Showing papers on "Monte Carlo molecular modeling published in 2009"
01 Jan 2009
TL;DR: The PENELOPE as mentioned in this paper computer code system performs Monte Carlo simulation of coupled electron-photon transport in arbitrary materials for a wide energy range, from a few hundred eV to about 1 GeV.
Abstract: The computer code system PENELOPE (version 2008) performs Monte Carlo simulation of coupled
electron-photon transport in arbitrary materials for a wide energy range, from a few hundred eV to
about 1 GeV. Photon transport is simulated by means of the standard, detailed simulation scheme.
Electron and positron histories are generated on the basis of a mixed procedure, which combines
detailed simulation of hard events with condensed simulation of soft interactions. A geometry package
called PENGEOM permits the generation of random electron-photon showers in material systems
consisting of homogeneous bodies limited by quadric surfaces, i.e., planes, spheres, cylinders, etc. This
report is intended not only to serve as a manual of the PENELOPE code system, but also to provide the
user with the necessary information to understand the details of the Monte Carlo algorithm.
1,675 citations
723 citations
Book•
27 Feb 2009
TL;DR: The Monte Carlo method has been used in many applications, e.g., for algebra, beyond numerical integration, this article, and for error and variance analysis for Halton sequences.
Abstract: The Monte Carlo method.- Sampling from known distributions.- Pseudorandom number generators.- Variance reduction techniques.- Quasi-Monte Carlo constructions.- Using quasi-Monte Carlo constructions.- Using quasi-Monte Carlo in practice.- Financial applications.- Beyond numerical integration.- Review of algebra.- Error and variance analysis for Halton sequences.- References.- Index.
517 citations
TL;DR: The aim of this paper is to present a comprehensive overview of SMC methods that have been proposed to perform static parameter estimation in general state-space models and discuss the advantages and limitations of these methods.
284 citations
TL;DR: In this paper, the authors investigated the feasibility of the Hybrid Monte Carlo method to solve higher-dimensional Bayesian model updating problems and proposed a new formulae for Markov chain convergence assessment.
Abstract: In recent years, Bayesian model updating techniques based on measured data have been applied to system identification of structures and to structural health monitoring. A fully probabilistic Bayesian model updating approach provides a robust and rigorous framework for these applications due to its ability to characterize modeling uncertainties associated with the underlying structural system and to its exclusive foundation on the probability axioms. The plausibility of each structural model within a set of possible models, given the measured data, is quantified by the joint posterior probability density function of the model parameters. This Bayesian approach requires the evaluation of multidimensional integrals, and this usually cannot be done analytically. Recently, some Markov chain Monte Carlo simulation methods have been developed to solve the Bayesian model updating problem. However, in general, the efficiency of these proposed approaches is adversely affected by the dimension of the model parameter space. In this paper, the Hybrid Monte Carlo method is investigated (also known as Hamiltonian Markov chain method), and we show how it can be used to solve higher-dimensional Bayesian model updating problems. Practical issues for the feasibility of the Hybrid Monte Carlo method to such problems are addressed, and improvements are proposed to make it more effective and efficient for solving such model updating problems. New formulae for Markov chain convergence assessment are derived. The effectiveness of the proposed approach for Bayesian model updating of structural dynamic models with many uncertain parameters is illustrated with a simulated data example involving a ten-story building that has 31 model parameters to be updated.
263 citations
TL;DR: The interlayer bonding properties of graphite are computed using an ab initio many-body theory and an equilibrium interlayer binding energy is found in good agreement with most recent experiments.
Abstract: We compute the interlayer bonding properties of graphite using an ab initio many-body theory. We carry out variational and diffusion quantum Monte Carlo calculations and find an equilibrium interlayer binding energy in good agreement with most recent experiments. We also analyze the behavior of the total energy as a function of interlayer separation at large distances comparing the results with the predictions of the random phase approximation.
260 citations
Posted Content•
TL;DR: In this article, an introduction to the Monte Carlo method is given and concepts such as Markov chains, detailed balance, critical slowing down, and ergodicity, as well as the Metropolis algorithm are explained.
Abstract: Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance, critical slowing down, and ergodicity, as well as the Metropolis algorithm are explained. The Monte Carlo method is illustrated by numerically studying the critical behavior of the two-dimensional Ising ferromagnet using finite-size scaling methods. In addition, advanced Monte Carlo methods are described (e.g., the Wolff cluster algorithm and parallel tempering Monte Carlo) and illustrated with nontrivial models from the physics of glassy systems. Finally, we outline an approach to study rare events using a Monte Carlo sampling with a guiding function.
255 citations
TL;DR: In this paper, the authors generalize the recently developed diagrammatic Monte Carlo techniques for quantum impurity models from an imaginary time to a Keldysh formalism suitable for real-time and nonequilibrium calculations.
Abstract: We generalize the recently developed diagrammatic Monte Carlo techniques for quantum impurity models from an imaginary time to a Keldysh formalism suitable for real-time and nonequilibrium calculations. Both weak-coupling and strong-coupling based methods are introduced, analyzed, and applied to the study of transport and relaxation dynamics in interacting quantum dots.
237 citations
TL;DR: The paper presents a technique for efficient Monte Carlo type simulation of samples of random vectors with prescribed marginals and a correlation structure, and it is shown that if the technique is applied for small-sample simulation with a variance reduction technique called Latin Hypercube Sampling, the outcome is a set of samples that match user-defined Marginals and covariances.
193 citations
01 Jan 2009
TL;DR: In these notes I discuss Monte Carlo simulations for the study of classical models in statistical mechanics and include a simple and direct proof that the method converges to the Boltzmann distribution.
Abstract: In these notes I discuss Monte Carlo simulations for the study of classical models in statistical mechanics. I include a simple and direct proof that the method converges to the Boltzmann distribution. Usually, physics articles discuss this important point by just giving a reference to the mathematical literature on “Markov chains”, where the proof is rather abstract. In these notes I give a proof of convergence which is self contained and uses only elementary algebra. In statistical mechanics one computes averages of a quantity A from the Boltzmann distribution, i.e. 〈A〉 = ∑
183 citations
TL;DR: In this article, the authors developed a Monte Carlo based method for estimating the reliability of structural systems by reformulating the reliability problem to depend on a parameter and exploiting the regularity of the failure probability as a function of this parameter.
TL;DR: Numerical simulations show that event-chain algorithms clearly outperform the conventional Metropolis method, and reversible versions of the algorithms, which violate detailed balance, improve the speed of the method even further.
Abstract: In this paper we present the event-chain algorithms, which are fast Markov-chain Monte Carlo methods for hard spheres and related systems. In a single move of these rejection-free methods, an arbitrarily long chain of particles is displaced, and long-range coherent motion can be induced. Numerical simulations show that event-chain algorithms clearly outperform the conventional Metropolis method. Irreversible versions of the algorithms, which violate detailed balance, improve the speed of the method even further. We also compare our method with a recent implementations of the molecular-dynamics algorithm.
TL;DR: In this paper, a numerically exact approach to nonequilibrium real-time dynamics that is applicable to quantum impurity models coupled to biased noninteracting leads, such as those relevant to quantum transport in nanoscale devices, is proposed.
Abstract: We propose a numerically exact approach to nonequilibrium real-time dynamics that is applicable to quantum impurity models coupled to biased noninteracting leads, such as those relevant to quantum transport in nanoscale devices. The method is based on a diagrammatic Monte Carlo sampling of the real-time perturbation theory along the Keldysh contour. We benchmark the method on a noninteracting resonant-level model and, as a first nontrivial application, we study zero-temperature nonequilibrium transport through a vibrating molecule.
TL;DR: In this paper, a Monte Carlo sampling based on collective atomic moves (wave moves) was introduced to access the long-wavelength limit for finite-size systems (up to 40 000 atoms) and they found a power-law behavior G(q)α q(-2+eta) with the same exponent eta approximate to 0.85 for both potentials.
Abstract: Structure and thermodynamics of crystalline membranes are characterized by the long-wavelength behavior of the normal-normal correlation function G(q). We calculate G(q) by Monte Carlo and molecular dynamics simulations for a quasiharmonic model potential and for a realistic potential for graphene. To access the long-wavelength limit for finite-size systems (up to 40 000 atoms) we introduce a Monte Carlo sampling based on collective atomic moves (wave moves). We find a power-law behavior G(q)alpha q(-2+eta) with the same exponent eta approximate to 0.85 for both potentials. This finding supports, from the microscopic side, the adequacy of the scaling theory of membranes in the continuum medium approach, even for an extremely rigid material such as graphene.
TL;DR: In this paper, the authors assess the validity of these approximations with grand canonical Monte Carlo simulations for a well-known Zn-based MOF (IRMOF-1), using potential parameters specifically derived for IRMOF, and compare the results with experimental results for hydrogen and xenon adsorption at room temperature.
Abstract: The gas storage capacity of metal−organic frameworks (MOFs) is well-known and has been investigated using both experimental and computational methods. Previous Monte Carlo computer simulations of gas adsorption by MOFs have made several questionable approximations regarding framework−framework and framework−adsorbate interactions: potential parameters from general force fields have been used, and framework atoms were fixed at their crystallographic coordinates (rigid framework). We assess the validity of these approximations with grand canonical Monte Carlo simulations for a well-known Zn-based MOF (IRMOF-1), using potential parameters specifically derived for IRMOF-1. Our approach is validated by comparison with experimental results for hydrogen and xenon adsorption at room temperature. The effects of framework flexibility on the adsorption of noble gases and hydrogen are described, as well as the selectivity of IRMOF-1 for xenon versus other noble gases. At both low temperature (78 K) and room temperatu...
TL;DR: A particle-based Monte Carlo formalism for the study of polymeric melts, where the interaction energy is given by a local density functional, as is done in traditional field-theoretic models, is introduced.
Abstract: We introduce a particle-based Monte Carlo formalism for the study of polymeric melts, where the interaction energy is given by a local density functional, as is done in traditional field-theoretic models. The method enables Monte Carlo simulations in arbitrary ensembles and direct calculation of free energies. We present results for the phase diagram and the critical point of a binary homopolymer blend. For a symmetric diblock copolymer, we compute the distribution of local stress in lamellae and locate the order-disorder transition.
DOI•
01 Jan 2009
TL;DR: This thesis proposes a new Monte Carlo framework in which an efficient high-dimensional proposal distributions are built using SMC methods, which allows for effective MCMC algorithms in complex scenarios where standard strategies fail.
Abstract: Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods have emerged as the two main tools to sample from high-dimensional probability distributions. Although asymptotic convergence of MCMC algorithms is ensured under weak assumptions, the performance of these latters is unreliable when the proposal distributions used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. In this thesis we propose a new Monte Carlo framework in which we build efficient high-dimensional proposal distributions using SMC methods. This allows us to design effective MCMC algorithms in complex scenarios where standard strategies fail. We demonstrate these algorithms on a number of example problems, including simulated tempering, nonlinear non-Gaussian state-space model, and protein folding.
TL;DR: In this paper, the physical principles and approximations employed in Monte Carlo simulations of coupled electron-photon transport are reviewed and a brief analysis of the assumptions underlying the trajectory picture used to generate random particle histories is presented.
Abstract: The physical principles and approximations employed in Monte Carlo simulations of coupled electron–photon transport are reviewed. After a brief analysis of the assumptions underlying the trajectory picture used to generate random particle histories, we concentrate on the physics of the various interaction processes of photons and electrons. For each of these processes we describe the theoretical models and approximations that lead to the differential cross sections employed in general-purpose Monte Carlo codes. References to relevant publications and data resources are also provided.
TL;DR: Conditions which favour multi-step, or dynamic estimation for multi- step forecasting are delineated and an analytical example shows how dynamic estimation may accomodateincorrectly-specified models as the forecast lead alters, improving forecast performance for some mis-specifications.
Abstract: We delineate conditions which favour multi-step, or dynamic, estimation for multi-step forecasting. An analytical example shows how dynamic estimation (DE) may accommodate incorrectly-specified models as the forecast lead alters, improving forecast performance for some misspecifications. However, in correctly-specified models, reducing finite-sample biases does not justify DE. In a Monte Carlo forecasting study for integrated processes, estimating a unit root in the presence of a neglected negative moving-average error may favour DE, though other solutions exist to that scenario. A second Monte Carlo study obtains the estimator biases and explains these using asymptotic approximations.
TL;DR: The resulting Monte Carlo algorithm is event-driven and asynchronous; each Brownian particle propagates inside its own protective domain and on its own time clock, which reproduces the statistics of the underlying Monte Carlo model exactly.
Abstract: We present a new effcient method for Monte Carlo simulations of diusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditionalsma ...
TL;DR: It is shown that Wang-Landau sampling, combined with suitable Monte Carlo trial moves, provides a powerful method for both the ground state search and the determination of the density of states for the hydrophobic-polar protein model and the interacting self-avoiding walk model for homopolymers.
Abstract: We show that Wang-Landau sampling, combined with suitable Monte Carlo trial moves, provides a powerful method for both the ground state search and the determination of the density of states for the hydrophobic-polar (HP) protein model and the interacting self-avoiding walk (ISAW) model for homopolymers. We obtain accurate estimates of thermodynamic quantities for HP sequences with >100 monomers and for ISAWs up to >500 monomers. Our procedure possesses an intrinsic simplicity and overcomes the limitations inherent in more tailored approaches making it interesting for a broad range of protein and polymer models.
01 Oct 2009
TL;DR: An overview of the methods and algorithms developed, and the new open-source code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator, for materials modeling applications, are described.
Abstract: The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applying it to materials modeling problems of interest to Sandia. In this report we give an overview of the methods and algorithms developed, and describe our new open-source code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator. We also highlight the development of several Monte Carlo models in SPPARKS for specific materials modeling applications, including grain growth, bubble formation, diffusion in nanoporous materials, defect formation in erbium hydrides, and surface growth and evolution.
TL;DR: An efficient Monte Carlo algorithm is developed that generates thousands of probable solutions from which the statistical properties of the solution can be analyzed and it is found that although all of the individual solutions are spiky, the mean solution spectrum is smooth and similar to the regularized solution.
Dissertation•
01 Jan 2009
TL;DR: In the thesis, a thorough review of the theoretical properties of these two Monte Carlo methods are given and it is shown that the choice of proposal density can have a marked effect on the performance of the algorithm.
Abstract: Monte Carlo methods are statistical methods that can be used to give approximate answers
to questions such as finding the distribution or expectation of a stochastic variable
through simulation. Two of the most widely used Monte Carlo methods are Markov
Chain Monte Carlo (MCMC) and particle filtering. In the thesis, a thorough review
of the theoretical properties of these two Monte Carlo methods is given. After having
established the theoretical foundation for the algorithms, the algorithms are used to do
inference in a Stochastic Volatility (SV) model.
For both the methods, the importance of choosing a good proposal distribution is emphasized,
and it is shown that the choice of proposal density can have a marked effect
on the performance of the algorithm. Several novel methods for choosing a good importance
density are proposed and implemented.
The standard SV model is extended in two ways. The first way it is extended is by
letting the volatility process be modeled by an autoregressive process of arbitrary order
p. The filtering and predictive properties of the MCMC method is investigated through
simulation of this extended SV model. The second way the standard SV model is extended
is by allowing the model parameters to vary over time. The particle filtering
algorithm is tested on synthetic data generated from this model. However, for the particle
filtering algorithm, the main focus will be on illustrating some of the problems
related to the algorithm, along with their solution.
Finally, the MCMC method is used to estimate parameters and volatility for two selected
financial time series.
TL;DR: An efficient O(N) cluster Monte Carlo method for Ising models with long-range interactions is presented that strictly fulfills the detailed balance and the realized stochastic dynamics is equivalent to that of the conventional Swendsen-Wang algorithm.
TL;DR: In this paper, a Monte Carlo sampling of the spectral integration in the heating rate calculation is used to estimate the energy associated with the spectral cascade from the large scale, even on the grid scale, and a scaling analysis shows that the errors introduced by the method diminish as flow features become well resolved.
Abstract: Large-eddy simulation (LES) refers to a class of calculations in which the large energy-rich eddies are
simulated directly and are insensitive to errors in the modeling of sub-grid scale processes. Flows represented
by LES are often driven by radiative heating and therefore require the calculation of radiative transfer along with the fluid-dynamical simulation. Current methods for detailed radiation calculations, even those using
simple one-dimensional radiative transfer, are far too expensive for routine use, while popular shortcuts are
either of limited applicability or run the risk of introducing errors on time and space scales that might affect the overall simulation.
A new approximate method is described that relies on Monte Carlo sampling of the spectral integration in the heating rate calculation and is applicable to any problem. The error introduced when using this method is substantial for individual samples (single columns at single times) but is uncorrelated in time and space and so does not bias the statistics of scales that are well resolved by the LES. The method is evaluated through simulation of two test problems; these behave as expected. A scaling analysis shows that the errors introduced by the method diminish as flow features become well resolved. Errors introduced by the approximation increase with decreasing spatial scale but the spurious energy introduced by the approximation
is less than the energy expected in the unperturbed flow, i.e. the energy associated with the spectral cascade from the large scale, even on the grid scale.
TL;DR: In this article, the authors proposed a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes, which uses a recently developed technique for exact simulation of diffusions, and involves no discretization error.
Abstract: This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s.\@ continuous estimators of the likelihood function for a family of diffusion models and its performance in numerical examples is computationally efficient. It uses a recently developed technique for the exact simulation of diffusions, and involves no discretization error. We show that, under regularity conditions, the Monte Carlo MLE converges a.s. to the true MLE. For datasize $n\to\infty$, we show that the number of Monte Carlo iterations should be tuned as $\mathcal{O}(n^{1/2})$ and we demonstrate the consistency properties of the Monte Carlo MLE as an estimator of the true parameter value.
TL;DR: The present contribution addresses uncertainty quantification and uncertainty propagation in structural mechanics using stochastic analysis using Monte Carlo methods for studying the variability in the structural properties and for their propagation to the response.
Abstract: The present contribution addresses uncertainty quantification and uncertainty propagation in structural mechanics using stochastic analysis Presently available procedures to describe uncertainties in load and resistance within a suitable mathematical framework are shortly addressed Monte Carlo methods are proposed for studying the variability in the structural properties and for their propagation to the response The general applicability and versatility of Monte Carlo Simulation is demonstrated in the context with computational models that have been developed for deterministic structural analysis After
discussing Direct Monte Carlo Simulation for the assessment of the response variability, some recently developed advanced Monte Carlo methods applied for reliability assessment are described, such as Importance Sampling for linear uncertain structures subjected to Gaussian loading, Line Sampling in linear dynamics and Subset simulation The numerical example demonstrates the applicability of Line Sampling to general linear uncertain FE systems under Gaussian distributed excitation
TL;DR: In this paper, the results of the unified Monte Carlo chemical model with the modified-rate equation (MRE) method under a wide range of interstellar conditions, using a full gas-grain chemical network.
Abstract: We compare the results of the unified Monte Carlo chemical model with the new modified-rate equation (MRE) method under a wide range of interstellar conditions, using a full gas-grain chemical network. In most of the explored parameter space, the new MRE method reproduces very well the results of the exact approach. Small disagreements between the methods may be remedied by the use of a more complete surface chemistry network, appropriate to the full range of temperatures employed here.
TL;DR: The results suggest that in simulating metal-hydride systems it is very important to apply accurate methods that go beyond traditional mean-field approaches as a benchmark of their performance for a given material, and QMC is an appealing method to provide such a benchmark due to its high level of accuracy and favorable scaling (N(3)) with the number of electrons.
Abstract: We calculated the desorption energy of MgH2 clusters using the highly accurate quantum Monte Carlo (QMC) approach, which can provide desorption energies with chemical accuracy (within ∼1 kcal/mol) ...