Showing papers on "Dynamic Monte Carlo method published in 1978"
TL;DR: In this paper, the authors propose a method to solve the problem of the problem: this paper...,.. ].. ).. ]... )...
Abstract: CONTENTS
820 citations
TL;DR: In this paper, a method of introducing a controlled degree of skew and kurtosis for Monte Carlo studies was derived, and the form of such a transformation on normal deviates [X ≈N(0, 1)] isY =a +bX +cX2 +dX3.
Abstract: A method of introducing a controlled degree of skew and kurtosis for Monte Carlo studies was derived. The form of such a transformation on normal deviates [X ≈N(0, 1)] isY =a +bX +cX
2 +dX
3. Analytic and empirical validation of the method is demonstrated.
673 citations
TL;DR: In this paper, the authors performed fermion Monte Carlo variational calculations to determine the equation of state of the uniform electron one-component plasma in two and three dimensions, and showed that the ground state excess energies calculated by the Monte Carlo method are very precise and in agreement with those of other calculations in the metallic density range and in the very low-density Wigner crystals.
Abstract: We have performed fermion Monte Carlo variational calculations to determine the equation of state of the uniform electron one-component plasma in two and three dimensions. The ground-state excess energies calculated by the Monte Carlo method are very precise and in agreement with those of other calculations in the metallic density range and in the very-low-density Wigner crystals. Three phases have been investigated: the Wigner crystal, the normal or unpolarized fluid, and the polarized fluid. The Wigner crystal has the lowest energy for ${r}_{s}g67$ in three dimensions and ${r}_{s}g33$ in two dimensions. The totally polarized quantum fluid is stable for $26l{r}_{s}l67$ in three dimensions and for $13l{r}_{s}l33$ in two dimensions, and the normal or unpolarized fluid is stable at higher densities ${r}_{s}l26$ in three dimensions and ${r}_{s}l13$ in two dimensions. A pseudopotential with no adjustable parameters, derived from the random-phase approximation, is found to give excellent energies. The present results lend support to earlier conjectures that the ground state of the electron gas will be spin polarized at intermediate densities.
486 citations
TL;DR: In this paper, a new Monte Carlo simulation procedure is developed which is expected to produce more rapid convergence than the standard Metropolis method, and the trial particle moves are chosen in accord with a Brownian dynamics algorithm rather than at random.
Abstract: A new Monte Carlo simulation procedure is developed which is expected to produce more rapid convergence than the standard Metropolis method. The trial particle moves are chosen in accord with a Brownian dynamics algorithm rather than at random. For two model systems, a string of point masses joined by harmonic springs and a cluster of charged soft spheres, the new procedure is compared to the standard one and shown to manifest a more rapid convergence rate for some important energetic and structural properties.
481 citations
242 citations
TL;DR: It is almost certain that the first Monte Carlo simulation of a gas was carried out by William Anderson, the secretary and assistant to Lord Kelvin, and requires the introduction of the Knudsen number Kn as a distinct dimensionless parameter.
Abstract: It is almost certain that the first Monte Carlo simulation of a gas was carried out by William Anderson, the secretary and assistant to Lord Kelvin. As reported by Kelvin (1901), Anderson generated random numbers by shuffling decks of numbered cards and calculated· with "unfailingly faithful perseverance" a total of five thousand molecular impacts with surfaces and three hundred intermolecular collisions. The use of random numbers is the distinguishing feature of a Monte Carlo procedure, and the essentially probabilistic nature of a gas flow at the molecular level makes it an obvious subject for a simulation approach based directly on the physics of the individual molecular interactions. However, prior to the advent. of the digital computer, the approach was effectively ruled out by the enormous number of repetitive arithmetical computations that are required for its application, even to the simplest problem. Typical computer runs of Monte Carlo simulation programs now involve the computation of as many as ten million intermolecular collisions, together with millions of molecule-surface interactions. The molecular or microscopic model of a gas flow must, of course, be viewed against the familiar macroscopic or continuum model. This requires the introduction of the Knudsen number Kn as a distinct dimensionless parameter. The usual definition is
228 citations
TL;DR: In this article, a new algorithm is presented in which the Monte Carlo moves are biased in the direction of the forces and torques acting on the individual molecule, which shows that this new method is much more rapidly convergent.
160 citations
TL;DR: The authors compare the results using nonmetric analysis, full factorial designs, and rank data with quicker and less expensive methods of metric analysis, orthogonal arrays and stimulus ratings to indicate that metric analysis using ratings data and orthogonic arrays is very robust.
Abstract: In many industrial applications of conjoint analysis the use of nonmetric algorithms to analyze respondent ranks of products described by more than eight or 10 attributes is time consuming and very...
148 citations
TL;DR: The structure and energetics of the solvent, both ordered and disordered, in a small peptide crystal and in the triclinic lysozyme crystal have been simulated using the Monte Carlo method to provide insight into the role of solvent structure around biological macromolecules in solution.
Abstract: The structure and energetics of the solvent, both ordered and disordered, in a small peptide crystal and in the triclinic lysozyme crystal have been simulated using the Monte Carlo method. The results are in good agreement with the experimental data and provide insight into the role of solvent structure around biological macromolecules in solution.
136 citations
TL;DR: In this paper, an exact, computer-oriented Monte Carlo procedure is derived for numerically simulating continuous-time/discrete-state random walks in which the transition probability per unit time from state Sm to state Sn may depend upon the residence time τ in the state Sm. Conditions for applicational feasibility of the simulation procedure are briefly indicated, and explicit stepping algorithms for simple τ-dependencies are obtained.
133 citations
TL;DR: In this article, the mean square end-to-end distance and radius of gyration are found to vary exponentially with chain length, and the results are similar to those obtained in Monte Carlo and self-avoiding walk studies.
Abstract: Molecular dynamics simulation techniques have been used to study the equilibrium configurational properties of freely moving polymer chains constructed from linked elastic spheres. The mean square end-to-end distance and radius of gyration are found to vary exponentially with chain length, and the results are similar to those obtained in Monte Carlo and self-avoiding walk studies. It is suggested that molecular dynamics is capable of yielding results of the same quality as Monte Carlo, while avoiding the inherent sampling problems.
TL;DR: In this article, Monte Carlo simulations for correlation functions in various solid-on-solid models, some of which are equivalent to the $F$ model, the two-dimensional Coulomb gas, and the planar model are performed.
Abstract: We have performed Monte Carlo simulations for correlation functions in various solid-on-solid models, some of which are equivalent to the $F$ model, the two-dimensional Coulomb gas, and the planar model. Our results for the $F$ model can be quantitatively represented using the theory of Kosterlitz and Thouless. We use this theory to help determine the transition temperatures in other systems.
TL;DR: In this article, a non-random method of approximating multidimensional integrals is compared to the traditional Monte Carlo method in the determination of average energy transfer values from classical trajectories.
Abstract: A nonrandom method of approximating multidimensional integrals is compared to the traditional Monte Carlo method in the determination of average energy transfer values from classical trajectories. Two atom–diatomic molecule collision systems are studied. Estimates of error show that, for a given number of trajectories, the nonrandom method tends to be more accurate than the Monte Carlo method.
TL;DR: In this article, Monte Carlo computer simulations have been carried out for fluid systems of 256 and 500 heteronuclear and homonuclear hard diatomic molecules, each consisting of fused hard spheres of diameters σAA and σBB with centers separated by distance L. The atom-atom distribution functions gαβ(r), for these models are described in detail, and the discontinuities in their first derivatives at distances σαβ+L, predicted by cluster expansion theory, are shown to have a simple explanation in molecular geometry.
Abstract: Monte Carlo computer simulations have been carried out for fluid systems of 256 and 500 heteronuclear and homonuclear hard diatomic molecules, each consisting of fused hard spheres of diameters σAA and σBB with centers separated by distance L. Nineteen different models have been studied, with elongations L*=L/σAA in the range 0.05⩽L*⩽0.75, and diameter ratios γ=σBB/σAA in the range 0.5⩽γ⩽1.0. The atom–atom distribution functions gαβ(r), for these models are described in detail, and the discontinuities in their first derivatives at distances σαβ+L, predicted by cluster expansion theory, are shown to have a simple explanation in molecular geometry. Pressures have been calculated from a virial‐like equation and used to examine trends in pressure with changes in molecular geometry. Structure factors S (K) and direct correlation functions c (r) have been calculated by Fourier transform of the gαβ(r), and the dependence of these functions on molecular geometry has been examined.
TL;DR: In this paper, the effects of features such as large-angle scattering and the interaction between straggling and scattering are studied and a description based on the near linearity of the transport mean free path lambda tr(s) is used to obtain empirical corrections in some cases of the total transmission and back-scattering simulation and empirical estimates of the (Bethe) range and the transport means free path.
Abstract: Simplified models, based on stopping power, transport mean free path and classical straggling, are shown to give results rather good agreement with experiment and comparable with the results of more detailed, direct Monte Carlo procedure hitherto constructed. The small effects of features such as large-angle scattering and the interaction between straggling and scattering are studied. A description based on the near linearity of the transport mean free path lambda tr(s) is used to obtain empirical corrections in some cases of the total transmission and back-scattering simulation and empirical estimates of the (Bethe) range and the transport mean free path. The estimates of the range are consistent with a rough calculation of the effect of large binding energies.
TL;DR: In this article, the surface ionisation function phi (0) is calculated for a wide range of elements and overvoltages using a Monte Carlo program which simulates electron interactions in solids.
Abstract: Values of the surface ionisation function phi (0) are calculated for a wide range of elements and overvoltages using a Monte Carlo program which simulates electron interactions in solids. From the data it is shown that phi (0) is simply a function of electron back-scatter coefficient and overvoltage, and an analytical expression for phi (0) is derived in terms of these parameters. Values of phi (0) obtained using the expression are compared with previous results.
TL;DR: In this paper, the simpler ARMA type models are examined with respect to properties of a variety of proposed estimators of unknown parameters, and the authors suggest that if only one estimation method were available to a researcher, the choice should probably be maximum likelihood.
TL;DR: In this paper, the Monte Carlo computer simulation technique of classical statistical mechanics is employed to determine the structure and thermodynamics of binary microclusters of Lennard-Jones atoms as a function of cluster size, composition and temperature.
TL;DR: In this paper, the authors used Markov chains to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process, and verified the speed and accuracy of this formalism for finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering.
Abstract: The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.
01 Jun 1978
TL;DR: In this paper, a computer program using a variation of the Monte Carlo method was developed to predict radiative exchange factors in three-dimensional configurations with curved surfaces, allowing for arbitrary emission, absorption, and reflection characteristics and for radiation exchange between surfaces as well as external irradiation through openings.
Abstract: A computer program using a variation of the Monte Carlo method was developed to predict radiative exchange factors in three-dimensional configurations with curved surfaces. The model allows for arbitrary emission, absorption, and reflection characteristics and for radiation exchange between surfaces as well as external irradiation through openings. It was shown that exchange factors can be determined efficiently by using the normal Monte Carlo method for closed configurations and/or high surface emissivities, while energy partitioning is vastly superior in the case of open configurations and/or low surface emissivities. Comparison with some experiments performed on the Space Shuttle heat rejection system demonstrates the model's accuracy as well as its superiority over a simplified diffuse-surface analysis, which requires similar amounts of computer time.
TL;DR: In this article, the effects of density and shape on the structure of the fluid have been observed by using the expansion in spherical harmonics of the pair distribution function, and the equation of state has been calculated at various densities.
TL;DR: In this paper, a generalization of the TRIM computer program such that the target atom trajectories are followed in addition to those of the incident particles is presented, and a model of the sputtering process has been developed for physically defining the surface and bulk binding energies necessary for calculations.
TL;DR: A computer model is developed to predict the central axis dose distributions arising from the interaction between an external beam of radiation and an inhomogeneous medium and results are presented on the centralaxis dose distribution both within and beyond lung and bone inhomogeneities.
Abstract: A computer model is developed to predict the central axis dose distributions arising from the interaction between an external beam of radiation and an inhomogeneous medium. The principal features of the Monte Carlo simulation are discussed. Results are presented on the central axis does distribution both within and beyond lung and bone inhomogeneities.
TL;DR: In this article, the Monte Carlo method is applied to a threedimensional Ising model with nearest neighbour ferromagnetic interactions and next nearest neighbour antiferromagnetic interaction along one axis only.
Abstract: The Monte Carlo method is applied to a threedimensional Ising model with nearest neighbour ferromagnetic interactions and next nearest neighbour antiferromagnetic interactions along one axis only Special emphasis is given to the critical behaviour near the Lifshitz point
TL;DR: In this article, two correlated Monte Carlo methods, the similar flight path and the identical flight path methods, have been improved to evaluate up to the second order change of the reactivity perturbation.
Abstract: Two correlated Monte Carlo methods, the similar flight path and the identical flight path methods, have been improved to evaluate up to the second order change of the reactivity perturbation. Secondary fission neutrons produced by neutrons having passed through perturbed regions in both unperturbed and perturbed systems are followed in a way to have a strong correlation between secondary neutrons in both the systems. These techniques are incorporated into the general purpose Monte Carlo code MORSE, so as to be able to estimate also the statistical error of the calculated reactivity change. The control rod worths measured in the FCA V-3 assembly are analyzed with the present techniques, which are shown to predict the measured values within the standard deviations. The identical flight path method has revealed itself more useful than the similar flight path method for the analysis of the control rod worth.