Showing papers on "Dynamic Monte Carlo method published in 2006"

Monte carlo methods for solving multivariable problems

Abstract: This paper opens with a brief general introduction on the nature of Monte Carlo methods that can be skipped by readers acquainted with them. I then deal more specifically with the application of these methods to multivariable problems, and I indicate certain relatively unexplored areas of this field where further research might be profitable. As I believe is appropriate, some of my material is exploratory, speculative, and controversial, and accordingly I hope it will stimulate discussion.

Fixed-width output analysis for Markov chain Monte Carlo

Abstract: Markov chain Monte Carlo is a method of producing a correlated sample to estimate features of a target distribution through ergodic averages. A fundamental question is when sampling should stop; that is, at what point the ergodic averages are good estimates of the desired quantities. We consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user-specified value. Hence calculating a Monte Carlo standard error is a critical step in assessing the simulation output. We consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution. We give sufficient conditions for the strong consistency of both methods and investigate their finite-sample properties in various examples.

Sequential Monte Carlo Methods

Abstract: Algorithm 1 Bootstrap particle filter (for i = 1, . . . , N) 1. Initialization (t = 0): (a) Sample x i 0 ∼ p(x0). (b) Set initial weights: w i 0 = 1/N. 2. for t = 1 to T do (a) Resample: sample ancestor indices ai t ∼ C({w j t−1}j=1). (b) Propagate: sample x i t ∼ p(xt | x ai t t−1). x i 0:t = {x ai t 0:t−1, x i t}. (c) Weight: compute w̃ i t = p(yt | x i t) and normalize w i t = w̃ i t/ ∑N j=1 w̃ j t . The ancestor indices {ai t}i=1 allow us to keep track of exactly what happens in each resampling step. Note the bookkeeping added to the propagation step 2b. 2/22 Bookkeeping – ancestral path

Feedback-optimized parallel tempering Monte Carlo

Abstract: We introduce an algorithm for systematically improving the efficiency of parallel tempering Monte Carlo simulations by optimizing the simulated temperature set. Our approach is closely related to a recently introduced adaptive algorithm that optimizes the simulated statistical ensemble in generalized broad-histogram Monte Carlo simulations. Conventionally, a temperature set is chosen in such a way that the acceptance rates for replica swaps between adjacent temperatures are independent of the temperature and large enough to ensure frequent swaps. In this paper, we show that by choosing the temperatures with a modified version of the optimized ensemble feedback method we can minimize the round-trip times between the lowest and highest temperatures which effectively increases the efficiency of the parallel tempering algorithm. In particular, the density of temperatures in the optimized temperature set increases at the 'bottlenecks' of the simulation, such as phase transitions. In turn, the acceptance rates are now temperature dependent in the optimized temperature ensemble. We illustrate the feedback-optimized parallel tempering algorithm by studying the two-dimensional Ising ferromagnet and the two-dimensional fully frustrated Ising model, and briefly discuss possible feedback schemes for systems that require configurational averages, such as spin glasses.

Retrospective exact simulation of diffusion sample paths with applications

Abstract: We present an algorithm for exact simulation of a class of Ito's diffusions. We demonstrate that when the algorithm is applicable, it is also straightforward to simulate diffusions conditioned to hit specific values at predetermined time instances. We also describe a method that exploits the properties of the algorithm to carry out inference on discretely observed diffusions without resorting to any kind of approximation apart from the Monte Carlo error.

A Monte Carlo modeling of electron interaction with solids including cascade secondary electron production

Abstract: A new Monte Carlo simulation approach has been developed to describe electron scattering and secondary electron generation processes in solids. This approach is based on the uses of Mott's elastic scattering cross section and Penn's dielectric function. A very good agreement has been found on the energy distribution of backscattered electrons between theoretical calculations and accurate experimental measurement recently made by Goto et al. (1994). This fact confirms that the present Monte Carlo model is very useful for more comprehensive understanding of basic phenomena in electron spec-troscopy and microscopy, particularly in the sub-keV energy region where cascade secondary electrons play a dominant role. In this paper the details of the Monte Carlo procedure are described and further application to the mechanism of secondary electron generation is presented.

Beyond the locality approximation in the standard diffusion Monte Carlo method

Abstract: We present a way to include nonlocal potentials in the standard diffusion Monte Carlo method without using the locality approximation. We define a stochastic projection based on a fixed node effective Hamiltonian, whose lowest energy is an upper bound of the true ground-state energy, even in the presence of nonlocal operators in the Hamiltonian. The variational property of the resulting algorithm provides a stable diffusion process, even in the case of divergent nonlocal potentials, like the hard-core pseudopotentials. It turns out that the modification required to improve the standard diffusion Monte Carlo algorithm is simple.

Inhomogeneous backflow transformations in quantum Monte Carlo calculations.

Abstract: An inhomogeneous backflow transformation for many-particle wave functions is presented and applied to electrons in atoms, molecules, and solids. We report variational and diffusion quantum Monte Carlo (VMC and DMC) energies for various systems and study the computational cost of using backflow wave functions. We find that inhomogeneous backflow transformations can provide a substantial increase in the amount of correlation energy retrieved within VMC and DMC calculations. The backflow transformations significantly improve the wave functions and their nodal surfaces.

Universality in three-dimensional Ising spin glasses: A Monte Carlo study

Abstract: We study universality in three-dimensional Ising spin glasses by large-scale Monte Carlo simulations of the Edwards-Anderson Ising spin glass for several choices of bond distributions, with particular emphasis on Gaussian and bimodal interactions. A finite-size scaling analysis suggests that three-dimensional Ising spin glasses obey universality.

Worm algorithm for continuous-space Path Integral Monte Carlo simulations

Abstract: We present a new approach to path integral Monte Carlo (PIMC) simulations based on the worm algorithm, originally developed for lattice models and extended here to continuous-space many-body systems. The scheme allows for efficient computation of thermodynamic properties, including winding numbers and off-diagonal correlations, for systems of much greater size than that accessible to conventional PIMC simulations. As an illustrative application of the method, we simulate the superfluid transition of 4He in two dimensions.

Molecular modeling of porous carbons using the hybrid reverse Monte Carlo method.

Abstract: We apply a simulation protocol based on the reverse Monte Carlo (RMC) method, which incorporates an energy constraint, to model porous carbons. This method is called hybrid reverse Monte Carlo (HRMC), since it combines the features of the Monte Carlo and reverse Monte Carlo methods. The use of the energy constraint term helps alleviate the problem of the presence of unrealistic features (such as three- and four-membered carbon rings), reported in previous RMC studies of carbons, and also correctly describes the local environment of carbon atoms. The HRMC protocol is used to develop molecular models of saccharose-based porous carbons in which hydrogen atoms are taken into account explicitly in addition to the carbon atoms. We find that the model reproduces the experimental pair correlation function with good accuracy. The local structure differs from that obtained with a previous model (Pikunic, J.; Clinard, C.; Cohaut, N.; Gubbins, K. E.; Guet, J. M.; Pellenq, R. J.-M.; Rannou, I.; Rouzaud, J. N. Langmuir 2003, 19 (20), 8565). We study the local structure by calculating the nearest neighbor distribution, bond angle distribution, and ring statistics.

Pfaffian pairing wave functions in electronic-structure quantum Monte Carlo simulations.

Abstract: We investigate the accuracy of trial wave functions for quantum Monte Carlo based on Pfaffian functional form with singlet and triplet pairing Using a set of first row atoms and molecules we find that these wave functions provide very consistent and systematic behavior in recovering the correlation energies on the level of 95% In order to get beyond this limit we explore the possibilities of multi-Pfaffian pairing wave functions We show that a small number of Pfaffians recovers another large fraction of the missing correlation energy comparable to the larger-scale configuration interaction wave functions We also find that Pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions

Comparison of a finite-element multigroup discrete-ordinates code with Monte Carlo for radiotherapy calculations

Abstract: Radiotherapy calculations often involve complex geometries such as interfaces between materials of vastly differing atomic number, such as lung, bone and/or air interfaces. Monte Carlo methods have been used to calculate accurately the perturbation effects of the interfaces. However, these methods can be computationally expensive for routine clinical calculations. An alternative approach is to solve the Boltzmann equation deterministically. We present one such deterministic code, Attila™. Further, we computed a brachytherapy example and an external beam benchmark to compare the results with data previously calculated by MCNPX and EGS4. Our data suggest that the presented deterministic code is as accurate as EGS4 and MCNPX for the transport geometries examined in this study.

Improved Monte-Carlo Search

Abstract: Monte-Carlo search has been successful in many non-deterministic games, and recently in deterministic games with high branching factor. One of the drawbacks of the current approaches is that even if the iterative process would last for a very long time, the selected move does not necessarily converge to a game-theoretic optimal one. In this paper we introduce a new algorithm, UCT, which extends a bandit algorithm for Monte-Carlo search. It is proven that the probability that the algorithm selects the correct move converges to 1. Moreover it is shown empirically that the algorithm converges rather fast even in comparison with alpha-beta search. Experiments in Amazons and Clobber indicate that the UCT algorithm outperforms considerably a plain Monte-Carlo version, and it is competitive against alpha-beta based game programs.

PROFASI: A Monte Carlo simulation package for protein folding and aggregation.

Abstract: We present a flexible and efficient program package written in C++, PROFASI, for simulating protein folding and aggregation. The systems are modeled using an all-atom description of the protein chains with only torsional degrees of freedom, and implicit water. The program package has a modular structure that makes the interaction potential easy to modify. The currently implemented potential is able to fold several peptides with about 20 residues, and has also been used to study aggregation and force-induced unfolding. The simulation methods implemented in PROFASI are Monte Carlo-based and include a semilocal move and simulated tempering. Adding new updates is easy. The code runs fast in both single- and multi-chain applications, as is illustrated by several examples.

Comparison of screened hybrid density functional theory to diffusion Monte Carlo in calculations of total energies of silicon phases and defects

Abstract: Nearly quantitative agreement between density functional theory DFT and diffusion Monte Carlo DMC calculations is shown for the prediction of defect properties using the Heyd-Scuseria-Ernzerhof HSE screened-exchange hybrid functional. The HSE functional enables accurate computations on complex systems, such as defects, where traditional DFT may be inadequate and DMC calculation computationally unfeasible. The screened-exchange hybrid functional retains the benefits of earlier hybrid functionals in terms of treating strongly correlated insulators but unlike them it can be applied to metallic phases. This study concentrates on the DFT energetic predictions of point defects in silicon and on phase energy differences between the diamond and metallic -tin phases.

First-passage Monte Carlo algorithm: diffusion without all the hops.

Abstract: We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions Using the theory of first-passage processes and time dependent Green’s functions, we break the di

The Monte Carlo method in science and engineering

Abstract: Since 1953, researchers have applied the Monte Carlo method to a wide range of areas. Specialized algorithms have also been developed to extend the method's applicability and efficiency. The author describes some of the algorithms that have been developed to perform Monte Carlo simulations in science and engineering

The nature of the calculation of the pressure in molecular simulations of continuous models from volume perturbations.

Abstract: We consider some fundamental aspects of the calculation of the pressure from simulations by performing volume perturbations. The method, initially proposed for hard-core potentials by Eppenga and Frenkel [Mol. Phys.52, 1303 (1984)] and then extended to continuous potentials by Harismiadis et al. [J. Chem. Phys. 105, 8469 (1996)], is based on the numerical estimate of the change in Helmholtz free energy associated with the perturbation which, in turn, can be expressed as an ensemble average of the corresponding Boltzmann factor. The approach can be easily generalized to the calculation of components of the pressure tensor and also to ensembles other than the canonical ensemble. The accuracy of the method is assessed by comparing simulation results obtained from the volume-perturbation route with those obtained from the usual virial expression for several prototype fluid models. Monte Carlo simulation data are reported for bulk fluids and for inhomogeneous systems containing a vapor-liquid interface.

Wang-Landau Monte Carlo simulation of the Blume-Capel model.

Abstract: We carry out a study of the two-dimensional Blume-Capel model using the Wang-Landau Monte Carlo method which estimates the density of states $g(E)$ directly. This work validates the applicability of this method to multiparametric systems, since only one computer run is needed for all range of macroscopic parameters (temperature, anisotropy, etc.). The location of the tricritical point is determined as ${k}_{B}{T}_{t}∕J=0.609(3)$, ${D}_{t}∕J=1.966(2)$ and is in excellent agreement with previous estimates. The free energy and the entropy, which are not directly accessible by conventional Monte Carlo simulations, are obtained simply using $g(E)$.

Calculation of Phase Coexistence Properties and Surface Tensions of n-Alkanes with Grand-Canonical Transition-Matrix Monte Carlo Simulation and Finite-Size Scaling

Abstract: Grand-canonical transition-matrix Monte Carlo is combined with configurational-bias and expanded ensemble Monte Carlo techniques to obtain saturated densities and vapor pressures of select n-alkanes. Surface tension values for butane, hexane, and octane are also computed via the finite-size scaling method of Binder. The exponential-6 model of Errington and Panagiotopoulos is used to describe the molecular interactions. The effect of the number of configurational-bias trial conformations on the efficiency of phase equilibra calculations is studied. We find that a broad range of trial conformation numbers give reasonable performance, with the optimal value increasing with decreasing temperature for a fixed chain length. Phase coexistence properties are in good agreement with literature values and are obtained with very reasonable computing resources. Similar to other recently developed n-alkane force fields, the exponential-6 model overestimates the surface tension relative to experimental values. Statistical uncertainties for coexistence properties obtained with the current approach are relatively small compared to existing methods.

The Fermi–Hubbard model at unitarity

Abstract: We simulate the dilute attractive Fermi-Hubbard model in the unitarity regime using a diagrammatic determinant Monte Carlo algorithm with worm-type updates. We obtain the dependence of the critical temperature on the filling factorand, by extrapolating to � ! 0, determine the universal critical temperature of the continuum unitary Fermi gas in units of Fermi energy: Tc/"F = 0.152(7). We also determine the thermodynamic functions and show how the Monte Carlo results can be used for accurate thermometry of a trapped unitary gas.

Towards hybrid molecular simulations

Abstract: In many biology, chemistry and physics applications molecular simulations can be used to study material and process properties. The level of detail needed in such simulations depends on the application. In some cases quantum mechanical simulations are indispensable. However, traditional ab-initio methods, usually employing plane waves or a linear combination of atomic orbitals as a basis, are extremely expensive in terms of computational as well as memory requirements. The well-known fact that electronic wave functions vary much more rapidly near the atomic nuclei than in inter-atomic regions calls for a multi-resolution approach, allowing one to use low resolution and to add extra resolution only in those regions where necessary, so limiting the costs. This is provided by an alternative basis formed of wavelets. Using such a wavelet basis, a method has been developed for solving electronic structure problems that has been applied successfully to 2D quantum dots and 3D molecular systems. In other cases, it suffices to use effective potentials to describe the atomic interaction instead of the use of the electronic structure, enabling the simulation of larger systems. Molecular dynamics simulations with such effective potentials have been used for a systematic study of surface wettability influence on particle and heat flow in nanochannels, showing that the effects at the solid-gas interface are crucial for the behavior of the whole nanochannel. Again in other cases even coarse grained models can be used where the average behavior of several atoms is combined into a single particle. Such a model, refraining from as much detail as possible while maintaining realistic behavior, has been developed for lipids and with this model the dynamics of membranes and vesicle formation have been studied in detail. A disadvantage of molecular dynamics simulations with effective potentials is that no reactions are possible. Therefore a new method has been developed, where molecular dynamics is coupled with stochastic reactions. Using this method, both unilamellar and multilamellar vesicle formation, and vesicle growth, bursting, and healing are shown. Still larger systems can be simulated using other methods, like the direct simulation Monte Carlo method. However, as shown for nanochannels, these methods are not always accurate enough. But, exploiting again that the finest level of detail is often only needed in part of the domain, a hybrid method has been developed coupling molecular dynamics, where needed for accuracy, and direct simulation Monte Carlo, where possible in order to speed up the calculation. Further development of such hybrid simulations will further increase molecular simulation’s scientific role.

Generation of atomistic models of periodic mesoporous silica by kinetic Monte Carlo simulation of the synthesis of the material.

Abstract: We have developed a molecular simulation method for the generation of realistic atomic-level models for periodic mesoporous silicas. Using simplified interaction potentials and simplified representations of the templating micelles, the simulation follows the reaction path of the hydrothermal synthesis and calcination of the silica material in a kinetic Monte Carlo (kMC) simulation. The only input to the simulation is the geometry of the micelle and the number of silicic acid monomers at the beginning of the synthesis. We simulated the adsorption properties of the PMS models using Grand Canonical Monte Carlo simulation. With use of MCM-41 materials of different pore sizes as a prototype material, experimental and simulated adsorption isotherms for nitrogen, ethane, and carbon dioxide were compared, showing good agreement between simulation and experiment.

Monte Carlo and quasi-Monte Carlo methods 2004

Abstract: Invariance Principles with Logarithmic Averaging for Ergodic Simulations.- Technical Analysis Techniques versus Mathematical Models: Boundaries of Their Validity Domains.- Weak Approximation of Stopped Dffusions.- Approximation of Stochastic Programming Problems.- The Asymptotic Distribution of Quadratic Discrepancies.- Weighted Star Discrepancy of Digital Nets in Prime Bases.- Explaining Effective Low-Dimensionality.- Selection Criteria for (Random) Generation of Digital (0,s)-Sequences.- Imaging of a Dissipative Layer in a Random Medium Using a Time Reversal Method.- A Stochastic Numerical Method for Diffusion Equations and Applications to Spatially Inhomogeneous Coagulation Processes.- Non-Uniform Low-Discrepancy Sequence Generation and Integration of Singular Integrands.- Construction of Good Rank-1 Lattice Rules Based on the Weighted Star Discrepancy.- Probabilistic Approximation via Spatial Derivation of Some Nonlinear Parabolic Evolution Equations.- Myths of Computer Graphics.- Illumination in the Presence of Weak Singularities.- Irradiance Filtering for Monte Carlo Ray Tracing.- On the Star Discrepancy of Digital Nets and Sequences in Three Dimensions.- Lattice Rules for Multivariate Approximation in the Worst Case Setting.- Randomized Quasi-Monte Carlo Simulation of Markov Chains with an Ordered State Space.- Experimental Designs Using Digital Nets with Small Numbers of Points.- Concentration Inequalities for Euler Schemes.- Fast Component-by-Component Construction, a Reprise for Different Kernels.- A Reversible Jump MCMC Sampler for Object Detection in Image Processing.- Quasi-Monte Carlo for Integrands with Point Singularities at Unknown Locations.- Infinite-Dimensional Highly-Uniform Point Sets Defined via Linear Recurrences in $$\mathbb{F}_{2^w } $$ .- Monte Carlo Studies of Effective Diffusivities for Inertial Particles.- An Adaptive Importance Sampling Technique.- MinT: A Database for Optimal Net Parameters.- On Ergodic Measures for McKean-Vlasov Stochastic Equations.- On the Distribution of Some New Explicit Inversive Pseudorandom Numbers and Vectors.- Error Analysis of Splines for Periodic Problems Using Lattice Designs.

Monte Carlo Simulation Study of Water Adsorption in Activated Carbon

Abstract: We present a Monte Carlo simulation study of adsorption and desorption for two molecular models of water in activated carbon, focusing on the temperature range for which the system exhibits hysteresis. The activated carbon is modeled using an adaptation of the platelet model developed by Segarra and Glandt (Chem. Eng. Sci. 1994, 49 (17), 2953−2965). The active sites in the carbon are modeled by placing interaction sites at the periphery of the platelets. To model water we have used two model potentials: the simple point charge (SPC) model and adaptation of the primitive model of water developed by Kolafa and Nezbeda (Mol. Phys. 1987, 61 (1), 161−175). We find that both models considered yield quite good qualitative agreement with the experimental data for water in BPL carbon obtained by Levan and co-workers (Ind. Eng. Chem. Res. 1992, 31 (4), 1122−1130). In particular both the shape of the hysteresis loops and their temperature dependence are correctly described by the simulation results. The sensitivity...