Showing papers on "Dynamic Monte Carlo method published in 2003"

Experimental benchmarks of the Monte Carlo code penelope

Abstract: The physical algorithms implemented in the latest release of the general-purpose Monte Carlo code penelope for the simulation of coupled electron–photon transport are briefly described. We discuss the mixed (class II) scheme used to transport intermediate- and high-energy electrons and positrons and, in particular, the approximations adopted to account for the energy dependence of the interaction cross-sections. The reliability of the simulation code, i.e. of the adopted interaction models and tracking algorithms, is analyzed by means of a comprehensive comparison of simulation results with experimental data available from the literature. The present analysis demonstrates that penelope yields a consistent description of electron transport processes in the energy range from a few keV up to about 1 GeV.

Direct calculation of liquid–vapor phase equilibria from transition matrix Monte Carlo simulation

Abstract: An approach for directly determining the liquid–vapor phase equilibrium of a model system at any temperature along the coexistence line is described. The method relies on transition matrix Monte Carlo ideas developed by Fitzgerald, Picard, and Silver [Europhys. Lett. 46, 282 (1999)]. During a Monte Carlo simulation attempted transitions between states along the Markov chain are monitored as opposed to tracking the number of times the chain visits a given state as is done in conventional simulations. Data collection is highly efficient and very precise results are obtained. The method is implemented in both the grand canonical and isothermal–isobaric ensemble. The main result from a simulation conducted at a given temperature is a density probability distribution for a range of densities that includes both liquid and vapor states. Vapor pressures and coexisting densities are calculated in a straightforward manner from the probability distribution. The approach is demonstrated with the Lennard-Jones fluid. Coexistence properties are directly calculated at temperatures spanning from the triple point to the critical point.

Structural modeling of porous carbons: Constrained reverse Monte Carlo method

Abstract: We present a constrained reverse Monte Carlo method for structural modeling of porous carbons. As in the original reverse Monte Carlo method, the procedure is to stochastically change the atomic positions of a system of carbon atoms to minimize the differences between the simulated and the experimental pair correlation functions. However, applying the original reverse Monte Carlo method without further constraints yields nonunique structures for carbons, due to the presence of strong three-body forces. In this respect, the uniqueness theorem of statistical mechanics provides a helpful guide to the design of reverse Monte Carlo methods that give reliable structures. In our method, we constrain the bond angle distribution and the average carbon coordination number to describe the three-body correlations. Using this procedure, we have constructed structural models of two highly disordered porous carbons prepared by pyrolysis of saccharose at two different temperatures. The resulting pair correlation function...

Gaussian Processes to Speed up Hybrid Monte Carlo for Expensive Bayesian Integrals

Abstract: Hybrid Monte Carlo (HMC) is often the method of choice for computing Bayesian integrals that are not analytically tractable. However the success of this method may require a very large number of evaluations of the (un-normalized) posterior and its partial derivatives. In situations where the posterior is computationally costly to evaluate, this may lead to an unacceptable computational load for HMC. I propose to use a Gaussian Process model of the (log of the) posterior for most of the computations required by HMC. Within this scheme only occasional evaluation of the actual posterior is required to guarantee that the samples generated have exactly the desired distribution, even if the GP model is somewhat inaccurate. The method is demonstrated on a 10 dimensional problem, where 200 evaluations suffice for the generation of 100 roughly independent points from the posterior. Thus, the proposed scheme allows Bayesian treatment of models with posteriors that are computationally demanding, such as models involving computer simulation.

A reappraisal of drug release laws using Monte Carlo simulations: the prevalence of the Weibull function.

Abstract: Purpose. To verify the Higuchi law and study the drug release from cylindrical and spherical matrices by means of Monte Carlo computer simulation.

Intrinsic profiles beyond the capillary wave theory: a Monte Carlo study.

Abstract: We develop and test an operational definition of the intrinsic surface for liquid-vapor interfaces. The application to the microscopic configurations along Monte Carlo computer simulations gives the statistical properties of the intrinsic surfaces and the intrinsic density profiles for simple fluid models. The results open a framework of quantitative description to close the gap between the mesoscopic capillary wave theory and the sharpest level of resolution for the intrinsic density distribution, relative to the first atomic layer in the liquid surface, as done in the interpretation of experimental x-ray reflectivity.

Convergence of the Monte Carlo expectation maximization for curved exponential families

Abstract: The Monte Carlo expectation maximization (MCEM) algorithm is a versatile tool for inference in incomplete data models, especially when used in combination with Markov chain Monte Carlo simulation methods. In this contribution, the almost-sure convergence of the MCEM algorithm is established. It is shown, using uniform versions of ergodic theorems for Markov chains, that MCEM converges under weak conditions on the simulation kernel. Practical illustrations are presented, using a hybrid random walk Metropolis Hastings sampler and an independence sampler. The rate of convergence is studied, showing the impact of the simulation schedule on the fluctuation of the parameter estimate at the convergence. A novel averaging procedure is then proposed to reduce the simulation variance and increase the rate of convergence.

Evaluating surface tension using grand-canonical transition-matrix Monte Carlo simulation and finite-size scaling.

Abstract: This Brief Report describes an approach for determining the surface tension of a model system that is applicable over the entire liquid-vapor coexistence region. At the heart of the method is a technique for determining coexistence properties that utilize transition probabilities of attempted Monte Carlo moves during a grand canonical simulation. Finite-size scaling techniques are implemented to determine the infinite system surface tension from a series of finite-size simulations. To demonstrate the method, the surface tension of the Lennard-Jones fluid is determined at temperatures ranging from the triple point to the critical point.

Fast Calculation of the Density of States of a Fluid by Monte Carlo Simulations

Abstract: Two related methods are proposed to calculate the density of states of a fluid from Monte Carlo simulations. In contrast to previous approaches, which require that histograms be accumulated in a stochastic manner, the methods proposed here rely on evaluation of the instantaneous temperature. In the first method, the temperature is calculated from the gradient of the forces. In the second, it is estimated from the kinetic contribution to the total energy. The validity and usefulness of the new approaches are demonstrated by presenting results from simulations of a Lennard-Jones fluid. It is shown that the new methods are considerably faster than previously available techniques.

An improved Monte Carlo method for direct calculation of the density of states

Abstract: We present an efficient Monte Carlo algorithm for determining the density of states which is based on the statistics of transition probabilities between states. By measuring the infinite temperature transition probabilities—that is, the probabilities associated with move proposal only—we are able to extract excellent estimates of the density of states. When this estimator is used in conjunction with a Wang–Landau sampling scheme [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)], we quickly achieve uniform sampling of macrostates (e.g., energies) and systematically refine the calculated density of states. This approach requires only potential energy evaluations, continues to improve the statistical quality of its results as the simulation time is extended, and is applicable to both lattice and continuum systems. We test the algorithm on the Lennard-Jones liquid and demonstrate good statistical convergence properties.

Zero-variance zero-bias principle for observables in quantum Monte Carlo: Application to forces

Abstract: A simple and stable method for computing accurate expectation values of observables with variational Monte Carlo (VMC) or diffusion Monte Carlo (DMC) algorithms is presented. The basic idea consists in replacing the usual “bare” estimator associated with the observable by an improved or “renormalized” estimator. Using this estimator more accurate averages are obtained: Not only the statistical fluctuations are reduced but also the systematic error (bias) associated with the approximate VMC or (fixed-node) DMC probability densities. It is shown that improved estimators obey a zero-variance zero-bias property similar to the usual zero-variance zero-bias property of the energy with the local energy as improved estimator. Using this property improved estimators can be optimized and the resulting accuracy on expectation values may reach the remarkable accuracy obtained for total energies. As an important example, we present the application of our formalism to the computation of forces in molecular systems. Cal...

A quantum correction based on Schrodinger equation applied to Monte Carlo device simulation

Abstract: A full-band Monte Carlo model has been coupled to a Schrodinger equation solver to account for the size quantization effects that occur at heterojunctions, such as the oxide interface in MOS devices. The overall model retains the features of the well-developed semi-classical approach, by treating self-consistently the Schrodinger solution as a correction to the particle-based Monte Carlo. The simulator has been benchmarked by comparing results for MOS capacitors and double gate structures with a self-consistent quantum solution, showing that the proposed approach is efficient and accurate. This quantum correction methodology is extended to device simulation, by accounting for the interplay between confinement and transport through a parameter which we call "transverse" temperature. This approach appears to be valid even for nanometer-scale devices in which nonequilibrium ballistic transport is occurring. We present simulations of a 25-nm MOSFET and compare results obtained with and without the quantum correction.

Accelerated Monte Carlo models to simulate fluorescence spectra from layered tissues

Abstract: Two efficient Monte Carlo models are described, facilitating predictions of complete time-resolved fluorescence spectra from a light-scattering and light-absorbing medium. These are compared with a third, conventional fluorescence Monte Carlo model in terms of accuracy, signal-to-noise statistics, and simulation time. The improved computation efficiency is achieved by means of a convolution technique, justified by the symmetry of the problem. Furthermore, the reciprocity principle for photon paths, employed in one of the accelerated models, is shown to simplify the computations of the distribution of the emitted fluorescence drastically. A so-called white Monte Carlo approach is finally suggested for efficient simulations of one excitation wavelength combined with a wide range of emission wavelengths. The fluorescence is simulated in a purely scattering medium, and the absorption properties are instead taken into account analytically afterward. This approach is applicable to the conventional model as well as to the two accelerated models. Essentially the same absolute values for the fluorescence integrated over the emitting surface and time are obtained for the three models within the accuracy of the simulations. The time-resolved and spatially resolved fluorescence exhibits a slight overestimation at short delay times close to the source corresponding to approximately two grid elements for the accelerated models, as a result of the discretization and the convolution. The improved efficiency is most prominent for the reverse-emission accelerated model, for which the simulation time can be reduced by up to two orders of magnitude.

Evaluating surface tension using grand-canonical transition-matrix Monte Carlo simulation and finite-size scaling

Abstract: This Brief Report describes an approach for determining the surface tension of a model system that is applicable over the entire liquid-vapor coexistence region At the heart of the method is a technique for determining coexistence properties that utilize transition probabilities of attempted Monte Carlo moves during a grand canonical simulation Finite-size scaling techniques are implemented to determine the infinite system surface tension from a series of finite-size simulations To demonstrate the method, the surface tension of the Lennard-Jones fluid is determined at temperatures ranging from the triple point to the critical point

Introduction to quantum Monte Carlo simulations for fermionic systems

Abstract: We tutorially review the determinantal Quantum Monte Carlo method for fermionic systems, using the Hubbard model as a case study. Starting with the basic ingredients of Monte Carlo simulations for classical systems, we introduce aspects such as importance sampling, sources of errors, and finite-size scaling analyses. We then set up the preliminary steps to prepare for the simulations, showing that they are actually carried out by sampling discrete Hubbard-Stratonovich auxiliary fields. In this process the Green’s function emerges as a fundamental tool, since it is used in the updating process, and, at the same time, it is directly related to the quantities probing magnetic, charge, metallic, and superconducting behaviours. We also discuss the as yet unresolved ‘minus-sign problem’, and two ways to stabilize the algorithm at low temperatures.

A Monte Carlo program for quantitative electron-induced X-ray analysis of individual particles.

Abstract: A versatile Monte Carlo program for quantitative particle analysis in electron probe X-ray microanalysis is presented. The program includes routines for simulating electron-solid interactions in microparticles lying on a flat surface and calculating the generated X-ray signal. Simulation of the whole X-ray spectrum as well as φ(z) curves is possible. The most important facility of the program is the reverse Monte Carlo quantification of the chemical composition of microparticles, including low-Z elements, such as C, N, O, and F. This quantification method is based on the combination of a single scattering Monte Carlo simulation and a robust successive approximation. An iteration procedure is employed; in each iteration step, the Monte Carlo simulation program calculates characteristic X-ray intensities, and a new set of concentration values for chemical elements in the particle is determined. When the simulated X-ray intensities converge to the measured ones, the input values of elemental concentrations u...

A Wigner function-based quantum ensemble Monte Carlo study of a resonant tunneling diode

Abstract: We present results of resonant tunneling diode operation achieved from a particle-based quantum ensemble Monte Carlo (EMC) simulation that is based on the Wigner distribution function (WDF). Methods of including the Wigner potential into the EMC, to incorporate natural quantum phenomena, via a particle property we call the affinity are discussed. Dissipation is included via normal Monte Carlo procedures and the solution is coupled to a Poisson solver to achieve fully selfconsistent results.

A Monte Carlo Hyper-Heuristic To Optimise Component Placement Sequencing For Multi Head Placement Machine

Abstract: In this paper we introduce a Monte Carlo based hyper-heuristic. The Monte Carlo hyper-heuristic manages a set of low level heuristics (in this case just simple 2-opt swaps but they could be any other heuristics). Each of the low level heuristics is responsible for creating a unique neighbour that may be impossible to create by the other low level heuristics. On each iteration, the Monte Carlo hyper heuristic randomly calls a low level heuristic. The new solution returned by the low level heuristic will be accepted based on the Monte Carlo acceptance criteria. The Monte Carlo acceptance criteria always accept an improved solution. Worse solutions will be accepted with a certain probability, which decreases with worse solutions, in order to escape local minima. We develop three hyper-heuristics based on a Monte Carlo method, these being Linear Monte Carlo Exponential Monte Carlo and Exponential Monte Carlo with counter. We also investigate four other hyper- heuristics to examine their performance and for comparative purposes. To demonstrate our approach we employ these hyper-heuristics to optimise component placement sequencing in order to improve the efficiency of the multi head placement machine. Experimental results show that the Exponential Monte Carlo hyper- heuristic is superior to the other hyper-heuristics and is superior to a choice function hyper-heuristic reported in earlier work.

Monte Carlo simulation of the energy loss of low-energy electrons in liquid water.

Abstract: A Monte Carlo code that performs detailed (i.e. event-by-event) simulation of the transport and energy loss of low-energy electrons (~50–10000 eV) in water in the liquid phase is presented. The inelastic model for energy loss is based on a semi-empirical dielectric-response function for the valence-shells of the liquid whereas an exchange corrected semi-classical formula was used for K-shell ionization. Following a methodology widely used for the vapour phase, we succeeded in parametrizing the dielectric cross-sections of the liquid in accordance with the Bethe asymptote, thus providing a unified approach for both phases of water and greatly facilitating the computations. Born-corrections at lower energies have been implemented in terms of a second-order perturbation term with a simple Coulomb-field correction and the use of a Mott-type exchange modification. Angular deflections were determined by empirical schemes established from vapour data. Electron tracks generated by the code were used to calculate energy- and interaction-point-kernel distributions at low electron energies in liquid water. The effect of various model assumptions (e.g., dispersion, Born-corrections, phase) on both the single-collision and slowing-down distributions is examined.

Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions

Abstract: We present results from Monte Carlo simulations of the one-dimensional Ising spin glass with power-law interactions at low temperature, using the parallel tempering Monte Carlo method. For a set of parameters where the long-range part of the interaction is relevant, we find evidence for large-scale dropletlike excitations with an energy that is independent of system size, consistent with replica symmetry breaking. We also perform zero-temperature defect energy calculations for a range of parameters and find a stiffness exponent for domain walls in reasonable but by no means perfect agreement with analytic predictions.

Monte Carlo backbone sampling for polypeptides with variable bond angles and dihedral angles using concerted rotations and a Gaussian bias

Abstract: An efficient concerted rotation algorithm for use in Monte Carlo statistical mechanics simulations of polypeptides is reported that includes flexible bond and dihedral angles. A Gaussian bias is applied with driver bond and dihedral angles to optimize the sampling efficiency. Jacobian weighting is required in the Metropolis test to correct for imbalances in resultant transition probabilities. Testing of the methodology includes Monte Carlo simulations for polyalanines with 8–14 residues and a 36-residue protein as well as a search to find the lowest-energy conformer of the pentapeptide Met-enkephalin. The results demonstrate the formal correctness and efficiency of the method.

Particle aggregation with simultaneous surface growth.

Abstract: Particle aggregation with simultaneous surface growth was modeled using a dynamic Monte Carlo method. The Monte Carlo algorithm begins in the particle inception zone and constructs aggregates via ensemble-averaged collisions between spheres and deposition of gaseous species on the sphere surfaces. Simulations were conducted using four scenarios. The first, referred to as scenario 0, is used as a benchmark and simulates aggregation in the absence of surface growth. Scenario 1 forces all balls to grow at a uniform rate while scenario 2 only permits them to grow once they have collided and stuck to each other. The last one is a test scenario constructed to confirm conclusions drawn from scenarios 0-2. The transition between the coalescent and the fully developed fractal aggregation regimes is investigated using shape descriptors to quantify particle geometry. They are used to define the transition between the coalescent and fractal growth regimes. The simulations demonstrate that the morphology of aggregating particles is intimately related to both the surface deposition and particle nucleation rates.

Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems.

Abstract: We apply the multicanonical Monte Carlo (MMC) method to compute the probability distribution of the received voltage in a chirped return-to-zero system. When computing the probabilities of very rare events, the MMC technique greatly enhances the efficiency of Monte Carlo simulations by biasing the noise realizations. Our results agree with the covariance matrix method over 20 orders of magnitude. The MMC method can be regarded as iterative importance sampling that automatically converges toward the optimal bias so that it requires less a priori knowledge of the simulated system than importance sampling requires. A second advantage is that the merging of different regions of a probability distribution function to obtain the entire function is not necessary in many cases.