in their ordered sequence.
Abstract: (1972). Machine-Generation of Order Statistics for Monte Carlo Computations. The American Statistician: Vol. 26, No. 1, pp. 26-27.
51 citations
TL;DR: In this paper, the authors used the Monte Carlo method to compute the triplet correlation function in a classical fluid with Lennard-Jones interactions and compared the results with the pair correlation function.
Abstract: The Monte Carlo method has been used to compute the triplet correlation function in a classical fluid with Lennard‐Jones interactions. The computations were performed for particular configurations at five thermodynamic states of high density. The structure of the triplet function is discussed in the liquid and dense gas regions. Several closure approximations, which express the triplet function in terms of the pair correlation function, are compared to the Monte Carlo results.
47 citations
TL;DR: In this paper, the authors present a systematic discussion of Monte Carlo methods for examining thermal excitation and dissociation in atomic and molecular systems, and the most important advantage of sampling inside the collision complex is that the reaction probability for excitation or dissociation can be increased sufficiently to make Monte Carlo calculations for these processes relatively efficient.
Abstract: Publisher Summary This chapter presents a systematic discussion of Monte Carlo methods for examining thermal excitation and dissociation in atomic and molecular systems. The efficiency of Monte Carlo calculation is influenced not only by the manner in which points are sampled on a given surface, but also by the choice of surface. The principal advantage of the impact parameter surfaces is that they permit a priori specification of the phase space density in the initial state. This is important if one wishes to simulate the results of beam experiments carried out for particles in precisely defined states if any appreciable averaging is involved, or if results are required for a sequence of initial conditions this advantage rapidly disappears. The most important advantage of sampling inside the collision complex is that the reaction probability for excitation and dissociation can be increased sufficiently to make Monte Carlo calculations for these processes relatively efficient.
TL;DR: In this paper, a Monte Carlo approach of statistically sampling the states available to the guest molecule inside the host water cage was used to evaluate the configurational properties including the free volume integral.
Abstract: Equilibrium dissociation pressures for monovariant three-phase (icesolid clathrate-gas) systems were predicted for water clathrates with Ar, Kr, Xe, N2, O2, CO2, and CH4 as the guest molecules. A Monte Carlo approach of statistically sampling the states available to the guest molecule inside the host water cage was used to evaluate the configurational properties including the free volume integral. The Lennard-Jones 6–12 potential adequately described the guest-host interaction for monatomic species, for example, Ar, Kr, and Xe, while the nonspherically symmetric Kihara potential with a fixed hard-core geometry was required for polyatomic guests. The simulated motion of the guest within the cell was consistent with the geometrical features of the host lattice.
TL;DR: In this article, a Monte Carlo transport code for calculating high-energy nucleon-meson cascades in thick targets is described, which uses an intra-nuclear-cascade-extrapolation-evaporation model.
Abstract: A Monte Carlo transport code for calculating high-energy nucleon-meson cascades in thick targets is described. The calculational method uses an intra-nuclear-cascade-extrapolation-evaporation model...
TL;DR: The authors examined the use of indirect Monte Carlo methods in investigating the finite-sample properties of econometric estimators and found that the two-antithetic-variate method is far better than straight-forward simulation in estimating the biases of the estimators.
Abstract: This note examines the use of indirect Monte Carlo methods in investigating the finite-sample properties of econometric estimators. It is found that the two-antithetic-variate method is far better than straight-forward simulation in estimating the biases of the estimators, but that a method combining the control-variate and the two-antithetic-variate techniques is better for estimating the dispersions. Comparisons with Nagar's approximations to the biases and dispersions are presented.
TL;DR: In this article, the effects of excluded volume interactions upon the dynamical behavior of random-coil polymer chains are studied by obtaining autocorrelation functions for vector end-to-end length of lattice-model chains of 9, 15, 33, and 63 beads by a Monte Carlo simulation technique.
Abstract: The effects of excluded volume interactions upon the dynamical behavior of random‐coil polymer chains are studied by obtaining autocorrelation functions for vector end‐to‐end length of lattice‐model chains of 9, 15, 33, and 63 beads by a Monte Carlo simulation technique. It is found that relaxation of the vector end‐to‐end length requires from 4 to 7 times as long as relaxation of its square, in contrast to the predictions of simple models without excluded volume effects.
TL;DR: In this article, the elastic constants of solid argon have been calculated using an accurate pairpotential together with the Monte Carlo method and the Axilrod-Teller three-body potential.
Abstract: Thermodynamic properties and elastic constants of solid argon have been calculated using an accurate pair-potential together with the Monte Carlo method and the Axilrod-Teller three-body potential. Excellent agreement is obtained with experimental values of the pressure and internal energy. However the calculated elastic constants show systematic deviations from the experimental values. These discrepancies are examined in some detail and possible reasons for them are given.
TL;DR: In this article, the ESR line shape in the slow modulation region is calculated from the Kubo-Anderson theory by using a Monte Carlo technique for averaging the relaxation function, and the problem of spurious peaks is solved by the means of a window technique.
Abstract: The ESR line shape in the slow modulation region is calculated from the Kubo‐Anderson theory by using a Monte Carlo technique for averaging the relaxation function. The problem of spurious peaks is solved by the means of a window technique. It is explicitly shown how to sample the relaxation function. The method is applied to axially symmetric and asymmetric secular g tensor and pseudosecular terms modulated by isotropic rotational diffusion. Other interactions, e.g., nonsecular terms, as well as other types of modulation may be included.
TL;DR: In this article, the authors extended the random coalescence model to the case of reactors for which the two separate reactant feed streams have differing residence time distributions, and the parameter characterising the micromixing is the average number of collisions each fluid element experiences in its sojourn in the reactor vessel.
TL;DR: In this article, an iterative method is proposed to include the electron-electron interaction in Monte Carlo calculations of semiconductor transport properties, making use of the distribution function obtained in the previous step.
TL;DR: In this paper, a general Monte Carlo procedure for the calculation of perturbations in the reactivity of a multiplying system due to changes in system parameters (e.g., temperature, control rod p...
Abstract: This paper gives a general Monte Carlo procedure for the calculation of perturbations in the reactivity of a multiplying system due to changes in system parameters (e.g., temperature, control rod p...
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TL;DR: The Monte Carlo method was used to generate canonical ensemble isotherms for N = 25, 64, 100, and 400 parallel hard squares in a two-dimensional periodic box as discussed by the authors.
Abstract: The Monte Carlo method was used to generate canonical‐ensemble isotherms for N=25, 64, 100, and 400 parallel hard squares in a two‐dimensional periodic box. The Monte Carlo realizations with their chain lengths ranging up to ∼ 8× 105 trials per particle were employed to ascertain statistical accuracy of the calculated pressures. The resulting isotherms are monotone increasing functions of the density with a possibility of a higher‐order transition but without showing any sign of a first‐order phase transition, with a density increment greater than 0.005ρ0 (ρ0 is the close‐packed density). This departs remarkably from the behavior of the hard‐disk isotherm, which displayed a van der Waals‐like loop for N ≳ 72. Instead, it resembles isotherms of the lattice‐gas systems (e.g., a square‐lattice system with the first and second nearest‐neighbor exclusion, or a system of dimers) which, like the present case, contain a residual degree of freedom at close packing. By numerically integrating the Monte Carlo isothe...
TL;DR: In this paper, Monte Carlo simulations of the transport of Doppler-broadened resonance radiation in certain ideal geometries are described, and the results corroborate the usual local thermodynamic equilibrium assumption.
Abstract: Monte Carlo simulations of the transport of Doppler‐broadened resonance radiation in certain ideal geometries are described. The results corroborate the usual local thermodynamic equilibrium assumption. Spectral line shapes, quenching probabilities, and resonance defects are discussed, and simple empirical formulations are noted.
TL;DR: The Metropolis Monte Carlo method as discussed by the authors is one of the main main approaches to computer simulation of liquid properties and has virtually always been employed within the canonical ensemble formalism, and it has been applied to the analysis of a closed, isothermal, isobaric system (isobaric ensemble conditions).
Abstract: The Metropolis Monte Carlo method is one of two main approaches to computer simulation of liquid properties. It has virtually always been employed within the canonical ensemble formalism. By including density as one of the variables for the random walk, the Metropolis method becomes applicable to the analysis of a closed, isothermal, isobaric system (isobaric ensemble conditions). The analysis is directed toward equilibrium properties of classical models of dense polyatomic liquids such as water. Density, compressibility, constant pressure heat capacity, enthalpy and coefficient of thermal expansion are obtained directly in terms of mean values and variances of a two‐dimensional distribution, g(U, V) of random walk steps. The method appears to be well suited to the study of liquids in the vicinity of the triple point.
TL;DR: In an effort to resolve a conflict in F ( τ ) values calculated by the Monte Carlo method, new results were obtained from an independently- formulated Monte Carlo programme.