Showing papers on "Dynamic Monte Carlo method published in 2013"

On the inner workings of Monte Carlo codes

Abstract: We review state-of-the-art Monte Carlo (MC) techniques for computing fluid coexistence properties (Gibbs simulations) and adsorption simulations in nanoporous materials such as zeolites and metal–o...

MCCCS Towhee: a tool for Monte Carlo molecular simulation

Abstract: The history of the Monte Carlo for complex chemical systems Towhee open source Monte Carlo molecular simulation tool is discussed. A proof is given that the Widom insertion method for computing the...

Mean Field Simulation for Monte Carlo Integration

Abstract: In the last three decades, there has been a dramatic increase in the use of interacting particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced particle algorithms include nonlinear interacting jump diffusions; quantum, diffusion, and resampled Monte Carlo methods; Feynman-Kac particle models; genetic and evolutionary algorithms; sequential Monte Carlo methods; adaptive and interacting Markov chain Monte Carlo models; bootstrapping methods; ensemble Kalman filters; and interacting particle filters.

Monte Carlo methods in Materials Studio

Abstract: We survey the use of the Monte Carlo method within the Materials Studio application, which integrates a large number of modules for molecular simulation. Several of these modules work by generating...

Hard-disk equation of state: first-order liquid-hexatic transition in two dimensions with three simulation methods.

Abstract: We report large-scale computer simulations of the hard-disk system at high densities in the region of the melting transition. Our simulations reproduce the equation of state, previously obtained using the event-chain Monte Carlo algorithm, with a massively parallel implementation of the local Monte Carlo method and with event-driven molecular dynamics. We analyze the relative performance of these simulation methods to sample configuration space and approach equilibrium. Our results confirm the first-order nature of the melting phase transition in hard disks. Phase coexistence is visualized for individual configurations via the orientational order parameter field. The analysis of positional order confirms the existence of the hexatic phase.

A warp-speed method for conducting monte carlo experiments involving bootstrap estimators

Abstract: We analyze fast procedures for conducting Monte Carlo experiments involving bootstrap estimators, providing formal results establishing the properties of these methods under general conditions.

Using perturbatively selected configuration interaction in quantum Monte Carlo calculations

Abstract: Defining accurate and compact trial wavefunctions leading to small statistical and fixed-node errors in quantum Monte Carlo (QMC) calculations is still a challenging problem. Here we propose to mak...

Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas

Abstract: We have studied the spin-polarized three-dimensional homogeneous electron gas using the diffusion quantum Monte Carlo method, with trial wave functions including backflow and three-body correlations in the Jastrow factor, and we have used twist averaging to reduce finite-size effects. Calculations of the pair-correlation function, including the on-top pair density, as well as the structure factor and the total energy, are reported for systems of 118 electrons in the density range rs=0.5–20 a.u., and for spin polarizations of 0, 0.34, 0.66, and 1. We consider the spin resolution of the pair-correlation function and structure factor, and the energy of spin polarization. We show that a control variate method can reduce the variance when twist averaging, and we have achieved higher accuracy and lower noise than earlier quantum Monte Carlo studies.

Quantum Monte Carlo applied to solids

Abstract: We apply diffusion quantum Monte Carlo to a broad set of solids, benchmarking the method by comparing bulk structural properties (equilibrium volume and bulk modulus) to experiment and density functional theory (DFT) based theories. The test set includes materials with many different types of binding including ionic, metallic, covalent, and van der Waals. We show that, on average, the accuracy is comparable to or better than that of DFT when using the new generation of functionals, including one hybrid functional and two dispersion corrected functionals. The excellent performance of quantum Monte Carlo on solids is promising for its application to heterogeneous systems and high-pressure/high-density conditions. Important to the results here is the application of a consistent procedure with regards to the several approximations that are made, such as finite-size corrections and pseudopotential approximations. This test set allows for any improvements in these methods to be judged in a systematic way.

Integral formulation of null-collision Monte Carlo algorithms

Abstract: At the kinetic level, the meaning of null-collisions is straightforward: they correspond to pure-forward scattering events. We here discuss their technical significance in integral terms. We first consider a most standard null-collision Monte Carlo algorithm and show how it can be rigorously justified starting from a Fredholm equivalent to the radiative transfer equation. Doing so, we also prove that null-collision algorithms can be slightly modified so that they deal with unexpected occurrences of negative values of the null-collision coefficient (when the upper bound of the heterogeneous extinction coefficient is nonstrict). We then describe technically, in full details, the resulting algorithm, when applied to the evaluation of the local net-power density within a bounded, heterogeneous, multiple scattering and emitting/absorbing medium. The corresponding integral formulation is then explored theoretically in order to distinguish the statistical significance of introducing null-collisions from that of the integral-structure underlying modification.

Photon beam diffusion: a hybrid Monte Carlo method for subsurface scattering

Abstract: We present photon beam diffusion, an efficient numerical method for accurately rendering translucent materials. Our approach interprets incident light as a continuous beam of photons inside the material. Numerically integrating diffusion from such extended sources has long been assumed computationally prohibitive, leading to the ubiquitous single-depth dipole approximation and the recent analytic sum-of-Gaussians approach employed by Quantized Diffusion. In this paper, we show that numerical integration of the extended beam is not only feasible, but provides increased speed, flexibility, numerical stability, and ease of implementation, while retaining the benefits of previous approaches. We leverage the improved diffusion model, but propose an efficient and numerically stable Monte Carlo integration scheme that gives equivalent results using only 3--5 samples instead of 20--60 Gaussians as in previous work. Our method can account for finite and multi-layer materials, and additionally supports directional incident effects at surfaces. We also propose a novel diffuse exact single-scattering term which can be integrated in tandem with the multi-scattering approximation. Our numerical approach furthermore allows us to easily correct inaccuracies of the diffusion model and even combine it with more general Monte Carlo rendering algorithms. We provide practical details necessary for efficient implementation, and demonstrate the versatility of our technique by incorporating it on top of several rendering algorithms in both research and production rendering systems.

Improvements and considerations for size distribution retrieval from small-angle scattering data by Monte Carlo methods.

Abstract: Monte Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve form-free particle size distributions from small-angle scattering patterns of non-interacting low-concentration scatterers such as particles in solution or precipitates in metals Improvements are presented to existing MC methods, such as a non-ambiguous convergence criterion, nonlinear scaling of contributions to match their observability in a scattering measurement, and a method for estimating the minimum visibility threshold and uncertainties on the resulting size distributions

Adjoint-Based k-Eigenvalue Sensitivity Coefficients to Nuclear Data Using Continuous-Energy Monte Carlo

Abstract: A continuous-energy Monte Carlo method is developed to compute adjoint-based k-eigenvalue sensitivity coefficients with respect to nuclear data. The method is implemented into MCNP6 and is based upon similar methodologies used to compute other adjoint-weighted quantities. The Monte Carlo tallies employed are explained. Verification of the method is performed by comparing results to analytic solutions, direct density perturbations, and those from other software packages such as TSUNAMI-3D and MONK. Results of analytic solutions agree within a few tenths of a percent. Direct density perturbations and comparisons with other software generally agree within a few percent.

DL_MONTE: a general purpose program for parallel Monte Carlo simulation

Abstract: Monte Carlo (MC) represents a powerful simulation tool that can be usefully applied to calculating thermodynamic data. However, such codes are normally bespoke for a particular problem and not widely applicable. In this paper, we report a new flexible and versatile MC code called DL_MONTE, which builds on the highly successful DL_POLY molecular dynamics code to allow the treatment of polymers, minerals, semiconductors and metals in a range of applications on both workstations and highly parallel supercomputers. In addition, to describe its features, we used a recent work to model the phase diagrams of mixed metal oxide nanoparticles using MgO/MnO as an illustration, adsorption of water at the MgO surface and, finally, the adsorption isotherms of CO2 in different microporous zeolites. The results demonstrate the flexibility of the methodology and how semi-grand and grand canonical MC can be readily applied.

Combining molecular dynamics with Monte Carlo simulations: implementations and applications

Abstract: In this contribution, we present an overview of the various techniques for combining atomistic molecular dynamics with Monte Carlo simulations, mainly in the context of condensed matter systems, as well as a brief summary of the main accelerated dynamics techniques. Special attention is given to the force bias Monte Carlo technique and its combination with molecular dynamics, in view of promising recent developments, including a definable timescale. Various examples of the application of combined molecular dynamics / Monte Carlo simulations are given, in order to demonstrate the enhanced simulation efficiency with respect to either pure molecular dynamics or Monte Carlo.

Dynamic Monte Carlo Method for Nuclear Reactor Kinetics Calculations

Abstract: In nuclear reactor physics, deterministic and hybrid calculation methods dominate the field of transient analysis. This implies that important safety assessments are subject to many approximations, which are needed by these methods. This paper proposes the Dynamic Monte Carlo method (Dynamic MC), which solves the coupled Boltzmann and kinetic equations with exact geometry and continuous energy, using only Monte Carlo techniques.For Dynamic MC a number of new techniques are developed, e.g., precursor tracking, forced decay for precursors, and the branchless method. Also, the particle source of the simulation has to be determined differently from what is current standard Monte Carlo practice, and the simulation scheme is adapted.A few example cases are simulated, demonstrating the effectiveness of Dynamic MC. The sample cases vary from simple homogeneous systems to full fuel assemblies with an asymmetric flux profile during the transient. Since Dynamic MC is implemented in the general-purpose Monte ...

Monte Carlo Simulations Applied to Uncertainty in Measurement

Abstract: Metrology is the science that covers all theoretical and practical concepts involved in a measurement, which when applied are able to provide results with appropriate accuracy and metrological reliability to a given measurement process. In any area in which a decision is made from a measurement result, all attention is critical to the metrological concepts in‐ volved. For example, the control panels of an aircraft are composed by several instruments that must be calibrated to perform measurements with metrological traceability and reliabil‐ ity, influencing the decisions that the pilot will make during the flight. In this way, it is clear that concepts involving metrology and reliability of measurements must be well established and harmonized to provide reliability and quality for products and services.

A local superbasin kinetic Monte Carlo method

Abstract: We present a local superbasin kinetic Monte Carlo (LSKMC) method that efficiently treats multiple-time-scale problems in kinetic Monte Carlo (KMC). The method is designed to solve the small-barrier problem created by groups of recurrent free-energy minima connected by low free-energy barriers and separated from the full phase space of the system by high barriers. We propose an algorithm to detect, on the fly, groups of recurrent free-energy minima connected by low free-energy barriers and to consolidate them into “superbasins,” which we treat with rate equations and/or absorbing Markov chains. We discuss various issues involved with implementing LSKMC simulations that contain local superbasins and non-superbasin events concurrently. These issues include the time distribution of superbasin escapes and interactions between superbasin and non-superbasin states. The LSKMC method is exact, as it introduces no new approximations into conventional KMC simulations. We demonstrate various aspects of LSKMC in several examples, which indicate that significant increases in computational efficiency can be achieved using this method.

A New Insight into the Formation of Polymer Networks: A Kinetic Monte Carlo Simulation of the Cross-Linking Polymerization of S/DVB

Abstract: The kinetic Monte Carlo simulation was used to predict the characteristics of the polymer network formation during pre- and postgelation regimes of free-radical cross-linking copolymerization. The simulation naturally considers the presence of multiradicals, primary and secondary cyclization with no preassumptions. The simulation was first validated in the pregel regime by comparing the microstructure with that given by a mean-field model. The Monte Carlo simulation was then used to predict the kinetics and development of the polymer microstructure of the sol and gel fractions up to full conversion, including the complete molecular weight distribution, cross-linking and pendant double bond densities, primary and secondary cyclization and the molecular weight distribution between cross-linking points. The simulation also allows studying the presence and evolution of multiradicals along the polymerization.

Strongly correlated systems : numerical methods

Abstract: 1. Ground State and Finite Temperature Lanczos Method.- 2. The Density Matrix Renormalization Group.- 3. Matrix Product State Algorithms: DMRG, TEBD and Relatives.- 4. Quantum Criticality with the Multi-scale Entanglement Renormalization Ansatz.- 5. The Time-Dependent Density Matrix Renormalization Groupd.- 6. Loop Algorithm.- 7. Stochastic Series Expansion Quantum Monte Carlo.- 8. Variatonal Monte Carlo and Markov Chanis for Computational Physics.- 9. Coupled Cluster Theories for Strongly Correlated Molecular Systems.- 10. Diagrammatic Monte Carlo and Worm Algorithm Techniques.- 11. Fermionic and Continuous Time Quantum Monte Carlo.

Multilevel Monte Carlo Methods for Stochastic Elliptic Multiscale PDEs

Abstract: In this paper Monte Carlo finite element approximations for elliptic homogenization problems with random coefficients, which oscillate on $n\in\mathbb{N}$ a priori known, separated microscopic length scales, are considered. The convergence of multilevel Monte Carlo finite element discretizations is analyzed. In particular, it is considered that the multilevel finite element discretization resolves the finest physical length scale, but the coarsest finite element mesh does not, so that the so-called resonance case occurs at intermediate multilevel Monte Carlo sampling levels. It is shown that for first order finite elements in two space dimensions, the multilevel Monte Carlo finite element method converges at the same rate as the corresponding single-level Monte Carlo finite element method, despite the majority of samples being underresolved in the multilevel Monte Carlo finite element estimator. It is proved that switching to a hierarchic multiscale finite element method such as the finite element heterog...

Molecular properties by Quantum Monte Carlo: an investigation on the role of the wave function ansatz and the basis set in the water molecule

Abstract: Quantum Monte Carlo methods are accurate and promising many body techniques for electronic structure calculations which, in the last years, are encountering a growing interest thanks to their favorable scaling with the system size and their efficient parallelization, particularly suited for the modern high performance computing facilities. The ansatz of the wave function and its variational flexibility are crucial points for both the accurate description of molecular properties and the capabilities of the method to tackle large systems. In this paper, we extensively analyze, using different variational ansatzes, several properties of the water molecule, namely: the total energy, the dipole and quadrupole momenta, the ionization and atomization energies, the equilibrium configuration, and the harmonic and fundamental frequencies of vibration. The investigation mainly focuses on variational Monte Carlo calculations, although several lattice regularized diffusion Monte Carlo calculations are also reported. Through a systematic study, we provide a useful guide to the choice of the wave function, the pseudo potential, and the basis set for QMC calculations. We also introduce a new strategy for the definition of the atomic orbitals involved in the Jastrow - Antisymmetrised Geminal power wave function, in order to drastically reduce the number of variational parameters. This scheme significantly improves the efficiency of QMC energy minimization in case of large basis sets.

Mean exit times and the multilevel Monte Carlo method

Abstract: Numerical methods for stochastic differential equations are relatively inefficient when used to ap- proximate mean exit times. In particular, although the basic Euler-Maruyama method has weak order equal to one for approximating the expected value of the solution, the order reduces to one half when it is used in a straightforward manner to approximate the mean value of a (stopped) exit time. Consequently, the widely used standard approach of combining an Euler-Maruyama discretization with a Monte Carlo simulation leads to a computationally expensive procedure. In this work, we show that the multilevel approach developed by Giles (Oper. Res., 56 (2008), pp. 607-617) can be adapted to the mean exit time context. In order to justify the algorithm, we analyze the strong error of the discretization method in terms of its ability to approximate the exit time. We then show that the resulting multilevel algorithm improves the expected computational complexity by an order of magnitude, in terms of the required accuracy. Numerical results are provided to illustrate the analysis.

Use of the Grand Canonical Transition-Matrix Monte Carlo Method to Model Gas Adsorption in Porous Materials

Abstract: We present grand canonical transition-matrix Monte Carlo (GC-TMMC) as an efficient method for simulating gas adsorption processes, with particular emphasis on subcritical gas adsorption in which capillary phase transitions are present. As in other applications of TMMC, the goal of the simulation is to compute a particle number probability distribution (PNPD), from which thermophysical properties of the system can be computed. The key advantage of GC-TMMC is that, by appropriate use of histogram reweighting, one can generate an entire adsorption isotherm, including those with hysteresis loops, from the PNPD generated by a single GC-TMMC simulation. We discuss how to determine various thermophysical properties of an adsorptive system from the PNPD, including the identification of capillary phases and capillary phase transitions, the equilibrium phase transition, other free energies, and the heat of adsorption. To demonstrate the utility of GC-TMMC for studies of adsorption, we apply the method to various sy...

A new adaptive importance sampling Monte Carlo method for structural reliability

Abstract: Monte Carlo simulation is a useful method for reliability analysis. But in Monte Carlo, a large number of simulations are required to assess small failure probabilities. Many methods, such as Importance sampling, have been proposed to reduce the computational time. In this paper, a new importance sampling Monte Carlo method is proposed that reduces the numbers of calculation of the limit state function. On the other hand, the proposed algorithm does not need the knowledge about the position of the design point or the shape of the limit state function. The key-idea of the proposed algorithm is that the mean of sampling density function is changed throughout the simulation. In fact, in random point generating process each point with lower absolute value of limit state function and nearer distance from space center is considered the mean of the sampling density function. Based on this, the centralization of the sampling will be on the important area.