Showing papers on "Monte Carlo molecular modeling published in 2005"
Book•
19 Sep 2005TL;DR: A review of Monte Carlo methods of computer simulation can be found in this article, where a brief review of other methods of simulation can also be found, as well as a brief introduction to Monte Carlo studies of biological molecules.
Abstract: Preface 1. Introduction 2. Some necessary background 3. Simple sampling Monte Carlo methods 4. Importance sampling Monte Carlo methods 5. More on importance sampling Monte Carlo methods of lattice systems 6. Off-lattice models 7. Reweighting methods 8. Quantum Monte Carlo methods 9. Monte Carlo renormalization group methods 10. Non-equilibrium and irreversible processes 11. Lattice gauge models: a brief introduction 12. A brief review of other methods of computer simulation 13. Monte Carlo simulations at the periphery of physics and beyond 14. Monte Carlo studies of biological molecules 15. Outlook Appendix Index.
2,055 citations
22 Jun 2005
TL;DR: In this paper, the authors describe the Monte Carlo method for the simulation of grain growth and recrystallization, and present a small subset of the broader use of Monte Carlo methods for which an excellent overview can be found in the book.
Abstract: This chapter is aimed at describing the Monte Carlo method for the simulation of grain growth and recrystallization. It has also been extended to phase transformations and hybrid versions (Monte Carlo coupled with Cellular Automaton) of the model can also accommodate diffusion. If reading this chapter inspires you to program your own version of the algorithm and try to solve some problems, then we will have succeeded! The method is simple to implement and it is fairly straightforward to apply variable material properties such as anisotropic grain boundary energy and mobility. There are, however, some important limitations of the method that must be kept in mind. These limitations include an inherent lattice anisotropy that manifests itself in various ways. For many purposes, however, if you pay attention to what has been found to previous work, the model is robust and highly efficient from a computational perspective. In many circumstances, it is best to use the model to gain insight into a physical system and then obtain a new theoretical understanding, in preference to interpreting the results as being directly representative of a particular material. Please also keep in mind that the “Monte Carlo Method” described herein is a small subset of the broader use of Monte Carlo methods for which an excellent overview can be found in the book by Landau and Binder (2000).
1,115 citations
Book•
20 May 2005
TL;DR: In this paper, Brownian Dynamics for the Simulation of Granular Flows is used to simulate the simulation of granular flows in a dynamical model with event-driven molecular dynamics.
Abstract: Molecular Dynamics.- Event-Driven Molecular Dynamics.- Direct Simulation Monte Carlo.- Rigid-Body Dynamics.- Cellular Automata.- Bottom-to-Top Reconstruction.- Brownian Dynamics for the Simulation of Granular Flows.
617 citations
01 Jan 2005
378 citations
01 Jan 2005
347 citations
TL;DR: Three different ways to build a Monte Carlo program for light propagation with polarization are given and comparison in between Monte Carlo runs and Adding Doubling program yielded less than 1 % error.
Abstract: Three Monte Carlo programs were developed which keep track of the status of polarization of light traveling through mono-disperse solutions of micro-spheres. These programs were described in detail in our previous article [1]. This paper illustrates a series of Monte Carlo simulations that model common experiments of light transmission and reflection of scattering media. Furthermore the codes were expanded to model light propagating through poly-disperse solutions of micro-spheres of different radii distributions.
324 citations
TL;DR: This work describes a sequential importance sampling procedure for analyzing two-way zero–one or contingency tables with fixed marginal sums, and produces Monte Carlo samples that are remarkably close to the uniform distribution, enabling one to approximate closely the null distributions of various test statistics about these tables.
Abstract: We describe a sequential importance sampling (SIS) procedure for analyzing two-way zero–one or contingency tables with fixed marginal sums. An essential feature of the new method is that it samples the columns of the table progressively according to certain special distributions. Our method produces Monte Carlo samples that are remarkably close to the uniform distribution, enabling one to approximate closely the null distributions of various test statistics about these tables. Our method compares favorably with other existing Monte Carlo-based algorithms, and sometimes is a few orders of magnitude more efficient. In particular, compared with Markov chain Monte Carlo (MCMC)-based approaches, our importance sampling method not only is more efficient in terms of absolute running time and frees one from pondering over the mixing issue, but also provides an easy and accurate estimate of the total number of tables with fixed marginal sums, which is far more difficult for an MCMC method to achieve.
270 citations
TL;DR: Ligand exit pathways are successfully modeled for different systems containing ligands of various sizes and reveal the potential of this new technique in mapping millisecond-time-scale processes.
Abstract: Combining protein structure prediction algorithms and Metropolis Monte Carlo techniques, we provide a novel method to explore all-atom energy landscapes. The core of the technique is based on a steered localized perturbation followed by side-chain sampling as well as minimization cycles. The algorithm and its application to ligand diffusion are presented here. Ligand exit pathways are successfully modeled for different systems containing ligands of various sizes: carbon monoxide in myoglobin, camphor in cytochrome P450cam, and palmitic acid in the intestinal fatty-acid-binding protein. These initial applications reveal the potential of this new technique in mapping millisecond-time-scale processes. The computational cost associated with the exploration is significantly less than that of conventional MD simulations.
198 citations
TL;DR: MC and SMC are introduced to sample and/or maximize high-dimensional probability distributions to perform likelihood or Bayesian inference for complex non-Gaussian signal processing problems.
Abstract: In this article, MCMC (Markov chain Monte Carlo methods) and SMC (sequential Monte Carlo methods) are introduced to sample and/or maximize high-dimensional probability distributions. These methods enable to perform likelihood or Bayesian inference for complex non-Gaussian signal processing problems.
197 citations
TL;DR: In this paper, the accept-reject version of the recursive Monte Carlo filter is compared with the more common sampling importance resampling version of particle filters. And the central limit theorem for particle filters is proved.
Abstract: Recursive Monte Carlo filters, also called particle filters, are a powerful tool to perform the computations in general state space models. We discuss and compare the accept-reject version with the more common sampling importance resampling version of the algorithm. In particular, we show how auxiliary variable methods and stratification can be used in the accept-reject version, and we compare dierent resampling techniques. In a second part, we show laws of large numbers and a central limit theorem for these Monte Carlo filters by simple induction arguments that need only weak conditions. We also show that under stronger conditions the required sample size is independent of the length of the observed series. AMS 2000 subject classifications. Primary 62M09; secondary 60G35, 60J22, 65C05.
167 citations
TL;DR: The generalized directed loop method is applied to the magnetization process of spin chains in order to compare its efficiency to that of previous directed loop schemes and finds that the optimal strategy depends not only on the model parameters but also on the observable of interest.
Abstract: Efficient quantum Monte Carlo update schemes called directed loops have recently been proposed, which improve the efficiency of simulations of quantum lattice models. We propose to generalize the detailed balance equations at the local level during the loop construction by accounting for the matrix elements of the operators associated with open world-line segments. Using linear programming techniques to solve the generalized equations, we look for optimal construction schemes for directed loops. This also allows for an extension of the directed loop scheme to general lattice models, such as high-spin or bosonic models. The resulting algorithms are bounce free in larger regions of parameter space than the original directed loop algorithm. The generalized directed loop method is applied to the magnetization process of spin chains in order to compare its efficiency to that of previous directed loop schemes. In contrast to general expectations, we find that minimizing bounces alone does not always lead to more efficient algorithms in terms of autocorrelations of physical observables, because of the nonuniqueness of the bounce-free solutions. We therefore propose different general strategies to further minimize autocorrelations, which can be used as supplementary requirements in any directed loop scheme. We show by calculating autocorrelation times for different observables that such strategies indeed lead to improved efficiency; however, we find that the optimal strategy depends not only on the model parameters but also on the observable of interest.
TL;DR: The algorithm proposed improves on similar existing methods by recovering EM's ascent property with high probability, being more robust to the effect of user‐defined inputs and handling classical Monte Carlo and Markov chain Monte Carlo methods within a common framework.
Abstract: Summary. The expectation–maximization (EM) algorithm is a popular tool for maximizing likelihood functions in the presence of missing data. Unfortunately, EM often requires the evaluation of analytically intractable and high dimensional integrals. The Monte Carlo EM (MCEM) algorithm is the natural extension of EM that employs Monte Carlo methods to estimate the relevant integrals. Typically, a very large Monte Carlo sample size is required to estimate these integrals within an acceptable tolerance when the algorithm is near convergence. Even if this sample size were known at the onset of implementation of MCEM, its use throughout all iterations is wasteful, especially when accurate starting values are not available. We propose a data-driven strategy for controlling Monte Carlo resources in MCEM. The algorithm proposed improves on similar existing methods by recovering EM’s ascent (i.e. likelihood increasing) property with high probability, being more robust to the effect of user-defined inputs and handling classical Monte Carlo and Markov chain Monte Carlo methods within a common framework. Because of the first of these properties we refer to the algorithm as ‘ascent-based MCEM’. We apply ascent-based MCEM to a variety of examples, including one where it is used to accelerate the convergence of deterministic EM dramatically.
TL;DR: In this paper, a new subset simulation approach is proposed for reliability estimation for dynamical systems subject to stochastic excitation, which employs splitting of a trajectory that reaches an intermediate failure level into multiple trajectories subsequent to the corresponding first passage time.
TL;DR: Numerical results demonstrate that the proposed method leads to a severalfold increase in the acceptance rate of MCMC and provides a practical approach to uncertainty quantification during subsurface characterization.
Abstract: [1] In this paper, we use a two-stage Markov chain Monte Carlo (MCMC) method for subsurface characterization that employs coarse-scale models. The purpose of the proposed method is to increase the acceptance rate of MCMC by using inexpensive coarse-scale runs based on single-phase upscaling. Numerical results demonstrate that our approach leads to a severalfold increase in the acceptance rate and provides a practical approach to uncertainty quantification during subsurface characterization.
TL;DR: It is found that the fluid-fluid critical point is metastable for both cases, with the case lambda = 1.25 being just below the threshold value for metastability.
Abstract: Various Monte Carlo techniques are used to determine the complete phase diagrams of the square-well model for the attractive ranges λ=1.15 and λ=1.25. The results for the latter case are in agreement with earlier Monte Carlo simulations for the fluid-fluid coexistence curve and yield new results for the liquidus-solidus lines. Our results for λ=1.15 are new. We find that the fluid-fluid critical point is metastable for both cases, with the case λ=1.25 being just below the threshold value for metastability. We compare our results with prior studies and with experimental results for the γII-crystallin.
01 Jul 2005
TL;DR: In this paper, an adjoint method was proposed to accelerate the calculation of Greeks by Monte Carlo simulation, which calculates price sensitivities along each path; but in contrast to a forward pathwise calculation, it works backward recursively using adjoint variables.
Abstract: This paper presents an adjoint method to accelerate the calculation of Greeks by Monte Carlo simulation. The method calculates price sensitivities along each path; but in contrast to a forward pathwise calculation, it works backward recursively using adjoint variables. Along each path, the forward and adjoint implementations produce the same values, but the adjointmethodrearrangesthecalculationstogeneratepotentialcomputational savings. The adjoint method outperforms a forward implementation in calculating the sensitivities of a small number of outputs to a large number of inputs. This applies, for example, in estimating the sensitivities of an interestratederivativesbooktomultiplepointsalonganinitialforwardcurveor thesensitivitiesofanequityderivativesbooktomultiplepointsonavolatilitysurface. Weillustratetheapplicationofthemethodinthesettingofthe LIBORmarketmodel. Numericalresultsconflrmthatthecomputationaladvantage of the adjoint method grows in proportion to the number of initial forward rates.
TL;DR: A Monte Carlo algorithm is introduced that in fact simulates systems with size L(d-1) x infinity, where L specifies the linear system size, and which can be regarded either as an extension of the Hoshen-Kopelman method or as a special case of the transfer-matrix Monte Carlo technique.
Abstract: We investigate the site-percolation problem on the square and simple-cubic lattices by means of a Monte Carlo algorithm that in fact simulates systems with size L(d-1) x infinity, where L specifies the linear system size. This algorithm can be regarded either as an extension of the Hoshen-Kopelman method or as a special case of the transfer-matrix Monte Carlo technique. Various quantities, such as the magnetic correlation function, are sampled in the finite directions of the above geometry. Simulations are arranged such that both bulk and surface quantities can be sampled. On the square lattice, we locate the percolation threshold at p(c) =0.592 746 5 (4) , and determine two universal quantities as Q(gbc) =0.930 34 (1) and Q(gsc) =0.793 72 (3) , which are associated with bulk and surface correlations, respectively. These values agree well with the exact values 2(-5/48) and 2(-1/3) , respectively, which follow from conformal invariance. On the simple-cubic lattice, we locate the percolation threshold at p(c) =0.311 607 7 (4) . We further determine the bulk thermal and magnetic exponents as y(t) =1.1437 (6) and y(h) =2.5219 (2) , respectively, and the surface magnetic exponent at the ordinary phase transition as y (o)(hs) =1.0248 (3) .
TL;DR: In this paper, a simple scheme for introducing the correct cusps at nuclei into orbitals obtained from Gaussian basis set electronic structure calculations was described, which greatly reduced the variance of the local energy in all cases and slightly improved the variational energy.
Abstract: A simple scheme is described for introducing the correct cusps at nuclei into orbitals obtained from Gaussian basis set electronic structure calculations. The scheme is tested with all-electron variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods for the Ne atom, the H2 molecule, and 55 molecules from a standard benchmark set. It greatly reduces the variance of the local energy in all cases and slightly improves the variational energy. This scheme yields a general improvement in the efficiency of all-electron VMC and DMC calculations using Gaussian basis sets.
TL;DR: As a model problem two well-known approximations of a Wiener integral are considered: the standard one and the Brownian bridge, and the advantage of theBrownian bridge is confirmed.
Abstract: Different Quasi-Monte Carlo algorithms corresponding to the same Monte Carlo algorithm are considered. Even in the case when their constructive dimensions are equal and the same quasi-random points are used, the efficiencies of these algorithms may differ. Global sensitivity analysis provides an insight into this situation. As a model problem two well-known approximations of a Wiener integral are considered: the standard one and the Brownian bridge. The advantage of the Brownian bridge is confirmed.
TL;DR: The generalized algorithm, motivated by the successes of the Wang–Landau algorithm in discrete systems, is generalized to continuous systems and provides a new method for Monte Carlo integration based on stochastic approximation and is an excellent tool for Monte Monte optimization.
Abstract: Inference for a complex system with a rough energy landscape is a central topic in Monte Carlo computation. Motivated by the successes of the Wang–Landau algorithm in discrete systems, we generalize the algorithm to continuous systems. The generalized algorithm has some features that conventional Monte Carlo algorithms do not have. First, it provides a new method for Monte Carlo integration based on stochastic approximation; second, it is an excellent tool for Monte Carlo optimization. In an appropriate setting, the algorithm can lead to a random walk in the energy space, and thus it can sample relevant parts of the sample space, even in the presence of many local energy minima. The generalized algorithm can be conveniently used in many problems of Monte Carlo integration and optimization, for example, normalizing constant estimation, model selection, highest posterior density interval construction, and function optimization. Our numerical results show that the algorithm outperforms simulated annealing an...
TL;DR: A sampling algorithm to explore the probability densities arising in Bayesian data analysis problems and is a multiparameter generalization of a replica-exchange Monte Carlo scheme.
Abstract: We develop a sampling algorithm to explore the probability densities arising in Bayesian data analysis problems. Our algorithm is a multiparameter generalization of a replica-exchange Monte Carlo scheme. The strategy relies on gradual weighing of experimental data and on Tsallis generalized statistics. We demonstrate the effectiveness of the method on nuclear magnetic resonance data for a folded protein.
TL;DR: The quality of both the optimized Jastrow factors and the nodal surfaces of the wave functions declines with increasing atomic number Z, but the DMC calculations are tractable and well behaved in all cases.
Abstract: We report all-electron variational and diffusion quantum Monte Carlo (VMC and DMC) calculations for the noble gas atoms He, Ne, Ar, Kr, and Xe. The calculations were performed using Slater-Jastrow wave functions with Hartree-Fock single-particle orbitals. The quality of both the optimized Jastrow factors and the nodal surfaces of the wave functions declines with increasing atomic number Z, but the DMC calculations are tractable and well behaved in all cases. We discuss the scaling of the computational cost of DMC calculations with Z.
TL;DR: An important feature of this method is the capability to predict the entire fluid-phase diagram of a binary mixture at fixed temperature in a single simulation.
Abstract: We present a novel computational methodology for determining fluid-phase equilibria in binary mixtures. The method is based on a combination of highly efficient transition-matrix Monte Carlo and histogram reweighting. In particular, a directed grand-canonical transition-matrix Monte Carlo scheme is used to calculate the particle-number probability distribution, after which histogram reweighting is used as a postprocessing procedure to determine the conditions of phase equilibria. To validate the methodology, we have applied it to a number of model binary Lennard-Jones systems known to exhibit nontrivial fluid-phase behavior. Although we have focused on monatomic fluids in this work, the method presented here is general and can be easily extended to more complex molecular fluids. Finally, an important feature of this method is the capability to predict the entire fluid-phase diagram of a binary mixture at fixed temperature in a single simulation.
TL;DR: In this article, a new computational scheme with the asymptotic method to achieve variance reduction of Monte Carlo simulation for numerical analysis especially in finance is proposed, which not only provides general scheme of their method, but also show its effectiveness through numerical examples such as computing optimal portfolio and pricing an average option.
Abstract: We shall propose a new computational scheme with the asymptotic method to achieve variance reduction of Monte Carlo simulation for numerical analysis especially in finance. We not only provide general scheme of our method, but also show its effectiveness through numerical examples such as computing optimal portfolio and pricing an average option. Finally, we show mathematical validity of our method. ∗Forthcoming in Journal of Japan Statistical Society, We thank referees for helpful and valuable comments on the previous version.
TL;DR: Several new sequential Monte Carlo algorithms for online estimation (filtering) of nonlinear dynamic systems and are efficient because they tend to utilize both the information in the state process and the observations and are easy to sample from.
Abstract: In this paper we present several new sequential Monte Carlo (SMC) algorithms for online estimation (filtering) of nonlinear dynamic systems. SMC has been shown to be a powerful tool for dealing with complex dynamic systems. It sequentially generates Monte Carlo samples from a proposal distribution, adjusted by a set of importance weight with respect to a target distribution, to facilitate statistical inferences on the characteristic (state) of the system. The key to a successful implementation of SMC in complex problems is the design of an efficient proposal distribution from which the Monte Carlo samples are generated. We propose several such proposal distributions that are efficient yet easy to generate samples from. They are efficient because they tend to utilize both the information in the state process and the observations. They are all Gaussian distributions hence are easy to sample from. The central ideas of the conventional nonlinear filters, such as extended Kalman filter, unscented Kalman filter and the Gaussian quadrature filter, are used to construct these proposal distributions. The effectiveness of the proposed algorithms are demonstrated through two applications--real time target tracking and the multiuser parameter tracking in CDMA communication systems.
TL;DR: A density-of-states Monte Carlo method is proposed for simulations of solid-liquid phase equilibria and provides a direct estimate of the relative density of states and thus the relative free energy within these regions, which is subsequently used to determine portions of the melting curve over wide ranges of pressure and temperature.
Abstract: A density-of-states Monte Carlo method is proposed for simulations of solid-liquid phase equilibria. A modified Wang–Landau density-of-states sampling approach is used to perform a random walk in regions of potential energy and volume relevant to solid-liquid equilibrium. The method provides a direct estimate of the relative density of states [Ω(U,V)] and thus the relative free energy within these regions, which is subsequently used to determine portions of the melting curve over wide ranges of pressure and temperature. The validity and usefulness of the method are demonstrated by performing crystallization simulations for the Lennard-Jones fluid and for NaCl.
TL;DR: In this paper, the authors exploit known properties of universal ratios, involving the radius of gyration Rg, the second and third virial coefficients B2 and B3, and the effective pair potential between the centers of mass of self-avoiding polymer chains with nearest-neighbor attraction, as well as Monte Carlo simulations, to investigate the crossover from good-to θ-solvent regimes of polymers of finite length L.
Abstract: We exploit known properties of universal ratios, involving the radius of gyration Rg, the second and third virial coefficients B2 and B3, and the effective pair potential between the centers of mass of self-avoiding polymer chains with nearest-neighbor attraction, as well as Monte Carlo simulations, to investigate the crossover from good- to θ-solvent regimes of polymers of finite length L. The scaling limit and finite-L corrections to scaling are investigated in the good-solvent case and close to the θ temperature. Detailed interpolation formulas are derived from Monte Carlo data and results for the Edwards two-parameter model, providing estimates of universal ratios as functions of the observable ratio A2=B2∕Rg3 over the whole temperature range, from the θ point to the good-solvent regime. The convergence with L(L⩽8000) is found to be satisfactory under good-solvent conditions, but longer chains would be required to match theoretical predictions near the θ point, due to logarithmic corrections. A quanti...
TL;DR: In this article, the impact of various improvements on simulations of dynamical overlap fermions using the Hybrid Monte Carlo algorithm is discussed, focusing on the usage of fat links and multiple pseudofermion fields.
Abstract: We discuss the impact of various improvements on simulations of dynamical overlap fermions using the Hybrid Monte Carlo algorithm. We focus on the usage of fat links and multiple pseudofermion fields.
TL;DR: It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore.
Abstract: The influence of silicalite-1 pores on the reaction equilibria and the selectivity of the propene metathesis reaction system in the temperature range between 300 and 600 K and the pressure range from 0.5 to 7 bars has been investigated with molecular simulations. The reactive Monte Carlo (RxMC) technique was applied for bulk-phase simulations in the isobaric-isothermal ensemble and for two phase systems in the Gibbs ensemble. Additionally, Monte Carlo simulations in the grand-canonical ensemble (GCMC) have been carried out with and without using the RxMC technique. The various simulation procedures were combined with the configurational-bias Monte Carlo approach. It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore. The confined environment can increase the conversion significantly. A large change in selectivity between the bulk phase and the pore phase is observed. Pressure and temperature have strong influences on both conversion and selectivity. At low pressure and temperature both conversion and selectivity have the highest values. The effect of confinement decreases as the temperature increases.