Showing papers on "Monte Carlo molecular modeling published in 2004"
TL;DR: In this article, an analytic method of smearing link variables in lattice QCD is proposed and tested, and the differentiability of the smearing scheme with respect to the link variables permits the use of modern Monte Carlo updating methods based on molecular dynamics evolution for gauge-field actions constructed using such smeared links.
Abstract: An analytic method of smearing link variables in lattice QCD is proposed and tested. The differentiability of the smearing scheme with respect to the link variables permits the use of modern Monte Carlo updating methods based on molecular dynamics evolution for gauge-field actions constructed using such smeared links. In examining the smeared mean plaquette and the static quark-antiquark potential, no degradation in effectiveness is observed as compared to link smearing methods currently in use, although an increased sensitivity to the smearing parameter is found.
541 citations
TL;DR: A central limit theorem for the Monte Carlo estimates produced by these computational methods is established in this paper, and applies in a general framework which encompasses most of the sequential Monte Carlo methods that have been considered in the literature, including the resample-move algorithm of Gilks and Berzuini [J. R. Stat. Ser. B Statol. 63 (2001) 127,146] and the residual resampling scheme.
Abstract: The term “sequential Monte Carlo methods” or, equivalently, “particle filters,” refers to a general class of iterative algorithms that performs Monte Carlo approximations of a given sequence of distributions of interest (πt). We establish in this paper a central limit theorem for the Monte Carlo estimates produced by these computational methods. This result holds under minimal assumptions on the distributions πt, and applies in a general framework which encompasses most of the sequential Monte Carlo methods that have been considered in the literature, including the resample-move algorithm of Gilks and Berzuini [J. R. Stat. Soc. Ser. B Stat. Methodol. 63 (2001) 127–146] and the residual resampling scheme. The corresponding asymptotic variances provide a convenient measurement of the precision of a given particle filter. We study, in particular, in some typical examples of Bayesian applications, whether and at which rate these asymptotic variances diverge in time, in order to assess the long term reliability of the considered algorithm.
481 citations
TL;DR: A critical appraisal of reliability procedures for high dimensions is presented and it is observed that some types of Monte Carlo based simulation procedures in fact are capable of treating high dimensional problems.
446 citations
TL;DR: In this article, a review of generalized ensemble algorithms for complex systems with many degrees of freedom such as spin glass and biomolecular systems is presented. And five new generalized-ensemble algorithms which are extensions of the above methods are presented.
Abstract: In complex systems with many degrees of freedom such as spin glass and biomolecular systems, conventional simulations in canonical ensemble suffer from the quasi-ergodicity problem. A simulation in generalized ensemble performs a random walk in potential energy space and overcomes this difficulty. From only one simulation run, one can obtain canonical ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review the generalized ensemble algorithms. Three well-known methods, namely, multicanonical algorithm (MUCA), simulated tempering (ST), and replica-exchange method (REM), are described first. Both Monte Carlo (MC) and molecular dynamics (MD) versions of the algorithms are given. We then present five new generalized-ensemble algorithms which are extensions of the above methods.
331 citations
TL;DR: In this paper, a Monte Carlo algorithm for doing simulations in classical statistical physics in a different way is described, where instead of sampling the probability distribution at a fixed temperature, a random walk is performed in energy space to extract an estimate for the density of states.
Abstract: We describe a Monte Carlo algorithm for doing simulations in classical statistical physics in a different way. Instead of sampling the probability distribution at a fixed temperature, a random walk is performed in energy space to extract an estimate for the density of states. The probability can be computed at any temperature by weighting the density of states by the appropriate Boltzmann factor. Thermodynamic properties can be determined from suitable derivatives of the partition function and, unlike “standard” methods, the free energy and entropy can also be computed directly. To demonstrate the simplicity and power of the algorithm, we apply it to models exhibiting first-order or second-order phase transitions.
237 citations
TL;DR: Molecular Dynamics Simulations of Water and Biomolecules with a Monte Carlo Constant Pressure Algorithm as discussed by the authors was used to simulate water and biomolecules in the simulation.
235 citations
TL;DR: A Monte Carlo code for indexing powder diffraction patterns is presented in this article, where cell parameters are generated randomly and tested against an idealized powder profile generated from the extracted d's and I's.
Abstract: A Monte Carlo code for indexing powder diffraction patterns is presented. Cell parameters are generated randomly and tested against an idealized powder profile generated from the extracted d’s and I’s. Limits with this program in solving problems associated with zeropoint errors and impurity lines are examined. Most problems (V 2 GHz processor); more time is needed for triclinic cases. Attempts are shown to be successful for the indexation of two-phase samples in simple cases (combining orthorhombic or higher symmetries). © 2004 International Centre for Diffraction Data.Key words: powder diffraction, indexing, Monte Carlo
200 citations
TL;DR: A procedure is proposed in which the numerical results from a Monte Carlo reliability estimation procedure are converted to a form that will allow the basic ideas of the first order reliability method to be employed and allows sensitivity estimates of low computational cost to be made.
178 citations
TL;DR: GEANT4 is a promising Monte Carlo simulation toolkit for low-energy medical applications and is compared to published results based on three Monte Carlo codes widely used in medical physics: MCNP, EGS4, and EGSnrc.
Abstract: GEANT4 (GEometry ANd Tracking 4) is an object-oriented Monte Carlo simulation toolkit that has been developed by a worldwide collaboration of scientists. It simulates the passage of particles through matter. In order to validate GEANT4 for medical physics applications, different simulations are conducted. The results are compared to published results based on three Monte Carlo codes widely used in medical physics: MCNP, EGS4, and EGSnrc. When possible, the simulation results are also compared to experimental data. Different geometries are tested (multilayer and homogeneous phantoms), different sources considered (point-source and broad parallel beam), and different primary particles simulated (photons and electrons) at different energies. For the heterogeneous media, there are notable differences between the Monte Carlo codes reaching up to over 5% in relative difference. For the monoenergetic electrons in a homogeneous medium, the difference between GEANT4 and the experimental measurements is similar to the difference between EGSnrc and the experimental measurements; for the depth-dose curves, the difference expressed as a fraction of the peak dose is always smaller than 4%. We conclude that GEANT4 is a promising Monte Carlo simulation toolkit for low-energy medical applications.
171 citations
TL;DR: A methodology for convergence analysis of Monte Carlo simulations and therefore for the reliability assessment of the inferred statistical moments is proposed, based on simple rules of statistical inference, which can be extended to different application fields.
Abstract: [1] Numerical Monte Carlo simulation is considered to be one of the main tools to be used in groundwater hydrology (1) to quantify the uncertainty in the flow predictions due to imperfect knowledge of aquifer architecture, hydraulic parameters, and forcing terms or (2) to assess the reliability of approximated moment-based equations for flow and/or transport. While the Monte Carlo framework is conceptually straightforward and very flexible, it is recognized as lacking well-established convergence criteria. Here we propose a methodology for convergence analysis of Monte Carlo simulations and therefore for the reliability assessment of the inferred statistical moments. The methodology, based on simple rules of statistical inference, is described with reference to a typical groundwater flow problem and can be extended to different application fields.
168 citations
TL;DR: The induced charge computation (ICC) method for the calculation of the polarization charges based on the variational formulation of Allen et al. is presented and results for electrolyte solutions in these special cases show that the ICC method is both accurate and efficient.
Abstract: The efficient calculation of induced charges in an inhomogeneous dielectric is important in simulations and coarse-grained models in molecular biology, chemical physics, and electrochemistry. We present the induced charge computation ~ICC! method for the calculation of the polarization charges based on the variational formulation of Allen et al. @Phys. Chem. Chem. Phys. 3, 4177 ~2001!#. We give a different solution for their extremum condition that produces a matrix formulation. The induced charges are directly calculated by solving the linear matrix equation Ah5c, where h contains the discretized induced charge density, c depends only on the source charges—the ions moved in the simulation—and the matrix A depends on the geometry of dielectrics, which is assumed to be unchanged during the simulation. Thus, the matrix need be inverted only once at the beginning of the simulation. We verify the efficiency and accuracy of the method by means of Monte Carlo simulations for two special cases. In the simplest case, a single sharp planar dielectric boundary is present, which allows comparison with exact results calculated using the method of electrostatic images. The other special case is a particularly simple case where the matrix A is not diagonal: a slab with two parallel flat boundaries. Our results for electrolyte solutions in these special cases show that the ICC method is both accurate and efficient.
TL;DR: The quantum annealing scheme, even with a drastically simple form of kinetic energy, appears definitely superior to the classical one, when tested on a 1002-city instance of the standard TSPLIB.
Abstract: We propose a path-integral Monte Carlo quantum annealing scheme for the symmetric traveling-salesman problem, based on a highly constrained Ising-like representation, and we compare its performance against standard thermal simulated annealing. The Monte Carlo moves implemented are standard, and consist in restructuring a tour by exchanging two links (two-opt moves). The quantum annealing scheme, even with a drastically simple form of kinetic energy, appears definitely superior to the classical one, when tested on a 1002-city instance of the standard TSPLIB.
TL;DR: An adaptive algorithm which optimizes the statistical-mechanical ensemble in a generalized broad-histogram Monte Carlo simulation to maximize the system's rate of round trips in total energy and substantially outperforms flat-histograms methods such as the Wang-Landau algorithm.
Abstract: We present an adaptive algorithm which optimizes the statistical-mechanical ensemble in a generalized broad-histogram Monte Carlo simulation to maximize the system's rate of round trips in total energy. The scaling of the mean round-trip time from the ground state to the maximum entropy state for this local-update method is found to be O ( [N ln N](2) ) for both the ferromagnetic and the fully frustrated two-dimensional Ising model with N spins. Our algorithm thereby substantially outperforms flat-histogram methods such as the Wang-Landau algorithm.
TL;DR: A novel, generally applicable Monte Carlo algorithm is presented, used to identify clusters of particles in such a manner that every cluster move is accepted, irrespective of the nature of the pair interactions.
Abstract: We present a novel, generally applicable Monte Carlo algorithm for the simulation of fluid systems. Geometric transformations are used to identify clusters of particles in such a manner that every cluster move is accepted, irrespective of the nature of the pair interactions. The rejection-free and nonlocal nature of the algorithm make it particularly suitable for the efficient simulation of complex fluids with components of widely varying size, such as colloidal mixtures. Compared to conventional simulation algorithms, typical efficiency improvements amount to several orders of magnitude.
TL;DR: A variance prediction method for a general built-up structure is presented here and is validated by comparison with Monte Carlo simulations of plate networks and structural-acoustic systems.
Abstract: In the statistical energy analysis (SEA) of high frequency noise and vibration, a complex engineering structure is represented as an assembly of subsystems. The response of the system to external excitation is expressed in terms of the vibrational energy of each subsystem, and these energies are found by employing the principle of power balance. Strictly the computed energy is an average taken over an ensemble of random structures, and for many years there has been interest in extending the SEA prediction to the variance of the energy. A variance prediction method for a general built-up structure is presented here. Closed form expressions for the variance are obtained in terms of the standard SEA parameters and an additional set of parameters alpha(k) that describe the nature of the power input to each subsystem k, and alpha(ks) that describe the nature of the coupling between subsystems k and s. The theory is validated by comparison with Monte Carlo simulations of plate networks and structural-acoustic systems.
TL;DR: It is argued that the efficiency of Monte Carlo simulations can be enhanced, sometimes dramatically, by properly sampling configurations that are normally rejected, and this method greatly improves the calculation of the order-parameter distribution of a two-dimensional Ising model.
Abstract: The Markov chain Monte Carlo method is an important tool to estimate the average properties of systems with a very large number of accessible states. This technique is used extensively in fields ranging from physics to genetics and economics. The rejection of trial configurations is a central ingredient in existing Markov chain Monte Carlo simulations. I argue that the efficiency of Monte Carlo simulations can be enhanced, sometimes dramatically, by properly sampling configurations that are normally rejected. This “waste-recycling” of microstates is useful in sampling schemes in which only one of a large set of trial configurations is accepted. It differs fundamentally from schemes that extract information about the density of macrostates from virtual Monte Carlo moves. As a simple illustration, I show that the method greatly improves the calculation of the order-parameter distribution of a two-dimensional Ising model. This method should enhance the efficiency of parallel Monte Carlo simulations significantly.
TL;DR: It is demonstrated that the swap efficiency of the parallel tempering method for condensed-phase systems decreases naturally to zero at least as fast as the inverse square root of the dimensionality of the physical system.
Abstract: We show that the acceptance probability for swaps in the parallel tempering Monte Carlo method for classical canonical systems is given by a universal function that depends on the average statistical fluctuations of the potential and on the ratio of the temperatures. The law, called the incomplete beta function law, is valid in the limit that the two temperatures involved in swaps are close to one another. An empirical version of the law, which involves the heat capacity of the system, is developed and tested on a Lennard-Jones cluster. We argue that the best initial guess for the distribution of intermediate temperatures for parallel tempering is a geometric progression and we also propose a technique for the computation of optimal temperature schedules. Finally, we demonstrate that the swap efficiency of the parallel tempering method for condensed-phase systems decreases naturally to zero at least as fast as the inverse square root of the dimensionality of the physical system.
TL;DR: In this paper, the generalized linear spatial models are used for parameter estimation and model selection using Markov chain Monte Carlo maximum likelihood is a feasible and very useful technique for estimating radionuclide concentrations on Rongelap Island.
Abstract: When using a model-based approach to geostatistical problems, often, due to the complexity of the models, inference relies on Markov chain Monte Carlo methods. This article focuses on the generalized linear spatial models, and demonstrates that parameter estimation and model selection using Markov chain Monte Carlo maximum likelihood is a feasible and very useful technique. A dataset of radionuclide concentrations on Rongelap Island is used to illustrate the techniques. For this dataset we demonstrate that the log-link function is not a good choice, and that there exists additional nonspatial variation which cannot be attributed to the Poisson error distribution. We also show that the interpretation of this additional variation as either micro-scale variation or measurement error has a significant impact on predictions. The techniques presented in this article would also be useful for other types of geostatistical models.
TL;DR: An adaptative variance reduction method for Monte Carlo simulations that uses importance sampling scheme based on a change of drift and develops two applications of the procedure for variance reduction in a Monte Carlo computation in finance and in reliability.
Abstract: In this article we propose an adaptative variance reduction method for Monte Carlo simulations. The method uses importance sampling scheme based on a change of drift. The change of drift is selected adaptatively through the Monte Carlo computation by using a suitable sequence of approximation. We state and prove theoretical results supporting the use of the method. We develop two applications of the procedure for variance reduction in a Monte Carlo computation in finance and in reliability.
TL;DR: The review offers a general study of the classical theories and algorithms that are foundational to Brownian Dynamics, Molecular Dynamics, and Monte Carlo simulations, and holds promising potential for effective modeling of transport in colloidal systems.
Book•
01 Oct 2004
TL;DR: Sampling, Statistics and Computer Code Error Analysis for Independent Random Variables Markov Chain Monte Carlo Error analysis forMarkov Chain Data Advanced Monte Carlo Parallel Computing Conclusions, History and Outlook.
Abstract: Sampling, Statistics and Computer Code Error Analysis for Independent Random Variables Markov Chain Monte Carlo Error Analysis for Markov Chain Data Advanced Monte Carlo Parallel Computing Conclusions, History and Outlook.
TL;DR: In this article, a stepwise constant-volume Monte Carlo simulation technique is developed to describe dispersed phase systems, which allows to use only several thousands simulation particles, even if the particle number concentration experiences changes of several orders of magnitude.
TL;DR: This study proposes a more realistic spike train generation model that incorporates both a description of "nontrivial" neuronal discharge statistics and of spike waveform dynamics and illustrates the way to build the transition matrix of the Markov chain with a simple, but realistic, model for data generation.
Abstract: Spike-sorting techniques attempt to classify a series of noisy electrical waveforms according to the identity of the neurons that generated them. Existing techniques perform this classification ign...
TL;DR: In this paper, an implementation of the Reverse Monte Carlo algorithm for the study of amorphous tetrahedral semiconductors is presented, taking into account a number of constraints.
Abstract: An implementation of the Reverse Monte Carlo algorithm is presented for the study of amorphous tetrahedral semiconductors. By taking into account a number of constraints that describe the tetrahedral bonding geometry along with the radial distribution function, we construct a model of amorphous silicon using the reverse monte carlo technique. Starting from a completely random configuration, we generate a model of amorphous silicon containing 500 atoms closely reproducing the experimental static structure factor and bond angle distribution and in improved agreement with electronic properties. Comparison is made to existing Reverse Monte Carlo models, and the importance of suitable constraints beside experimental data is stressed.
TL;DR: In this article, diffusion quantum Monte Carlo calculations of three-dimensional Wigner crystals in the density range rs=100−150 were performed. But none of the results improved upon the simple Gaussian form.
Abstract: We report diffusion quantum Monte Carlo calculations of three-dimensional Wigner crystals in the density range rs=100–150. We have tested different types of orbital for use in the approximate wave functions but none improve upon the simple Gaussian form. The Gaussian exponents are optimized by directly minimizing the diffusion quantum Monte Carlo energy. We have carefully investigated and sought to minimize the potential biases in our Monte Carlo results. We conclude that the uniform electron gas undergoes a transition from a ferromagnetic fluid to a body-centered-cubic Wigner crystal at rs=106±1. The diffusion quantum Monte Carlo results are compared with those from Hartree-Fock and Hartree theory in order to understand the role played by exchange and correlation in Wigner crystals. We also study “floating” Wigner crystals and give results for their pair-correlation functions.
TL;DR: In this article, a very efficient quantum Monte Carlo algorithm for the Holstein model with one electron was proposed, based on the canonical Lang-Firsov transformation of the Hamiltonian.
Abstract: Based on the canonical Lang-Firsov transformation of the Hamiltonian we develop a very efficient quantum Monte Carlo algorithm for the Holstein model with one electron. Separation of the fermionic degrees of freedom by a reweighting of the probability distribution leads to a dramatic reduction in computational effort. A principal component representation of the phonon degrees of freedom allows to sample completely uncorrelated phonon configurations. The combination of these elements enables us to perform efficient simulations for a wide range of temperature, phonon frequency, and electron-phonon coupling on clusters large enough to avoid finite-size effects. The algorithm is tested in one dimension and the data are compared with exact-diagonalization results and with existing work. Moreover, the ideas presented here can also be applied to the many-electron case. In the one-electron case considered here, the physics of the Holstein model can be described by a simple variational approach.
TL;DR: In this article, a determinantal grand-canonical method is proposed based on a stochastic series expansion for the partition function in the interaction representation for finite fermionic systems with non-local interactions.
Abstract: Numerically exact continuous-time Quantum Monte Carlo algorithm for finite fermionic systems with non-local interactions is proposed. The scheme is particularly applicable for general multi-band time-dependent correlations since it does not invoke Hubbard-Stratonovich transformation. The present determinantal grand-canonical method is based on a stochastic series expansion for the partition function in the interaction representation. The results for the Green function and for the time-dependent susceptibility of multi-orbital super-symmetric impurity model with a spin-flip interaction are presented.
TL;DR: In this article, a simple approach is described to calculate sample-specific standard errors for the concentrations predicted by a three-way parallel factor (PARAFAC) analysis model, which involves a first-order error propagation equation in which the correct sensitivity and leverage values are introduced.
Posted Content•
TL;DR: In this paper, a tutorial on Markov chain Monte Carlo simulations and their statistical analysis is presented, illustrated through many numerical assignments from the author's book on the subject. Computer code (in Fortran) is available for all subjects covered and can be downloaded from the web.
Abstract: This article is a tutorial on Markov chain Monte Carlo simulations and their statistical analysis. The theoretical concepts are illustrated through many numerical assignments from the author's book on the subject. Computer code (in Fortran) is available for all subjects covered and can be downloaded from the web.