Showing papers on "Dynamic Monte Carlo method published in 2008"
TL;DR: It is shown that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations.
Abstract: We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretisation, the computational cost to achieve an accuracy of O(e) is reduced from O(e-3) to O(e-2 (log e)2). The analysis is supported by numerical results showing significant computational savings.
1,619 citations
07 Dec 2008
TL;DR: This paper will briefly describe the nature and relevance of Monte Carlo simulation, the way to perform these simulations and analyze results, and the underlying mathematical techniques required for performing these simulations.
Abstract: This is an introductory tutorial on Monte Carlo simulation, a type of simulation that relies on repeated random sampling and statistical analysis to compute the results. In this paper, we will briefly describe the nature and relevance of Monte Carlo simulation, the way to perform these simulations and analyze results, and the underlying mathematical techniques required for performing these simulations. We will present a few examples from various areas where Monte Carlo simulation is used, and also touch on the current state of software in this area.
467 citations
TL;DR: The theoretical basis for calculating equilibrium properties of biological molecules by the Monte Carlo method is presented and a discussion of the estimation of errors in properties calculated by Monte Carlo is given.
Abstract: A description of Monte Carlo methods for simulation of proteins is given. Advantages and disadvantages of the Monte Carlo approach are presented. The theoretical basis for calculating equilibrium properties of biological molecules by the Monte Carlo method is presented. Some of the standard and some of the more recent ways of performing Monte Carlo on proteins are presented. A discussion of the estimation of errors in properties calculated by Monte Carlo is given.
401 citations
TL;DR: It is shown how spatially realistic Monte Carlo simulations of biological systems can be far more cost-effective than often is assumed, and provide a level of accuracy and insight beyond that of continuum methods.
Abstract: Many important physiological processes operate at time and space scales far beyond those accessible to atom-realistic simulations, and yet discrete stochastic rather than continuum methods may best represent finite numbers of molecules interacting in complex cellular spaces. We describe and validate new tools and algorithms developed for a new version of the MCell simulation program (MCell3), which supports generalized Monte Carlo modeling of diffusion and chemical reaction in solution, on surfaces representing membranes, and combinations thereof. A new syntax for describing the spatial directionality of surface reactions is introduced, along with optimizations and algorithms that can substantially reduce computational costs (e.g., event scheduling, variable time and space steps). Examples for simple reactions in simple spaces are validated by comparison to analytic solutions. Thus we show how spatially realistic Monte Carlo simulations of biological systems can be far more cost-effective than often is assumed, and provide a level of accuracy and insight beyond that of continuum methods.
318 citations
TL;DR: In this article, the problem of a single spin-down fermion resonantly interacting with a Fermi gas of spin-up particles was solved using the diagrammatic Monte Carlo approach.
Abstract: We use the diagrammatic Monte Carlo approach to solve the problem of a single spin-down fermion resonantly interacting with a Fermi gas of spin-up particles Our solution is important for understanding the phase diagram and properties of the crossover from the BCS regime to the Bose-Einstein condensate in the strongly imbalanced regime On the technical side, we develop a generic sign-problem-tolerant method for exact numerical solution of polaron-type models This is a characteristic example of how Monte Carlo methods can be used to simulate divergent sign-alternating diagrammatic series
241 citations
TL;DR: A constant-time algorithm, whose cost is independent of the number of reactions, enabled by a slightly more complex underlying data structure is presented, which is applicable to kinetic Monte Carlo simulations in general and its competitive performance on small- and medium-size networks is demonstrated.
Abstract: The time evolution of species concentrations in biochemical reaction networks is often modeled using the stochastic simulation algorithm SSAGillespie, J. Phys. Chem. 81, 2340 1977. The computational cost of the original SSA scaled linearly with the number of reactions in the network. Gibson and Bruck developed a logarithmic scaling version of the SSA which uses a priority queue or binary tree for more efficient reaction selection Gibson and Bruck, J. Phys. Chem. A 104, 1876 2000. More generally, this problem is one of dynamic discrete random variate generation which finds many uses in kinetic Monte Carlo and discrete event simulation. We present here a constant-time algorithm, whose cost is independent of the number of reactions, enabled by a slightly more complex underlying data structure. While applicable to kinetic Monte Carlo simulations in general, we describe the algorithm in the context of biochemical simulations and demonstrate its competitive performance on small- and medium-size networks, as well as its superior constant-time performance on very large networks, which are becoming necessary to represent the increasing complexity of biochemical data for pathways that mediate cell function. © 2008 American Institute of Physics. DOI: 10.1063/1.2919546
239 citations
TL;DR: In this paper, the problem of eliminating finite-size errors from quantum Monte Carlo (QMC) energy data has been analyzed and it has been shown that adding a recently proposed [ S. Chiesa et al. et al., 2006] finite size correction to the Ewald energy and using the model periodic Coulomb (MPC) interaction is a good solution to the problem.
Abstract: We analyze the problem of eliminating finite-size errors from quantum Monte Carlo (QMC) energy data. We demonstrate that both (i) adding a recently proposed [ S. Chiesa et al. Phys. Rev. Lett. 97 076404 (2006)] finite-size correction to the Ewald energy and (ii) using the model periodic Coulomb (MPC) interaction [ L. M. Fraser et al. Phys. Rev. B 53 1814 (1996); P. R. C. Kent et al. Phys. Rev. B 59 1917 (1999); A. J. Williamson et al. Phys. Rev. B 55 R4851 (1997)] are good solutions to the problem of removing finite-size effects from the interaction energy in cubic systems provided the exchange-correlation (XC) hole has converged with respect to system size. However, we find that the MPC interaction distorts the XC hole in finite systems, implying that the Ewald interaction should be used to generate the configuration distribution. The finite-size correction of Chiesa et al. Phys. Rev. Lett. 97 076404 (2006) is shown to be incomplete in systems of low symmetry. Beyond-leading-order corrections to the kinetic energy are found to be necessary at intermediate and high densities; we investigate the effect of adding such corrections to QMC data for the homogeneous electron gas. We analyze finite-size errors in two-dimensional systems and show that the leading-order behavior differs from that which has hitherto been supposed. We compare the efficiencies of different twist-averaging methods for reducing single-particle finite-size errors and we examine the performance of various finite-size extrapolation formulas. Finally, we investigate the system-size scaling of biases in diffusion QMC.
201 citations
05 Oct 2008
TL;DR: In this article, the authors describe methods, systems, devices and computer program code (software) products operable within a computer graphics system or other computer system enable quasi-Monte Carlo (QMC) light transport simulation by efficient ray tracing.
Abstract: Methods, systems, devices and computer program code (software) products operable within a computer graphics system or other computer system enable quasi-Monte Carlo (QMC) light transport simulation by efficient ray tracing.
196 citations
TL;DR: In this paper, a continuous-time Monte Carlo method for quantum impurity models is presented, which combines a weak-coupling expansion with an auxiliary-field decomposition.
Abstract: We present a continuous-time Monte Carlo method for quantum impurity models, which combines a weak-coupling expansion with an auxiliary-field decomposition. The method is considerably more efficient than Hirsch-Fye and free of time discretization errors, and is particularly useful as impurity solver in large cluster dynamical mean-field theory (DMFT) calculations.
192 citations
TL;DR: The statistical distribution of capture times is obtained from Monte Carlo calculations and shows a crossover from power-law to exponential behavior, and predicts the distribution function for a lattice with perfect mixing.
168 citations
TL;DR: In this paper, first-principles calculations and Monte Carlo simulation were used to predict ferromagnetic coupling in C doped CdS, resulting from carbon substitution of sulfur.
Abstract: Carbon doping of CdS is studied using first-principles calculations and Monte Carlo simulation. Our calculations predict ferromagnetism in C doped CdS, resulting from carbon substitution of sulfur. A single carbon substitution of sulfur favors a spin-polarized state with a magnetic moment of $1.22{\ensuremath{\mu}}_{B}$. Ferromagnetic coupling is generally observed between these magnetic moments. A transition temperature of $270\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is predicted through Monte Carlo simulation. The ferromagnetism of C doped CdS can be explained by the hole-mediated double exchange mechanism.
TL;DR: The adaptive kinetic Monte Carlo method uses minimum-mode following saddle point searches and harmonic transition state theory to model rare-event, state-to-state dynamics in chemical and material systems, focusing on low energy processes and asserting a minimum probability of finding any saddle.
Abstract: The adaptive kinetic Monte Carlo method uses minimum-mode following saddle point searches and harmonic transition state theory to model rare-event, state-to-state dynamics in chemical and material systems. The dynamical events can be complex, involve many atoms, and are not constrained to a grid—relaxing many of the limitations of regular kinetic Monte Carlo. By focusing on low energy processes and asserting a minimum probability of finding any saddle, a confidence level is used to describe the completeness of the calculated event table for each state visited. This confidence level provides a dynamic criterion to decide when sufficient saddle point searches have been completed. The method has been made efficient enough to work with forces and energies from density functional theory calculations. Finding saddle points in parallel reduces the simulation time when many computers are available. Even more important is the recycling of calculated reaction mechanisms from previous states along the dynamics. For systems with localized reactions, the work required to update the event table from state to state does not increase with system size. When the reaction barriers are high with respect to the thermal energy, first-principles simulations over long time scales are possible.
TL;DR: In this paper, the kinetic activation relaxation technique (k-ART) is proposed to identify and evaluate activation barriers using an off-lattice, self-learning, on-the-fly identification and evaluation.
Abstract: Many materials science phenomena, such as growth and self-organisation, are dominated by activated diffusion processes and occur on timescales that are well beyond the reach of standard-molecular dynamics simulations. Kinetic Monte Carlo (KMC) schemes make it possible to overcome this limitation and achieve experimental timescales. However, most KMC approaches proceed by discretizing the problem in space in order to identify, from the outset, a fixed set of barriers that are used throughout the simulations, limiting the range of problems that can be addressed. Here, we propose a more flexible approach -- the kinetic activation-relaxation technique (k-ART) -- which lifts these constraints. Our method is based on an off-lattice, self-learning, on-the-fly identification and evaluation of activation barriers using ART and a topological description of events. The validity and power of the method are demonstrated through the study of vacancy diffusion in crystalline silicon.
TL;DR: It is concluded that solvation free energy calculations with the GCMC/MD method can greatly improve the accuracy of the computed binding free energy compared to simulations with fixed number of water.
Abstract: The binding of a ligand to a receptor is often associated with the displacement of a number of bound water molecules. When the binding site is exposed to the bulk region, this process may be sampled adequately by standard unbiased molecular dynamics trajectories. However, when the binding site is deeply buried and the exchange of water molecules with the bulk region may be difficult to sample, the convergence and accuracy in free energy perturbation (FEP) calculations can be severely compromised. These problems are further compounded when a reduced system including only the region surrounding the binding site is simulated. To address these issues, we couple molecular dynamics (MD) with grand canonical Monte Carlo (GCMC) simulations to allow the number of water to fluctuate during an alchemical FEP calculation. The atoms in a spherical inner region around the binding pocket are treated explicitly while the influence of the outer region is approximated using the generalized solvent boundary potential (GSBP). At each step during thermodynamic integration, the number of water in the inner region is equilibrated with GCMC and energy data generated with MD is collected. Free energy calculations on camphor binding to a deeply buried pocket in cytochrome P450cam, which causes about seven water molecules to be expelled, are used to test the method. It concluded that solvation free energy calculations with the GCMC/MD method can greatly improve the accuracy of the computed binding free energy compared to simulations with fixed number of water.
TL;DR: In this paper, the authors compare the performance of mean field rate theory (MFRT) and Kinetic Monte Carlo (MC) models for point defect cluster dynamics modeling, which is relevant to the evolution of radiation-induced defect structures.
TL;DR: A novel scheme for fully scalable White Monte Carlo is developed and is used as a forward solver in the evaluation of experimental time-resolved spectroscopy, exploring the low albedo regime of time-domain photon migration in a regime where the diffusion approximation of radiative transport theory breaks down.
Abstract: A novel scheme for fully scalable White Monte Carlo (WMC) has been developed and is used as a forward solver in the evaluation of experimental time-resolved spectroscopy. Previously reported scaling problems are avoided by storing detection events individually, turning spatial and temporal binning into post-simulation activities. The approach is suitable for modeling of both interstitial and noninvasive settings (i.e., infinite and semi-infinite geometries). Motivated by an interest in in vivo optical properties of human prostate tissue, we utilize WMC to explore the low albedo regime of time-domain photon migration--a regime where the diffusion approximation of radiative transport theory breaks down, leading to the risk of overestimating both reduced scattering (mu(s)') and absorption (mu(a)). Experimental work supports our findings and establishes the advantages of Monte Carlo-based evaluation.
01 Jan 2008
TL;DR: In this article, the authors concentrate primarily on world-line methods with loop updates, for spins and also for spin-phonon systems, as well as on the auxiliary field quantum Monte Carlo (QMC) method.
Abstract: In this chapter we will concentrate primarily on world-line methods with loop updates, for spins and also for spin-phonon systems, as well as on the auxiliary field quantum Monte Carlo (QMC) method. Both approaches are based on a path integral formulation of the partition function which maps a d-dimensional quantum system onto a d+1 dimensional classical system. The additional dimension is nothing but the imaginary time. World-line based approaches for quantum spin systems offer a simple realization of the mapping from quantum to classical, and serve as a nice introduction to QMC methods for correlated systems. Auxiliary field QMC methods provide access to fermionic systems both at finite temperature and in the ground state. An important example is the Hirsch-Fye approach that allows for an efficient simulation of impurity models, such as the Kondo and Anderson models, and is widely used in the domain of dynamical mean field theories (DMFT).
TL;DR: The reaction ensemble Monte Carlo method (RxMC) as discussed by the authors has been applied to predict the equilibrium behavior of chemically reacting systems in highly non-ideal environments, including solvation, nanoporous materials, catalyst design, combustion and propulsion science, shock physics and many more.
Abstract: Understanding and predicting the equilibrium behaviour of chemically reacting systems in highly non-ideal environments is critical to many fields of science and technology, including solvation, nanoporous materials, catalyst design, combustion and propulsion science, shock physics and many more. A method with recent success in predicting the equilibrium behaviour of reactions under non-ideal conditions is the reaction ensemble Monte Carlo method (RxMC). RxMC has been applied to reactions confined in porous solids or near solid surfaces, reactions at high temperature and/or high pressure, reactions in solution and at phase interfaces. The only required information is a description of the intermolecular forces among the system molecules and standard free-energy data for the reacting components. Extensions of the original method include its combination with algorithms for systems involving phase equilibria, constant-enthalpy and constant-internal energy adiabatic conditions, a method to include reaction kine...
TL;DR: Two methods are presented-one that combines the use of inverted-list data structures with rejection Monte Carlo and a second that combines inverted lists with the Marsaglia-Norman-Cannon algorithm.
TL;DR: The CFC move can be combined with other Monte Carlo moves to enable efficient simulation of dense strongly associating fluids that are to this point infeasible to model with standard methods.
Abstract: The continuous fractional component Monte Carlo (CFC MC) move (J Chem Theory Comput, 2007, 3, 1451) is extended to the Gibbs ensemble The algorithm is validated against conventional simulations for the Lennard Jones fluid and a flexible water model The method is also used to compute the vapor-liquid coexistence densities of a model for SO2 The CFC molecule exchange move relies on the gradual insertion and deletion of molecules in conjunction with a self-adapting bias potential As a result, the method does not require the formation of spontaneous voids in the dense fluid phase to be successful, leading to molecule exchange acceptance probabilities that are nearly independent of temperature For example, over 1% of the vapor-liquid molecule exchange moves are successful for water at 280 K, whereas advanced rotational and configurational bias methods have success rates of less than 003% The CFC move can be combined with other Monte Carlo moves to enable efficient simulation of dense strongly associating fluids that are to this point infeasible to model with standard methods © 2008 Wiley Periodicals, Inc J Comput Chem, 2008
TL;DR: In this paper, the Anderson impurity model is extended to the case of fermionic continua with finite bandwidths, and the transient dynamics of the system depends sensitively on the bandwidth of the electrode material.
Abstract: We discuss the transient effects in the Anderson impurity model that occur when two fermionic continua with finite bandwidths are instantaneously coupled to a central level. We present results for the analytically solvable noninteracting resonant-level system first and then consistently extend them to the interacting case using the conventional perturbation theory and recently developed nonequilibrium Monte Carlo simulation schemes. The main goal is to gain an understanding of the full time-dependent nonlinear current-voltage characteristics and the population probability of the central level. We find that, contrary to the steady state, the transient dynamics of the system depends sensitively on the bandwidth of the electrode material.
TL;DR: Monte Carlo simulations in the constant pressure ensemble are performed and several important properties of the pressure effect are reproduced in a unified way with a microscopic mechanism for the first time.
Abstract: Pressure-induced phase transitions of spin-crossover materials are studied in a microscopic model taking into account the elastic interaction among distortions of lattice due to the difference of the molecular sizes between the high-spin state and the low-spin state. We perform Monte Carlo simulations in the constant pressure ensemble and reproduce several important properties of the pressure effect in a unified way with a microscopic mechanism for the first time. The simulation newly reveals how the temperature dependence of the ordering process changes with the pressure.
TL;DR: In this article, an unscented transform (UT) method is used to model the uncertainty in time and frequency-domain simulations of the transmission line matrix-based solvers, and the results show good agreement compared with Monte Carlo outcomes with much reduced simulator use.
Abstract: The objective of this work is to present a new approach to the modelling of uncertainty in electromagnetic simulations. This contribution enhances the practical utilisation of regular time- and frequency-domain models. The approach is based on the unscented transform (UT) method. The procedure shows results with accuracy similar to the Monte Carlo approach, but uses a smaller number of simulations. This work uses standard transmission line matrix-based solvers. Furthermore, the combination of the UT approach with other time- or frequency-domain electromagnetic simulators is straightforward. The validation of the technique used both time- and frequency-domain tests. The results show good agreement compared with Monte Carlo outcomes with much reduced simulator use.
TL;DR: Two free-energy-based methods for studying the wetting properties of a fluid in contact with a solid substrate are examined and good agreement is found between the results and those obtained via the mechanical definition of the interfacial tension.
Abstract: We examine two free-energy-based methods for studying the wetting properties of a fluid in contact with a solid substrate. Application of the first approach involves examination of the adsorption behavior of a fluid at a single substrate, while the second technique requires investigation of the properties of a system confined between two parallel substrates. Both of the techniques rely upon computation and analysis of the density dependence of a system’s surface free energy and provide the contact angle and solid-vapor and solid-liquid interfacial tensions for substrate-fluid combinations within the partial wetting regime. Grand canonical transition matrix Monte Carlo simulation is used to obtain the required free-energy curves. The methods examined within this work are general and are applicable to a wide range of molecular systems. We probe the performance of the methods by computing the interfacial properties for two systems in which an atomistic fluid interacts with a fcc crystal. For both of the systems studied we find good agreement between our results and those obtained via the mechanical definition of the interfacial tension.
TL;DR: In this article, the authors compare the results obtained by the Monte Carlo method for the two examples compared to the corresponding results when applying the Guide to the Expression of Uncertainty in Measurement (GUM).
Abstract: The Guide to the Expression of Uncertainty in Measurement (GUM) is the de facto standard for the evaluation of measurement uncertainty in metrology. Recently, evaluation of measurement uncertainty has been proposed on the basis of probability density functions (PDFs) using a Monte Carlo method. The relation between this PDF approach and the standard method described in the GUM is outlined. The Monte Carlo method required for the numerical calculation of the PDF approach is described and illustrated by its application to two examples. The results obtained by the Monte Carlo method for the two examples are compared to the corresponding results when applying the GUM.
TL;DR: Direct Monte Carlo simulations on the liquid-vapor interfaces of pure water, carbon dioxide, and hydrogen sulfide are reported and the different contributions to the surface tension due to the repulsion-dispersion and electrostatic interactions are discussed.
Abstract: We report direct Monte Carlo (MC) simulations on the liquid-vapor interfaces of pure water, carbon dioxide, and hydrogen sulfide. In the case of water, the recent TIP4P/2005 potential model used with the MC method is shown to reproduce the experimental surface tension and to accurately describe the coexistence curves. The agreement with experiments is also excellent for CO2 and H2S with standard nonpolarizable models. The surface tensions are calculated by using the mechanical and the thermodynamic definitions via profiles along the direction normal to the surface. We also discuss the different contributions to the surface tension due to the repulsion-dispersion and electrostatic interactions. The different profiles of these contributions are proposed in the case of water.
TL;DR: In this paper, two methodologies to propagate the uncertainties on the nuclide inventory in combined Monte Carlo-spectrum and burn-up calculations are presented, based on sensitivity/uncertainty and random sampling techniques.
TL;DR: In this article, the spatial relaxation of the electrons and benchmark calculations of spatially resolved non-conservative electron transport in model gases have been carried out using a Monte Carlo simulation technique.
Abstract: An investigation of the spatial relaxation of the electrons and benchmark calculations of spatially resolved non-conservative electron transport in model gases has been carried out using a Monte Carlo simulation technique. The Monte Carlo code has been specifically developed to study the spatial relaxation of electrons in an idealized steady-state Townsend (SST) experiment in the presence of non-conservative collisions. Calculations have been performed for electron transport properties with the aim of providing the benchmark required to verify the codes used in plasma modelling. Both the spatially uniform values and the relaxation profiles of the electron transport properties may serve as an accurate test for such codes. The explicit effects of ionization and attachment on the spatial relaxation profiles are considered using physical arguments. We identify the relations for the conversion of hydrodynamic transport properties to those found in the SST experiment. Our Monte Carlo simulation code and sampling techniques appropriate to these experiments have provided us with a way to test these conversion formulae and their convergence.
TL;DR: In this article, the authors studied the zero and finite-temperature properties of a system of harmonically trapped one-dimensional spin1 2 fermions with short-range interactions and found that the Thomas-Fermi approximation fails to capture small Friedel-like spin and density oscillations.
Abstract: Using exact continuous quantum Monte Carlo techniques, we study the zero- and finite-temperature properties of a system of harmonically trapped one-dimensional spin1 2 fermions with short-range interactions. Motivated by experimental searches for modulated Fulde-Ferrel-Larkin-Ovchinikov states, we systematically examine the impact of a spin imbalance on the density profiles. We quantify the accuracy of the Thomas-Fermi approximation, finding that for sufficiently large particle numbers N100 it quantitatively reproduces most features of the exact density profile. The Thomas-Fermi approximation fails to capture small Friedel-like spin and density oscillations and overestimates the size of the fully paired region in the outer shell of the trap. Based on our results, we suggest a range of experimentally tunable parameters to maximize the visibility of the double-shell structure of the system and the Fulde-Ferrel-Larkin-Ovchinikov state in the one-dimensional harmonic trap. Furthermore, we analyze the fingerprints of the attractive contact interactions in the features of the momentum and pair momentum distributions.