Showing papers on "Monte Carlo molecular modeling published in 1973"
TL;DR: In this paper, a formal power series expansion of the initial terms of a power-series expansion with respect to the number of observations has been proposed, in most cases down to 4 observations per parameter.
Abstract: Maximum likelihood type robust estimates of regression are defined and their asymptotic properties are investigated both theoretically and empirically. Perhaps the most important new feature is that the number $p$ of parameters is allowed to increase with the number $n$ of observations. The initial terms of a formal power series expansion (essentially in powers of $p/n$) show an excellent agreement with Monte Carlo results, in most cases down to 4 observations per parameter.
2,221 citations
TL;DR: In this article, Monte Carlo studies of the dielectric properties of water-like models were performed in order to understand the properties of the water-based models in terms of their dielectrics.
Abstract: (1973). Monte Carlo studies of the dielectric properties of water-like models. Molecular Physics: Vol. 26, No. 3, pp. 789-792.
665 citations
TL;DR: In this article, a formal physical cluster theory for an imperfect gas, valid for an arbitrary definition of a ''physical cluster'' is described and the role of the definition of the physical cluster is stressed.
Abstract: A formal physical cluster theory for an imperfect gas, valid for an arbitrary definition of a ``physical cluster,'' is described The role of the definition of the physical cluster is stressed For a particular definition of the physical cluster, which may be appropriate in nucleation theory, the Helmholtz free energy of 13‐, 43‐, 60‐, 70‐, 80‐, 87‐, and 100‐atom argon clusters is calculated in the classical limit for temperatures ranging from absolute zero to 100°K using Monte Carlo techniques It is found that a cluster's free energy is almost independent of its definition provided that the definition is reasonable and the temperature is sufficiently low The results are compared with the predictions using the harmonic approximation
378 citations
TL;DR: In this paper, the perturbation approach developed by Weeks, Chandler, and Andersen (WCA) and by Verlet and Weis (VW) for pure systems is generalized to the case of mixtures and the radial distribution functions generated are used to test the VW representation for the correlation functions of hard-sphere mixtures.
Abstract: The perturbation approach developed by Weeks, Chandler, and Andersen (WCA) and by Verlet and Weis (VW) for pure systems is here generalized to the case of mixtures. We study binary mixtures of molecules interacting with the 12–6 Lennard-Jones potential, for which Monte Carlo simulations are available for comparison. The work is divided into two parts: The first part presents results of Monte Carlo calculations on mixtures of hard spheres of 864 and 1000 particles. The radial distribution functions generated are used to test the VW representation for the correlation functions of hard-sphere mixtures. This representation is found to work satisfactorily within the expected error limits. The second part deals with the two-step perturbation procedure for calculating the thermodynamic quantities of the Lennard-Jones system. The Lennard-Jones potential is divided into a reference potential, which is strictly repulsive, and an attractive part. The system of the reference potential is represented by a system of ha...
255 citations
TL;DR: A numerical integration technique based upon the use of nonrandom number sequences is examined with test integrations of a simple, analytical function and shows that the error of the new method decreases faster as more points are used in the calculation.
Abstract: A numerical integration technique based upon the use of nonrandom number sequences is examined with test integrations of a simple, analytical function. A comparison of the nonrandom technique with the familiar Monte Carlo method shows that the error of the new method decreases faster as more points are used in the calculation. Moreover, the new method needs fewer points to calculate an integral to an accuracy of 10% than does the Monte Carlo method.
247 citations
TL;DR: In this paper, the Monte Carlo sampling technique is used to calculate the equilibrium thermodynamics of fluids and magnets, and the questions of convergence and accuracy of this method can be understood in terms of the dynamics of the appropriate stochastic model.
Abstract: By means of the Monte Carlo sampling technique the equilibrium thermodynamics of fluids and magnets can be calculated numerically. We show that the questions of convergence and accuracy of this method can be understood in terms of the dynamics of the appropriate stochastic model. Also, we discuss to what extent various choices of transition probabilities lead to different dynamic properties of the system. As examples of applications, we consider Ising and Heisenberg spin systems. The numerical results about the dynamic correlation functions are compared to simple approximations taken from the theory of the kinetic Ising model.
214 citations
TL;DR: In this article, Monte Carlo free energy results for a fluid of point dipoles embedded in hard spheres are reported for a multistage sampling method compared with thermodynamic integration techniques, and the resulting free energies are compared with recent theoretical results obtained from the mean spherical model approximation and from a perturbation theory approach.
118 citations
01 Jan 1973
TL;DR: In this article, numerical calculations of the L2 discrepancy for several types of quasi-Monte Carlo formulae are presented, and the L 2 discrepancy is associated with the set of points used in the integration.
Abstract: The quasi-Monte Carlo method of integration offers an attractive solution to the problem of evaluating integrals in a large number of dimensions; however, the associated error bounds are difficult to obtain theoretically. Since these bounds are associated with the L2 discrepancy of the set of points used in the integration. Numerical calculations of the L2 discrepancy for several types of quasi-Monte Carlo formulae are presented.
102 citations
TL;DR: Gast and Candelore as discussed by the authors pointed out that the standard method of computing confidence limits in Monte Carlo calculations is invalid for iterated-source calculations and developed a new method to compute confidence limits.
Abstract: Gast and Candelore have recently pointed out that the standard method of computing confidence limits in Monte Carlo calculations is invalid for iterated-source calculations. This note develops a fo...
44 citations
TL;DR: In this article, a method of estimating the prediction coefficients from the usual "windowed" estimates of spectral density function is put forward and a Monte Carlo comparison of this method with the more usual regression method of finding the best fitting autoregressive process by recursively solving the Yule-Walker equations is carried out.
Abstract: We consider the question of estimating the linear, least-squares predictor of the future values of a real-valued, discrete, purely nondeterministic, stationary time series from its known past. A method of estimating the prediction coefficients from the usual ‘windowed’ estimates of spectral density function is put forward and a Monte Carlo comparison of this method with the more usual regression method of finding the best fitting autoregressive process by recursively solving the Yule-Walker equations is carried out.
31 citations
TL;DR: In this paper, a simple Monte Carlo sampling method is used to illustrate the principles of statistical mechanics as applied to a simple magnetic system and the concepts of ensembles, statistical averages, and responses are clarified particularly with respect to the role of statistical fluctuations.
Abstract: A simple Monte Carlo sampling method is used to illustrate the principles of statistical mechanics as applied to a simple magnetic system. The concepts of ensembles, statistical averages, and responses are clarified particularly with respect to the role of statistical fluctuations. The basic properties of magnetic phase transitions are also demonstrated using small systems of interacting moments.
TL;DR: In this article, a Monte Carlo simulation model for radiation-induced plasmas with nonlinear properties due to recombination has been developed employing a piecewise-linearized predict-correct technique.
Abstract: A Monte Carlo simulation model for radiation-induced plasmas with nonlinear properties due to recombination has been developed employing a piecewise-linearized predict-correct technique. Several va...
TL;DR: Comments are given on the combined use of Monte Carlo and sensitivity analysis as an efficient and accurate way of improving thermal analysis.
Abstract: Alternatives to "worst-case" thermal analysis are discussed, and a Monte Carlo method is developed for treating the uncertainties inherent in property data for such analysis. Comparison is made with another treatment of such problems using sensitivity analysis. Comments are given on the combined use of Monte Carlo and sensitivity analysis as an efficient and accurate way of improving thermal analysis. Comparison of various analytical treatments is given by means of an example problem.
01 Jan 1973
TL;DR: In this paper, a method for solving the radiative transport equation with Monte Carlo was developed, in which the photon source is expressed as the sum of an extraneous source term plus a pseudoscattering term by utilizing the RTE equation.
Abstract: A method ia developed to solve the radiative transport equation with Monte Carlo. The photon source aT4 ia expressed aa the sum of an extraneoussource term plus a pseudoscatteringterm by utilizing the radiative energy balance equation. This resulting photon source is sampled directly in the Monte Carlo calculationwith an extrapolation of croaa aectiona and equation-of-statedata from the previous time step.
TL;DR: In this paper, the Helmholtz free energy difference between unconstrained and single occupancy classical fluids is calculated in a Monte Carlo experiment at a single density by using special sampling techniques to measure the fraction of unconstrains configurations that show single occupancy.
Abstract: The Helmholtz free energy difference between unconstrained and ``single occupancy'' classical fluids may be calculated in a Monte Carlo experiment at a single density by using special sampling techniques to measure the fraction of unconstrained configurations that show single occupancy. Results obtained by this method for the hard sphere fluid are in agreement with values obtained by Hoover and Ree by the numerical integration of machine generated pressure‐density data. The relative merits of these two methods for locating the melting transitions of model systems are discussed.
TL;DR: In this paper, the diffusion of a sorbate in a solid body bisected by a narrow straight grain boundary has been simulated using a combination of the so-called floating random walk Monte Carlo technique and a modified technique of that sort, particularly applicable to the study of random walks inside narrow grain boundaries.
Abstract: The diffusion of a sorbate in a solid body bisected by a narrow straight grain boundary has been simulated using a combination of the so‐called floating random walk Monte Carlo technique and a modified technique of that sort, particularly applicable to the study of random walks inside narrow grain boundaries. The results have been compared to the published solutions obtained from deterministic methods. Complex composite processes involving simultaneous bulk, grain boundary, and surface diffusion have been simulated as well, using the techniques so developed, so as to show that the computations are quite feasible, even though at this point the results cannot always be verified by comparison to known solutions.
TL;DR: In this article, the numerical methods and computing techniques needed to obtain an electron atom collision cross section by the Monte Carlo classical trajectory method are described and illustrated by examples, and the need for classical cross sections is briefly presented.
TL;DR: In this article, a non-random method for approximating multidimensional integrations is compared to traditional ''random'' Monte Carlo techniques for determining reaction cross sections from quasiclassical trajectories.
Abstract: A nonrandom method for approximating multidimensional integrations is compared to traditional ``random'' Monte Carlo techniques for determining reaction cross sections from quasiclassical trajectories. Reaction cross sections are calculated for the H + H2 collision system to determine the relative rates of convergence for each method as a function of the number of trajectories employed in the calculation. Estimates of the maximum probable error for the nonrandom integrations of a given number of trajectories compare favorably with the errors expected for Monte Carlo integrations and seem to imply that nonrandom integrations are more accurate than Monte Carlo calculations. However, the error of a Monte Carlo integration is easily estimated while that of a nonrandom integration is not. Thus the nonrandom method's advantage in accuracy may be overcome by other characteristics of the Monte Carlo method. For classical trajectory calculations, the nonrandom method should be considered as an alternative, but not...
TL;DR: The discontinuous function frequently employed for describing the target molecules' velocity distribution is replaced here by a continuous analytic function, the form of calculations, which simplifies the calculations, reduces the computer storage requirements, and facilities the application of the method to multi-dimensional problems.
TL;DR: In this article, an alternative approach to the calculation of transmission factors is given, and several variance-reducing techniques are discussed, and a comparison with earlier attempts is made, and some results are listed.
Abstract: An alternative approach to the calculation of transmission factors is given. Several variance-reducing techniques are discussed. A comparison with earlier attempts is made. Description of a program is given. Some results are listed. Typical computing time is 0.3 sec per reflexion (cpu) on an IBM 360/65.
01 Mar 1973
TL;DR: This volume provides a straightforward approach and associated techniques for selecting the most appropriate probability distributions for use in Monte Carlo simulations.
Abstract: : The document is the first of three volumes which present techniques and methods for developing efficient Monte Carlo simulation. The volume provides a straightforward approach and associated techniques for selecting the most appropriate probability distributions for use in Monte Carlo simulations. Part 1, Basic Considerations, presents the underlying concepts and principles for selecting probability distributions. Part 2, Selection of Distributions, gives the mathematical models representing stochastic processes and presents step-by- step procedures for identification and selection of the appropriate probability distributions based upon the degree of knowledge and available data for the ramdom variable under study.
TL;DR: In this paper, a modified Monte Carlo approach, termed the simultaneity procedure, has been developed to hasten the classical Monte Carlo application, which can be adapted more widely, so that the techniques of a parallel simultaneous procedure and a successive simultaneous procedure can be devised and demonstrated.
Abstract: The advantages of applying the Monte Carlo methods to problems of water movement in soils have shown that very difficult problems can often be treated easily and that solutions at only a few points in a flow system can be obtained independently. A modified Monte Carlo application presented herein, termed the simultaneity procedure, has been developed to hasten the classical Monte Carlo application. So that the simultaneity procedure can be adapted more widely, the techniques of a parallel simultaneity procedure and a successive simultaneity procedure are devised and demonstrated. Examples are presented not only for the problems of groundwater movement and Thiessen coefficients but also for the problems of general mathematics. Comparisons of results indicate that the simultaneity procedure has the same accuracy as the classical Monte Carlo method, but the computing time is reduced by approximately 30–60% by using the simultaneity procedure.
TL;DR: In this paper, an alternative procedure which overcomes some of the difficiencies in their treatment and extends the study to physical circumstances which their treatment excludes (e.g., background inhomogeneity, crossover into cutoff regions, etc.).
Abstract: Hochstim and Martens were the first to use Monte Carlo computations to study scattering characteristics of scalar waves from randomly fluctuating slabs with an exponential spatial correlation. This paper describes an alternative procedure which overcomes some of the difficiencies in their treatment and extends the study to physical circumstances which their treatment excludes (e.g., background inhomogeneity, crossover into cutoff regions, etc.). The two-point correlation function characterizing the medium fluctuations (more directly the spectral density) may be arbitrarily selected and is no longer restricted to an exponential. The correlation properties of the medium are virtually independent of the length of the elementary slabs comprising the overall slab region, whence the medium may be structured by equal sized slab realizations-a major advantage whenever a background profile is superimposed. Furthermore, the statistics associated with the reflection and transmission of both the coherent as well as the incoherent waves are calculated separately. The results so obtained yield solutions with which appropriate analytical theories can be conveniently compared and they provide information additional to that found in previous studies. As examples, the syntheses of Gaussian and exponential correlation functions are shown. For the exponential, propagation calculations for a homogeneous random slab were made using the new technique and compared with results using Hochstim and Martens' approach.
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TL;DR: In this article, an alternative derivation of a Monte Carlo method that has been used to study robust estimators is given, and extensions of the technique to the regression case are also considered and some computational points are briefly mentioned.
Abstract: This paper gives an alternative derivation of a Monte Carlo method that has been used to study robust estimators. Extensions of the technique to the regression case are also considered and some computational points are briefly mentioned.