Showing papers on "Dynamic Monte Carlo method published in 2018"
TL;DR: This work has investigated the critical behavior of the simple cubic Ising Model, using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic.
Abstract: While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from ${16}^{3}$ to ${1024}^{3}$. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature ${K}_{c}=0.221\phantom{\rule{0.16em}{0ex}}654\phantom{\rule{0.16em}{0ex}}626(5)$ and the critical exponent of the correlation length $\ensuremath{
u}=0.629\phantom{\rule{0.16em}{0ex}}912(86)$ with precision that exceeds all previous Monte Carlo estimates.
127 citations
TL;DR: The first QMC EOS is calculated at 6000 K for a H-He mixture of a protosolar composition, and the crucial influence of He on the H metallization pressure is shown.
Abstract: Understanding planetary interiors is directly linked to our ability of simulating exotic quantum mechanical systems such as hydrogen (H) and hydrogen-helium (H-He) mixtures at high pressures and temperatures. Equation of state (EOS) tables based on density functional theory are commonly used by planetary scientists, although this method allows only for a qualitative description of the phase diagram. Here we report quantum Monte Carlo (QMC) molecular dynamics simulations of pure H and H-He mixture. We calculate the first QMC EOS at 6000 K for a H-He mixture of a protosolar composition, and show the crucial influence of He on the H metallization pressure. Our results can be used to calibrate other EOS calculations and are very timely given the accurate determination of Jupiter's gravitational field from the NASA Juno mission and the effort to determine its structure.
84 citations
TL;DR: In this paper, a hybrid quantum Monte Carlo (HQMC) method is used to simulate negative sign free lattice fermion models with subcubic scaling in system size.
Abstract: A unique feature of the hybrid quantum Monte Carlo (HQMC) method is the potential to simulate negative sign free lattice fermion models with subcubic scaling in system size. Here we will revisit the algorithm for various models. We will show that for the Hubbard model the HQMC suffers from ergodicity issues and unbounded forces in the effective action. Solutions to these issues can be found in terms of a complexification of the auxiliary fields. This implementation of the HQMC that does not attempt to regularize the fermionic matrix so as to circumvent the aforementioned singularities does not outperform single spin flip determinantal methods with cubic scaling. On the other hand we will argue that there is a set of models for which the HQMC is very efficient. This class is characterized by effective actions free of singularities. Using the Majorana representation, we show that models such as the Su-Schrieffer-Heeger Hamiltonian at half filling and on a bipartite lattice belong to this class. For this specific model subcubic scaling is achieved.
65 citations
TL;DR: This work addresses the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity, and considers different variants of the Monte Carlo and Multilevel Monte Carlo methods.
Abstract: We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity This problem is equivalent to estimating the weak solution of the limiting McKean–Vlasov SDE To that end, our approach uses systems with finite numbers of particles and a time-stepping scheme In this case, there are two discretization parameters: the number of time steps and the number of particles Based on these two parameters, we consider different variants of the Monte Carlo and Multilevel Monte Carlo (MLMC) methods and show that, in the best case, the optimal work complexity of MLMC, to estimate the functional in one typical setting with an error tolerance of $$\mathrm {TOL}$$
, is when using the partitioning estimator and the Milstein time-stepping scheme We also consider a method that uses the recent Multi-index Monte Carlo method and show an improved work complexity in the same typical setting of Our numerical experiments are carried out on the so-called Kuramoto model, a system of coupled oscillators
36 citations
TL;DR: Various ways of optimizing population annealing Monte Carlo are presented using 2-local spin-glass Hamiltonians as a case study to demonstrate how the algorithm can be optimized from an implementation, algorithmic accelerator, as well as scalable parallelization point of view.
Abstract: Population annealing Monte Carlo is an efficient sequential algorithm for simulating k-local Boolean Hamiltonians. Because of its structure, the algorithm is inherently parallel and therefore well suited for large-scale simulations of computationally hard problems. Here we present various ways of optimizing population annealing Monte Carlo using 2-local spin-glass Hamiltonians as a case study. We demonstrate how the algorithm can be optimized from an implementation, algorithmic accelerator, as well as scalable parallelization points of view. This makes population annealing Monte Carlo perfectly suited to study other frustrated problems such as pyrochlore lattices, constraint-satisfaction problems, as well as higher-order Hamiltonians commonly found in, e.g., topological color codes.
33 citations
TL;DR: In this article, a review of the main processes used for semiconductor industries to manufacture transistor from semiconductor materials, namely implantation, annealing and epitaxial growth are reviewed.
32 citations
TL;DR: This article considers static Bayesian parameter estimation for partially observed diffusions that are discretely observed under the assumption that one must resort to discretizing the underlying diffusion process, for instance, using the Euler--Maruyama method.
Abstract: In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for instance, using the Euler--Maruyama method. Given this assumption, we show how one can use Markov chain Monte Carlo (MCMC) and particularly particle MCMC [C. Andrieu, A. Doucet, and R. Holenstein, J. R. Stat. Soc. Ser. B Stat. Methodol., 72 (2010), 269--342] to implement a new approximation of the multilevel (ML) Monte Carlo (MC) collapsing sum identity. Our approach comprises constructing an approximate coupling of the posterior density of the joint distribution over parameter and hidden variables at two different discretization levels and then correcting by an importance sampling method. The variance of the weights are independent of the length of the observed data set. The utility of such a method is that, for a prescribed level of mean square error, the cost of this MLMC m...
32 citations
TL;DR: In this article, the authors use the Gutzwiller Monte Carlo approach to simulate the dissipative $XYZ$ model in the vicinity of a dissipative phase transition and identify a ferromagnetic and two paramagnetic phases.
Abstract: We use the Gutzwiller Monte Carlo approach to simulate the dissipative $XYZ$ model in the vicinity of a dissipative phase transition. This approach captures classical spatial correlations together with the full on-site quantum behavior while neglecting nonlocal quantum effects. By considering finite two-dimensional lattices of various sizes, we identify a ferromagnetic and two paramagnetic phases, in agreement with earlier studies. The greatly reduced numerical complexity of the Gutzwiller Monte Carlo approach facilitates efficient simulation of relatively large lattice sizes. The inclusion of the spatial correlations allows to capture parts of the phase diagram that are completely missed by the widely applied Gutzwiller decoupling of the density matrix.
31 citations
TL;DR: In this paper, the phase diagrams and the magnetic properties of a single nano-graphene layer with next-nearest neighbors coupling J 2 and four-spin interaction J 4 were studied.
27 citations
TL;DR: A new, asymptotic-preserving Monte Carlo method that is stable independently of the scaling parameter and degenerates to a standard probabilistic approach for solving the limiting equation in the diffusion limit.
Abstract: We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit when the scaling parameter tends to zero. Classical Monte Carlo methods suffer severe time step limitations in these situations, due to the fact that the characteristic speeds go to infinity in the diffusion limit. This makes the problem a real challenge, since the scaling parameter may differ by several orders of magnitude in the domain. To circumvent these time step limitations, we construct a new, asymptotic-preserving Monte Carlo method that is stable independently of the scaling parameter and degenerates to a standard probabilistic approach for solving the limiting equation in the diffusion limit. The method uses an implicit time discretization to formulate a modified equation in which the characteristic speeds do not grow indefinitely when the scaling factor tend...
27 citations
TL;DR: The cumulative migration method (CMM) as discussed by the authors was proposed for computing lattice-homogenized multi-group neutron diffusion coefficients and transport cross sections from Monte Carlo, which is shown to be both rigorous and computationally efficient, while eliminating inaccuracies inherent in commonly applied transport approximations.
TL;DR: In this article, the authors survey two common approaches widely used to study the kinetics of heterogeneous catalytic reactions: kinetic Monte Carlo simulations and micro-kinetic modeling, and discuss typical assumptions, advantages, drawbacks, and differences of these two methodologies.
Abstract: In the present article, we survey two common approaches widely used to study the kinetics of heterogeneous catalytic reactions. These are kinetic Monte Carlo simulations and microkinetic modeling. We discuss typical assumptions, advantages, drawbacks, and differences of these two methodologies. We also illustrate some wrong concepts and inaccurate procedures used too often in this kind of kinetics studies. Thus, several issues as for instance minimum energy diagrams, diffusion processes, lateral interactions, or the accuracy of the reaction rates are discussed. Some own examples mainly based on water gas shift reaction over Cu(111) and Cu(321) surfaces are chosen to explain the different developed topics on the kinetics of heterogeneous catalytic reactions.
TL;DR: This work applied and compared derivative-free optimization algorithms to incorporate KMC simulations and find synthesis conditions for achieving property targets and minimizing reaction time, advancing the ability to carry out the design of polymer microstructures and control polymerization processes.
TL;DR: In this article, a differentially weighted operator splitting Monte Carlo (DWOSMC) method was developed to solve complex aerosol dynamic processes by coupling the DWOSMC method and the operator splitting technique.
TL;DR: In this paper, the authors investigated the tunneling time of projective QMC simulations based on the diffusion Monte Carlo (DMC) algorithm without guiding functions, showing that it scales as $1/
Abstract: In simple ferromagnetic quantum Ising models characterized by an effective double-well energy landscape the characteristic tunneling time of path-integral Monte Carlo (PIMC) simulations has been shown to scale as the incoherent quantum-tunneling time, i.e., as $1/{\mathrm{\ensuremath{\Delta}}}^{2}$, where $\mathrm{\ensuremath{\Delta}}$ is the tunneling gap. Since incoherent quantum tunneling is employed by quantum annealers (QAs) to solve optimization problems, this result suggests that there is no quantum advantage in using QAs with respect to quantum Monte Carlo (QMC) simulations. A counterexample is the recently introduced shamrock model (Andriyash and Amin, arXiv:1703.09277), where topological obstructions cause an exponential slowdown of the PIMC tunneling dynamics with respect to incoherent quantum tunneling, leaving open the possibility for potential quantum speedup, even for stoquastic models. In this work we investigate the tunneling time of projective QMC simulations based on the diffusion Monte Carlo (DMC) algorithm without guiding functions, showing that it scales as $1/\mathrm{\ensuremath{\Delta}}$, i.e., even more favorably than the incoherent quantum-tunneling time, both in a simple ferromagnetic system and in the more challenging shamrock model. However, a careful comparison between the DMC ground-state energies and the exact solution available for the transverse-field Ising chain indicates an exponential scaling of the computational cost required to keep a fixed relative error as the system size increases.
TL;DR: In this article, the authors showed how the clusters free energies are constrained by the coagulation probability, and explained various anomalies observed during the precipitation kinetics in coagulated water.
Abstract: In a recent paper, the authors showed how the clusters free energies are constrained by the coagulation probability, and explained various anomalies observed during the precipitation kinetics in co...
TL;DR: Considering the uncertainties in the Monte Carlo simulation, derivative-free method is applied for the CCD-target optimization and a successive boundary shrinkage (SBS) formulation is developed to improve the convergence of problem solving.
TL;DR: The optimal values of the parameters of the numerical method such as the mesh sizes of the spatial discretization and the numbers of quasi-points are calculated in order to minimize the overall computational cost for solving the stationary stochastic drift–diffusion-Poisson system.
TL;DR: Upper and lower bounds for the additional error caused by this are determined and compared to those of |E-N [Y - Y-n]|, which are found to be smaller than the corresponding results for multilevel Monte Carlo estimators.
TL;DR: In this paper, a generalized perturbation theory (GPT) formulation suited for the Monte Carlo (MC) eigenvalue calculations is newly developed to estimate sensitivities of a general MC tally to input data.
Abstract: A generalized perturbation theory (GPT) formulation suited for the Monte Carlo (MC) eigenvalue calculations is newly developed to estimate sensitivities of a general MC tally to input data. In the ...
TL;DR: The consortium for Advanced Simulation of Light Water Reactors aims to provide real-time information about the design and operation of light water Reactors to improve the simulation quality of the Reactors.
TL;DR: In this paper, a 3D discrete ordinates-Monte Carlo (SN-MC) coupling method was proposed to combine the advantage of the SN method with high efficiency and the MC method with fine geometrical modeling.
TL;DR: For a nuclear system in which the entire -eigenvalue spectrum is known, eigenfunction expansion yields the time-dependent flux response to any arbitrary source as mentioned in this paper, and applications in which this response...
Abstract: For a nuclear system in which the entire -eigenvalue spectrum is known, eigenfunction expansion yields the time-dependent flux response to any arbitrary source. Applications in which this response ...
TL;DR: In this article, a new random geometry method was developed in Monte Carlo code RMC to simulate the particle transport in polytype particle/pebble in double heterogeneous geometry systems.
TL;DR: Modern variants of Monte Carlo methods for Uncertainty Quantification (UQ) of the Neutron Transport Equation, when it is approximated by the discrete ordinates method with diamond differencing are described.
Abstract: We describe modern variants of Monte Carlo methods for Uncertainty Quantification (UQ) of the Neutron Transport Equation, when it is approximated by the discrete ordinates method with diamond differencing. We focus on the mono-energetic 1D slab geometry problem, with isotropic scattering, where the cross-sections are log-normal correlated random fields of possibly low regularity. The paper includes an outline of novel theoretical results on the convergence of the discrete scheme, in the cases of both spatially variable and random cross-sections. We also describe the theory and practice of algorithms for quantifying the uncertainty of a functional of the scalar flux, using Monte Carlo and quasi-Monte Carlo methods, and their multilevel variants. A hybrid iterative/direct solver for computing each realisation of the functional is also presented. Numerical experiments show the effectiveness of the hybrid solver and the gains that are possible through quasi-Monte Carlo sampling and multilevel variance reduction. For the multilevel quasi-Monte Carlo method, we observe gains in the computational e-cost of up to two orders of magnitude over the standard Monte Carlo method, and we explain this theoretically. Experiments on problems with up to several thousand stochastic dimensions are included.
TL;DR: This paper evaluates the performance of Monte Carlo forecasting by analyzing it in the context of Markov chain Monte Carlo (MCMC) theory, and shows that for a special class of nonlinear systems that have zero divergence, the propagated kernel is in detailed balance with the true state probability density function.
TL;DR: In this article, an efficient kinetic Monte Carlo scheme is presented to determine the Helmholtz free energy and entropy of bulk fluids and adsorption systems. The method is made possible because this technique enables the accurate determination of the chemical potential.
TL;DR: A group of mesh datasets generated by Iso2Mesh software are designed and used to evaluate the performance of four Monte Carlo-based simulation packages, including Monte Carlo model of steady-state light transport in multi-layered tissues (MCML), tetrahedron-based inhomogeneous Monte Carlo optical simulator (TIMOS), Molecular Optical Simulation Environment (MOSE), and Mesh-based Monte Carlo (MMC).
Abstract: Monte Carlo simulation of light propagation in turbid medium has been studied for years. A number of software packages have been developed to handle with such issue. However, it is hard to compare these simulation packages, especially for tissues with complex heterogeneous structures. Here, we first designed a group of mesh datasets generated by Iso2Mesh software, and used them to cross-validate the accuracy and to evaluate the performance of four Monte Carlo-based simulation packages, including Monte Carlo model of steady-state light transport in multi-layered tissues (MCML), tetrahedron-based inhomogeneous Monte Carlo optical simulator (TIMOS), Molecular Optical Simulation Environment (MOSE), and Mesh-based Monte Carlo (MMC). The performance of each package was evaluated based on the designed mesh datasets. The merits and demerits of each package were also discussed. Comparative results showed that the TIMOS package provided the best performance, which proved to be a reliable, efficient, and stable MC simulation package for users.
TL;DR: In this article, the partial current-based coarse mesh finite difference (p-CMFD) feedback was applied to the Monte Carlo (MC) kinematic analysis of a 3D continuous-energy whole-core reactor.
Abstract: In the three-dimensional (3-D) continuous-energy whole-core reactor analysis, the partial current–based coarse mesh finite difference (p-CMFD) feedback was applied to the Monte Carlo (MC) k...
TL;DR: Various new schemes such as deterministic decay of precursors in each time step, adjustment of weights of neutrons and precursor for population control, use of mean number of secondaries per collision, and particle splitting/Russian roulette to reduce the variance in neutron power are proposed.
Abstract: The use of the Monte Carlo (MC) method for space-time reactor kinetics is expected to be much more accurate than the presently used deterministic methods largely based on few-group diffusion theory. However, the development of the MC method for space-time reactor kinetics poses challenges because of the vastly different timescales of neutrons and delayed neutron precursors and their vastly different populations that also change with time by several orders of magnitude. In order to meet these challenges in MC-based space kinetics, we propose various new schemes such as deterministic decay of precursors in each time step, adjustment of weights of neutrons and precursors for population control, use of mean number of secondaries per collision, and particle splitting/Russian roulette to reduce the variance in neutron power. The efficacy of these measures is first tested in a simpler point-kinetics version of the MC method against analytical or accurate numerical solutions of point-kinetics equations. T...