Showing papers on "Monte Carlo method published in 1982"
TL;DR: In this article, a method for inducing a desired rank correlation matrix on a multivariate input random variable for use in a simulation study is introduced, which preserves the exact form of the marginal distributions on the input variables, and may be used with any type of sampling scheme for which correlation of input variables is a meaningful concept.
Abstract: A method for inducing a desired rank correlation matrix on a multivariate input random variable for use in a simulation study is introduced in this paper. This method is simple to use, is distribution free, preserves the exact form of the marginal distributions on the input variables, and may be used with any type of sampling scheme for which correlation of input variables is a meaningful concept. A Monte Carlo study provides an estimate of the bias and variability associated with the method. Input variables used in a model for study of geologic disposal of radioactive waste provide an example of the usefulness of this procedure. A textbook example shows how the output may be affected by the method presented in this paper.
1,571 citations
1,196 citations
TL;DR: In this article, the ground state energies of H2, LiH, Li2, and H2O are calculated by a fixed-node quantum Monte Carlo method, which is presented in detail.
Abstract: The ground‐state energies of H2, LiH, Li2, and H2O are calculated by a fixed‐node quantum Monte Carlo method, which is presented in detail. For each molecule, relatively simple trial wave functions ΨT are chosen. Each ΨT consists of a single Slater determinant of molecular orbitals multiplied by a product of pair‐correlation (Jastrow) functions. These wave functions are used as importance functions in a stochastic approach that solves the Schrodinger equation by treating it as a diffusion equation. In this approach, ΨT serves as a ‘‘guiding function’’ for a random walk of the electrons through configuration space. In the fixed‐node approximation used here, the diffusion process is confined to connected regions of space, bounded by the nodes (zeros) of ΨT. This approximation simplifies the treatment of Fermi statistics, since within each region an electronic probability amplitude is obtained which does not change sign. Within these approximate boundaries, however, the Fermi problem is solved exactly. The e...
893 citations
TL;DR: In this article, an approximate technique is presented for the evaluation of the mean and variance of the power sums with log-normal components, and exact expressions for the moments with two components are developed and then used in a nested fashion to obtain the moments of the desired sum.
Abstract: An approximate technique is presented for the evaluation of the mean and variance of the power sums with log-normal components. Exact expressions for the moments with two components are developed and then used in a nested fashion to obtain the moments of the desired sum. The results indicate more accurate estimates of these quantities over a wider range of individual component variances than any previously reported procedure. Coupling our estimates with the Gaussian assumption for the power sum provides a characterization of the cumulative distribution function which agrees remarkably well with a Monte Carlo simulation in the 1 to 99 percent range of the variate. Simple polynomial expressions obtained for the moments lead to an effective analytical tool for various system performance studies. They allow quick and accurate calculation of quantities such as cochannel interference caused by shadowing in mobile telephony.
675 citations
TL;DR: In this article, the influence of a hard wall on the configurations of long flexible polymer chains near the wall is studied, in the presence of a short-range attractive force between monomers and the wall.
Abstract: The influence of a hard wall on the configurations of long flexible polymer chains near the wall is studied, in the presence of a short‐range attractive force between monomers and the wall. Particular attention is paid to the region around the temperature Ta below which the polymer becomes adsorbed to the wall, i.e., where the typical polymer linear dimensions perpendicular to the wall become independent of chain length. Both ideal noninteracting chains and chains with excluded volume interactions are treated. Polymer linear dimensions parallel and perpendicular to the wall and their probability distributions are studied, as well as the behavior of the monomer fraction at the surface and a distance z in the interior. The relation of polymer statistics to the problem of correlation functions in the n‐vector model of magnetism in the limit n→0 is exploited to express both the exponents describing the various power laws and the crossover scaling functions near Ta in terms of results for the analogous problem of the critical behavior of magnets with a free surface. The predictions of this scaling theory are confirmed by Monte Carlo studies of self‐avoiding walks on the tetrahedral lattice with a free surface, and estimates for the exponents involved are presented. A new sampling technique with a bias in favor of adsorbed polymer configurations is developed.
582 citations
TL;DR: In this paper, the authors present a review of the main components of calculation methods, based on the solution of conservation equations in differential form, for the velocity, temperature and concentration fields in turbulent combusting flows.
522 citations
TL;DR: The turning bands method (TBM) for the simulation of multidimensional random fields is presented in this paper, which can be general applied to any two-dimensional covariance function and which is easily extended to anisotropic and areal averaged processes.
Abstract: The turning bands method (TBM) for the simulation of multidimensional random fields is presented. These fields commonly occur in the Monte Carlo simulation of hydrologic processes, particularly groundwater flow and mass transport. The general TBM equations for two- and three-dimensional fields are derived with particular emphasis on the more complicated two-dimensional case. For stationary two-dimensional fields the unidimensional line process is generated by a simple spectral method, a technique which can be generally applied to any two-dimensional covariance function and which is easily extended to anisotropic and areal averaged processes. Theoretically and by example the TBM is shown to be ergodic even for a finite number of lines, and it is demonstrated that it rapidly converges to the true statistics of the field. Guidelines are presented for the selection of model parameters which will be helpful in the design of simulation experiments. The TBM is compared to other methods in terms of cost and accuracy, demonstrating that the TBM is as accurate as and much less expensive than multidimensional spectral techniques and more accurate than the most expensive approaches which use matrix inversion, such as the nearest neighbor approach. The unidimensional spectral technique presented here permits, for the first time, the inexpensive and accurate TBM simulation of any proper two-dimensional covariance function and should be of some help in the stochastic analysis of hydrologic processes.
498 citations
TL;DR: In this paper, a Monte Carlo procedure based on a discrete point representation of the path integral for the density matrix is explored, and it is found that the variance of the estimator used to evaluate the energy grows as the square root of the number of discrete points used, and is therefore to be avoided in highly quantum mechanical systems.
Abstract: A Monte Carlo procedure based on a discrete point representation of the path integral for the density matrix is explored. It is found that the variance of the estimator used to evaluate the energy grows as the square root of the number of discrete points used, and is therefore to be avoided in highly quantum mechanical systems, where the number of discrete points must be large. A new energy estimator based on the virial theorem is proposed and shown to be well behaved. The main points of the paper are illustrated, using the harmonic oscillator as an example.
422 citations
TL;DR: In this paper, two approaches are described to the analysis of spatial patterns consisting of several types of points, and some distributional results are given in each case, and a method of Monte Carlo testing conditional on the marginal structure is described.
Abstract: Two approaches are described to the analysis of spatial patterns consisting of several types of points. The first approach uses a method of asymptotically unbiased estimation of the second moment distribution; the second uses methods based on regions of empty space in the patterns. Some distributional results are given in each case, and a method of Monte Carlo testing conditional on the marginal structure is described. The methods are illustrated by being applied to some physiological data.
404 citations
TL;DR: In this paper, it is shown that the interface free energy between bulk phases with a macroscopically flat interface can be estimated from the variation of certain probability distribution functions of finite blocks with block size.
Abstract: It is suggested that the interface free energy between bulk phases with a macroscopically flat interface can be estimated from the variation of certain probability distribution functions of finite blocks with block size. For a liquid-gas system the probability distribution of the density would have to be used. The method is particularly suitable for the critical region where other methods are hard to apply. As a test case, the two-dimensional lattice-gas model is treated and it is shown that already, from rather small blocks, one obtains results consistent with the exact soluion of Onsager for the surface tension, by performing appropriate extrapolations. The surface tension of the three-dimensional lattice-gas model is also estimated and found to be reasonably consistent with the expected critical behavior. The universal amplitude of the surface tension of fluids near their critical point is estimated and shown to be in significantly better agreement with experimental data than the results of Fisk and Widom and the first-order 4-d renormalization-group expansion. Also the universal amplitude ratio used in nucleation theory near the critical point is estimated.
379 citations
TL;DR: In this article, a quenched version of the Eguchi-Kawai model is proposed, which gives good behavior at weak couplings, based on an analytic investigation and on Monte Carlo simulations.
TL;DR: In this paper, the transport of neutral atoms and molecules in the edge and divertor regions of fusion experiments has been calculated using Monte-Carlo techniques using a pseudocollision method.
TL;DR: In this article, a Monte Carlo method for studying the steady-state behavior of charged species under the influence of a non-uniform electric field is described, using a null-collision technique based on determination of the increase in kinetic energy between two collisions, avoiding calculation of the time variations of the phase space coordinates of the charged species.
Abstract: A Monte Carlo method for studying the steady-state behaviour of charged species under the influence of a non-uniform electric field is described. This method, using a null-collision technique based on determination of the increase in kinetic energy between two collisions, avoids calculation of the time variations of the phase space coordinates of the charged species. The electron behaviour in the cathode region of a glow discharge has been analysed using this method; spatial variations of the energy and angular electron distribution functions, and of the macroscopic electron parameters are discussed.
TL;DR: In this article, the authors derived exact statistical mechanical relations for polyelectrolyte systems within the primitive model using the cell model and determined the osmotic pressure through an explicit evaluation of the derivative of the partition function.
Abstract: Some exact statistical mechanical relations have been derived for polyelectrolyte systems within the primitive model. Using the cell model, the osmotic pressure is determined through an explicit evaluation of the derivative of the partition function. Planar, cylindrical, and spherical systems are considered and for a planar charged wall the contact value theorem [Henderson and Blum, J. Chem. Phys. 69, 5441 (1978)] is obtained as a special case. Analogous relations are derived for the cylindrical and spherical geometries. It is argued that the exact relations can be used as consistency tests for analytical approximations. It is pointed out that one merit of the Poisson–Boltzmann approximation is that the validity of the exact equations is retained. Finally, a simple method is devised for determining the osmotic pressure from Monte Carlo simulations. Results from such simulations are used to assess the accuracy of the osmotic pressure calculated using the Poisson–Boltzmann equation. For monovalent ions, the pressure is overestimated by 10%–50% in the cases studied, while with divalent counterions the error is substantially larger and a discrepancy of one order of magnitude is found.
TL;DR: In this paper, a new computer simulation technique to evaluate the chemical potential in dense fluids, where the usual test particle method fails, is described, based on the use of the well known Widom test particle equation in conjunction with another equation which is the inverse of the Widom equation.
Abstract: We describe a new computer simulation technique to evaluate the chemical potential in dense fluids, where the usual test particle method fails. The method rests on the use of the well known Widom test particle equation in conjunction with another equation which is the inverse of the Widom equation. We show that the distribution functions (f and g, respectively) that describe the distribution of the test particle interaction energy u t for these two equations are exactly related (equation (10) below), and that g can be obtained accurately for the values of u t that are needed to calculate the chemical potential. This equation provides the basis for the method. We also propose a further refinement called ‘restricted umbrella sampling’, which improves the efficiency of placing the test particle in the fluid for a fixed configuration of real molecules. Detailed tests of the method are presented using the Monte Carlo technique, for both pure Lennard-Jones (LJ) fluids and LJ mixtures. We find that the method wo...
TL;DR: In this paper, the dynamics of interfaces where the normal component of an interface velocity is proportional to the curvature of the interface is studied and the dynamic structure function due to the motion of random interfaces is shown to satisfy a scaling law.
Abstract: The dynamics of interfaces where the normal component of an interface velocity is proportional to the curvature is studied. The dynamic structure function due to the motion of random interfaces is shown to satisfy a scaling law. The results are compared with Monte Carlo simulations of the kinetics of the order-disorder transition in a quenched system.
TL;DR: In this paper, a probabilistic language based on stochastic models of population growth is proposed for a standard language to be used in environmental assessment, which is measured by the probability of quasiextinction.
Abstract: A probabilistic language based on stochastic models of population growth is proposed for a standard language to be used in environmental assessment. Environmental impact on a population is measured by the probability of quasiextinction. Density-dependent and independent models are discussed. A review of one-dimensional stochastic population growth models, the implications of environmental autocorrelation, finite versus “infinite” time results, age-structured models, and Monte Carlo simulations are included. The finite time probability of quasiextinction is presented for the logistic model. The sensitivity of the result with respect to the mean growth rate and the amplitude of environmental fluctuations are examined. Stochastic models of population growth form a basis for formulating reasonable criteria for environmental impact estimates.
TL;DR: In this article, a method for calibrating the light output of NE 213 scintillation detectors by means of "monoenergetic" photon sources is described, where the position of the Compton edge can be precisely determined by comparing the measured pulse-height spectrum with a Monte Carlo simulated distribution properly folded with the pulse height dependent resolution.
TL;DR: The internal energy of the classical one-component plasma is calculated using a Monte Carlo technique for 128, 250, 432, 686, and 1024 particles for 1.
Abstract: We calculate the internal energy of the classical one-component plasma using a Monte Carlo technique for 128, 250, 432, 686, and 1024 particles for $1l\ensuremath{\Gamma}l300$ in order to determine the effect of a differing number of particles on the thermodynamics. By fitting the internal energy to a function of $\ensuremath{\Gamma}$ and $N$ (the particle number), we find the free energy for both the liquid and solid for an infinite number of particles.
TL;DR: In this article, the authors present results from extensive Monte Carlo simulations of the fluid phase of the two-dimensional classical one-component plasma (OCP) and compare these results to those obtained for a planar system with screened Coulomb interactions and periodic boundary conditions.
Abstract: We present results from extensive Monte Carlo simulations of the fluid phase of the two-dimensional classical one-component plasma (OCP). The difficulties associated with the infinite range of the logarithmic Coulomb interaction are eliminated by confining the particles to the surface of a sphere. The results are compared to those obtained for a planar system with screened Coulomb interactions and periodic boundary conditions; in this case the infinite tail of the Coulomb interaction is treated as a perturbation. The “exact” simulation results are used to test various approximate theories, including a semiempirical modification of the hypernetted-chain (HNC) integral equation. The OCP freezing transition is located at a couplingγ= e2/kBT−140.
TL;DR: In this article, the hypernetted chain integral equations (HNC/MSA version) for the reduced density profiles of a model electrolyte near a charged electrode are solved and the resulting density and potential profiles are compared with recent Monte Carlo calculations.
Abstract: The hypernetted chain integral equations (HNC/MSA version) for the reduced density profiles of a model electrolyte near a charged electrode (the so‐called electrical double layer problem) are solved and the resulting density and potential profiles are compared with recent Monte Carlo calculations. Good agreement is found when the bulk electrolyte direct correlation functions are calculated from the mean spherical approximation. In particular, the HNC/MSA correctly predicts that for divalent salts, the potential profile is nonmonotonic and changes sign. As a result, there is charge oscillation or a layering of charge. That is, near the electrode the ions predominately have the opposite charge as the electrode but in some situations the ions at a greater distance generally have the same charge as the electrode. In contrast, the Gouy–Chapman theory gives poor results. The Gouy–Chapman density and potential profiles are always monotonic. Thus, the widely used practice of estimating the effects of solvent or n...
TL;DR: The general conclusion reached is that the three methods produce results that are equivalent, and several important trends were observed.
Abstract: Factor analysis and component analysis represent two broad classes of methods employed generally with similar types of problems. The purpose of the present study is to determine the extent to which and under what conditions the methods produce different patterns. Principal component analysis, image component analysis, and maximum likelihood factor analysis were performed on simulated data matrices. Comparisons were made between each of the three methods and to ideal patterns. Sample size, saturation, and type of pattern were systematically varied. The general conclusion reached is that the three methods produce results that are equivalent. In addition, several important trends were observed.
TL;DR: In this paper, the effect of surface polarization on the properties of electrical double layers is studied by means of Monte Carlo calculations on a primitive model electrolyte next to a planar charged surface bounding a semi-infinite dielectric.
Abstract: The effect of surface polarization (i.e., image forces) on the properties of electrical double layers is studied by means of Monte Carlo calculations on a primitive model electrolyte next to a planar charged surface bounding a semi‐infinite dielectric. Two cases are considered, that of a conducting material for which an ion is attracted by its own image and that of an insulator for which the self‐image force is repulsive. At low surface charge densities the image forces cause quite dramatic changes in the ionic densities near the wall; the effect on the electrostatic potential is small but increases with surface charge density. The modified Poisson–Boltzmann theory of Outhwaite is quite successful in describing the Monte Carlo results for the range of parameters studied. A screened self‐image model of image effects is also considered for which both Monte Carlo calculations and numerical solution of the HNC equation have been obtained.
TL;DR: In this article, the potential energy surface of the LiH molecule was calculated using the Green's function Monte Carlo method and the calculated correlation energy is 0.078±0.001 hartree and the binding energy is 2.56 eV.
Abstract: The potential energy surface of the LiH molecule is calculated using the Green’s function Monte Carlo method. The calculated correlation energy is 0.078±0.001 hartree and the binding energy is 2.56 eV. These results are within 6% and 2% of the experimental values, respectively. The Green’s function Monte Carlo method is discussed in some detail with particular emphasis on problems of chemical interest.
TL;DR: In this article, the effects of scatter and attenuation on single photon emission computed tomography (SPECT) images can be analyzed with the aid of sophisticated Monte Carlo simulation, which enables control of components which govern the emission and transport of radiation through the source and attenuating medium.
Abstract: The effects of scatter and attenuation on single photon emission computed tomography (SPECT) images can be analyzed with the aid of sophisticated Monte Carlo simulation. Correction procedures can be evaluated by comparing corrected images with images absent of scatter and attenuation. The simulation enables control of components which govern the emission and transport of radiation through the source and attenuating medium. The basic calculation involves sampling the probability density functions (pdf) which govern the photon transport process. First, the origin of a photon is selected by sampling. Variance reduction is applied so that a detection is "forced" and weighted by the probability of an initial direction within the acceptance angle of the collimator multiplied by the probability that the photon is not attenuated. Second, the photon history is continued by sampling for a direction. The photon is forced to interact within the attenuating medium and an appropriate weight is calculated. Variance reduction is again applied with a weight determined by the product of the probability of interaction within the attenuating medium, the probability of scatter, the probability of scattering into the acceptance angle of the collimator, and the probability that the photon reaches the detector. Finally, a new direction and energy is selected. If the new energy is below the baseline energy, the history is terminated; otherwise, the second step is repeated. Presently, the collimator's geometric efficiency is considered without septal penetration.
TL;DR: The first numerical determination of the thermodynamic isotropic-nematic transition in a simple three-dimensional model fluid, viz., a system of infinitely thin hard platelets, is reported in this article.
Abstract: The first numerical determination of the thermodynamic isotropic-nematic transition in a simple three-dimensional model fluid, viz., a system of infinitely thin hard platelets, is reported. Thermodynamic properties were studied with use of the constant-pressure Monte Carlo method; Widom's particle-insertion method was used to measure the chemical potential. The phase diagram is found to differ considerably from predictions of a second-virial ("Onsager") theory. Virial coefficients up to the fifth were computed; b5 is found to be negative.
TL;DR: In this paper, Monte Carlo simulations have been performed on a system of 91 hard spheres representing water-like molecules with extremely simple short-range interactions and the agreement between the energy, entropy and free energy of physical water and of the model is reasonable.
Abstract: In an attempt to understand the salient thermodynamic features of liquid water in relation to the molecular interactions in the system, Monte Carlo simulations have been performed on a system of 91 hard spheres representing waterlike molecules with extremely simple short-range interactions. The thermodynamic equilibrium properties, including the free energy and equation of state, are evaluated. The agreement between the energy, entropy and free energy of physical water and of the model is reasonable. It appears that an anomaly in the thermal expansion, as exists in physical water, can be observed when a preference for tetrahedral coordination is superimposed on the hard spheres. When additionally the spheres are made polar, the anomaly persists.
TL;DR: In this article, the authors studied lattice g0φ4 field theory for all g0 and fixed renormalized mass M in one and two dimensions using Monte Carlo techniques.
TL;DR: In this article, the authors used the Monte Carlo method to evaluate the internal energy, the heat capacity and the second rank orientational order parameter of a nematogen, and the potential of mean torque was found to be linear in the order parameter as required by the Maier-Saupe theory.
Abstract: The Lebwohl-Lasher model of a nematogen provides a simple system with which to study the order-disorder transition and to examine the properties of the nematic phase. We have investigated the model containing 203 particles over a small temperature range characteristic of that for real nematogens using the Monte Carlo method to evaluate the internal energy, the heat capacity and the second rank orientational order parameter. Our results are in reasonable agreement with those of other simulations and are compared with the predictions of theories based on a cluster expansion of the free energy. The temperature dependence of the order parameter is used to investigate the validity of the singlet orientational distribution function predicted by the Maier-Saupe theory. The potential of mean torque is found to be linear in the order parameter as required by the theory although the orientational free energy is in error. The simulated properties are in reasonable but not complete accord with those of a real nematog...
TL;DR: The results from the present numerical study indicate that the experimental application of fluorescence energy transfer measurements in multicomponent membrane systems can be used to obtain organizational parameters that accurately reflect the lateral distribution of protein and lipid molecules within the bilayer membrane.