Showing papers on "Monte Carlo molecular modeling 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, 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: 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.
112 citations
110 citations
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.
75 citations
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: A procedure is developed to obtain practical numerical results in connection with the m-out-of-n sliding-window detection problem, motivated by difficulties with previous approaches involving approximation, Markov models, and Monte Carlo simulation.
Abstract: A procedure is developed to obtain practical numerical results in connection with the m-out-of-n sliding-window detection problem. This effort was motivated by difficulties with previous approaches involving approximation, Markov models, and Monte Carlo simulation. Generating-function methods were found to be unsatisfactory for window lengths greater than 6 due to their complexity. Instead, a Markov model is described that is then constructively reduced to the minimum number of state variables. The results are derived for binary strings with intersymbol correlation. Computational aids are discussed for obtaining design information, such as quantiles, from the minimal-order Markov models. Numerical results are given comparing the methods of the paper with a "jumping" window approximation for an 8/10 problem.
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 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: 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, the authors examined the relationship between analytic continuation of transfer matrix eigenvalues and metastability in the Ising model and the Monte Carlo model, and provided quantitative support for the critical droplet model for decay.
Abstract: Metastability in the Ising model is studied in two ways In a dynamical Monte Carlo model, metastable magnetization and lifetime are measured for various magnetic fields and low temperatures Following up a proposed relation between analytic continuation of transfer matrix eigenvalues and metastability, transfer matrix eigenvalues are studied We examine the extent to which these approaches agree The Monte Carlo data also provide quantitative support for the critical droplet model for decay
TL;DR: In this paper, the authors developed stress distributions using Kruskal's second stress formula based upon a null hypothesis of equal likelihood in the ranking of a set of proximities.
Abstract: Researchers in the past ten years have studied various parameters involved in nonmetric multidimensional scaling by utilizing Monte Carlo procedures. This paper develops stress distributions using Kruskal's second stress formula based upon a null hypothesis of equal likelihood in the ranking of a set of proximities. These distributions can serve to determine whether a set of data has other than random structure.
TL;DR: In this article, the fictitious scattering radiation transport model was extended for use in deep-penetration calculations by using Monte Carlo applications in geometrically complex systems, and the model was used for deep penetration calculations.
Abstract: The fictitious scattering radiation transport model, suitable for Monte Carlo applications in geometrically complex systems, has been extended for use in deep-penetration calculations by the develo...
TL;DR: In this article, the authors compared and discussed several random ranking studies and suggested that the use of a principal components decomposition of the doubly centered matrix of dissimilarities, or some transformation thereof, will yield an initial configuration which is superior to a randomly chosen one.
Abstract: In response to Arabie several random ranking studies are compared and discussed. Differences are typically very small, however it is noted that those studies which used arbitrary configurations tend to produce slightly higher stress values. The choice of starting configuration is discussed and we suggest that the use of a principal components decomposition of the doubly centered matrix of dissimilarities, or some transformation thereof, will yield an initial configuration which is superior to a randomly chosen one.
TL;DR: In this article, Monte Carlo calculations of X-ray light curves for binary systems surrounded by clouds with simple density distributions, chemical compositions, and ionization structures are presented for the cases of a uniform-density cloud with a radius four times the binary orbital separation, a steady-state constant-velocity stellar wind emanating from the companion star, and a spherically symmetric shell or "cocoon" of the type proposed for Cyg X-3.
Abstract: Results are presented for Monte Carlo calculations of X-ray light curves for binary systems surrounded by clouds with simple density distributions, chemical compositions, and ionization structures. Occultation of the X radiation by the companion star is taken into account along with Compton scattering and photoionization within the clouds. The models are used to examine the effect of various cloud geometries and ionization structures on the emergent X-ray flux as a function of orbital phase and X-ray energy. The results demonstrate the sensitivity of observed light curves and phase-dependent spectra with respect to the optical depth, geometry, and ionization structure of a surrounding cloud for the cases of a uniform-density cloud with a radius four times the binary orbital separation, a steady-state constant-velocity stellar wind emanating from the companion star, and a spherically symmetric shell or 'cocoon' of the type proposed for Cyg X-3. It is concluded that X-ray binary systems are unlikely to be surrounded by obscuring clouds.
TL;DR: In this article, Monte Carlo simulation was performed for finite two-dimensional single spin flip kinetic Ising model which is quenched from a thermodynamically stable to an unstable state.
TL;DR: In this paper, the temperature dependence of the limiting reduced free energy per step for self-avoiding walks on the cubic and face centred cubic lattices, interacting with a plane (square lattice) surface, was studied by exact enumeration and extrapolation techniques as well as by Monte Carlo methods.
Abstract: The temperature dependence of the limiting reduced free energy per step for self-avoiding walks on the cubic and face centred cubic lattices, interacting with a plane (square lattice) surface, is studied by exact enumeration and extrapolation techniques as well as by Monte Carlo methods. These data, together with the locations of the zeros of the partition, functions, are used to estimate the locations of the adsorption transitions.
TL;DR: In this article, the Amster and Djomehri theory is generalized to allow the score distribution functions to depend on the coordinates of two successive collisions, and the expected contributions to the track-length estimator are also treated.
Abstract: Present theories for predicting expected Monte Carlo errors in neutron transport calculations apply to estimates of flux-weighted integrals sampled directly by scoring individual collisions. To treat track-length estimators, the recent theory of Amster and Djomehri is generalized to allow the score distribution functions to depend on the coordinates of two successive collisions. It has long been known that the expected track length in a region of phase space equals the expected flux integrated over that region, but that the expected statistical error of the Monte Carlo estimate of the track length is different from that of the flux integral obtained by sampling the sum of the reciprocals of the cross sections for all collisions in the region. These conclusions are shown to be implied by the generalized theory, which provides explicit equations for the expected values and errors of both types of estimators. Sampling expected contributions to the track-length estimator is also treated. Other general properties of the errors for both estimators are derived from the equations and physically interpreted. The actual values of these errors are then obtained and interpreted for a simple specific example.
TL;DR: In this paper, Monte Carlo simulations of the two-dimensional discrete Gaussian model of roughening are used to obtain the thermodynamic properties of the Coulomb lattice gas and the Villain XY model.
Abstract: Monte Carlo simulations of the two-dimensional discrete Gaussian model of roughening are used to obtain the thermodynamic properties of the Coulomb lattice gas and the Villain XY model. A comparison of the results with the first four terms in the low-temperature expansion of the discrete Gaussian model and the independent-pair approximation in the Coulomb gas representation confirms the accuracy and reliability of the Monte Carlo method generally, but reveals difficulties in the neighborhood of the transition. Various types of Monte Carlo simulations are compared and their consequences in different representations are discussed.