Showing papers on "Monte Carlo molecular modeling published in 2002"

Monte Carlo Simulation in Statistical Physics: An Introduction

Abstract: Introduction - purpose and scope of this volume, and some general comments theoretical foundation of the Monte Carlo method and its application in statistical physics guide to practical work with the Monte Carlo method some important recent developments of the Monte Carlo methodology.

Extending the Time Scale in Atomistic Simulation of Materials

Abstract: ▪ Abstract Obtaining a good atomistic description of diffusion dynamics in materials has been a daunting task owing to the time-scale limitations of the molecular dynamics method. We discuss promising new methods, derived from transition state theory, for accelerating molecular dynamics simulations of these infrequent-event processes. These methods, hyperdynamics, parallel replica dynamics, temperature-accelerated dynamics, and on-the-fly kinetic Monte Carlo, can reach simulation times several orders of magnitude longer than direct molecular dynamics while retaining full atomistic detail. Most applications so far have involved surface diffusion and growth, but it is clear that these methods can address a wide range of materials problems.

Monte Carlo methods in finance

Abstract: An invaluable resource for quantitative analysts who need to run models that assist in option pricing and risk management. This concise, practical hands on guide to Monte Carlo simulation introduces standard and advanced methods to the increasing complexity of derivatives portfolios. Ranging from pricing more complex derivatives, such as American and Asian options, to measuring Value at Risk, or modelling complex market dynamics, simulation is the only method general enough to capture the complexity and Monte Carlo simulation is the best pricing and risk management method available. The book is packed with numerous examples using real world data and is supplied with a CD to aid in the use of the examples.

Monte Carlo analysis of inverse problems

Abstract: Monte Carlo methods have become important in analysis of nonlinear inverse problems where no analytical expression for the forward relation between data and model parameters is available, and where linearization is unsuccessful. In such cases a direct mathematical treatment is impossible, but the forward relation materializes itself as an algorithm allowing data to be calculated for any given model. Monte Carlo methods can be divided into two categories: the sampling methods and the optimization methods. Monte Carlo sampling is useful when the space of feasible solutions is to be explored, and measures of resolution and uncertainty of solution are needed. The Metropolis algorithm and the Gibbs sampler are the most widely used Monte Carlo samplers for this purpose, but these methods can be refined and supplemented in various ways of which the neighbourhood algorithm is a notable example. Monte Carlo optimization methods are powerful tools when searching for globally optimal solutions amongst numerous local optima. Simulated annealing and genetic algorithms have shown their strength in this respect, but they suffer from the same fundamental problem as the Monte Carlo sampling methods: no provably optimal strategy for tuning these methods to a given problem has been found, only a number of approximate methods.

Self-driven lattice-model Monte Carlo simulations of alloy thermodynamic properties and phase diagrams

Abstract: Monte Carlo (MC) simulations of lattice models are a widely used way to compute thermodynamic properties of substitutional alloys. A limitation to their more widespread use is the difficulty of driving a MC simulation in order to obtain the desired quantities. To address this problem, we have devised a variety of high-level algorithms that serve as an interface between the user and a traditional MC code. The user specifies the goals sought in a high-level form that our algorithms convert into elementary tasks to be performed by a standard MC code. For instance, our algorithms permit the determination of the free energy of an alloy phase over its entire region of stability within a specified accuracy, without requiring any user intervention during the calculations. Our algorithms also enable the direct determination of composition-temperature phase boundaries without requiring the calculation of the whole free energy surface of the alloy system.

Bayesian Monte Carlo

Abstract: We investigate Bayesian alternatives to classical Monte Carlo methods for evaluating integrals. Bayesian Monte Carlo (BMC) allows the incorporation of prior knowledge, such as smoothness of the integrand, into the estimation. In a simple problem we show that this outperforms any classical importance sampling method. We also attempt more challenging multidimensional integrals involved in computing marginal likelihoods of statistical models (a.k.a. partition functions and model evidences). We find that Bayesian Monte Carlo outperformed Annealed Importance Sampling, although for very high dimensional problems or problems with massive multimodality BMC may be less adequate. One advantage of the Bayesian approach to Monte Carlo is that samples can be drawn from any distribution. This allows for the possibility of active design of sample points so as to maximise information gain.

On the acceptance probability of replica-exchange Monte Carlo trials

Abstract: An analysis is presented of the average probability of accepting an exchange trial in the parallel-tempering Monte Carlo molecular simulation method. Arguments are given that this quantity should be related to the entropy difference between the phases, and results from simulations of a simple Lennard-Jones system are presented to support this argument qualitatively. Another analysis based on the energy distributions of a replica pair is presented, and an exact expression for the trial-move acceptance probability in terms of the overlap of these distributions is derived. A more detailed expression is presented using an approximation of constant heat capacity, and an asymptotic form for this result, good for large system sizes, is reported. The detailed analyses are in quantitative agreement with the simulation data. It is further shown that treatment of the energy distributions as Gaussians is an inappropriate way to analyze the acceptance probability.

A Novel Monte Carlo Scheme for the Rapid Equilibration of Atomistic Model Polymer Systems of Precisely Defined Molecular Architecture

Abstract: Two novel connectivity-altering atomistic Monte Carlo moves are presented for the fast equilibration of condensed phases of long-chain systems with a variety of chain architectures. With the new moves, isotropic or oriented melts of linear or long-chain branched polymers, dense brushes of terminally grafted macromolecules, and cyclic peptides can be simulated. Results concerning the structural, conformational, and volumetric properties of linear, monodisperse polyethylene melts, simulated with a new united-atom molecular model, are in excellent agreement with experimental data.

ARTICLES On the acceptance probability of replica-exchange Monte Carlo trials

Abstract: An analysis is presented of the average probability of accepting an exchange trial in the parallel-tempering Monte Carlo molecular simulation method. Arguments are given that this quantity should be related to the entropy difference between the phases, and results from simulations of a simple Lennard-Jones system are presented to support this argument qualitatively. Another analysis based on the energy distributions of a replica pair is presented, and an exact expression for the trial-move acceptance probability in terms of the overlap of these distributions is derived. A more detailed expression is presented using an approximation of constant heat capacity, and an asymptotic form for this result, good for large system sizes, is reported. The detailed analyses are in quantitative agreement with the simulation data. It is further shown that treatment of the energy distributions as Gaussians is an inappropriate way to analyze the acceptance probability. © 2002 American Institute of Physics. @DOI: 10.1063/1.1507776#

Density-of-states Monte Carlo method for simulation of fluids

Abstract: A Monte Carlo method based on a density-of-states sampling is proposed for study of arbitrary statistical mechanical ensembles in a continuum A random walk in the two-dimensional space of particle number and energy is used to estimate the density of states of the system; this density of states is continuously updated as the random walk visits individual states The validity and usefulness of the method are demonstrated by applying it to the simulation of a Lennard-Jones fluid Results for its thermodynamic properties, including the vapor–liquid phase coexistence curve, are shown to be in good agreement with high-accuracy literature data

Lectures on Monte Carlo Methods

Abstract: Introduction Generating random numbers Variance reduction techniques Markov chain Monte Carlo Statistical analysis of simulation output The Ising model and related examples Bibliography.

Benchmark quantum Monte Carlo calculations

Abstract: Fixed node diffusion Monte Carlo (FN-DMC) atomization energies are calculated for a benchmark set of 55 molecules. Using single determinant trial wave functions, comparison with experiment yields an average absolute deviation of 2.9 kcal/mol, placing this simplest form of FN-DMC roughly at the same level of accuracy as the CCSD(T)/aug-cc-pVQZ method. However, unlike perturbative wave function expansion approaches, FN-DMC is applicable to systems containing thousands of valence electrons. For the P2 molecule, a number of possible sources of error are explored in detail. Results show that the main error is due to the fixed-node approximation and that this can be improved significantly with multireference trial wave functions.

Quantum annealing by the path-integral Monte Carlo method: The two-dimensional random Ising model

Abstract: Quantum annealing was recently found experimentally in a disordered spin-$\frac{1}{2}$ magnet to be more effective than its classical, thermal counterpart. We use the random two-dimensional Ising model as a test example and perform on it both classical and quantum (path-integral) Monte Carlo annealing. A systematic study of the dependence of the final residual energy on the annealing Monte Carlo time quantitatively demonstrates the superiority of quantum relative to classical annealing in this system. In order to determine the parameter regime for optimal efficiency of the quantum annealing procedure we explore a range of values of Trotter slice number P and temperature T. This identifies two different regimes of freezing with respect to efficiency of the algorithm, and leads to useful guidelines for the optimal choice of quantum annealing parameters.

Atomistic Monte Carlo simulation of strictly monodisperse long polyethylene melts through a generalized chain bridging algorithm

Abstract: This work is concerned with the atomistic simulation of the volumetric, conformational and structural properties of monodisperse polyethylene (PE) melts of molecular length ranging from C78 up to C1000. In the past, polydisperse models of these melts have been simulated in atomistic detail with the end-bridging Monte Carlo algorithm [Pant and Theodorou, Macromolecules 28, 7224 (1995); Mavrantzas et al., Macromolecules 32, 5072 (1999)]. In the present work, strictly monodisperse as well as polydisperse PE melts are simulated using the recently introduced double bridging and intramolecular double rebridging chain connectivity-altering Monte Carlo moves [Karayiannis et al., Phys. Rev. Lett. 88, 105503 (2002)]. These algorithms constitute generalizations of the EB move, since they entail the construction of two trimer bridges between two properly chosen pairs of dimers along the backbones of two different chains or along the same chain. In the simulations, a new molecular model is employed which is a hybrid o...

Stochastic roadmap simulation: an efficient representation and algorithm for analyzing molecular motion

Abstract: Classic techniques for simulating molecular motion, such as the Monte Carlo and molecular dynamics methods, generate individual motion pathways one at a time and spend most of their time trying to escape from the local minima of the energy landscape of a molecule. Their high computational cost prevents them from being used to analyze many pathways. We introduce Stochustic Roadmap Sirrrcllation (SRS), a new approach for exploring the kinetics of molecular motion by simultaneously examining multiple pathways encoded compactly in a graph, called a roadmap. A roadmap is computed by sampling a molecule's conformation space at random. The computation does not suffer from the localminima problem encountered with existing methods. Each path in the roadmap represents a potential motion pathway and is associated with a probability indicating the likelihood that the molecule follows this pathway. By viewing the roadmap as a Markov chain, we can efficiently compute kinetic properties of molecular motion over the entire molecular energy landscape. We also prove that, in the limit, SRS converges to the same distribution as Monte Carlo simulation. To test the effectiveness of our approach, we apply it to the computation of the transmission coefficients for protein folding, an important order parameter that measures the "kinetic distance" of a protein's conformation to its native state Our computational studies show that SRS obtains more accurate results and achieves several orders- of- magnitude reduction in computation time, compared with Monte Carlo simulatio.

Hybrid approach for generating realistic amorphous carbon structure using metropolis and reverse Monte Carlo

Abstract: An improved method for the modelling of carbon structures based on a hybrid reverse Monte Carlo (HRMC) method is presented. This algorithm incorporates an accurate environment dependent interaction potential (EDIP) in conjunction with the commonly used constraints derived from experimental data. In this work, we compare this new method with other modelling results for a small system of 2.9 g/cc amorphous carbon. We find that the new approach greatly improves the structural description, alleviating the common problem in standard reverse Monte Carlo method (RMC) of generating structures with a high proportion of unphysical small rings. The advantage of our method is that larger systems can now be modelled, allowing the incorporation of mesoscopic scale features.

The full Monte

Abstract: This paper deals with computing based on various forms of random sampling, or Monte Carlo methods. The author illustrates with applications to evaluate integrals and simple simulation, before explaining the prescription that inspired the paper.

Kinetic Monte Carlo Simulation of Chemical Vapor Deposition

Abstract: ▪ Abstract The kinetic Monte Carlo method is a powerful tool for exploring the evolution and properties of a wide range of problems and systems. Kinetic Monte Carlo is ideally suited for modeling the process of chemical vapor deposition, which involves the adsorption, desorption, evolution, and incorporation of vapor species at the surface of a growing film. Deposition occurs on a time scale that is generally not accessible to fully atomistic approaches such as molecular dynamics, whereas an atomically resolved Monte Carlo method parameterized by accurate chemical kinetic data is capable of exploring deposition over long times (min) on large surfaces (mm2). There are many kinetic Monte Carlo approaches that can simulate chemical vapor deposition, ranging from coarse-grained model systems with hypothetical input parameters to physically realistic atomic simulations with accurate chemical kinetic input. This article introduces the kinetic Monte Carlo technique, reviews some of the major approaches, details ...

Vapour—liquid equilibrium of the square-well fluid of variable range via a hybrid simulation approach

Abstract: The equilibrium between vapour and liquid in a square-well system has been determined by a hybrid simulation approach combining chemical potentials calculated via the Gibbs ensemble Monte Carlo technique with pressures calculated by the standard NVT Monte Carlo method. The phase equilibrium was determined from the thermodynamic conditions of equality of pressure and chemical potential between the two phases. The results of this hybrid approach were tested by independent NPT and μPT calculations and are shown to be of much higher accuracy than those of conventional GEMC simulations. The coexistence curves, vapour pressures and critical points were determined for SW systems of interaction ranges λ = 1.25, 1.5, 1.75 and 2. The new results show a systematic dependence on the range λ, in agreement with results from perturbation theory where previous work had shown more erratic behaviour.

Local simulation algorithms for Coulomb interactions.

Abstract: We consider a problem in dynamically constrained Monte Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever having to evaluate pair potentials or solve the Poisson equation. We discuss a simple implementation of a charged lattice gas as well as more elaborate off-lattice versions of the algorithm. There are analogies between our formulation of electrostatics and the bosonic Hubbard model in the phase approximation. Cluster methods developed for this model further improve the efficiency of the electrostatics algorithm.

Vibrational relaxation rates in the direct simulation Monte Carlo method

Abstract: Exact relationship is developed that connects the vibrational relaxation number, ZvDSMC, used in the direct simulation Monte Carlo method and that employed in continuum simulations. An approximate expression for ZvDSMC is also derived that is cost-effective and applicable when translational temperature is larger than vibrational temperature.

Monte Carlo simulation of the homogeneous cooling state for a granular mixture

Abstract: The Direct Simulation Monte Carlo (DSMC) method is used to numerically solve the Enskog equation for a granular binary mixture in the homogeneous cooling state (HCS). The fourth velocity moments, the temperature ratio, and also the velocity distribution functions are obtained and compared with approximate analytical results derived recently from a Sonine polynomial expansion [V. Garzo and J. W. Dufty, Phys. Rev. E 60, 5706 (1999)]. The comparison shows an excellent agreement between both approaches, even for strong dissipation or disparate values of the mechanical parameters of the mixture. In contrast to previous studies, the partial temperatures of each species are clearly different, so that the total energy is not equally distributed between both species. Finally, in the same way as in the one-component case, the simulation as well as the theory show a high energy tail of the distribution functions.

An Unfolding Method for High Energy Physics Experiments

Abstract: Finite detector resolution and limited acceptance require one to apply unfolding methods in high energy physics experiments. Information on the detector resolution is usually given by a set of Monte Carlo events. Based on the experience with a widely used unfolding program (RUN) a modified method has been developed. The first step of the method is a maximum likelihood fit of the Monte Carlo distributions to the measured distribution in one, two or three dimensions; the finite statistics of the Monte Carlo events is taken into account by the use of Barlow’s method with a new method of solution. A clustering method is used before combining bins in sparsely populated areas. In the second step a regularization is applied to the solution, which introduces only a small bias. The regularization parameter is determined from the data after a diagonalization and rotation procedure. 1 THE UNFOLDING PROBLEM A standard task in high energy physics experiments is the measurement of a distribution of some kinematical quantity . With an ideal detector one could measure the quantity in every event and could obtain by a simple histogram of the quantity . With real detectors the determination of is complicated by three effects: Limited acceptance: The probability to observe a given event, the detector acceptance, is less than 1. The acceptance depends on the kinematical variable . Transformation: Instead of the quantity a different, but related quantity is measured. The transformation from to can be caused by the non-linear response of a detector component. Finite resolution: The measured quantity is smeared out due to the finite resolution (or limited measurement accuracy) of the detector. Thus there is only a statistical relation between the true kinematical variable and the measured quantity . The really difficult effect in the data correction for experimental effects, or data transformation from to is the finite resolution, causing a smearing of the measured quantities. Mathematically the relation between the distribution of the true variable , to be determined in an experiment, and the measured distribution of the measured quantity is given by the integral equation, d (1) called a Fredholm integral equation of the first kind. In practice often a known (measured or simulated) background contribution has to be added to the right-hand side of equation (1); this contribution is ignored in this paper. The resolution function represents the effect of the detector. For a given value the function describes the response of the detector in the variable for that fixed value . The problem in determining the distribution from measured distributions is called unfolding; it is called an inverse problem. Unfolding of course requires the knowledge of the resolution function , i.e. all the effects of limited acceptance, transformation and finite resolution.

Monte Carlo transition probabilities. II.

Abstract: Transition probabilities governing the interaction of energy packets and matter are derived that allow Monte Carlo NLTE transfer codes to be constructed without simplifying the treatment of line formation. These probabilities are such that the Monte Carlo calculation asymptotically recovers the local emissivity of a gas in statistical equilibrium. Numerical experiments with one-point statistical equilibrium problems for Fe II and Hydrogen confirm this asymptotic behaviour. In addition, the resulting Monte Carlo emissivities are shown to be far less sensitive to errors in the populations of the emitting levels than are the values obtained with the basic emissivity formula.

Monte carlo method to solve multidimensional bioheat transfer problem

Abstract: The Monte Carlo method is implemented to solve the direct bioheat transfer problems, which are often encountered in the treatment planning of cancer hyperthermia. Several algorithms were developed to solve for the temperature transients inside the biological bodies with various time or space-dependent boundary conditions, blood perfusion, metabolic rate, and volumetric heat source for the tissues. The computer code thus compiled was validated through comparison with a theoretical solution. To illustrate the applications of the present numerical strategy, heat transfer in several three-dimensional cases was particularly studied. Parametric calculations were performed to test the technical adaptability of the present Monte Carlo algorithms. Some mathematical issues thus raised are discussed.