Showing papers on "Dynamic Monte Carlo method published in 2000"
TL;DR: It is demonstrated that EGSnrc allows for an artifact free Monte Carlo simulation of ion chamber response and backscattering, situations that have been considered in the past as the two of the most stringent tests of condensed history Monte Carlo codes.
Abstract: In this report a new EGS4 version, called EGSnrc to reflect the substantial changes made to the original code is reported, which incorporates a new any-angle multiple elastic scattering theory, an improved electron-step algorithm, a correct implementation of the fictitious cross section method for sampling distances between discrete interactions, a more accurate evaluation of energy loss, as well as an exact boundary crossing algorithm It is demonstrated that EGSnrc allows for an artifact free Monte Carlo simulation of ion chamber response and backscattering, situations that have been considered in the past as the two of the most stringent tests of condensed history Monte Carlo codes A detailed discussion of the effect of the various components of the condensed history simulation of electron transport on the simulated ion chamber response is given in the accompanying paper
934 citations
TL;DR: Prokof'ev and Svistunov as mentioned in this paper performed a detailed study of the Fr\"ohlich polaron model on the basis of diagrammatic quantum Monte Carlo method.
Abstract: A detailed study of the Fr\"ohlich polaron model is performed on the basis of diagrammatic quantum Monte Carlo method [N. V. Prokof'ev and B. V. Svistunov, Phys. Rev. Lett. $81,$ 2514 (1998)]. The method is further developed both quantitatively (performance) and qualitatively (new estimators), and is enhanced by spectral analysis of the polaron Green's function, within an approach developed in the present paper. We present up to date results for the binding energy, and make available precise data for the effective mass, including the region of intermediate and strong couplings. We look at the structure of the polaron cloud and answer such questions as the average number of phonons in the cloud and their number/momentum distribution. The spectral analysis reveals nontrivial structure of the spectral density at intermediate and large coupling: the spectral continuum features pronounced peaks that we attribute to unstable excited states of the polaron.
273 citations
TL;DR: An overview of Monte Carlo methods for simulations of the phase behaviour of fluids can be found in this article, where the Gibbs ensemble method and histogram-reweighting Monte Carlo techniques are described in detail.
Abstract: This article presents an overview of Monte Carlo methods for simulations of the phase behaviour of fluids. The Gibbs ensemble method and histogram-reweighting Monte Carlo techniques are described in detail. The Gibbs ensemble method is based on simulations of two regions coupled via volume change and particle transfer moves so that the conditions for phase coexistence are satisfied in a statistical sense. Histogram-reweighting methods obtain the free energy of a system over a broad range of conditions from a small set of grand canonical Monte Carlo calculations. The histogram methods can produce highly accurate data, especially in the vicinity of critical points. Other methods described briefly include interfacial simulations, the NPT + test particle method, Gibbs-Duhem integration and pseudo-ensembles. Configurational-bias sampling techniques and expanded ensembles can be used for multisegment molecules to increase the efficiency of the simulations. The last section of the review covers applications to both model and realistic systems that have appeared since 1995.
254 citations
TL;DR: It is shown that if the corresponding random functions are convex piecewise linear and the distribution is discrete, then an optimal solution of the approximating problem provides an exact optimal solution to the true problem with probability one for sufficiently large sample size.
Abstract: In this paper we discuss Monte Carlo simulation based approximations of a stochastic programming problem. We show that if the corresponding random functions are convex piecewise linear and the distribution is discrete, then an optimal solution of the approximating problem provides an exact optimal solution of the true problem with probability one for sufficiently large sample size. Moreover, by using the theory of large deviations, we show that the probability of such an event approaches one exponentially fast with increase of the sample size. In particular, this happens in the case of linear two- (or multi-) stage stochastic programming with recourse if the corresponding distributions are discrete. The obtained results suggest that, in such cases, Monte Carlo simulation based methods could be very efficient. We present some numerical examples to illustrate the ideas involved.
252 citations
22 Nov 2000
235 citations
Proceedings Article•
30 Jul 2000
TL;DR: Experimental results with physical robots and an analysis of the formulation of a new proposal distribution for the Monte Carlo sampling step suggest that the new algorithm is significantly more robust and accurate than plain MCL.
Abstract: Monte Carlo localization (MCL) is a Bayesian algorithm for mobile robot localization based on particle filters, which has enjoyed great practical success. This paper points out a limitation of MCL which is counter-intuitive, namely that better sensors can yield worse results. An analysis of this problem leads to the formulation of a new proposal distribution for the Monte Carlo sampling step. Extensive experimental results with physical robots suggest that the new algorithm is significantly more robust and accurate than plain MCL. Obviously, these results transcend beyond mobile robot localization and apply to a range of particle filter applications.
214 citations
01 Feb 2000
203 citations
TL;DR: In this paper, a Monte Carlo simulation technique was developed to describe dispersed phase systems with emphasis on coagulation and aggregation, and the particle evolution was computed as a stochastic game, computing the time step after each collision.
Abstract: A Monte Carlo simulation technique developed describes dispersed-phase systems with emphasis on coagulation and aggregation. The method does not use particle trajectories, but is based on the transformation of known collision frequencies into collision probabilities of particle pairs. The particle evolution was computed as a stochastic game, computing the time step after each collision. The simulations were validated by comparing with exact mathematical solutions for aggregation of solid particles and with numerical solutions based on sectional methods for coagulation of droplets. The direct simulation Monte Carlo (DSMC) method is advantageous, because the simulation of complex, multidimensional systems results in very elaborate models when using sectional models and is implemented very easily. Two examples of industrial importance are chemical reaction in coagulating droplets and coating of particles with small solid particles.
180 citations
TL;DR: In this article, a path integral ground state Monte Carlo method was proposed to calculate ground state expectation values without the extrapolations often used with Green's function and diffusion Monte Carlo methods.
Abstract: Ground state expectation values are obtained by using a path integral ground state Monte Carlo method. The method allows calculations of ground state expectation values without the extrapolations often used with Green’s function and diffusion Monte Carlo methods. We compare our results with those of Green’s function Monte Carlo by calculating some ground state properties of the van der Waals complex He2Cl2 as well as the infinite systems liquid and solid 4He. Advantages and disadvantages of the present method with respect to previous ones are discussed.
174 citations
TL;DR: In this paper, a continuous-time formulation of the direct simulation Monte Carlo was proposed, which allows the evaluation of the transport coefficient dependence on the time step through the use of the Green-Kubo theory.
Abstract: We propose a continuous-time formulation of the direct simulation Monte Carlo that allows the evaluation of the transport coefficient dependence on the time step through the use of the Green–Kubo theory. Our results indicate that the error exhibits quadratic dependence on the time step, and that for time steps of the order of one mean free time the error is of the order of 5%. Our predictions for the transport coefficients are in good agreement with numerical experiments. The calculation of the cell size dependence, first obtained by Alexander et al. [Phys. Fluids 10, 1540 (1998)], is reviewed and a correction is pointed out.
172 citations
TL;DR: In this article, a parallel tempering Monte Carlo algorithm was proposed for the 38-atom Lennard-Jones cluster with microcanonical and molecular dynamics ensembles to overcome quasiergodicity and to extract both equilibrium and dynamical properties.
Abstract: We study the 38-atom Lennard-Jones cluster with parallel tempering Monte Carlo methods in the microcanonical and molecular dynamics ensembles. A new Monte Carlo algorithm is presented that samples rigorously the molecular dynamics ensemble for a system at constant total energy, linear and angular momenta. By combining the parallel tempering technique with molecular dynamics methods, we develop a hybrid method to overcome quasiergodicity and to extract both equilibrium and dynamical properties from Monte Carlo and molecular dynamics simulations. Several thermodynamic, structural, and dynamical properties are investigated for LJ38, including the caloric curve, the diffusion constant and the largest Lyapunov exponent. The importance of insuring ergodicity in molecular dynamics simulations is illustrated by comparing the results of ergodic simulations with earlier molecular dynamics simulations.
TL;DR: This model is a simple model for isolated magnetic particles in a uniform field with an oblique angle to the easy axis of the particles, where the characteristic time of the magnetization reversal are in excellent agreement with asymptotic solutions for the Neel-Brown model.
Abstract: For the description of thermally activated dynamics in systems of classical magnetic moments numerical methods are desirable. We consider a simple model for isolated magnetic particles in a uniform field with an oblique angle to the easy axis of the particles. For this model, a comparison of the Monte Carlo method with Langevin dynamics yields new insight to the interpretation of the Monte Carlo process, leading to the implementation of a new algorithm where the Monte Carlo step is time quantified. The numeric results for the characteristic time of the magnetization reversal are in excellent agreement with asymptotic solutions for the Neel-Brown model.
TL;DR: In this article, a novel aggregation-volume-bias Monte Carlo (AVBMC) algorithm is presented which greatly enhances the efficiency of sampling the phase space of fluid systems consisting of strongly associating molecules.
Abstract: A novel aggregation-volume-bias Monte Carlo (AVBMC) algorithm is presented which greatly enhances the efficiency of sampling the phase space of fluid systems consisting of strongly associating molecules. The algorithm is compared to the bond-bias Monte Carlo algorithm by Tsangaris and de Pablo (J. Chem. Phys. 1994, 101, 1477) and the monomer-addition-subtraction algorithm by Visco and Kofke (J. Chem. Phys. 1999, 110, 5493). The AVBMC algorithm is easy to implement, generally applicable, and robust. Its efficiency is demonstrated for a large variety of processes and systems, including the vaporization of a liquid methane droplet or a water cluster, an investigation of the temperature- and pressure-dependent properties of superheated hydrogen fluoride vapor, and the vapor−liquid coexistence curve of acetic acid.
TL;DR: In this paper, Monte Carlo simulations of symmetric diblock copolymers confined between two hard, flat and homogeneous surfaces have been performed in an expanded grand-canonical ensemble, where the chemical potential and temperature of the confined films are specified and the density is allowed to fluctuate.
Abstract: Thin films of symmetric diblock copolymers confined between two hard, flat and homogeneous surfaces have been investigated by means of Monte Carlo simulations on a simple cubic lattice. For such simulations, the match between bulk lamellar period L0 and the simulation box size is crucial to obtain meaningful results. The simulations have been performed in an expanded grand-canonical ensemble, where the chemical potential and the temperature of the confined films are specified and the density is allowed to fluctuate. The dependence of morphology, density, and chain conformation in the confined films on the type of surfaces, surface separation, and the strength of surface-block interactions has been studied systematically. Our results are consistent with experimental findings.
Book•
01 Jan 2000
TL;DR: Introduction: Basic Concepts in Systems Engineering Basic concepts in Monte Carlo Methods Additional Applications Elements of Uncertainty and Uncertainties Analysis, System Transport, Realisation of System Transport.
Abstract: Introduction: Basic Concepts in Systems Engineering Basic Concepts in Monte Carlo Methods Additional Applications Elements of Uncertainty and Uncertainty Analysis, System Transport, Realisation of System Transport.
TL;DR: In this paper, a new Monte Carlo method for solving the population balance problem with multiple growth processes is presented, which samples a constant number of particles regardless of whether the actual growth process results in increase or decrease of the particle concentration.
TL;DR: In this paper, the structure and thermodynamics of inhomogeneous polymer solutions in the framework of a coarse-grained off-lattice model were investigated, and properties of the liquid-vapor interface and the packing of the solution were investigated.
Abstract: We investigate the structure and thermodynamics of inhomogeneous polymer solutions in the framework of a coarse-grained off-lattice model. Properties of the liquidvapor interface and the packing of...
TL;DR: Hadjiconstantinou et al. as mentioned in this paper found that the time step truncation error in direct simulation Monte Carlo calculations is O(Δt2) for a variety of simple flows, both transient and steady state.
Abstract: The time step truncation error in direct simulation Monte Carlo calculations is found to be O(Δt2) for a variety of simple flows, both transient and steady state. The measured errors in the transport coefficients (viscosity, thermal conductivity, and self-diffusion) are in good agreement with predictions from Green-Kubo analysis [N. Hadjiconstantinou, Phys. Fluids 12, 2634 (2000)].
01 Jan 2000
TL;DR: In this paper, a simple atomistic model of diffusion by vacancy jumps is presented for coherent precipitation in weakly super-saturated substitutional solid solutions by the Monte Carlo method.
Abstract: We present a study on the kinetics of coherent precipitation in weakly super-saturated substitutional solid solutions by the Monte Carlo method. Our simulations are based on a simple atomistic model of diffusion by vacancy jumps. The whole precipitation process (from early stages to late stage coarsening) is followed for various supersaturations and temperatures, and typical behaviors observed in the simulations are compared to those predicted by the classical theories. Special emphasis is placed on the first stages of the decomposition (incubation and nucleation) and on the effects of the vacancy diffusion mechanism. Finally we consider the addition of a third (impurity) element, which can be used to control the kinetic pathway: such effects are quantitatively explored with the Monte Carlo method.
TL;DR: In this paper, the authors examined the roughening behavior of a shadowing model, with lateral growth, for (2 11)-dimensional systems, and showed that the growth exponent b51 for growth and b50 for etching is 1/z50.
Abstract: Through numerical calculations and Monte Carlo simulations, we examine the roughening behavior of a shadowing model, with lateral growth, for (2 11)-dimensional systems. The results show that the roughening growth exponent b51 for growth and b50 for etching. For the Monte Carlo simulation of the growth model, tall columns are formed, and the correlation length obeys j}(t2t 0) 1/z , with 1/z50.9360.1. For the Monte Carlo simulation of the etching model, we obtain 1/z50, and the height-height correlation function H(r )i s proportional to log(r) for r!j. The results are compared to previous computational studies of shadowing and to experimental studies of sputter deposition.
TL;DR: Numerical results for long molecules indicate that the new hyperparallel tempering Monte Carlo method can be significantly more efficient than previously available techniques.
Abstract: A new hyperparallel tempering Monte Carlo method is proposed for simulation of complex fluids, including polymeric systems. The method is based on a combination of the expanded grand canonical ensemble (or simple tempering) and the multidimensional parallel tempering techniques. Its usefulness is established by applying it to polymer solutions and blends with large molecular weights. Our numerical results for long molecules indicate that the new algorithm can be significantly more efficient than previously available techniques.
TL;DR: The techniques for calculation of the electronic structure of relatively large molecular systems with very high accuracy, from positron complexes to silicon crystal structures of 250 atoms and 1000 valence electrons are reviewed.
Abstract: Quantum Monte Carlo methods have recently made it possible to calculate the electronic structure of relatively large molecular systems with very high accuracy. These large systems range from positron complexes [NH2,Ps] with ∼10 electrons to C20 isomers with 120 electrons, to silicon crystal structures of 250 atoms and 1000 valence electrons. The techniques for such calculations and a sampling of applications are reviewed.
TL;DR: In this paper, a full-band cellular automaton (CA) code for simulation of electron and hole transport in Si and GaAs is presented, where the entire Brillouin zone is discretized using a non-uniform mesh in k-space, and a transition table is generated between all initial and final states.
Abstract: We present a fullband cellular automaton (CA) code for simulation of electron and hole transport in Si and GaAs. In this implementation, the entire Brillouin zone is discretized using a nonuniform mesh in k-space, and a transition table is generated between all initial and final states on the mesh, greatly simplifying the final state selection of the conventional Monte Carlo algorithm. This method allows for fully anisotropic scattering rates within the fullband scheme, at the cost of increased memory requirements for the transition table itself. Good agreement is obtained between the CA model and previously reported results for the velocity-field characteristics and high field distribution function, which illustrate the potential accuracy of the technique. A hybrid CA/Monte Carlo algorithm is introduced which helps alleviate the memory problems of the CA method while preserving the speed up and accuracy.
TL;DR: A rigorous proof of the divergence of pure diffusion Monte Carlo methods (DMC without branching in which the weights are carried along trajectories) is given and a bias-free Monte Carlo method combining DMC and PDMC approaches, and based on a minimal stochastic reconfiguration of the population is discussed.
Abstract: In this paper we discuss various aspects of diffusion Monte Carlo methods using a fixed number of walkers. First, a rigorous proof of the divergence of pure diffusion Monte Carlo (PDMC) methods (DMC without branching in which the weights are carried along trajectories) is given. Second, a bias-free Monte Carlo method combining DMC and PDMC approaches, and based on a minimal stochastic reconfiguration of the population, is discussed. Finally, some illustrative calculations for a system of coupled quantum rotators are presented.
TL;DR: In this article, a dynamic lattice Monte Carlo (DLMC) simulation approach to describe ion transport in dielectric environments is presented, where the simulated system is embedded in a bigger system that determines the average electrostatic potential and the ionic concentrations at its boundaries.
Abstract: A dynamic lattice Monte Carlo (DLMC) simulation approach to the description of ion transport in dielectric environments is presented. Conventional approaches using periodic boundary conditions are inefficient for nonequilibrium situations in inhomogeneous systems. Instead, the simulated system is embedded in a bigger system that determines the average electrostatic potential and the ionic concentrations at its boundaries. Two issues are of special importance: implementing the given boundary conditions in the treatment of dynamical processes at and near the boundaries, and efficient evaluation of ion−ion interaction in the heterogeneous dielectric medium during the Monte Carlo simulation. The performance of the method is checked by comparing numerical results to exact solutions for simple geometries, and to mean field (Poisson−Nernst−Planck, PNP) theory in a system where the latter should provide a reasonable description. Other examples in which the PNP theory fails in various degrees are shown and discus...
TL;DR: In this paper, the ab initio potential of mean force for the formic acid-water system is calculated in a Monte Carlo simulation using a classical fluctuating charge molecular mechanics potential to guide Monte Carlo updates.
Abstract: In this paper the ab initio potential of mean force for the formic acid–water system is calculated in a Monte Carlo simulation using a classical fluctuating charge molecular mechanics potential to guide Monte Carlo updates. The ab initio energies in the simulation are calculated using density-functional theory (DFT) methods recently developed by Salahub et al. [J. Chem. Phys. 107, 6770 (1997)] to describe hydrogen-bonded systems. Importance sampling methods are used to investigate structural changes and it is demonstrated that using a molecular mechanics importance function can improve the efficiency of a DFT simulation by several orders of magnitude. Monte Carlo simulation of the system in a canonical ensemble at T=300 K reveals two chemical processes at intermediate time scales: The rotation of the H2O bonded to HCOOH, which takes place on a time scale of 3 ps, and the dissociation of the complex which occurs in 24 ps. It is shown that these are the only important structural “reactions” in the formic ac...
TL;DR: Using the maximum likelihood method, a formalism is derived to analyze a series of biased Monte Carlo or molecular dynamics simulations as mentioned in this paper, which is applied to different examples, in particular the estimation of thermodynamic properties of molecular systems such as potentials of mean force and free energy differences.
TL;DR: In this paper, the sign problem arising in Monte Carlo simulations of frustrated quantum spin systems was discussed and it was shown that for a class of semi-rustrated systems [Heisenberg models with ferromagnetic coupling] it is NP-hard.
Abstract: We discuss the: sign problem arising in Monte Carlo simulations of frustrated quantum spin systems. We show that for a class of semifrustrated systems [Heisenberg models with ferromagnetic coupling ...