Showing papers on "Monte Carlo method published in 1981"

Simulation and the Monte Carlo Method

Abstract: From the Publisher: Provides the first simultaneous coverage of the statistical aspects of simulation and Monte Carlo methods, their commonalities and their differences for the solution of a wide spectrum of engineering and scientific problems. Contains standard material usually considered in Monte Carlo simulation as well as new material such as variance reduction techniques, regenerative simulation, and Monte Carlo optimization.

Monte Carlo calculations of coupled boson-fermion systems. I

Abstract: We present a formalism for carrying out Monte Carlo calculations of field theories with both boson and fermion degrees of freedom. The basic approach is to integrate out the fermion degrees of freedom and obtain an effective action for the boson fields to which standard Monte Carlo techniques can be applied. We study the structure of the effective action for a wide class of theories. We develop a procedure for making rapid calculations of the variation in the effective action due to local changes in the boson fields, which is essential for practical numerical calculations.

A new radiation solution method for incorporation in general combustion prediction procedures

Abstract: A new numerical solution method for the calculation of the thermal radiation transfer in combustors is described. It has been especially developed for incorporation in general combustor prediction procedures for the flow, and chemical reaction. It combines features and advantages of the zone, Monte Carlo, and flux model solution methods while avoiding their shortcomings. It is based on the solving of representatively directed beams of radiation within the enclosure between the known wall boundary conditions and on the subsequent computing of the radiation sources which arise within the finite difference control volumes of the flow procedure due to the passage of the beams. It is fast, exact applicable to complex geometries, and it retains in evidence the physics of the problem by avoiding complex mathematics.

Analytic expression for the dielectric screening function of strongly coupled electron liquids at metallic and lower densities

Abstract: We propose a fitting formula for the dielectric screening function of the degenerate electron liquids at metallic and lower densities which accurately reproduces the recent Monte Carlo results as well as those of the microscopic calculations and which satisfies the self-consistency conditions in the compressibility sum rule and the short-range correlation.

A Monte Carlo study of thirty internal criterion measures for cluster analysis.

Abstract: A Monte Carlo evaluation of thirty internal criterion measures for cluster analysis was conducted. Artificial data sets were constructed with clusters which exhibited the properties of internal cohesion and external isolation. The data sets were analyzed by four hierarchical clustering methods. The resulting values of the internal criteria were compared with two external criterion indices which determined the degree of recovery of correct cluster structure by the algorithms. The results indicated that a subset of internal criterion measures could be identified which appear to be valid indices of correct cluster recovery. Indices from this subset could form the basis of a permutation test for the existence of cluster structure or a clustering algorithm.

Simulation and the Monte Carlo Method (Wiley Series in Probability and Statistics)

Abstract: * The authoritative resource for understanding the power behind Monte Carlo Methods. * Most ideas are introduced and explained by way of concrete examples, algorithms, and practical experiments * A new co-author has now been added to enliven the writing style and to provide modern day expertise on new topics * An extensive range of exercises is provided at the end of each chapter, with more difficult sections and exercises marked accordingly * Examples of cross-entropy programs, written in MATLAB, are given in an appendix

Evaluation Methods and Accuracy in Probabilistic Load Flow Solutions

Abstract: This paper presents a new method for obtaining a probabilistic load flow solution using a discrete frequency domain convolution technique. It is shown that this method has greater accuracy while providing a breakthrough in computational speed. A detailed example compares the numerical results with a Monte Carlo simulation. The effects of nonlinearity in the network equations are discussed.

A Monte Carlo Method for the PDF Equations of Turbulent Reactive Flow

Abstract: —A Monte Carlo method is presented which simulates the transport equations of joint probability density functions (pdf's) in turbulent flows. (Finite-difference solutions of the equations are impracticable, mainly because of the large dimensionality of the pdf's). Attention is focused on an equation for the joint pdf of chemical and thermodynamic properties in turbulent reactive flows. It is shown that the Monte Carlo method provides a true simulation of this equation, and that the amount of computation required increases only linearly with the number of properties considered. Consequently, the method can be used to solve the pdf equation for turbulent flows involving many chemical species and complex reaction kinetics. Test calculations are reported that demonstrate the method and determine the influence of the numerical parameters. The method is then used to calculate pdf's of temperature in a turbulent mixing layer, and the calculations are found to be in good agreement with the measurements o...

Monte Carlo evaluation of transport coefficients

Abstract: A method is developed for evaluating transport coefficients in asymmetric geometries using the Monte Carlo method. The method is applied to the stellarator.

Optimal sampling times for pharmacokinetic experiments

Abstract: A sequential estimation procedure is presented which uses optimal sampling times to estimate the parameters of a model from data obtained from a group of subjects. This optimal sampling sequential estimation procedure utilizes parameter estimates from previous subjects in the group to determine the optimal sampling times for the next subject. Parameter estimates obtained from the optimal sampling procedure are compared to those obtained from a conventional sampling scheme by using Monte Carlo simulations which include noise terms for both assay error and intersubject variability. The results of these numerical experiments, for the two examples considered here, show that the parameter estimates obtained from data collected at optimal sampling times have significantly less variability than those generated using the conventional sampling procedure. We conclude that optimal sampling and preexperiment simulation may be useful tools for designing informative pharmacokinetic experiments.

Band-structure-dependent transport and impact ionization in GaAs

Abstract: We have performed a Monte Carlo simulation of high-field transport in GaAs including a realistic band structure to study the band-structure dependence of electron transport and impact ionization. The band structure has been calculated using the empirical pseudopotential method. Unlike previous theories of impact ionization, our method is capable of calculating various parameters, such as mean free path, from first principles. The calculated electron mean free path, drift velocity, and impact ionization rate are in reasonable agreement with the experimental data in spite of several simplifications of the model. Within statistical uncertainty we do not observe any orientation dependence of the ionization rate in contradiction to the interpretation of recently reported experimental results. We also find that the contribution of ballistic electrons to impact ionization is negligibly small. Based on the results of the calculation, a general discussion of impact ionization is given.

A Family of Distributions for Modelling Non-Elliptically Symmetric Multivariate Data

Abstract: SUMMARY The paucity of distributions that can be used as an aid to modelling the structure of multivariate data is a recognized limitation. We present a relatively simple family of distributions for use in describing data which are not elliptically symmetric. Properties of the family are discussed and it is shown that multivariate Pareto, Burr and Logistic distributions are special cases. In addition, simulation methods for applications in Monte Carlo robustness studies are outlined and, finally, the fit to a data set on uranium exploration is compared to that obtained using the usual bivariate normal distribution.

A Review Of Monte Carlo Tests Of Cluster Analysis

Abstract: A review of Monte Carlo validation studies of clustering algorithms is presented. Several validation studies have tended to support the view that Ward's minimum variance hierarchical method gives the best recovery of cluster structure. However, a more complete review of the validation literature on clustering indicates that other algorithms may provide better recovery under a variety of conditions. Applied researchers are cautioned concerning the uncritical selection of Ward's method for empirical research. Alternative explanations for the differential recovery performance are explored and recommendations are made for future Monte Carlo experiments.

Monte Carlo approach to the analysis of the rotational diffusion of wormlike chains

Abstract: Synopsis A Monte Carlo analysis is presented which establishes a relationship between the rotational diffusion coefficients and the flexibility (persistence length, P) of short, wormlike chains. The results of this analysis are presented in terms of experimentally observable quantities; namely, the rotational relaxation times for the field-free decay of optical anisotropy. The pertinent theoretical quantity is R, defined as the ratio of the longest rotational relaxation time of a wormlike chain to the transverse rotational relaxation time of a rigid cylinder having the same axial length (L) and segmental volume. R, so defined, is essentially independent of the axial ratio of the cylinder for any value of LIP within the range of validity of the present analysis (axial ratio > 20; 0.1 < L/P < 5). It is pointed out that P can be determined with reasonable accuracy even in the absence of a precise knowledge of the local hydrodynamic radius of the chain.

Over-relaxation method for the Monte Carlo evaluation of the partition function for multiquadratic actions

Abstract: I formulate a successive over-relaxation (SOR) procedure for the Monte Carlo evaluation of the Euclidean partition function for multiquadratic actions (such as the Yang-Mills action with canonical gauge fixing). A convergence analysis for the quadratic-action (Abelian) case shows that as thermalization proceeds the mean nodal fields relax according to the difference equation arising from the standard SOR analysis of the associated classical Euclidean field equation. Hence, SOR should accelerate the thermalization process, just as it accelerates convergence in the numerical solution of second-order elliptic differential equations.

A Perspective on the Use of Control Variables to Increase the Efficiency of Monte Carlo Simulations

Abstract: This is a survey paper on the application of control variables to increase the efficiency of discrete event simulations. The emphasis is on the practical problems and potential of applying the method in the simulation of complex systems. The basic theory of control variables is reviewed and the equivalence of control variables and multiple estimators is discussed. Techniques for generating control variables are described. Inefficiencies resulting from the statistical estimation of control variable coefficients and the problem of confidence interval generation are treated. This is done both within the context of the method of independent replications and the regenerative method. The application literature is reviewed and the conditions under which control variables could be profitably applied in practical simulations are described. Finally, there is a set of recommended directions for future research.

Finite size scaling analysis of ising model block distribution functions

Abstract: The distribution functionP L (s) of the local order parameters in finite blocks of linear dimensionL is studied for Ising lattices of dimensionalityd=2, 3 and 4. Apart from the case where the block is a subsystem of an infinite lattice, also the distribution in finite systems with free [P (s)] and periodic [P ] boundary conditions is treated. Above the critical pointT c , these distributions tend for largeL towards the same gaussian distribution centered around zero block magnetization, while belowT c these distributions tend towards two gaussians centered at ±M, whereM is the spontaneous magnetization appearing in the infinite systems. However, belowT c the wings of the distribution at small |s| are distinctly nongaussian, reflecting two-phase coexistence. Hence the distribution functions can be used to obtain the interface tension between ordered phases. At criticality, the distribution functions tend for largeL towards scaled universal forms, though dependent on the boundary conditions. These scaling functions are estimated from Monte Carlo simulations. For subsystem-blocks, good agreement with previous renormalization group work of Bruce is obtained. As an application, it is shown that Monte Carlo studies of critical phenomena can be improved in several ways using these distribution functions:(i) standard estimates of order parameter, susceptibility, interface tension are improved(ii) T c can be estimated independent of critical exponent estimates(iii) A Monte Carlo “renormalization group” similar to Nightingale's phenomenological renormalization is proposed, which yields fairly accurate exponent estimates with rather moderate effort(iv) Information on coarse-grained hamiltonians can be gained, which is particularly interesting if the method is extended to more general Hamiltonians.

Monte Carlo studies of the structure of dilute aqueous sclutions of Li+, Na+, K+, F−, and Cl−

Abstract: Monte Carlo–Metropolis statistical thermodynamic computer simulations are reported for dilute aqueous solutions of Li+, Na+, K+, F−, and Cl−. The calculations are carried out on systems consisting of one ion and 215 water molecules at 25 °C and experimental densities. The condensed phase environment is modeled using periodic boundary conditions. The configurational energies are developed under the assumption of pairwise additivity by means of potential functions representative of nonempirical quantum mechanical calculations of the ion–water and water–water energies. The internal energies, radial distribution functions, and related thermodynamic properties are calculated for each system. The structure of the local solution environment around each dissolved ion is analyzed in terms of quasicomponent distribution functions. The results are compared with analogous calculations on a smaller system to estimate the effect of long‐range forces in the ion–water potential function on the calculated results.

Monte Carlo simulation of fast secondary electron production in electron beam resists

Abstract: Monte Carlo calculations of fast secondary electron production have been performed with a hybrid model for the discrete and continuous energy‐loss processes. The Moller theory was adopted for the differential inelastic scattering cross‐section which determines the production rate of fast secondary electrons. The calculations were made for both a bulk polymethyl methacrylate (PMMA) sample and 4000‐A‐thin films of PMMA (with and without a silicon substrate) at 10 and 20 keV. The new model is discussed and comparison made with results obtained from the old model, which is based on the continuous slowing down approximation of Bethe for energy loss and the screened Rutherford equation for elastic angular scattering. The new model predicts a larger absorbed energy density than the old model for an isolated line source exposure on a resist film. The consequences of this fast secondary electron contribution on the ultimate limit in electron lithography is discussed.

Electron' drift velocity and diffusivity in germanium

Abstract: Experimental results for electron drift velocity and diffusivity in germanium, obtained with the time-of-flight technique in hyperpure material, are presented for temperatures between 8 and 240 K and fields between 1 and ${10}^{4}$ V/cm oriented along $〈111〉$ and $〈100〉$ directions. An anisotropy of the drift velocity and of the diffusion coefficient is found with the electric field applied along $〈111〉$ and $〈100〉$ directions, the latter due to the intervalley diffusion. The effect of the electron-electron interaction in the anisotropy properties has also been investigated. Theoretical Monte Carlo calculations have been performed with a model which includes lower, $〈111〉$, nonparabolic bands as well as upper bands at the center of the Brillouin zone and along the $〈100〉$ directions. Acoustic scattering with proper energy relaxation, optical scattering, and intervalley scattering between equivalent and nonequivalent valleys has been taken into account. Besides drift velocities and diffusion coefficients, other quantities such as mean electron energy, electron distribution function, and valley repopulation have been obtained from the Monte Carlo simulation.

Phase diagram of the two-dimensional Lennard-Jones system; Evidence for first-order transitions

Abstract: There has recently been extensive interest in the nature of the melting/freezing transition for a two-dimensional system of molecules interacting with Lennard-Jones 6:12 potentials, which is a prototype for physisorbed systems. We have therefore made a detailed study of the thermodynamics of the phase diagram for this system. We first made calculations using liquid-state perturbation theory for the fluid state and a self-consistent cell theory for the solid state to determine thermodynamic functions; these results led to ordinary first-order phase transitions between solid/fluid and liquid/gas phases, in agreement with the constant-pressure Monte Carlo results of Abraham. We refined the calculations by using constant-pressure and constant-density Monte Carlo results to improve the accuracy of the calculated free energies, and we determined the two-phase equilibria by making direct Monte Carlo calculations for two-phase systems. The results are internally consistent and lead to a phase diagram qualitatively similar to the three-dimensional Lennard-Jones system.