Showing papers on "Dynamic Monte Carlo method published in 1998"
TL;DR: In this paper, the authors presented an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques, and showed Monte Carlo to be very robust but also slow.
Abstract: Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N−1/2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Carlo quadrature is attained using quasi-random (also called low-discrepancy) sequences, which are a deterministic alternative to random or pseudo-random sequences. The points in a quasi-random sequence are correlated to provide greater uniformity. The resulting quadrature method, called quasi-Monte Carlo, has a convergence rate of approximately O((logN)kN−1). For quasi-Monte Carlo, both theoretical error estimates and practical limitations are presented. Although the emphasis in this article is on integration, Monte Carlo simulation of rarefied gas dynamics is also discussed. In the limit of small mean free path (that is, the fluid dynamic limit), Monte Carlo loses its effectiveness because the collisional distance is much less than the fluid dynamic length scale. Computational examples are presented throughout the text to illustrate the theory. A number of open problems are described.
1,708 citations
Book•
01 Jan 1998
TL;DR: Simulating Random Numbers from a Uniform Distribution * Quality of Random Number Generation * Quasirandom Numbers * Transformations of Uniform Deviates: General Methods * Simulating Random numbers from Specific Distributions
Abstract: Simulating Random Numbers from a Uniform Distribution * Quality of Random Number Generation * Quasirandom Numbers * Transformations of Uniform Deviates: General Methods * Simulating Random Numbers from Specific Distributions * Generation of Random Samples, Permutations, and Stochastic Processes * Monte Carlo Methods * Software for Random Number Generation * Monte Carlo Studies in Statistics
860 citations
TL;DR: It is proved that the minimalworst case error of quasi-Monte Carlo algorithms does not depend on the dimensiondiff the sum of the weights is finite, and the minimal number of function values in the worst case setting needed to reduce the initial error by ? is bounded byC??p, where the exponentp? 1, 2], andCdepends exponentially on thesum of weights.
686 citations
26 Mar 1998
TL;DR: In this paper, a sequence of Monte Carlo methods, namely importance sampling, rejection sampling, the Metropolis method, and Gibbs sampling, are described and a discussion of advanced methods, including methods for reducing random walk behaviour is presented.
Abstract: This chapter describes a sequence of Monte Carlo methods: importance sampling, rejection sampling, the Metropolis method, and Gibbs sampling. For each method, we discuss whether the method is expected to be useful for high—dimensional problems such as arise in inference with graphical models. After the methods have been described, the terminology of Markov chain Monte Carlo methods is presented. The chapter concludes with a discussion of advanced methods, including methods for reducing random walk behaviour.
590 citations
TL;DR: In this paper, a new order parameter, S, is introduced to test for tetrahedral configurations, which is applied to analyse the results of three simulations: (1) molecular dynamics simulation of ice Ih (hexagonal ice) at 200 K, using the SPC/E water potential; (2) Monte Carlo simulation of aqueous solution of methane, using OPLS methane potential and the TIP4P water potential.
Abstract: A new order parameter, S, is introduced to test for tetrahedral configurations. It is applied to analyse the results of three simulations: (1) molecular dynamics simulation of ice Ih (hexagonal ice) at 200 K, using the SPC/E water potential; (2) Monte Carlo simulation of aqueous solution of methane, using the OPLS methane potential and the TIP4P water potential; and (3) Monte Carlo simulation of Lennard-Jones spheres. The quasi-tetrahedral configurations of water molecules in different states can be adequately described using S.
464 citations
TL;DR: In this paper, a modified force field is proposed that provides good agreement with experimental phase equilibrium and second virial coefficient data over wide ranges of temperature and chain length over short and long alkanes.
Abstract: A Monte Carlo simulation study has been conducted to assess the ability of recently proposed force fields to predict orthobaric densities, second virial coefficients, and P-V-T data for short and long alkanes. A new, modified force field is proposed that provides good agreement with experimental phase equilibrium and second virial coefficient data over wide ranges of temperature and chain length.
425 citations
TL;DR: In this article, Monte Carlo statistical mechanics simulations have been carried out with the TIP3P, SPC, and TIP4P models for liquid water at 13 temperatures from −50°C to 100°C at 1 atm.
Abstract: Monte Carlo statistical mechanics simulations have been carried out with the TIP3P, SPC, and TIP4P models for liquid water at 13 temperatures from −50°C to 100°C at 1 atm. Long runs with 512 water molecules provided definitive results for densities. Although the TIP4P model yields a flat region in the density profile and a temperature of maximum density near −15°C, the SPC and TIP3P models show monotonically increasing density with decreasing temperature. Results for heats of vaporization, isothermal compressibilities, and coefficients of thermal expansion and their convergence characteristics are also reported. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1179–1186, 1998
406 citations
TL;DR: In this paper, the Monte Carlo maximum likelihood (MCMCMC) method is used to estimate stochastic volatility (SV) models, which can be expressed as a linear state space model with log chi-square disturbances and decompose it into a Gaussian part, constructed by the Kalman filter, and a remainder function whose expectation is evaluated by simulation.
347 citations
TL;DR: In this article, the relationship between Monte Carlo and quasi-Monte Carlo methods is analyzed from both theoretical and practical points of view with special emphasis on high-dimensional integration with a focus on high dimensional integration.
274 citations
TL;DR: In this paper, the authors show that the most effective update strategy involves the motion of worldline discontinuities (both in space and time), i.e., the evaluation of the Green's function.
Abstract: We show how the worldline quantum Monte Carlo procedure, which usually relies on an artificial time discretization, can be formulated directly in continuous time, rendering the scheme exact. For an arbitrary system with discrete Hilbert space, none of the configuration update procedures contain small parameters. We find that the most effective update strategy involves the motion of worldline discontinuities (both in space and time), i.e., the evaluation of the Green’s function. Being based on local updates only, our method nevertheless allows one to work with the grand canonical ensemble and nonzero winding numbers, and to calculate any dynamical correlation function as easily as expectation values of, e.g., total energy. The principles found for the update in continuous time generalize to any continuous variables in the space of discrete virtual transitions, and in principle also make it possible to simulate continuous systems exactly.
250 citations
Journal Article•
TL;DR: In this paper, Monte Carlo methods for simulation of the dynamic behavior of surface reactions are developed, based on the chemical master equation, in a general framework which makes them applicable to a variety of models.
Abstract: Monte Carlo methods for the simulation of the dynamic behavior of surface reactions are developed, based on the chemical master equation. The methods are stated in a general framework which makes them applicable to a variety of models. Three methods are developed. A comparative analysis of the performance of the three methods, both theoretically and empirically, is included.
TL;DR: In this paper, the dependence of the viscosity and thermal conductivity on cell size for stochastic particle methods such as direct simulation Monte Carlo (DSMC) and its generalization, the consistent Boltzmann algorithm (CBA) was investigated.
Abstract: Using the Green–Kubo theory, the dependence of the viscosity and thermal conductivity on cell size is obtained explicitly for stochastic particle methods such as direct simulation Monte Carlo (DSMC) and its generalization, the consistent Boltzmann algorithm (CBA). These analytical results confirm empirical observations that significant errors occur when the cell dimensions are larger than a mean free path.
11 Nov 1998-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this article, a new simulation of nuclear γ cascades by the Monte Carlo method is described, which makes it possible to generate artificially individual events of the γ-cascade decay of an isolated, highly excited initial level in a medium and heavy nucleus.
Abstract: A new simulation of nuclear γ cascades by the Monte Carlo method is described. It makes it possible to generate artificially individual events of the γ-cascade decay of an isolated, highly excited initial level in a medium and heavy nucleus. A broad class of quantities, associated with the process of γ-cascade de-excitation, can be modelled. The main advantage of the method is the possibility of a full quantitative control over the influence of the Porter–Thomas fluctuations of partial radiation widths on uncertainties of the modelled cascade-related quantities. For assessment of these uncertainties and a control over the accuracy of the method, a special statistical formalism has been developed.
TL;DR: In this paper, a quantum Monte Carlo scheme was proposed for the analysis of large disordered systems, using a pair of worldline discontinuities for sampling the extended configuration space of the system which includes both closed and disconnected worldlines.
TL;DR: In this paper, the correlation energy of the homogeneous three-dimensional interacting electron gas is calculated using the variational and fixed-node diffusion Monte Carlo methods, with trial functions that include backflow and three-body correlations.
Abstract: The correlation energy of the homogeneous three-dimensional interacting electron gas is calculated using the variational and fixed-node diffusion Monte Carlo methods, with trial functions that include backflow and three-body correlations. In the high-density regime ( r s<5) the effects of backflow dominate over those due to three-body correlations, but the relative importance of the latter increases as the density decreases. Since the backflow correlations vary the nodes of the trial function, this leads to improved energies in the fixed-node diffusion Monte Carlo calculations. The effects are comparable to those found for the two-dimensional electron gas, leading to much improved variational energies and fixed-node diffusion energies similar to the releasednode energies of Ceperley and Alder. @S0163-1829~98!00135-0#
01 Jan 1998
TL;DR: In this article, the performance of ordinary Monte Carlo and quasi Monte Carlo methods in valuing moderate-and high-dimensional options was compared, where the dimensionality of the problems arises either from the number of time steps along a single path or from the underlying assets.
Abstract: This article compares the performance of ordinary Monte Carlo and quasi Monte Carlo methods in valuing moderate-and high-dimensional options The dimensionality of the problems arises either from the number of time steps along a single path or from the number of underlying assets We compare ordinary Monte Carlo with and without antithetic variates against Sobol’, Faure, and Generalized Faure sequences and three constructions of a discretely sampled Brownian path We test the standard random walk construction with all methods, a Brownian bridge construction proposed by Caflisch and Morokoff with Sobol’ points and an alternative construction based on principal components analysis also with Sobol’ points We find that the quasi Monte Carlo methods outperform ordinary Monte Carlo; the Brownian bridge construction generally outperforms the standard construction; and the principal components construction generally outperforms the Brownian bridge construction and is more widely applicable We interpret both the Brownian bridge and principal components constructions in terms of orthogonal expansions of Brownian motion and note an optimality property of the principal components construction
TL;DR: In this article, a new method for the stabilization of the sign problem in the Green Function Monte Carlo technique is devised for real lattice Hamiltonians and is based on an iterative ''stochastic reconfiguration'' scheme which introduces some bias but allows a stable simulation with constant sign.
Abstract: A new method for the stabilization of the sign problem in the Green Function Monte Carlo technique is proposed. The method is devised for real lattice Hamiltonians and is based on an iterative ''stochastic reconfiguration'' scheme which introduces some bias but allows a stable simulation with constant sign. The systematic reduction of this bias is in principle possible. The method is applied to the frustrated J1-J2 Heisenberg model, and tested against exact diagonalization data. Evidence of a finite spin gap for J2/J1 >~ 0.4 is found in the thermodynamic limit.
TL;DR: Comparisons of the performance (defined as the variance of the results multiplied by the CPU time required for solution) are presented for three common methods used in Monte Carlo solution.
Abstract: A review of various strategies for implementing Monte Carlo analysis of radiative media is presented. Comparisons of the performance (defined as the variance of the results multiplied by the CPU time required for solution) are presented for three common methods used in Monte Carlo solution. Methods of treating complex geometries are also explored and compared, and a ray-tracing technique based on finite-element models of the geometry is presented. The finite-element models allow use of commercial codes for describing complex geometries, and also allow efficient coupling of the Monte Carlo radiative model with other finite-element-based thermal models. The utility and performance of the direct simulation Monte Carlo ray-tracing methods in engineering problems involving realistic properties are examined. Strategies are compared for treating anisotropic scattering distributions, nonuniform temperatures and radiative properties, and spectral property variations. The effects of scattering on ray tracing and the necessary modifications to the algorithms are evaluated, and the performance and accuracy of these algorithms are evaluated and recommendations are suggested. The difficulties in handling inhomogeneous properties and spectrally dependent properties are presented, and some possible approaches are proposed and compared. Monte Carlo strategies for solving radiative transfer in participating media are described for use on parallel processors using different common architectures. An example benchmark problem is carried out to demonstrate the degree of speedup that can be obtained.
TL;DR: This work reviews and discusses some recent progress in the theory of Markov-chain Monte Carlo applications and attempts to assess the relevance of this theory for practical applications.
Abstract: We review and discuss some recent progress in the theory of Markov-chain Monte Carlo applications, particularly oriented to applications in statistics. We attempt to assess the relevance of this theory for practical applications.
TL;DR: In this paper, the conditions of adsorption of a uniformly charged polyelectrolyte onto oppositely charged planar and spherical surfaces have been investigated by using off-lattice Monte Carlo simulations.
Abstract: By using off-lattice Monte Carlo simulations, the conditions of adsorption of a uniformly charged polyelectrolyte onto oppositely charged planar and spherical surfaces have been investigated. These conditions are functions of the strength of the electrostatic interaction, Debye screening length, chain length, and charge density and curvature of the surface. The adsorption can be tuned by using any one of these parameters. The chain’s conformation, adsorption energy and thickness of the adsorbed polymer are obtained under different adsorption conditions. We find the Monte Carlo simulation data to be in good agreement with the theoretical prediction derived previously by using the assumptions of ground state dominance and separability.
TL;DR: In this article, the authors compute two-time correlation and response functions and find that, as expected from the exact solution of a certain mean-field model, in the limit of $N$ going to infinity, this parameter is equal to one (no violation of FDT) in the quasiequilibrium regime (short separation of times), and zero in the aging regime.
Abstract: Numerical simulations of various domain growth systems are reported in order to compute the parameter describing the violation of fluctuation-dissipation theorem (FDT) in aging phenomena. We compute two-time correlation and response functions and find that, as expected from the exact solution of a certain mean-field model [equivalent to the $O(N)$ model in three dimensions, in the limit of $N$ going to infinity], this parameter is equal to one (no violation of FDT) in the quasiequilibrium regime (short separation of times), and zero in the aging regime.
TL;DR: The reliability and robustness of the new method should enable its routine application in model building protocols based on various (very sparse) experimentally derived structural restraints, and increasing the number of tertiary restraints improves the accuracy of the assembled structures.
Abstract: A new, efficient method for the assembly of protein tertiary structure from known, loosely encoded secondary structure restraints and sparse information about exact side chain contacts is proposed and evaluated. The method is based on a new, very simple method for the reduced modeling of protein structure and dynamics, where the protein is described as a lattice chain connecting side chain centers of mass rather than Calphas. The model has implicit built-in multibody correlations that simulate short- and long-range packing preferences, hydrogen bonding cooperativity and a mean force potential describing hydrophobic interactions. Due to the simplicity of the protein representation and definition of the model force field, the Monte Carlo algorithm is at least an order of magnitude faster than previously published Monte Carlo algorithms for structure assembly. In contrast to existing algorithms, the new method requires a smaller number of tertiary restraints for successful fold assembly; on average, one for every seven residues as compared to one for every four residues. For example, for smaller proteins such as the B domain of protein G, the resulting structures have a coordinate root mean square deviation (cRMSD), which is about 3 A from the experimental structure; for myoglobin, structures whose backbone cRMSD is 4.3 A are produced, and for a 247-residue TIM barrel, the cRMSD of the resulting folds is about 6 A. As would be expected, increasing the number of tertiary restraints improves the accuracy of the assembled structures. The reliability and robustness of the new method should enable its routine application in model building protocols based on various (very sparse) experimentally derived structural restraints.
TL;DR: In this paper, the effect of finite chain length on the collapse transition of stiff-chain macromolecules was studied by means of a Monte Carlo simulation within the framework of the bond fluctuation lattice model.
Abstract: We study the effect of finite chain length on the collapse transition of stiff-chain macromolecules by means of a Monte Carlo simulation within the framework of the bond fluctuation lattice model. Variable stiffness of the chains was modeled by introducing a potential depending on the angle between successive bonds and we introduced an additional quasi-Lennard-Jones potential between monomer units which are not nearest neighbors along the chain to model the quality of the solvent. Chains of length up to 200 monomer units were simulated. For the flexible case these chains are long enough to determine the θ-temperature, but for higher stiffnesses we show systematic effects in the dependence of the apparent transition temperature on the stiffness. For fixed chain lengths we determine apparent phase diagrams and give the apparent transition points and points of ideal chain size as a function of stiffness. We report on the occurrence of a toroidal structure in our model and characterize this structure by local and global packing and orientational ordering.
TL;DR: It is demonstrated that the recently proposed pruned‐enriched Rosenbluth method (PERM) leads to extremely efficient algorithms for the folding of simple model proteins and gives detailed information about the thermal spectrum and thus allows one to analyze thermodynamic aspects of the folding behavior of arbitrary sequences.
Abstract: We demonstrate that the recently proposed pruned-enriched Rosenbluth method (PERM) (Grassberger, Phys. Rev. E 56:3682, 1997) leads to extremely efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare it to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and thus allows one to analyze thermodynamic aspects of the folding behavior of arbitrary sequences. Proteins 32:52–66, 1998. © 1998 Wiley-Liss, Inc.
TL;DR: In this article, an efficient path-integral quantum Monte Carlo algorithm for the lattice polaron is presented, based on Feynman's integration of phonons and subsequent simulation of the resulting singleparticle self-interacting system.
Abstract: An efficient continuous-time path-integral quantum Monte Carlo algorithm for the lattice polaron is presented. It is based on Feynman's integration of phonons and subsequent simulation of the resulting single-particle self-interacting system. The method is free from the finite-size and finite-time-step errors and works in any dimensionality and for any range of electron-phonon interaction. The ground-state energy and effective mass of the polaron are calculated for several models. The polaron spectrum can be measured directly by Monte Carlo, which is of general interest.
TL;DR: In this paper, a new approach to cluster simulation is developed in the context of nucleation theory, which preferentially and automatically generates the physical clusters, defined as the density fluctuations that lead to nucleation, and determines their equilibrium distribution.
Abstract: A new approach to cluster simulation is developed in the context of nucleation theory. This approach is free of any arbitrariness involved in the definition of a cluster. Instead, it preferentially and automatically generates the physical clusters, defined as the density fluctuations that lead to nucleation, and determines their equilibrium distribution in a single simulation, thereby completely bypassing the computationally expensive free energy evaluation that is necessary in a conventional approach. The validity of the method is demonstrated for a single component system using a model potential for water under several values of supersaturation.