Showing papers on "Monte Carlo method published in 1983"
TL;DR: In this paper, the basic principles of the Monte Carlo method, as applied to the solution of transport problems in semiconductors, are presented in a comprehensive and tutorial form, with the aim of showing the power of the method in obtaining physical insights into the processes under investigation.
Abstract: This review presents in a comprehensive and tutorial form the basic principles of the Monte Carlo method, as applied to the solution of transport problems in semiconductors. Sufficient details of a typical Monte Carlo simulation have been given to allow the interested reader to create his own Monte Carlo program, and the method has been briefly compared with alternative theoretical techniques. Applications have been limited to the case of covalent semiconductors. Particular attention has been paid to the evaluation of the integrated scattering probabilities, for which final expressions are given in a form suitable for their direct use. A collection of results obtained with Monte Carlo simulations is presented, with the aim of showing the power of the method in obtaining physical insights into the processes under investigation. Special technical aspects of the method and updated microscopic models have been treated in some appendixes.
2,081 citations
1,897 citations
TL;DR: In this paper, two formulas for estimating the significance of positive observations in searching gamma-ray sources or lines were proposed for analyzing the results of Gamma-ray astronomy experiments, which were tested with the aid of Monte Carlo simulations.
Abstract: The procedures in current use for analyzing the results of gamma-ray astronomy experiments are assessed. Two formulas are proposed for estimating the significance of positive observations in searching gamma-ray sources or lines. The correctness of the formulas is tested with the aid of Monte Carlo simulations. One formula is derived by immediately estimating the standard deviation of the observed signal NS; the other is derived by applying the method of the statistical hypotheses test.
1,211 citations
TL;DR: In this paper, the effects of number and interdependence in evaluating the collective significance of finite sets of statistics are frequently non-trivial, especially for spatial networks of time-averaged meteorological data, and the effects can be taken into account in two steps: by first prescreening for significance assuming data independence and then, if necessary, by taking into consideration dependence through the use of estimated effective degrees of freedom and the binomial distribution or, failing that, Monte Carlo simulation.
Abstract: The effects of number and interdependence in evaluating the collective significance of finite sets of statistics are frequently non-trivial, especially for spatial networks of time-averaged meteorological data. These effects can be taken into account in two steps: By first prescreening for significance assuming data independence and then, if necessary, by taking into consideration dependence through the use of estimated effective degrees of freedom and the binomial distribution or, failing that, Monte Carlo simulation. Seasonal averages of 700 mb height data are used to illustrate the problem and to demonstrate how the data set properties are taken into account. Papers by Hancock and Yarger (1979), Nastrom and Belmont (1980) and Williams (1980) are critically examined in light of these considerations and Monte Carlo strategies for clarification of ambiguities suggested.
1,110 citations
TL;DR: In this article, a modele decrivant le processus de croissance de amas par agregation d'amas is introduced, which is based on the methode de Monte Carlo.
Abstract: On introduit un modele decrivant le processus de croissance d'amas par agregation d'amas. On effectue l'etude par la methode de Monte Carlo. On trouve que les amas sont invariants d'echelle
822 citations
TL;DR: A Monte Carlo computer model has been used to predict the distribution of absorbed dose in homogeneous tissues of different absorption/scattering ratios, for illumination both by external light beams and via implanted optical fibers.
Abstract: A Monte Carlo computer model has been developed to study the propagation of light in tissues. Light attenuation is assumed to result from absorption and isotropic scattering. The model has been used to predict the distribution of absorbed dose in homogeneous tissues of different absorption/scattering ratios, for illumination both by external light beams and via implanted optical fibers. The photon flux into optical fibers placed in the tissue as detectors has also been investigated. The results are interpreted in relation to the use of visible light irradiation for photo radiation therapy.
688 citations
TL;DR: A least squares algorithm for fitting additive trees to proximity data using a penalty function to enforce the four point condition on the estimated path length distances is described.
Abstract: A least squares algorithm for fitting additive trees to proximity data is described. The algorithm uses a penalty function to enforce the four point condition on the estimated path length distances. The algorithm is evaluated in a small Monte Carlo study. Finally, an illustrative application is presented.
514 citations
TL;DR: In this article, the Lagrange multiplier is used to evaluate the safety index and the location of the design point, and Monte Carlo techniques are recommended for use in estimating limit state probabilities as a practical alternative to other methods.
Abstract: The present study reviews some of the more significant recent developments in the area of structural reliability analysis, proposes new interpretations for and emphasis in some of these crucial theoretical developments, and introduces additional useful quantities. To be specific, the first‐order second‐moment methods are reviewed. It is then shown that the Lagrange multiplier formulation (and thus any algorithm associated with it) can be used to evaluate the safety index and the location of the design point. Monte Carlo techniques are recommended for use in estimating limit state probabilities as a practical alternative to other methods. The use of the Stokes and Gauss divergence theorem in two‐ and three‐dimensional integral expressions of a limit state probability is suggested in order to reduce the dimensionality of the integrations by one. Finally, it is recommended that the point of maximum likelihood be used as an alternative to the design point based on the advanced firstorder second‐moment method.
499 citations
TL;DR: A new algorithm for the simulation of statistical systems that produces a random walk through configurations of a constant total energy and is applicable to systems of both discrete and continuous variables.
Abstract: A new algorithm for the simulation of statistical systems is presented. The procedure produces a random walk through configurations of a constant total energy. It is computationally simple and applicable to systems of both discrete and continuous variables.
429 citations
07 Nov 1983
TL;DR: A simple but very general Monte-Carlo technique for the approximate solution of enumeration and reliability problems and several applications are given.
Abstract: 1. Introduction We present a simple but very general Monte-Carlo technique for the approximate solution of enumeration and reliability problems. Several applications are given, including: 1. Estimating the number of triangulated plane maps with a given number of ver-tices; 2. Estimating the cardinality of a union of sets; 3. Estimating the number of input combinations for which a boolean function, presented in disjunctive normal form,
342 citations
TL;DR: In this paper, a Monte Carlo comparison of the estimators is presented, showing improvement of the bias and mean squared error over some estimators commonly used in practice, and compared when auxiliary information is available.
Abstract: Variance estimators under several sample designs are proposed and compared when auxiliary information is available. Improvement of the bias and mean squared error over some estimators commonly used in practice is illustrated. A Monte Carlo comparison of the estimators is also presented.
TL;DR: In this paper, the Davidson-MacKinnon J -test and Fisher-McAleer test were used for non-nested regression models and the F -test applied to the comprehensive model is also included in the simulation experiments.
TL;DR: In this article, the formulation of gauge theories on Euclidean space-time lattices and the application of the Monte Carlo computational technique to the ensuing systems are reviewed and a variety of numerical results obtained for lattice gauge theories are presented and discussed.
TL;DR: In this paper, the mean square displacement of a tagged particle is calculated for all times by an approximate theory and compared to results from Monte Carlo simulations, and the overall agreement is quite good.
Abstract: The dynamical process of the diffusion of tagged particles in a one-dimensional concentrated lattice gas is investigated. The particles are noninteracting except that double occupancy is forbidden. The mean-square displacement of a tagged particle is calculated for all times by an approximate theory and compared to results from Monte Carlo simulations. The overall agreement is quite good. For an infinite chain and for large time t the mean-square displacement is found to increase proportionally to t1/2 in agreement with existing results. For periodic chains it increases as 2Dtrt for large times, with a coefficient of tracer diffusion Dtr inversely proportional to the number of particles on the chain. This, too, is in agreement with the results of older calculations. In the case of hard reflecting walls finally the mean-square displacement asymptotically approaches a constant, which can be calculated simply.
TL;DR: In this article, a more accurate fluctuation potential problem is considered in the modified Poisson-Boltzmann theory, and numerical solutions of the resulting new equation are compared with those of the previous theory and 1 : 1, 1 : 2, 2 : 2 Monte Carlo calculations.
Abstract: A more accurate fluctuation potential problem is considered in the modified Poisson–Boltzmann theory Numerical solutions of the resulting new equation are compared with those of the previous theory and 1 : 1, 1 : 2, 2 : 2 Monte Carlo calculations The new modified Poisson–Boltzmann equation is found to be much more successful in predicting the Monte Carlo results, especially for the higher-valency electrolytes
TL;DR: In this paper, Monte Carlo simulations of electron impact ionization in silicon are presented which include the pseudopotential band structure as well as collision broadening and higher order effects in the electron phonon interaction.
Abstract: Monte Carlo simulations of electron impact ionization in silicon are presented which include the pseudopotential band structure as well as collision broadening and higher order effects in the electron phonon interaction. Conduction in the two lowest conduction bands of silicon is considered. We also present new results for the impact ionization probability and deformation potential constants which are obtained by comparing our theory with a variety of experimental results.
TL;DR: In this paper, a simple iterative scheme which greatly facilitates the evaluation of discretized path integrals is presented, applied to study the motion of a proton in a bistable potential and the resulting configurational distribution function is compared to both the path integral Monte Carlo calculation and to the "exact" result.
Abstract: A simple iterative scheme which greatly facilitates the evaluation of discretized path integrals is presented. The method is applied to study the motion of a proton in a bistable potential and the resulting configurational distribution function is compared to both the path integral Monte Carlo calculation and to the ‘‘exact’’ result. As a second illustration we present calculations of the radial distribution function for an Ar2 van der Waals dimer at two temperatures.
TL;DR: In this article, a method of analyzing ergodic magnetic fields is given, including a generalization of magnetic coordinates to such fields, which can be used in existing Monte Carlo codes to assess the enhanced transport associated with imperfect surfaces.
Abstract: A method of analyzing ergodic magnetic fields is given, including a generalization of magnetic coordinates to such fields. The results of this analysis can be used in existing Monte Carlo codes to assess the enhanced transport associated with imperfect surfaces. The Hamiltonian for a general magnetic field is given as part of this analysis.
TL;DR: In this article, the ground states of droplets of $N$ atoms of $^{4}\mathrm{He}$ were calculated using variational Monte Carlo and Green's function Monte Carlo methods.
Abstract: Quantum mechanical calculations of the ground states of droplets of $N$ atoms of $^{4}\mathrm{He}$ are reported. The calculations have been made by the variational Monte Carlo method for $4l~Nl~728$ and by the Green's function Monte Carlo method for $3l~Nl~112$. The energies, rms radii, and density distributions are reported; liquid-drop fits to the energies and radii are discussed.
TL;DR: In this article, a detailed Monte Carlo proton transport code in water vapor is described, where all important interaction types (elastic scattering, five levels of ionization, 12 types of excitation) are considered explicitly.
Abstract: In the first of a series of papers on the application of track-structure calculations to radiobiology, a detailed Monte Carlo proton transport code in water vapor is described. In the code all important interaction types (elastic scattering, five levels of ionization, 12 types of excitation) are considered explicitly. All cross sections are based closely on experimental data. The proton energy range considered is 0.3-1.5 MeV since this is the range of available experimental ionization cross sections. Results are presented in terms of energy partitions, w values, stopping powers, and radial dose distributions, all showing agreement with the experiment.
TL;DR: In this paper, a complete classification of states that can be constructed from spacelike Wilson loop operators up to length 8 is given, and the set of operators is considered in a Monte Carlo variational calculation.
TL;DR: In this article, a Monte Carlo method for calculating quantum mechanical time correlation functions is presented, where the time correlation function is calculated at several values along the pure imaginary axis of the complex time plane such that 0 < it < β, where β is the temperature of the system.
Abstract: A Monte Carlo method for calculating quantum mechanical time correlation functions is presented. In this method the time correlation function is calculated at several values along the pure imaginary axis of the complex time plane such that 0
TL;DR: In this article, a perturbation theory to account for anisotropic long-ranged terms is described, giving two dið-electric constant estimates from one simulation, and the results are illustrated with Monte Carlo simulations of the Stockmayer system at reduced density 0.8, reduced square dipole moment 2.0 and scaled temperature 1.35.
Abstract: This paper makes some developments and clarifications of the theory for the application of periodic boundary conditions to the numerical simulation of the statistical mechanics of a cubic sample of dipolar particles. The reaction-field effect is treated rigorously. The anisotropies inherent in the periodic boundary condition Hamiltonian are allowed for in the derivation of a new fluctuation formula. A perturbation theory to account for anisotropic long-ranged terms is described, giving two di-electric constant estimates from one simulation. These new results are illustrated with Monte Carlo simulations of the Stockmayer system at reduced density 0.8, reduced square dipole moment 2.0 and scaled temperature 1.35, giving a dielectric constant estimate of 25 ± 2 from all the data, and showing that the perturbation theories are very accurate. It appears possible to claim that periodic boundary conditions should be used with infinite external dielectric constant in almost all circumstances, because they then give a chain of configurations that provide comparatively very stable estimates of dielectric constant.
TL;DR: In this paper, a model for describing the imaging of monochromatic ocean waves by synthetic aperture radar (SAR) is extended to relate ocean wave spectra to SAR image spectra.
Abstract: A theoretical model previously developed for describing the imaging of monochromatic ocean waves by synthetic aperture radar (SAR) is extended to relate ocean wave spectra to SAR image spectra. Since the SAR response to the moving ocean surface is nonlinear for a large range of ocean wave parameters, this relationship can, in general, not be described by a linear mapping transfer function. SAR image spectra are calculated from given ocean wave spectra by applying Monte Carlo simulation techniques. The computer simulations are performed with varying SAR parameters and for a unidirectional wave field propagating in azimuth direction. Though the model calculations are only one dimensional, they reveal the following basic features of the SAR imaging mechanism: (1) If the nonlinearity of the imaging is sufficiently strong, then the peak of the SAR image spectrum is shifted towards lower azimuthal wave numbers. (2) One parameter suitable for characterizing the degree of nonlinearity is the average velocity bunching parameter , which for SEASAT-SAR is given by , where λm is the dominant wavelength and Hs the significant waveheight in meters, and ϕ the azimuth angle (ϕ = O for azimuthally traveling waves). (3) The amount of the azimuthal shift of the spectral peak depends on c, SAR integration time, and on the width of the ocean wave spectrum. It increases with integration time and spectral width. (4) In case of a fully developed wind sea, shifts of spectral peaks toward lower azimuthal wave numbers become significant for SEASAT-SAR if . For , the relative azimuthal wavenumber shift is of the order of 1/2. If , the peak of the image spectrum is located near zero wave number and no wave information can be extracted from the SEASAT-SAR image spectrum.
TL;DR: The study verified that the sampling schemes used in the program can produce random samples according to the theoretical probability distribution functions which describe the photon-scattering process.
Abstract: A computer program using Monte Carlo methods has been developed for the simulation of photon scattering in tissue-equivalent phantoms for incident x-rays in the diagnostic energy range. The study verified that the sampling schemes used in the program can produce random samples according to the theoretical probability distribution functions which describe the photon-scattering process. The Monte Carlo program was applied to determinations of the scatter fractions and edge responses for various phantom sizes, X-ray energies, and recording systems. These quantities were also measured experimentally under comparable imaging conditions. Excellent agreement was obtained between the predicted and experimental results. This investigation established the validity of our Monte Carlo calculations for studies of the physical characteristics of scattered radiation in diagnostic radiology.
TL;DR: In this paper, Monte Carlo calculations are presented of the detailed evolution of chemical species around the tracks of individual electrons that are stopped in liquid water, starting with the spatial trajectory of a single electron.
Abstract: Monte Carlo calculations are presented of the detailed evolution of chemical species around the tracks of individual electrons that are stopped in liquid water. The work begins with the spatial tra...
01 Jan 1983
TL;DR: In this article, a Monte Carlo simulation and nonlinear least-squares estimation of a vertical transport submodel for Lake Nantua was used to predict water quality in the Bedford Ouse watershed.
Abstract: One: Introduction- Uncertainty, system identification, and the prediction of water quality- The validity and credibility of models for badly defined systems- Two: Uncertainty and Model Identification- An approach to the analysis of behavior and sensitivity in environmental systems- Distribution and transformation of fenitrothion sprayed on a pond: modeling under uncertainty- Input data uncertainty and parameter sensitivity in a lake hydrodynamic model- Maximum likelihood estimation of parameters and uncertainty in phytoplankton models- Model identification methods applied to two Danish lakes- Analysis of prediction uncertainty: Monte Carlo simulation and nonlinear least-squares estimation of a vertical transport submodel for Lake Nantua- Multidimensional scaling approach to clustering multivariate data for water-quality modeling- Nonlinear steady-state modeling of river quality by a revised group method of data handling- Three: Uncertainty, Forecasting, and Control- Parameter uncertainty and model predictions: a review of Monte Carlo results- A Monte Carlo approach to estimation and prediction- The need for simple approaches for the estimation of lake model prediction uncertainty- Statistical analysis of uncertainty propagation and model accuracy- Modeling and forecasting water quality in nontidal rivers: the Bedford Ouse study- Adaptive prediction of water quality in the River Cam- Uncertainty and dynamic policies for the control of nutrient inputs to lakes- Four: Commentary- Uncertainty and forecasting of water quality: reflections of an ignorant Bayesian
TL;DR: In this paper, the relation between lattice and local operators used in Monte Carlo simulations to evaluate the meson decay constants was computed, at first order in perturbation theory.
TL;DR: Application of these methods to neurophysiological data has shown that a large proportion of spike trains have favored patterns, and the quantized Monte Carlo method is presented, which identifies and establishes significance for favored patterns whose detailed timing may vary but that do not have extra or missing spikes.
Abstract: Traditional spike-train analysis methods cannot identify patterns of firing that occur frequently but at arbitrary times. It is appropriate to search for recurring patterns because such patterns could be used for information transfer. In this paper, we present two methods for identifying "favored patterns" --patterns that occur more often than is reasonably expected at random. The quantized Monte Carlo method identifies and establishes significance for favored patterns whose detailed timing may vary but that do not have extra or missing spikes. The template method identifies favored patterns whose occurrences may have extra or missing spikes. This method is useful when employed after the results of the first method are known. Studies with simulated spike trains containing known interpolated patterns are used to establish the sensitivity and accuracy of the quantized Monte Carlo method. Certain trends with regard to parameters of the detected patterns and of the analysis methods are described. Application of these methods to neurophysiological data has shown that a large proportion of spike trains have favored patterns. These findings are described in the accompanying paper (3).