Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study

In this paper, we report a fully ab initio variational Monte Carlo study of the linear and periodic chain of hydrogen atoms, a prototype system providing the simplest example of strong electronic correlation in low dimensions. In particular, we prove that numerical accuracy comparable to that of benchmark density-matrix renormalization-group calculations can be achieved by using a highly correlated Jastrow-antisymmetrized geminal power variational wave function. Furthermore, by using the so-called "modern theory of polarization" and by studying the spin-spin and dimer-dimer correlations functions, we have characterized in detail the crossover between the weakly and strongly correlated regimes of this atomic chain. Our results show that variational Monte Carlo provides an accurate and flexible alternative to highly correlated methods of quantum chemistry which, at variance with these methods, can be also applied to a strongly correlated solid in low dimensions close to a crossover or a phase transition.

Quantum annealing of an ising spin-glass by Green's function Monte Carlo

We present an implementation of quantum annealing (QA) via lattice Green's function Monte Carlo (GFMC), focusing on its application to the Ising spin glass in transverse field. In particular, we study whether or not such a method is more effective than the path-integral Monte Carlo- (PIMC) based QA, as well as classical simulated annealing (CA), previously tested on the same optimization problem. We identify the issue of importance sampling, i.e., the necessity of possessing reasonably good (variational) trial wave functions, as the key point of the algorithm. We performed GFMC-QA runs using such a Boltzmann-type trial wave function, finding results for the residual energies that are qualitatively similar to those of CA (but at a much larger computational cost), and definitely worse than PIMC-QA. We conclude that, at present, without a serious effort in constructing reliable importance sampling variational wave functions for a quantum glass, GFMC-QA is not a true competitor of PIMC-QA.

Monte Carlo simulation of cluster growth in surface defects induced by the tip of a scanning tunnelling microscope

First steps are taken to model the electrochemical deposition of metals in nanometer-sized cavities. In the present work, the electrochemical deposition of Cu atoms in nanometer-sized holes dug on Au(111) is investigated through Monte Carlo simulations using the embedded atom method to represent particle interactions. By sweeping the chemical potential of Cu, a cluster is allowed to grow within the hole rising four atomic layers above the surface. Its lateral extension remains confined to the area defined by the borders of the original defect. (C) 2004 Elsevier B.V. All rights reserved.

Monte Carlo simulation of properties of monolayers and metal islands adsorbed on metallic (111) surfaces

To obtain the surface stress changes due to the adsorption of metal monolayers onto metallic surfaces, a new model derived from thermodynamic considerations is presented. Such a model is based on continuum Monte Carlo simulations with embedded atom method potentials in the canonical ensemble, and it is extended to consider the behavior on different islands adsorbed onto (111) substrate surfaces. Homoepitaxial and heteroepitaxial systems are studied. Pseudomorphic growth is not observed for small metal islands with considerable positive misfit with the substrate. Instead, the islands become compressed upon increase of their size. A simple model is proposed to interpolate between the misfits of atoms in small islands and the pseudomorphic behavior of the monolayer.

Anisotropic seismic inversion using a multigrid Monte Carlo approach

We propose a new approach for the inversion of anisotropic P-wave data based on Monte Carlo methods combined with a multigrid approach. Simulated annealing facilitates objective minimization of the functional characterizing the misfit between observed and predicted traveltimes, as controlled by the Thomsen anisotropy parameters (epsilon, delta). Cycling between finer and coarser grids enhances the computational efficiency of the inversion process, thus accelerating the convergence of the solution while acting as a regularization technique of the inverse problem. Multigrid perturbation samples the probability density function without the requirements for the user to adjust tuning parameters. This increases the probability that the preferred global, rather than a poor local, minimum is attained. Undertaking multigrid refinement and Monte Carlo search in parallel produces more robust convergence than does the initially more intuitive approach of completing them sequentially. We demonstrate the usefulness of the new multigrid Monte Carlo (MGMC) scheme by applying it to (a) synthetic, noise-contaminated data reflecting an isotropic subsurface of constant slowness, horizontally layered geologic media and discrete subsurface anomalies; and (b) a crosshole seismic data set acquired by previous authors at the Reskajeage test site in Cornwall, UK. Inverted distributions of slowness (s) and the Thomson anisotropy parameters (epsilon, delta) compare favourably with those obtained previously using a popular matrix-based method. Reconstruction of the Thomsen epsilon parameter is particularly robust compared to that of slowness and the Thomsen delta parameter, even in the face of complex subsurface anomalies. The Thomsen epsilon and delta parameters have enhanced sensitivities to bulk-fabric and fracture-based anisotropies in the TI medium at Reskajeage. Because reconstruction of slowness (s) is intimately linked to that epsilon and delta in the MGMC scheme, inverted images of phase velocity reflect the integrated effects of these two modes of anisotropy. The new MGMC technique thus promises to facilitate rapid inversion of crosshole P-wave data for seismic slownesses and the Thomsen anisotropy parameters, with minimal user input in the inversion process.

Nonrigid Structure-From-Motion From 2-D Images Using Markov Chain Monte Carlo

In this paper we present a new method for simultaneously determining three dimensional (3-D) shape and motion of a non-rigid object from uncalibrated two dimensional (2- D) images without assuming the distribution characteristics. A non-rigid motion can be treated as a combination of a rigid rotation and a non-rigid deformation. To seek accurate recovery of deformable structures, we estimate the probability distribution function of the corresponding features through random sampling, incorporating an established probabilistic model. The fitting between the observation and the projection of the estimated 3-D structure will be evaluated using a Markov chain Monte Carlo based expectation maximisation algorithm. Applications of the proposed method to both synthetic and real image sequences are demonstrated with promising results.

A Monte Carlo model of DNA double-strand break clustering and rejoining kinetics for the analysis of pulsed-field gel electrophoresis data

In studies of radiation-induced DNA fragmentation and repair, analytical models may provide rapid and easy-to-use methods to test simple hypotheses regarding the breakage and rejoining mechanisms involved. The random breakage model, according to which lesions are distributed uniformly and independently of each other along the DNA, has been the model most used to describe spatial distribution of radiation-induced DNA damage. Recently several mechanistic approaches have been proposed that model clustered damage to DNA. In general, such approaches focus on the study of initial radiation-induced DNA damage and repair, without considering the effects of additional (unwanted and unavoidable) fragmentation that may take place during the experimental procedures. While most approaches, including measurement of total DNA mass below a specified value, allow for the occurrence of background experimental damage by means of simple subtractive procedures, a more detailed analysis of DNA fragmentation necessitates a more accurate treatment. We have developed a new, relatively simple model of DNA breakage and the resulting rejoining kinetics of broken fragments. Initial radiation-induced DNA damage is simulated using a clustered breakage approach, with three free parameters: the number of independently located clusters, each containing several DNA double-strand breaks (DSBs), the average number of DSBs within a cluster (multiplicity of the cluster), and the maximum allowed radius within which DSBs belonging to the same cluster are distributed. Random breakage is simulated as a special case of the DSB clustering procedure. When the model is applied to the analysis of DNA fragmentation as measured with pulsed-field gel electrophoresis (PFGE), the hypothesis that DSBs in proximity rejoin at a different rate from that of sparse isolated breaks can be tested, since the kinetics of rejoining of fragments of varying size may be followed by means of computer simulations. The problem of how to account for background damage from experimental handling is also carefully considered. We have shown that the conventional procedure of subtracting the background damage from the experimental data may lead to erroneous conclusions during the analysis of both initial fragmentation and DSB rejoining. Despite its relative simplicity, the method presented allows both the quantitative and qualitative description of radiation-induced DNA fragmentation and subsequent rejoining of double-stranded DNA fragments. (C) 2004 by Radiation Research Society.

Monte Carlo radiation hydrodynamics:Methods, tests and application to Type Ia supernova ejecta

In astrophysical systems, radiation-matter interactions are important in transferring energy and momentum between the radiation field and the surrounding material. This coupling often makes it necessary to consider the role of radiation when modelling the dynamics of astrophysical fluids. During the last few years, there have been rapid developments in the use of Monte Carlo methods for numerical radiative transfer simulations. Here, we present an approach to radiation hydrodynamics that is based on coupling Monte Carlo radiative transfer techniques with finite-volume hydrodynamical methods in an operator-split manner. In particular, we adopt an indivisible packet formalism to discretize the radiation field into an ensemble of Monte Carlo packets and employ volume-based estimators to reconstruct the radiation field characteristics. In this paper the numerical tools of this method are presented and their accuracy is verified in a series of test calculations. Finally, as a practical example, we use our approach to study the influence of the radiation-matter coupling on the homologous expansion phase and the bolometric light curve of Type Ia supernova explosions. © 2012 The Authors Monthly Notices of the Royal Astronomical Society © 2012 RAS.

Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials

A numerical method is developed to simulate complex two-dimensional crack propagation in quasi-brittle materials considering random heterogeneous fracture properties. Potential cracks are represented by pre-inserted cohesive elements with tension and shear softening constitutive laws modelled by spatially varying Weibull random fields. Monte Carlo simulations of a concrete specimen under uni-axial tension were carried out with extensive investigation of the effects of important numerical algorithms and material properties on numerical efficiency and stability, crack propagation processes and load-carrying capacities. It was found that the homogeneous model led to incorrect crack patterns and load–displacement curves with strong mesh-dependence, whereas the heterogeneous model predicted realistic, complicated fracture processes and load-carrying capacity of little mesh-dependence. Increasing the variance of the tensile strength random fields with increased heterogeneity led to reduction in the mean peak load and increase in the standard deviation. The developed method provides a simple but effective tool for assessment of structural reliability and calculation of characteristic material strength for structural design.

Root Cause Analysis by a Combined Sparse Classification and Monte Carlo Approach

Classification methods with embedded feature selection capability are very appealing for the analysis of complex processes since they allow the analysis of root causes even when the number of input variables is high. In this work, we investigate the performance of three techniques for classification within a Monte Carlo strategy with the aim of root cause analysis. We consider the naive bayes classifier and the logistic regression model with two different implementations for controlling model complexity, namely, a LASSO-like implementation with a L1 norm regularization and a fully Bayesian implementation of the logistic model, the so called relevance vector machine. Several challenges can arise when estimating such models mainly linked to the characteristics of the data: a large number of input variables, high correlation among subsets of variables, the situation where the number of variables is higher than the number of available data points and the case of unbalanced datasets. Using an ecological and a semiconductor manufacturing dataset, we show advantages and drawbacks of each method, highlighting the superior performance in term of classification accuracy for the relevance vector machine with respect to the other classifiers. Moreover, we show how the combination of the proposed techniques and the Monte Carlo approach can be used to get more robust insights into the problem under analysis when faced with challenging modelling conditions.

Self-consistent modelling of line-driven hot-star winds with Monte Carlo radiation hydrodynamics

Radiative pressure exerted by line interactions is a prominent driver of outflows in astrophysical systems, being at work in the outflows emerging from hot stars or from the accretion discs of cataclysmic variables, massive young stars and active galactic nuclei. In this work, a new radiation hydrodynamical approach to model line-driven hot-star winds is presented. By coupling a Monte Carlo radiative transfer scheme with a finite volume fluid dynamical method, line-driven mass outflows may be modelled self-consistently, benefiting from the advantages of Monte Carlo techniques in treating multiline effects, such as multiple scatterings, and in dealing with arbitrary multidimensional configurations. In this work, we introduce our approach in detail by highlighting the key numerical techniques and verifying their operation in a number of simplified applications, specifically in a series of self-consistent, one-dimensional, Sobolev-type, hot-star wind calculations. The utility and accuracy of our approach are demonstrated by comparing the obtained results with the predictions of various formulations of the so-called CAK theory and by confronting the calculations with modern sophisticated techniques of predicting the wind structure. Using these calculations, we also point out some useful diagnostic capabilities our approach provides. Finally, we discuss some of the current limitations of our method, some possible extensions and potential future applications.

Density functional and Monte Carlo studies of sulfur. I. Structure and bonding in S-n rings and chains (n=2-18) (vol 118, pg 9257, 2003)

Density functional calculations have been performed for ring isomers of sulfur with up to 18 atoms, and for chains with up to ten atoms. There are many isomers of both types, and the calculations predict the existence of new forms. Larger rings and chains are very flexible, with numerous local energy minima. Apart from a small, but consistent overestimate in the bond lengths, the results reproduce experimental structures where known. Calculations are also performed on the energy surfaces of S8 rings, on the interaction between a pair of such rings, and the reaction between one S8 ring and the triplet diradical S8 chain. The results for potential energies, vibrational frequencies, and reaction mechanisms in sulfur rings and chains provide essential ingredients for Monte Carlo simulations of the liquid–liquid phase transition. The results of these simulations will be presented in Part II.

Density functional and Monte Carlo studies of sulfur. II. Equilibrium polymerization of the liquid phase

The equilibrium polymerization of sulfur is investigated by Monte Carlo simulations. The potential energy model is based on density functional results for the cohesive energy, structural, and vibrational properties as well as reactivity of sulfur rings and chains [Part I, J. Chem. Phys. 118, 9257 (2003)]. Liquid samples of 2048 atoms are simulated at temperatures 450less than or equal toTless than or equal to850 K and P=0 starting from monodisperse S-8 molecular compositions. Thermally activated bond breaking processes lead to an equilibrium population of unsaturated atoms that can change the local pattern of covalent bonds and allow the system to approach equilibrium. The concentration of unsaturated atoms and the kinetics of bond interchanges is determined by the energy DeltaE(b) required to break a covalent bond. Equilibrium with respect to the bond distribution is achieved for 15less than or equal toDeltaE(b)less than or equal to21 kcal/mol over a wide temperature range (Tgreater than or equal to450 K), within which polymerization occurs readily, with entropy from the bond distribution overcompensating the increase in enthalpy. There is a maximum in the polymerized fraction at temperature T-max that depends on DeltaE(b). This fraction decreases at higher temperature because broken bonds and short chains proliferate and, for Tless than or equal toT(max), because entropy is less important than enthalpy. The molecular size distribution is described well by a Zimm-Schulz function, plus an isolated peak for S-8. Large molecules are almost exclusively open chains. Rings tend to have fewer than 24 atoms, and only S-8 is present in significant concentrations at all T. The T dependence of the density and the dependence of polymerization fraction and degree on DeltaE(b) give estimates of the polymerization temperature T-f=450+/-20 K. (C) 2003 American Institute of Physics.