Showing papers on "Dynamic Monte Carlo method published in 2012"
Book•
05 Dec 2012
TL;DR: This paper presents a meta-modelling framework that automates the very labor-intensive and therefore time-heavy and expensive process of manually cataloging samples and generating random numbers.
Abstract: Introduction.- Estimating Volume and Count.- Generating Samples.- Increasing Efficiency.- Random Tours.- Designing and Analyzing Sample Paths.- Generating Pseudorandom Numbers.
2,215 citations
TL;DR: A significant impact of Monte Carlo dose calculation can be expected in complex geometries where local range uncertainties due to multiple Coulomb scattering will reduce the accuracy of analytical algorithms and in these cases Monte Carlo techniques might reduce the range uncertainty by several mm.
Abstract: The main advantages of proton therapy are the reduced total energy deposited in the patient as compared to photon techniques and the finite range of the proton beam. The latter adds an additional degree of freedom to treatment planning. The range in tissue is associated with considerable uncertainties caused by imaging, patient setup, beam delivery and dose calculation. Reducing the uncertainties would allow a reduction of the treatment volume and thus allow a better utilization of the advantages of protons. This paper summarizes the role of Monte Carlo simulations when aiming at a reduction of range uncertainties in proton therapy. Differences in dose calculation when comparing Monte Carlo with analytical algorithms are analyzed as well as range uncertainties due to material constants and CT conversion. Range uncertainties due to biological effects and the role of Monte Carlo for in vivo range verification are discussed. Furthermore, the current range uncertainty recipes used at several proton therapy facilities are revisited. We conclude that a significant impact of Monte Carlo dose calculation can be expected in complex geometries where local range uncertainties due to multiple Coulomb scattering will reduce the accuracy of analytical algorithms. In these cases Monte Carlo techniques might reduce the range uncertainty by several mm.
1,027 citations
264 citations
TL;DR: In this article, the authors applied an analytical method that combined the cumulant method with the Cornish-Fisher expansion to solve the voltage regulation problem in photovoltaic distributed generation.
162 citations
Book•
31 May 2012
TL;DR: A Stochastic Model for the Description of Surface Reaction Systems and Kinetic Monte Carlo Algorithms to Modeling Surface Reactions and Examples is presented.
Abstract: Introduction.- Stochastic Model for the Description of Surface Reaction Systems.- Kinetic Monte Carlo Algorithms.- How to Get Kinetic Parameters.- Modeling Surface Reactions I.- Modeling Surface Reactions II.- Examples.- New Developments.- Glossary.- Index.
151 citations
TL;DR: In this paper, the authors obtained a finite-basis energy for the homogeneous electron gas (HEG) with respect to a basis set incompleteness error of 0.5 a.u.
Abstract: Highly accurate results for the homogeneous electron gas (HEG) have only been achieved to date within a diffusion Monte Carlo (DMC) framework. Here, we introduce a recently developed stochastic technique, full configuration interaction quantum Monte Carlo (FCIQMC), which samples the exact wave function expanded in plane-wave Slater determinants. Despite the introduction of a basis-set incompleteness error, we obtain a finite-basis energy, which is significantly and variationally lower than any previously published work for the 54-electron HEG at ${r}_{s}$ $=$ 0.5 a.u., in a Hilbert space of ${10}^{108}$ Slater determinants. At this value of ${r}_{s}$, as well as of 1.0 a.u., we remove the remaining basis-set incompleteness error by extrapolation, yielding results comparable to state-of-the-art DMC backflow energies. In doing so, we demonstrate that it is possible to yield highly accurate results with the FCIQMC method in periodic systems.
131 citations
TL;DR: A Monte Carlo method to sample the classical configurational canonical ensemble is introduced, where all particles move simultaneously, and a straight event-chain implementation is introduced.
Abstract: A Monte Carlo method to sample the classical configurational canonical ensemble is introduced. In contrast to the Metropolis algorithm, where trial moves can be rejected, in this approach collisions take place. The implementation is event-driven; i.e., at scheduled times the collisions occur. A unique feature of the new method is that smooth potentials (instead of only step-wise changing ones) can be used. In addition to an event-driven approach, where all particles move simultaneously, we introduce a straight event-chain implementation. As proof of principle, a system of Lennard-Jones particles is simulated.
128 citations
TL;DR: A review of recent developments in Monte Carlo methods in the field of ultracold gases, including developments in diagrammatic Monte Carlo for the Fermi polaron problem and the Hubbard model, and the connection with dynamical mean-field theory.
Abstract: This is a review of recent developments in Monte Carlo methods in the field of ultra cold gases. For bosonic atoms in an optical lattice we discuss path integral Monte Carlo simulations with worm updates and show the excellent agreement with cold atom experiments. We also review recent progress in simulating bosonic systems with long-range interactions, disordered bosons, mixtures of bosons, and spinful bosonic systems. For repulsive fermionic systems determinantal methods at half filling are sign free, but in general no sign-free method exists. We review the developments in diagrammatic Monte Carlo for the Fermi polaron problem and the Hubbard model, and show the connection with dynamical mean-field theory. We end the review with diffusion Monte Carlo for the Stoner problem in cold gases.
119 citations
TL;DR: It is explained how cancellation of the positive and negative particles sampling the wave function ensures convergence to a stochastic representation of the many-fermion ground state and accounts for the characteristic population dynamics observed in simulations.
Abstract: The recently proposed full configuration interaction quantum Monte Carlo method allows access to essentially exact ground-state energies of systems of interacting fermions substantially larger than previously tractable without knowledge of the nodal structure of the ground-state wave function. We investigate the nature of the sign problem in this method and how its severity depends on the system studied. We explain how cancellation of the positive and negative particles sampling the wave function ensures convergence to a stochastic representation of the many-fermion ground state and accounts for the characteristic population dynamics observed in simulations.
115 citations
TL;DR: In this article, a combination of spectral, velocity-dependent, Implicit Monte Carlo and discrete-diffusion Monte Carlo methods was proposed for neutrino transport calculations in core-collapse supernovae.
Abstract: Monte Carlo approaches to radiation transport have several attractive properties such as simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are relatively easy to extend to multiple spatial dimensions, which makes them potentially interesting in modeling complex multi-dimensional astrophysical phenomena such as core-collapse supernovae. The aim of this paper is to explore Monte Carlo methods for modeling neutrino transport in core-collapse supernovae. We generalize the Implicit Monte Carlo photon transport scheme of Fleck & Cummings and gray discrete-diffusion scheme of Densmore et al. to energy-, time-, and velocity-dependent neutrino transport. Using our 1D spherically-symmetric implementation, we show that, similar to the photon transport case, the implicit scheme enables significantly larger timesteps compared with explicit time discretization, without sacrificing accuracy, while the discrete-diffusion method leads to significant speed-ups at high optical depth. Our results suggest that a combination of spectral, velocity-dependent, Implicit Monte Carlo and discrete-diffusion Monte Carlo methods represents a robust approach for use in neutrino transport calculations in core-collapse supernovae. Our velocity-dependent scheme can easily be adapted to photon transport.
112 citations
TL;DR: In this article, the self-energy and vertex function of the Anderson impurity model was measured using higher-order correlation functions related to the quantities being sought through the equation of motion.
Abstract: We propose efficient measurement procedures for the self-energy and vertex function of the Anderson impurity model within the hybridization expansion continuous-time quantum Monte Carlo algorithm. The method is based on the measurement of higher-order correlation functions related to the quantities being sought through the equation of motion, a technique previously introduced in the numerical renormalization-group context. For the case of interactions of density-density type, the additional correlators can be obtained at essentially no additional computational cost. In combination with a recently introduced method for filtering the Monte Carlo noise using a representation in terms of orthogonal polynomials, we obtain data with unprecedented accuracy. This leads to an enhanced stability in analytical continuations of the self-energy or in two-particle-based theories such as the dual fermion approach. As an illustration of the method we reexamine the previously reported spin-freezing and high-spin to low-spin transitions in a two-orbital model with density-density interactions. In both cases, the vertex function undergoes significant changes, which suggests significant corrections to the dynamical mean-field solutions in dual fermion calculations.
TL;DR: In this article, a stochastic method for taking the effect of thermal motion into account on the fly in a Monte Carlo neutron transport calculation is introduced, which is based on explicit treatme...
Abstract: This paper introduces a new stochastic method for taking the effect of thermal motion into account on the fly in a Monte Carlo neutron transport calculation. The method is based on explicit treatme...
TL;DR: This algorithm does away with the integral transformation as the hotspot of the usual algorithms, has a far superior size dependence of cost, does not suffer from the sign problem of some quantum Monte Carlo methods, and is potentially easily parallelizable and extensible to other more complex electron-correlation theories.
Abstract: With the aid of the Laplace transform, the canonical expression of the second-order many-body perturbation correction to an electronic energy is converted into the sum of two 13-dimensional integrals, the 12-dimensional parts of which are evaluated by Monte Carlo integration. Weight functions are identified that are analytically normalizable, are finite and non-negative everywhere, and share the same singularities as the integrands. They thus generate appropriate distributions of four-electron walkers via the Metropolis algorithm, yielding correlation energies of small molecules within a few mEh of the correct values after 108 Monte Carlo steps. This algorithm does away with the integral transformation as the hotspot of the usual algorithms, has a far superior size dependence of cost, does not suffer from the sign problem of some quantum Monte Carlo methods, and potentially easily parallelizable and extensible to other more complex electron-correlation theories.
01 Mar 2012-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: This work presents the theory and sample code for a Geant4 process which allows the cross-section of a G4VDiscreteProcess to be scaled, while adjusting track weights so as to mitigate the effects of altered primary beam depletion induced by theCross-section change.
Abstract: In Monte Carlo particle transport codes, it is often important to adjust reaction cross-sections to reduce the variance of calculations of relatively rare events, in a technique known as non-analog Monte Carlo. We present the theory and sample code for a Geant4 process which allows the cross-section of a G4VDiscreteProcess to be scaled, while adjusting track weights so as to mitigate the effects of altered primary beam depletion induced by the cross-section change. This makes it possible to increase the cross-section of nuclear reactions by factors exceeding 10 4 (in appropriate cases), without distorting the results of energy deposition calculations or coincidence rates. The procedure is also valid for bias factors less than unity, which is useful in problems that involve the computation of particle penetration deep into a target (e.g. atmospheric showers or shielding studies).
01 Jan 2012
TL;DR: This paper presents QMC algorithms, which are ideal candidates for acceleration in the many-core paradigm because they offer multiple forms of parallelism.
Abstract: More accurate than mean-field methods and more scalable than quantum chemical methods, continuum quantum Monte Carlo (QMC) is an invaluable tool for predicting the properties of matter from fundamental principles. Because QMC algorithms offer multiple forms of parallelism, they're ideal candidates for acceleration in the many-core paradigm.
TL;DR: It is demonstrated the existence of a unique Monte Carlo time scale that allows for a direct comparison between Monte Carlo and Brownian dynamics simulations, and the agreement between Brownian and Monte Carlo dynamics under the most general conditions is excellent.
Abstract: We report on the diffusion of purely repulsive and freely rotating colloidal rods in the isotropic, nematic, and smectic liquid crystal phases to probe the agreement between Brownian and Monte Carlo dynamics under the most general conditions. By properly rescaling the Monte Carlo time step, being related to any elementary move via the corresponding self-diffusion coefficient, with the acceptance rate of simultaneous trial displacements and rotations, we demonstrate the existence of a unique Monte Carlo time scale that allows for a direct comparison between Monte Carlo and Brownian dynamics simulations. To estimate the validity of our theoretical approach, we compare the mean square displacement of rods, their orientational autocorrelation function, and the self-intermediate scattering function, as obtained from Brownian dynamics and Monte Carlo simulations. The agreement between the results of these two approaches, even under the condition of heterogeneous dynamics generally observed in liquid crystalline phases, is excellent.
TL;DR: The fixed-shift phase of the i-FCIQMC can be used to effectively assess stochastic and initiator error, and the computational cost scales linearly with the plane wave basis set size, which is justifiable on physical grounds.
Abstract: Using the homogeneous electron gas (HEG) as a model, we investigate the sources of error in the `initiator' adaptation to Full Configuration Interaction Quantum Monte Carlo (i-FCIQMC), with a view to accelerating convergence. In particular we find that the fixed shift phase, where the walker number is allowed to grow slowly, can be used to effectively assess stochastic and initiator error. Using this approach we provide simple explanations for the internal parameters of an i-FCIQMC simulation. We exploit the consistent basis sets and adjustable correlation strength of the HEG to analyze properties of the algorithm, and present finite basis benchmark energies for N=14 over a range of densities $0.5 \leq r_s \leq 5.0$ a.u. A \emph{single-point extrapolation} scheme is introduced to produce complete basis energies for 14, 38 and 54 electrons. It is empirically found that, in the weakly correlated regime, the computational cost scales linearly with the plane wave basis set size, which is justifiable on physical grounds. We expect the fixed shift strategy to reduce the computational cost of many \iFCIQMC calculations of weakly correlated systems. In addition, we provide benchmarks for the electron gas, to be used by other quantum chemical methods in exploring periodic solid state systems.
TL;DR: This study proposes a novel method of spectral deconvolution based on Bayesian estimation with the exchange Monte Carlo method, which is an application of the integral approximation of stochastic complexity and the exchangeMonte Carlo method.
TL;DR: This paper presents an extension of DDMC for frequency-dependent radiative transfer based on a frequency-integrated diffusion equation for frequencies below a specified threshold, as optical thickness is typically a decreasing function of frequency.
TL;DR: Two computer simulation methods are formulated: a kinetic Monte Carlo (KMC) and a cellular particle dynamics (CPD) method, which are capable of describing and predicting the shape evolution in time of three-dimensional multicellular systems during their biomechanical relaxation.
Abstract: Computer modeling of multicellular systems has been a valuable tool for interpreting and guiding in vitro experiments relevant to embryonic morphogenesis, tumor growth, angiogenesis and, lately, structure formation following the printing of cell aggregates as bioink particles Here we formulate two computer simulation methods: (1) a kinetic Monte Carlo (KMC) and (2) a cellular particle dynamics (CPD) method, which are capable of describing and predicting the shape evolution in time of three-dimensional multicellular systems during their biomechanical relaxation Our work is motivated by the need of developing quantitative methods for optimizing postprinting structure formation in bioprinting-assisted tissue engineering The KMC and CPD model parameters are determined and calibrated by using an original computational-theoretical-experimental framework applied to the fusion of two spherical cell aggregates The two methods are used to predict the (1) formation of a toroidal structure through fusion of spherical aggregates and (2) cell sorting within an aggregate formed by two types of cells with different adhesivities
TL;DR: This method allows for stable sampling with respect to collapse to lower energy states and requires no uncontrolled approximations, and it is shown that the propagator can directly yield frequency-domain correlation functions and spectral functions such as the density of states which are difficult to obtain within a traditional quantum Monte Carlo framework.
Abstract: In this communication, we propose a method for obtaining isolated excited states within the full configuration interaction quantum Monte Carlo framework. This method allows for stable sampling with respect to collapse to lower energy states and requires no uncontrolled approximations. In contrast with most previous methods to extract excited state information from quantum Monte Carlo methods, this results from a modification to the underlying propagator, and does not require explicit orthogonalization, analytic continuation, transient estimators, or restriction of the Hilbert space via a trial wavefunction. Furthermore, we show that the propagator can directly yield frequency-domain correlation functions and spectral functions such as the density of states which are difficult to obtain within a traditional quantum Monte Carlo framework. We demonstrate this approach with pilot applications to the neon atom and beryllium dimer.
TL;DR: This NP+LEMC technique can be used in systems with diffusion of charged or uncharged particles in complex three-dimensional geometries, including systems with low concentrations and small applied voltages that are difficult for other particle simulation techniques.
Abstract: We propose a procedure to compute the steady-state transport of charged particles based on the Nernst–Planck (NP) equation of electrodiffusion. To close the NP equation and to establish a relation between the concentration and electrochemical potential profiles, we introduce the Local Equilibrium Monte Carlo (LEMC) method. In this method, Grand Canonical Monte Carlo simulations are performed using the electrochemical potential specified for the distinct volume elements. An iteration procedure that self-consistently solves the NP and flux continuity equations with LEMC is shown to converge quickly. This NP+LEMC technique can be used in systems with diffusion of charged or uncharged particles in complex three-dimensional geometries, including systems with low concentrations and small applied voltages that are difficult for other particle simulation techniques.
TL;DR: In this article, the authors focus on the challenges facing full-core Monte Carlo for keff calculations and the prospects for Monte Carlo becoming a routine tool for reactor analysis, and discuss the advantages of using Monte Carlo methods to analyze fullcore reactor configurations.
TL;DR: In this article, the authors derive a uniform acceptance force-bias Monte Carlo (UFMC) method starting from basic thermodynamic principles, which leads to an intuitive and unambiguous formalism.
Abstract: Monte Carlo (MC) methods have a long-standing history as partners of molecular dynamics (MD) to simulate the evolution of materials at the atomic scale. Among these techniques, the uniform-acceptance force-bias Monte Carlo (UFMC) method [ G. Dereli Mol. Simul. 8 351 (1992)] has recently attracted attention [ M. Timonova et al. Phys. Rev. B 81 144107 (2010)] thanks to its apparent capacity of being able to simulate physical processes in a reduced number of iterations compared to classical MD methods. The origin of this efficiency remains, however, unclear. In this work we derive a UFMC method starting from basic thermodynamic principles, which leads to an intuitive and unambiguous formalism. The approach includes a statistically relevant time step per Monte Carlo iteration, showing a significant speed-up compared to MD simulations. This time-stamped force-bias Monte Carlo (tfMC) formalism is tested on both simple one-dimensional and three-dimensional systems. Both test-cases give excellent results in agreement with analytical solutions and literature reports. The inclusion of a time scale, the simplicity of the method, and the enhancement of the time step compared to classical MD methods make this method very appealing for studying the dynamics of many-particle systems.
TL;DR: In this paper, a simulation of the SU(3) spin model with chemical potential using a recently proposed flux representation is presented, where the complex phase problem is avoided and a Monte Carlo simulation in terms of the fluxes becomes possible.
TL;DR: The key feature of the kMC is the absence of discarded trial moves of molecules, which ensures larger number of configurations that are collected for time averaging, which results in significantly fewer errors for the same number of Monte Carlo steps.
TL;DR: A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented and it is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.
Abstract: A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.
TL;DR: In this paper, the authors apply a standard Monte Carlo Metropolis procedure for the treatment of a mechanoelastic model, in order to study the evolution of clusters in open boundary hexagonal spin-crossover systems, composed of molecules in a triangular lattice and linked by springs.
Abstract: In this paper we apply a standard Monte Carlo Metropolis procedure for the treatment of a mechanoelastic model, in order to study the evolution of clusters in open boundary hexagonal spin-crossover systems, composed of molecules in a triangular lattice and linked by springs. The temperature-driven transition between the paramagnetic high-spin phase and the diamagnetic low-spin phase is reproduced by taking into account the lattice elastic energy change in addition to the energy variation of spin-active molecules. This method allows us to determine where higher amounts of energies are stored and where the spins are more probable to flip and to form clusters. The spreading of clusters from the corners, similar to recently published experimental data, is well reproduced. We also analyze here the lattice deformation during the transition and we show that the deformation increases as the spring constant diminishes. A systematic comparison with results obtained in the framework of our previous Arrhenius approach of the mechanoelastic system is provided.
TL;DR: A Monte Carlo study of energy depositions due to protons, alpha particles and carbon ions of the same linear-energy-transfer (LET) in liquid water using the Geant4-DNA toolkit and an adapted version of the DBSCAN clustering algorithm.
Abstract: This work presents a Monte Carlo study of energy depositions due to protons, alpha particles and carbon ions of the same linear-energy-transfer (LET) in liquid water. The corresponding track structures were generated using the Geant4-DNA toolkit, and the energy deposition spatial distributions were analyzed using an adapted version of the DBSCAN clustering algorithm. Combining the Geant4 simulations and the clustering algorithm it was possible to compare the quality of the different radiation types. The ratios of clustered and single energy depositions are shown versus particle LET and frequency-mean lineal energies. The estimated effect of these types of radiation on biological tissues is then discussed by comparing the results obtained for different particles with the same LET.