Showing papers on "Monte Carlo method published in 1977"

Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features.

Abstract: A new procedure is discussed which fits either the weighted or simple Euclidian model to data that may (a) be defined at either the nominal, ordinal, interval or ratio levels of measurement; (b) have missing observations; (c) be symmetric or asymmetric; (d) be conditional or unconditional; (e) be replicated or unreplicated; and (f) be continuous or discrete. Various special cases of the procedure include the most commonly used individual differences multidimensional scaling models, the familiar nonmetric multidimensional scaling model, and several other previously undiscussed variants. The procedure optimizes the fit of the model directly to the data (not to scalar products determined from the data) by an alternating least squares procedure which is convergent, very quick, and relatively free from local minimum problems. The procedure is evaluated via both Monte Carlo and empirical data. It is found to be robust in the face of measurement error, capable of recovering the true underlying configuration in the Monte Carlo situation, and capable of obtaining structures equivalent to those obtained by other less general procedures in the empirical situation.

Monte Carlo simulation of a many-fermion study

Abstract: The Metropolis Monte Carlo method is used to sample the square of an antisymmetric wave function composed of a product of a Jastrow wave function and a number of Slater determinants. We calculate variational energies for $^{3}\mathrm{He}$ and several models of neutron matter. The first-order Wu-Feenberg expansion is shown always to underestimate the energy, sometimes seriously. The phase diagram for ground-state Yukawa matter is determined. There is a class of Yukawa potentials which do not lead to a crystal phase at any density.

Simple Monte Carlo Tests for Spatial Pattern

Abstract: The Monte Carlo approach to testing a simple null hypothesis is reviewed briefly and several examples of its application to problems involving spatial distributions are presented. These include spatial point pattern, pattern similarity, space‐time interaction and scales of pattern. The aim is not to present specific “recommended tests” but rather to illustrate the value of the general approach, particularly at a preliminary stage of analysis.

Do Robust Estimators Work with Real Data

Abstract: Most studies of robust estimators of location parameters have relied upon mathematical theory, computer simulated data, or a combination of these. This paper presents a comparison of the performances of eleven estimators using real data sets. Twenty sets of data from 1761 determinations of the parallax of the sun, from 1798 measurements of the mean density of the earth, and from circa 1880 measurements of the speed of light, are employed in the study, with the current values of these physical constants being compared with the estimators' realized values. We find that light trimming provides some improvement over the sample mean, but that the sample mean itself compares favorably with many recent proposals. The bias and nonnormality of the data sets is considered, and the data sets are presented and discussed in an appendix.

Computer simulation of a gas–liquid surface. Part 1

Abstract: The gas–liquid surface of a system of Lennard-Jones (12, 6) molecules has been simulated by Monte Carlo and by Molecular Dynamic methods at temperatures which span most of the liquid range. For systems of 255 molecules the two methods lead to similar results and this agreement confirms that the density profile, as a function of height, falls monotonically from the density of the bulk liquid to that of the gas. The thickness of the surface layer is sensitive to the surface area, and appears to approach its thermodynamic limit for surface areas of 400σ2 for a system of 4080 molecules. The density profile can be represented by a hyperbolic tangent of an appropriately scaled height. The thickness of the surface is of the order of two molecular diameters at temperatures near the triple point and increases rapidly as the critical point is approached. The computed surfacetens ions agree well with those calculated by statistical perturbation theory.Monte Carlo and Molecular Dynamic simulation of a binary mixture shows clearly the adsorption of the component of higher vapour pressure; the amount absorbed agrees with that calculated from Gibbs's isotherm.

A Method of Scaling with Applications to the 1968 and 1972 Presidential Elections

Abstract: A method of scaling is proposed to estimate the positions of candidates and voters on a common issue dimension. The scaling model assumes that candidates occupy true positions in an issue space and that individual level perceptual data arise from this in a two step process. The first step consists of a stochastic component, satisfying the standard Gauss Markov assumptions, which reflects true misperception. The second step consists of a linear distortion which is introduced in the survey situation. Estimates of the parameters of the model are developed by applying the least squares criterion, and distributions of the estimates are investigated by Monte Carlo methods.The scaling technique is applied to the seven-point issue scales asked in the 1968 and 1972 SRC survey. The resulting ideal point estimates are related to candidate positions in 1968 to test a simple Downsian voting model.

The simplicial approximation approach to design centering

Abstract: The basis of a method for designing circuits in the face of parameter uncertainties is described. This method is computationally cheaper than those methods which employ Monte Carlo analysis and nonlinear programming techniques, gives more useful information, and more directly addresses the central problem of design centering. The method, called simplicial approximation, locates and approximates the boundary of the feasible region of an n -dimensional design space with a polyhedron of bounding ( n - 1 )-simplices. The design centering problem is solved by determining the location of the center of the maximal hyperellipsoid inscribed within this polyhedron. The axis lengths of this ellipsoid can be used to solve the tolerance assignment problem. In addition, this approximation can be used to estimate the yield by performing an inexpensive Monte Carlo analysis in the parameter space without any need for the usual multitude of circuit simulations.

The development of electron avalanches in argon at high E/N values. II. Boltzmann equation analysis

Abstract: For pt.I see ibid., vol.10, no.7, p.1035 (1977). The electron swarm parameters for the steady-state Townsend, pulsed Townsend and time-of-flight experiments are calculated using a Boltzmann equation for argon at E/N values from 85 to 566 Td, when electron impact ionization is appreciable. The results suggest that the value of an electron swarm parameter depends on the type of the experiments involved, because of the presence of the ionization, in agreement with the Monte Carlo simulation work in the previous paper. The drift velocities and diffusion coefficients when ionization is present, are discussed.

Multiple scattering in reflection nebulae. I - A Monte Carlo approach. II - Uniform plane-parallel nebulae with foreground stars. III - Nebulae with embedded illuminating stars

Abstract: A method for calculating the surface brightness distribution on a plane-parallel reflection nebula of uniform density illuminated by a star located either in front of, behind, or arbitrarily inside the scattering medium is proposed. The Monte Carlo technique is used to find solutions to the radiative transfer problem. The scattering properties of the nebular particles are parameterized by the albedo for single scattering and a three-parameter analytic phase function. Calculations are then presented for the surface brightness distribution across the face of such nebulae with (1) a foreground star and (2) immersed stars. The calculations include the full effects of multiple scattering, are independent of a particular assumed grain material or size distribution, and are applicable to any wavelength region for which observations can be obtained.

Monte Carlo simulation of ion motion in drift tubes

Abstract: The motion of a swarm of ions in a uniform electric field is studied by simulating the motion of a single ion through many collisions with neutral atoms in order to obtain the drift velocity, average energy, and velocity distribution for the ions. For K+ ions in He at low field strengths, the results agree well with the solutions of the Boltzmann equation by Kumar and Robson; and for K+ in Ar at all field strengths, the computed mobilities demonstrate that the Viehland–Mason moment method can give useful results, especially if carried through to third order. The velocity distributions computed for O+ ions in He and Ar are used in the accompanying paper by Albritton et al. to analyze drift tube measurements of O+ reaction rates. Significant deviations from the Maxwell–Boltzmann form have been found and are seen to have important effects in that application. Velocity distributions have also been obtained for Li+ in He. The sensitivity of ionic mobilities to changes in the ion–atom interaction potential is examined with particular reference to K+ ions in Ar.

Monte Carlo Simulation of Quantum Spin Systems. I

Abstract: A general explicit formulation of Monte Carlo simulation for quantum systems is given in this paper on the basis of the previous fundamental proposal by Suzuki. This paper also demonstrates explicitly the possibility of it and gives new interesting physical results on the two-dimensional XY-model. That is, the present preliminary simulation seems to indicate a phase transition with a divergent susceptibility, and a very weak singularity of specific heat if it exists, and without long-range order.

Some Properties of Tests for Specification Error in a Linear Regression Model

Abstract: This article considers the test reset which is intended to detect a nonzero mean of the disturbance in a linear regression model. Analysis of an approximation to the test statistic's distribution and Monte Carlo experiments reveal that the power of the test may decline as the size of the disturbance mean increases. However, the possibility is remote and declines with increasing sample size. Alternative sets of test variables are considered, and their effect on the power of the test is studied in Monte Carlo experiments. The best set seems to be composed of powers of the explanatory variables.

Monte Carlo study of a phase‐separating liquid mixture by umbrella sampling

Abstract: Recently developed nonphysical sampling methods—umbrella sampling—have been used to obtain the free energy and other properties of a binary liquid mixture exhibiting phase separation with an upper critical solution point. The system is a mixture of two identical Lennard‐Jones liquids in which the interactions between the components are characterized by a range parameter σ12 obeying the Lorentz rule, but an energy parameter e12= (1−α) (e11e22)1/2 violating the Berthelot rule. The sampling methods enable one to cover wide ranges of temperature and composition with few Monte Carlo experiments, successfully sampling the metastable regions and obtaining the coexistence curve. The case α=0.25 is studied in detail, and compared with some theoretical predictions. An estimate is made of the minimum value of α required for phase separation at low pressures.

Stochastic process for extrapolating concrete creep

Abstract: Creep of concrete is modeled as a process with independent increments of locally gamma distribution. The process is transformed to a stationary gamma process. The mean prediction agrees with the deterministic double power law established previously. Infinite divisibility of the increment distribution is assumed. This is justified by additivity of deformations and of stresses, and also by considerations of the microscopic mechanism of creep, assuming creep to be due to migrations of widely spaced solid particles along micropore passages whose length is statistically distributed. The treatment of creep as a stochastic process allows extracting considerable information from measurements even on one specimen, although a greater number of specimens is preferable. The main use of the model is in extrapolation of short time creep data into long times, and calculation of confidence limits. Methods of determining process parameters from creep test data are given. Monte Carlo simulations demonstrate reasonable agreement with test data.

An integral equation theory for the dense dipolar hard-sphere fluid

Abstract: An integral equation theory based upon a simple linearization of the hypernetted-chain closure approximation is solved numerically for dipolar hard spheres. The pair-correlation function and thermodynamic properties are found to be in excellent agreement with Monte Carlo results. The dielectric constant in this approximation is larger than that predicted by previous theories.

Phase transitions in small clusters of atoms

Abstract: The Monte Carlo method is used to calculate the average thermodynamic properties of small (N?13) clusters of atoms. All cluster sizes studied exhibit fairly sharp solid–liquid, as well as liquid–gas, transitions. In addition, some of the larger clusters also undergo structural transitions between different isomeric forms. The solid–liquid transition temperature is determined by four independent tests. The melting points predicted by these tests do not differ by more than 5%.

A Guide to Monte Carlo for Statistical Mechanics: 2. Byways

Abstract: Monte Carlo techniques are methods of estimating the values of many-dimensional integrals by sampling with the help of random numbers.(1,2) It is obvious that this makes them methods appropriate to equilibrium statistical mechanics. Among the integrals of interest in classical statistical mechanics are ensemble averages of any “mechanical” quantity M(ξ), $$\left\langle M \right\rangle =\int M\left( \xi \right)p\left( \xi \right)d\xi$$ (1) where p(ξ) is the ensemble’s probability density function in the space of the variables ξ defining the microscopic mechanical state of the system. Conventional Monte Carlo work is concerned with the estimation of such averages for model systems, and is the subject of the present chapter.

The development of electron avalanches in argon at high E/N values. I. Monte Carlo simulation

Abstract: The behaviour of electron avalanches in argon when appreciable electron impact ionization occurs, is studied by a Monte Carlo simulation. The values of electron swarm parameters are obtained for steady-state Townsend, pulsed Townsend and time-of-flight experiments, by applying sampling techniques appropriate to the respective experiments. The results suggest that the value of an electron swarm parameter, such as the ionization frequency or the electron drift velocity, depends on the type of experiments for which there is appreciable electron impact ionization. The properties of electron avalanches in an electron energy non-equilibrium region, for example the variation of the electron energy distribution with distance from the cathode, and the effect of anisotropic scattering of electrons on the swarm parameters very close to the anode, are also studied.

Monte carlo and perturbation theory studies of the equation of state of the two-dimensional Lennard-Jones fluid

Abstract: Monte Carlo values for the equation of state of the two-dimensional Lennard-Jones fluid are reported. The agreement with previous simulations is good, with the exception of the critical point region. However, the estimates of the critical temperature and density given here are lower than those previously reported. The first and second-order Barker-Henderson and first-order Weeks-Chandler-Andersen perturbation theories are applied to this system and are found to be satisfactory only at high densities. A semiempirical correction term to the second-order Barker-Henderson theory is constructed. The resulting parameterization of the Monte Carlo data is found to be accurate and useful at all densities and temperatures for which the Monte Carlo data exist.

A Detailed Comparison of Four Approaches to the Calculation of the Sensitivity of Optical Fiber System Receivers

Abstract: In this paper four approaches to the calculation of error rates for optical fiber system repeaters are compared ("Exact" calculation, Monte Carlo simulation, Chernoff bounds and the Gaussian approximation). We conclude that the "Exact" and Monte Carlo calculations are in complete agreement. This allows the Monte Carlo results to be used to calibrate other methods. The relatively simple Chernoff bound is in very good agreement with the above, and should be used whenever computational facilities allow. For simpler calculations, or analytical expressions for the effects of parameter variations, the Guassian approximation gives a reasonable good estimate of the receiver sensitivity. However, it tends to underestimate the threshold setting and overestimate the optimal avalanche gain.

A Monte Carlo study of dipolar hard spheres The pair distribution function and the dielectric constant

Abstract: This paper is a systematic investigation of the effects of boundary conditions upon Monte Carlo calculations for dipolar fluids. Results are reported for the minimum image (MI), spherical cut-off (SC) and uniform reaction field methods. All three approximations are shown to give different pair distribution functions, g(12), and none yields the infinite system result. It is concluded that theories giving g(12) for an infinite system should not be evaluated by direct comparison with Monte Carlo results. Two alternative methods by which meaningful comparisons can be made are described in the text. The dependence of the thermodynamic properties upon boundary conditions is important only at large values of the dipole moment. For small to moderate dipoles both MI and SC are found to give reasonable estimates of the dielectric constant.