Showing papers on "Monte Carlo method published in 1978"
TL;DR: A new general purpose algorithm for multidimensional integration is described, an iterative and adaptive Monte Carlo scheme that is considerably more efficient than several others currently in use for a number of sample integrals of high dimension.
1,348 citations
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
TL;DR: In this article, it was shown that the probability of obtaining a good short-exposure image corresponds to a hyperspace integral in which the spatial dimensions are the independent random coefficients in the orthonormal series expansion.
Abstract: In short-exposure imaging through turbulence, there is some probability that the image will be nearly diffraction limited because the instantaneous wave-front distortion over the aperture was negligible. A number of years ago in a rather brief paper, Hufnagel (1966) argued heuristically that the probability of getting a good image would decrease exponentially with aperture area. This paper undertakes a rigorous quantitative analysis of the probability. We find that the probability of obtaining a good short-exposure image is Prob ≈ 5.6 exp[−0.1557 (D/r0)2] (for D/r0 ≥ 3.5), where D is the aperture diameter and r0 is the coherence length of the distorted wave front, as defined by Fried (1967). A good image is taken to be one for which the squared wave-front distortion over the aperture is 1 rad2 or less. The analysis is based on the decomposition of the distorted wave front over the aperture, in an orthonormal series with randomly independent coefficients. The orthonormal functions used are the eigenfunctions of a Karhunen-Loeve integral equation. The integral equation is solved using a separation of variables into radial and azimuthal dependence. The azimuthal dependence was solved analytically and the radial, numerically. The first 569 radial eigenfunctions and eigenvalues were obtained. The probability of obtaining a good short-exposure image corresponds to a hyperspace integral in which the spatial dimensions are the independent random coefficients in the orthonormal series expansion. It is equal to the probability that a randomly chosen point in the hyperspace will lie within a hypersphere of unit radius, the points in the hyperspace being randomly chosen in accordance with the product of independent Gaussian probability distribution—one distribution for each dimension. The variance of these distrbutions is directly proportional to the eigenvalues of the Karhunen-Loeve equation. This hyperspace integral (involving up to several hundred dimensions) has been evaluated using Monte Carlo techniques.
357 citations
TL;DR: A computer study of the previously published methods designed to avoid bias shows that while no single method is “best” under all circumstances, a judicious choice of method can increase the accuracy and decrease the bias with which the true slope is estimated.
317 citations
TL;DR: In this article, a failure criterion for a laminated composite is presented and a salient nature of this criterion is the use of "in situ shear strength" measured in the form of cross-ply laminate.
Abstract: A failure criterion for a laminated composite is presented. A salient nature of this criterion is the use of "in situ shear strength" measured in the form of cross-ply laminate. Then by statistical consideration, the model was further modified to incorporate probabilistic nature of composite fail ure. Rigorous mathematical development of probability was simply re placed by Monte Carlo simulation. As a result, the proposed model was proved simple and effective in predicting failure in both deterministic and probabilistic sense.
264 citations
242 citations
TL;DR: In this paper, the steady-state stellar distribution around a central black hole in a star cluster was determined by means of a direct numerical integration of the Fokker-Planck equation in energy-angular momentum space.
Abstract: We determine the steady-state stellar distribution around a central black hole in a star cluster by means of a direct numerical integration of the Fokker-Planck equation in energy-angular momentum space. The loss cone in phase space resulting from tidal destruction of stars is treated by means of a detailed boundary layer analysis. The process of stellar destruction by direct physical collisions is treated by use of the physical collision cross section.We present the two-dimensional steady-state distribution function, the density and velocity dispersion profiles of the stellar distribution, and stellar consumption rates for black holes in globular cluster environments. The distribution function we obtain is in reasonable agreement with that resulting from the Monte Carlo simulations of Shapiro and Marchant; our loss rate is larger than theirs by a factor of 2.
231 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, the Monte Carlo simulation method was used to study the interfacial liquid density profile for several systems; Lennard Jones (LJ) fluid/LJ (100) solid fcc face, L‐J fluid/lj (10−4) wall, L•J fluid /Boltzmann averaged wall, l•J fluids/hard wall, and hard-sphere fluid/Boltzman averaged wall.
Abstract: Using the Monte Carlo simulation method, we study the interfacial liquid density profile for several systems; Lennard‐Jones (L‐J) fluid/L‐J (100) solid fcc face, L‐J fluid/L‐J (10–4) wall, L‐J fluid/’’Boltzmann averaged’’ wall, L‐J fluid/hard wall, and hard‐sphere fluid/Boltzmann averaged wall. Upon comparing the simulation results, we conclude that the Boltzmann averaged wall is a good effective one‐dimensional potential for a (100) structured wall, and that the attractive interactions between the fluid atoms significantly influence the interfacial fluid density profile.
TL;DR: In this paper, the Monte Carlo value of the density profile and pair distribution function of a hard-sphere fluid near a hard wall is reported for four densities, and it is shown that the density is extremely high near the wall, in agreement with earlier simulation and integral equation studies.
Abstract: Monte Carlo value of the density profile and pair distribution function of a hard‐sphere fluid near a hard wall are reported for four densities. The density profile is found to be extremely high near the wall, in agreement with earlier simulation and integral equation studies. However, the number of molecules near the wall is no higher than in a comparable volume of the bulk fluid. The high density near the wall is caused by the fact that the molecules near the wall are generally constrained to remain near the wall and undergo a quasi‐two‐dimensional random walk. A layering is also observed in the pair distribution function.
TL;DR: Monte Carlo methods are used to study the ability of nearest available Mahalanobis metric matching to make the means of matching variables more similar in matched samples than in random samples.
Abstract: SUMMARY
Monte Carlo methods are used to study the ability of nearest available Mahalanobis metric matching to make the means of matching variables more similar in matched samples than in random samples.
TL;DR: In this article, a technique is described for the estimation of the influence of random potential alloy scattering on the high field transport properties of quaternary III-V semiconductors obtained by Monte Carlo simulation.
Abstract: A technique is described for the estimation of the influence of random potential alloy scattering on the high field transport properties of quaternary III–V semiconductors obtained by Monte Carlo simulation. The approach is based on an extension of a theoretical model for scattering in the ternary alloys. The magnitude of the scattering potential is an important parameter in alloy scattering, and three proposed models for calculating this potential are discussed. These are the energy bandgap difference, the electron affinity difference, and the heteropolar energy difference for the appropriate binary compounds. The technique is used in the Monte Carlo method to study the influence of alloy scattering on the transport properties of III–V quaternary alloys. The results of this study are used in a device model to estimate device parameters for FETs.
TL;DR: In this paper, the long-time behavior of a labeled particle on a one-dimensional chain is studied and it is shown that the long time behavior is dominated by density fluctuations leading to a ε(n 2 ) dependence of the mean square deviation in agreement with Monte Carlo results of Richards.
Abstract: The diffusion of a labeled particle on a one-dimensional chain is discussed. It is shown that the long-time behavior is dominated by density fluctuations leading to a ${t}^{\frac{1}{2}}$ dependence of the mean-square deviation in agreement with Monte Carlo results of Richards.
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.
TL;DR: The authors compare the results using nonmetric analysis, full factorial designs, and rank data with quicker and less expensive methods of metric analysis, orthogonal arrays and stimulus ratings to indicate that metric analysis using ratings data and orthogonic arrays is very robust.
Abstract: In many industrial applications of conjoint analysis the use of nonmetric algorithms to analyze respondent ranks of products described by more than eight or 10 attributes is time consuming and very...
TL;DR: In this paper, two independent methods have been devised to analyse the process of surface diffusion at a planar surface using Monte Carlo simulation and order-disorder theory in the quasi-chemical approximation to provide an analytical expression for the influence of lateral interactions on surface diffusion profiles.
TL;DR: In this paper, Monte Carlo techniques have been used to calculate neutral gas distributions in tokamaks, using track length estimators, suppression of absorption, and splitting with Russian roulette to reduce the variance.
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.
01 Jan 1978
TL;DR: In this paper, a Monte Carlo model applied to a wide range of cloud widths and heights, and for an analytical model restricted in its application to cuboidally shaped clouds whose length, breadth, and depth may be varied independently; the clouds must be internally homogeneous with respect to their intrinsic radiative properties.
Abstract: Results are presented for a Monte Carlo model applied to a wide range of cloud widths and heights, and for an analytical model restricted in its application to cuboidally shaped clouds whose length, breadth, and depth may be varied independently; the clouds must be internally homogeneous with respect to their intrinsic radiative properties. Comparative results from the Monte Carlo method and the derived analytical model are presented for a wide range of cloud sizes, with special emphasis on the effects of varying the single scatter albedo, the solar zenith angle, and the scattering phase angle.
TL;DR: In this article, the surface peak intensity of the backscattering spectrum was calculated using Monte Carlo techniques. But the results were not expressed as a function of one parameter, thus permitting the generation of an almost universal curve for surface peak estimates.
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.
TL;DR: In this paper, a Monte Carlo approach is used to solve the radiant energy balance equation and to get the distribution of the local rate of energy absorption as a function of the most significant parameters.
TL;DR: In this article, Monte Carlo results for the equation of state of a fluid in which the intermolecular potential consists of a hard core of diameter σ and an attractive tail which is of the form of a Yukawa function are presented.
Abstract: We present Monte Carlo results for the equation of state of a fluid in which the intermolecular potential consists of a hard core of diameter σ and an attractive tail which is of the form of a Yukawa function, - e exp -λ(r - σ)tr with λ=1·8/σ. These results are compared with those obtained from perturbation theory, the mean spherical approximation (MSA), and three related approximation schemes. While perturbation theory works rather well for this system, the MSA is considerably less satisfactory. However, the exponential and linearized exponential modifications of the MSA and the generalized MSA all give good results for this system.
TL;DR: In this article, the transport of electrons in molecular nitrogen and air has been studied in the energy range between 50 eV and 5 keV using the Monte Carlo method and simulating the trajectories of the electrons directly from elastic and inelastic cross-section data avoiding the continuous slowing down approximation and multiple scattering theories.
TL;DR: This chapter will give an updated survey on computer simulations, which are relevant for crystal growth since surveys on the other subjects are published elsewhere.
TL;DR: In this paper, Monte Carlo simulations for the site percolation problem are presented for lattices up to 64 x 106 sites, where distinct trends with bond-length are found for critical concentrations and for the critical exponents.
Abstract: Monte Carlo simulations for the site percolation problem are presented for lattices up to 64 x 106 sites. We investigate for the square lattice the variablerange percolation problem, where distinct trends with bond-length are found for the critical concentrations and for the critical exponents/~ and 7. We also investigate the layer problem for stacks of square lattices added to approach a simple cubic lattice, yielding critical concentrations as a functional of layer number as well as the correlation length exponent u. We also show that the exciton migration probability for a common type of ternary lattice system can be described by a cluster model and actually provides a cluster generating function.