Showing papers on "Dynamic Monte Carlo method published in 2010"

Monte Carlo Simulation of Single Event Effects

Abstract: In this paper, we describe a Monte Carlo approach for estimating the frequency and character of single event effects based on a combination of physical modeling of discrete radiation events, device simulations to estimate charge transport and collection, and circuit simulations to determine the effect of the collected charge. A mathematical analysis of the procedure reveals it to be closely related to the rectangular parallelepiped (RPP) rate prediction method. The results of these simulations show that event-to-event variation may have a significant impact when predicting the single-event rate in advanced spacecraft electronics. Specific criteria for supplementing established RPP-based single event analysis with Monte Carlo computations are discussed.

Introduction To Monte Carlo Simulation.

Abstract: This paper reviews the history and principles of Monte Carlo simulation, emphasizing techniques commonly used in the simulation of medical imaging.

A Markov Chain Monte Carlo technique to sample transport and source parameters of Galactic cosmic rays - II. Results for the diffusion model combining B/C and radioactive nuclei

Abstract: Context. Ongoing measurements of the cosmic radiation (nuclear, electronic, and γ-ray) are providing additional insight into cosmicray physics. A comprehensive picture of these data relies on an accurate determination of the transport and source parameters of propagation models. Aims. A Markov Chain Monte Carlo method is used to obtain these parameters in a diffusion model. By measuring the B/C ratio and radioactive cosmic-ray clocks, we calculate their probability density functions, placing special emphasis on the halo size L of the Galaxy and the local underdense bubble of size rh. We also derive the mean, best-fit model parameters and 68% confidence level for the various parameters, and the envelopes of other quantities. Methods. The analysis relies on the USINE code for propagation and on a Markov Chain Monte Carlo technique previously developed by ourselves for the parameter determination. Results. The B/C analysis leads to a most probable diffusion slope δ = 0.86 +0.04

Applications of quantum Monte Carlo methods in condensed systems

Abstract: The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schroedinger equation for atoms, molecules, solids and a variety of model systems. The algorithms are intrinsically parallel and are able to take full advantage of the present-day high-performance computing systems. This review article concentrates on the fixed-node/fixed-phase diffusion Monte Carlo method with emphasis on its applications to electronic structure of solids and other extended many-particle systems.

Clustering effects in Ga(AsBi)

Abstract: The photoluminescence from a Ga(AsBi) sample is investigated as a function of pump power and lattice temperature. The disorder-related features are analyzed using a Monte Carlo simulation technique. A two-scale approach is introduced to separately account for cluster localization and alloy disorder effects. The corresponding characteristic energy scales of 11 and 45 meV are deduced from the detailed comparison between experiment and simulation.

Dynamic Monte Carlo versus Brownian dynamics: A comparison for self-diffusion and crystallization in colloidal fluids.

Abstract: Here we present a comparative study of dynamic Monte Carlo and Brownian dynamics simulations of colloidal systems with repulsive interactions. We show that if the Monte Carlo time is rescaled with the acceptance probability, the estimates of the self-diffusion coefficient and of the crystallization times are, respectively, in good and fair agreement with the Brownian dynamics simulations. We also analyze the case of a particle in a one-dimensional potential, where we show that the convergence of a Monte Carlo procedure to the Brownian dynamics result is faster when time is rescaled by the acceptance probability, which gives a theoretical basis for this practical recipe.

Size-consistent variational approaches to nonlocal pseudopotentials: Standard and lattice regularized diffusion Monte Carlo methods revisited

Abstract: We propose improved versions of the standard diffusion Monte Carlo (DMC) and the lattice regularized diffusion Monte Carlo (LRDMC) algorithms. For the DMC method, we refine a scheme recently devised to treat nonlocal pseudopotential in a variational way. We show that such scheme—when applied to large enough systems—maintains its effectiveness only at correspondingly small enough time-steps, and we present two simple upgrades of the method which guarantee the variational property in a size-consistent manner. For the LRDMC method, which is size-consistent and variational by construction, we enhance the computational efficiency by introducing: (i) an improved definition of the effective lattice Hamiltonian which remains size-consistent and entails a small lattice-space error with a known leading term and (ii) a new randomization method for the positions of the lattice knots which requires a single lattice-space

Hybrid Monte Carlo Simulations Combined with a Phase Mixture Model to Predict the Structural Transitions of a Porous Metal−Organic Framework Material upon Adsorption of Guest Molecules

Abstract: Anisotropic isobaric/isothermal molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) techniques are combined in a hybrid scheme to get an osmotic Monte Carlo approach able to deal with a guest-assisted structural transition of a metal organic framework (MOF) porous solid corresponding to a large reversible breathing of its structure. This strategy based on (i) a consideration of a more general expression of the partition functions and (ii) a rigorous homogenization of the MD and MC parts allows us to capture the structural transition of the MIL-53(Cr) MOF-type solid in relation to the CO2 pressure. Further, we show that combining this revisited hybrid osmotic Monte Carlo (HOMC) approach to a newly developed “phase mixture” model, which is based on the existence of a pressure domain where several structural forms of MIL-53(Cr) are present, is an efficient way to accurately predict the adsorption behavior of this solid in the whole range of pressures.

Weak-coupling quantum Monte Carlo calculations on the Keldysh contour: theory and application to the current-voltage characteristics of the Anderson model

Abstract: We present optimized implementations of the weak-coupling continuous-time Monte Carlo method defined for nonequilibrium problems on the Keldysh contour. We describe and compare two methods of preparing the system before beginning the real-time calculation: the ``interaction quench'' and the ``voltage quench,'' which are found to be suitable for large and small voltage biases, respectively. We also discuss technical optimizations which increase the efficiency of the real-time measurements. The methods allow the accurate simulation of transport through quantum dots over wider interaction ranges and longer times than have heretofore been possible. The current-voltage characteristics of the particle-hole symmetric Anderson-impurity model is presented for interactions $U$ up to ten times the intrinsic level width $\ensuremath{\Gamma}$. We compare the Monte Carlo results to fourth-order perturbation theory, finding that perturbation theory is accurate up to $U\ensuremath{\approx}4\ensuremath{\Gamma}$ or for a voltage bias $V\ensuremath{\gtrsim}4\ensuremath{\Gamma}$. The interplay of voltage and temperature and the Coulomb blockade conductance regime are studied.

Progress and Outlook in Monte Carlo Simulations

Abstract: In 1953, Metropolis et al. introduced an ingenious stochastic method for sampling points in a multidimensional space, according to a prescribed probability distribution defined on that space. One of the great intellectual achievements of the 20th century, Metropolis Monte Carlo has found application in a wide range of scientific and engineering fields. Here, we are mainly concerned with the prediction of thermodynamic properties based on the principles of statistical mechanics. The multidimensional space sampled is the configuration space, spanned by the (generalized) coordinates of the molecules constituting the system plus possibly a few macroscopic extensive variables that are allowed to fluctuate, and the probability density Feq is set by an equilibrium ensemble. Sampled configuration-space points, or “states,” form a Markov chain, with each state being formed from the previous one in a Monte Carlo (MC) step. In the original MR2T2 algorithm, each MC step is executed in two stages. One first attempts an elementary move from the current state i into a new state j with probability R(ifj), where the stochastic matrix of attempt probabilities is symmetric, satisfying the condition

A Monte Carlo multimodal inversion of surface waves

Abstract: SUMMARY The analysis of surface wave propagation is often used to estimate the S-wave velocity profile at a site. In this paper, we propose a stochastic approach for the inversion of surface waves, which allows apparent dispersion curves to be inverted. The inversion method is based on the integrated use of two-misfit functions. A misfit function based on the determinant of the Haskell–Thomson matrix and a classical Euclidean distance between the dispersion curves. The former allows all the modes of the dispersion curve to be taken into account with a very limited computational cost because it avoids the explicit calculation of the dispersion curve for each tentative model. It is used in a Monte Carlo inversion with a large population of profiles. In a subsequent step, the selection of representative models is obtained by applying a Fisher test based on the Euclidean distance between the experimental and the synthetic dispersion curves to the best models of the Monte Carlo inversion. This procedure allows the set of the selected models to be identified on the basis of the data quality. It also mitigates the influence of local minima that can affect the Monte Carlo results. The effectiveness of the procedure is shown for synthetic and real experimental data sets, where the advantages of the two-stage procedure are highlighted. In particular, the determinant misfit allows the computation of large populations in stochastic algorithms with a limited computational cost.

McVol - a program for calculating protein volumes and identifying cavities by a Monte Carlo algorithm.

Abstract: In this paper, we describe a Monte Carlo method for determining the volume of a molecule. A molecule is considered to consist of hard, overlapping spheres. The surface of the molecule is defined by rolling a probe sphere over the surface of the spheres. To determine the volume of the molecule, random points are placed in a three-dimensional box, which encloses the whole molecule. The volume of the molecule in relation to the volume of the box is estimated by calculating the ratio of the random points placed inside the molecule and the total number of random points that were placed. For computational efficiency, we use a grid-cell based neighbor list to determine whether a random point is placed inside the molecule or not. This method in combination with a graph-theoretical algorithm is used to detect internal cavities and surface clefts of molecules. Since cavities and clefts are potential water binding sites, we place water molecules in the cavities. The potential water positions can be used in molecular dynamics calculations as well as in other molecular calculations. We apply this method to several proteins and demonstrate the usefulness of the program. The described methods are all implemented in the program McVol, which is available free of charge from our website at http://www.bisb.uni-bayreuth.de/software.html.

Diagrammatic Monte Carlo for correlated fermions

Abstract: We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC) can be used for tackling hard fermionic quantum many-body problems in the thermodynamic limit by presenting accurate results for the repulsive Hubbard model in the correlated Fermi liquid regime. Sampling Feynman's diagrammatic series for the single-particle self-energy, we can study moderate values of the on-site repulsion (U/t~4) and temperatures down to T/t=1/40. We compare our results with high-temperature series expansions and with single-site and cluster dynamical mean-field theory.

Monte Carlo Simulation for Particle and γ-Ray Emissions in Statistical Hauser-Feshbach Model

Abstract: Monte Carlo simulations for particle and γ-ray emissions from a compound nucleus based on the Hauser-Feshbach statistical theory with pre-equilibrium emission are performed. The simulation yields reliable nuclear-reaction-wise energy spectra, or so-called exclusive spectra, for emitted neutrons and γ-rays, which are required in particle transport calculations for nuclear applications. The Monte Carlo method is applied to neutron-induced nuclear reactions on 56Fe, and the results are compared with a traditional deterministic method. The neutron and γ-ray emission correlation is examined by gating on an 847 keV γ-ray that is produced by an inelastic scattering process. The partial γ-ray energy spectra for different γ-ray multiplicities are inferred using this Monte Carlo method. In addition, we investigate a correlation between two neutrons in the (n,2n) reaction.

Methodological assessment of kinetic Monte Carlo simulations of organic photovoltaic devices: the treatment of electrostatic interactions.

Abstract: The kinetic Monte Carlo (KMC) method provides a versatile tool to investigate the mechanisms underlying photocurrent generation in nanostructured organic solar cells. Currently available algorithms can already support the development of more cost-efficient photovoltaic devices, but so far no attempt has been made to test the validity of some fundamental model assumptions and their impact on the simulation result. A meaningful example is given by the treatment of the electrostatic interactions. In most KMC models, electrostatic interactions are approximated by means of cutoff based potentials, irrespective of the long-range nature of the Coulomb interaction. In this paper, the reliability of such approximation is tested against the exact Ewald sum. The results under short-circuit and flat-band conditions show that use of cutoff-based potentials tends to underestimate real device performance, in terms of internal quantum efficiency and current density. Together with this important finding, we formalize other methodological aspects which have been scarcely discussed in the literature.

An energy basin finding algorithm for kinetic Monte Carlo acceleration

Abstract: We present an energy basin finding algorithm for identifying the states in absorbing Markov chains used for accelerating kinetic Monte Carlo (KMC) simulations out of trapping energy basins. The algorithm saves groups of states corresponding to basic energy basins in which there is (i) a minimum energy saddle point and (ii) in moving away from the minimum the saddle point energies do not decrease between successive moves. When necessary, these groups are merged to help the system escape basins of basins. Energy basins are identified either as the system visits states, or by exploring surrounding states before the system visits them. We review exact and approximate methods for accelerating KMC simulations out of trapping energy basins and implement them within our algorithm. Its flexibility to store varying numbers of states, and ability to merge sets of saved states as the program runs, allows it to efficiently escape complicated trapping energy basins. Through simulations of vacancy-As cluster dissolution in Si, we demonstrate our algorithm can be several orders of magnitude faster than standard KMC simulations.

Distribution System Reliability Evaluation Using Enhanced Samples in a Monte Carlo Approach

Abstract: This letter revisits the calculation of distribution system reliability indices using Monte Carlo simulation. The concept of enhanced samples is introduced in order to reduce calculation time. A bootstrap and compensation method is also presented. These methods are found to enhance accuracy and reduce calculation speed for distribution system reliability calculations.

Implicit and electrostatic particle-in-cell/Monte Carlo model in two-dimensional and axisymmetric geometry: I. Analysis of numerical techniques

Abstract: We developed an implicit particle-in-cell/Monte Carlo model in two-dimensional and axisymmetric geometry for simulations of radio-frequency discharges, by introducing several numerical schemes which include variable weights and a multigrid field solver Compared with the standard explicit models, we found that the computational efficiency is significantly increased and the accuracy is maintained Numerical schemes are discussed and benchmark results are presented The code can be used to simulate practical reactors

Benchmark all-electron ab initio quantum Monte Carlo calculations for small molecules.

Abstract: We study the efficiency, precision and accuracy of all-electron variational and diffusion quantum Monte Carlo calculations using Slater basis sets. Starting from wave functions generated by Hartree–Fock and density functional theory, we describe an algorithm to enforce the electron-nucleus cusp condition by linear projection. For the 55 molecules in the G2 set, the diffusion quantum Monte Carlo calculations recovers an average of 95% of the correlation energy and reproduces bond energies to a mean absolute deviation of 3.2 kcal/mol. Comparing the individual total energies with essentially exact values, we investigate the error cancellation in atomization and chemical reaction path energies, giving additional insight into the sizes of nodal surface errors.

Finite-size scaling of mutual information in Monte Carlo simulations: Application to the spin- 1 2 X X Z model

Abstract: We develop a quantum Monte Carlo procedure to compute the Renyi mutual information of an interacting quantum many-body system at nonzero temperature Performing simulations on a spin-$\frac{1}{2}$ $XXZ$ model, we observe that for a subregion of fixed size embedded in a system of size $L$, the mutual information converges at large $L$ to a limiting function which displays nonmonotonic temperature behavior corresponding to the onset of correlations For a region of size $L/2$ embedded in a system of size $L$, the mutual information divided by $L$ converges to a limiting function of temperature, with apparently nontrivial corrections near critical points

Kinetic Monte Carlo study of activated states and correlated shear-transformation-zone activity during the deformation of an amorphous metal

Abstract: Shear transformation zone (STZ) dynamics simulations, which are based on the kinetic Monte Carlo algorithm, are used to model the mechanical response of amorphous metals and provide insight into the collective aspects of the microscopic events underlying deformation. The present analysis details the activated states of STZs in such a model, as well as the statistics of their activation and how these are affected by imposed conditions of stress and temperature. The analysis sheds light on the spatial and temporal correlations between the individual STZ activations that lead to different macroscopic modes of deformation. Three basic STZ correlation behaviors are observed: uncorrelated activity, nearest-neighbor correlation, and self-reactivating STZs. These three behaviors correspond well with the macroscopic deformation modes of homogeneous flow, inhomogeneous deformation, and elastic behavior, respectively. The effect of pre-existing stresses in the simulation cell is also studied and found to have a homogenizing effect on STZ correlations, suppressing the tendency for localization.

Wave functions for quantum Monte Carlo calculations in solids: Orbitals from density functional theory with hybrid exchange-correlation functionals

Abstract: We investigate how the fixed-node diffusion Monte Carlo energy of solids depends on single-particle orbitals used in Slater-Jastrow wave functions. We demonstrate that the dependence can be significant, in particular in the case of $3d$ transition-metal compounds, which we adopt as examples. We illustrate how exchange-correlation functionals with variable exact-exchange component can be exploited to reduce the fixed-node errors. On the basis of these results we argue that the fixed-node quantum Monte Carlo provides a variational approach for optimization of effective single-particle Hamiltonians with parameters.

Failure of Conventional Density Functionals for the Prediction of Molecular Crystal Polymorphism: A Quantum Monte Carlo Study

Abstract: We have applied the diffusion Monte Carlo method, for the first time, to an organic molecular crystal (para-diiodobenzene) in order to determine the relative stability of its two well-known polymor...

Real-time dynamics in quantum impurity models with diagrammatic Monte Carlo

Abstract: We extend the recently developed real-time diagrammatic Monte Carlo method, in its hybridization expansion formulation, to the full Kadanoff-Baym-Keldysh contour. This allows us to study real-time dynamics in correlated impurity models starting from an arbitrary, even interacting, initial density matrix. As a proof of concept, we apply the algorithm to study the nonequilibrium dynamics after a local quantum quench in the Anderson impurity model. Being a completely general approach to real-time dynamics in quantum impurity models, it can be used as a solver for nonequilibrium dynamical mean field theory.