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We obtain the phase diagram of the hard core lattice gas with third nearest neighbor exclusion on the triangular lattice using Monte Carlo simulations that are based on a rejection-free flat histogram algorithm. In a recent paper [Darjani et al., J. Chem. Phys. 151, 104702 (2019)], it was claimed that the lattice gas with third nearest neighbor exclusion undergoes two phase transitions with increasing density with the phase at intermediate densities exhibiting hexatic order with continuously varying exponents. Although a hexatic phase is expected when the exclusion range is large, it has not been seen earlier in hard core lattice gases with short range exclusion. In this paper, by numerically determining the entropies for all densities, we show that there is only a single phase transition in the system between a low-density fluid phase and a high density ordered sublattice phase and that a hexatic phase is absent. The transition is shown to be first order in nature, and the critical parameters are determined accurately. [ABSTRACT FROM AUTHOR]

In a recent paper, we proposed the adaptive shift method for correcting undersampling bias of the initiator-full configuration interaction (FCI) quantum Monte Carlo. The method allows faster convergence with the number of walkers to the FCI limit than the normal initiator method, particularly for large systems. However, in its application to some systems, mostly strongly correlated molecules, the method is prone to overshooting the FCI energy at intermediate walker numbers, with convergence to the FCI limit from below. In this paper, we present a solution to the overshooting problem in such systems, as well as further accelerating convergence to the FCI energy. This is achieved by offsetting the reference energy to a value typically below the Hartree–Fock energy but above the exact energy. This offsetting procedure does not change the exactness property of the algorithm, namely, convergence to the exact FCI solution in the large-walker limit, but at its optimal value, it greatly accelerates convergence. There is no overhead cost associated with this offsetting procedure and is therefore a pure and substantial computational gain. We illustrate the behavior of this offset adaptive shift method by applying it to the N2 molecule, the ozone molecule at three different geometries (an equilibrium open minimum, a hypothetical ring minimum, and a transition state) in three basis sets (cc-pVXZ, X = D, T, Q), and the chromium dimer in the cc-pVDZ basis set, correlating 28 electrons in 76 orbitals. We show that in most cases, the offset adaptive shift method converges much faster than both the normal initiator method and the original adaptive shift method. [ABSTRACT FROM AUTHOR]

In a recent paper, Lucco Castello et al. (arXiv:2107.03537) provided an accurate parameterization of classical one-component plasma bridge functions that was embedded in a novel dielectric scheme for strongly coupled electron liquids. Here, this approach is rigorously formulated, its set of equations is formally derived, and its numerical algorithm is scrutinized. A systematic comparison with available and new path integral Monte Carlo simulations reveals a rather unprecedented agreement especially in terms of the interaction energy and the long wavelength limit of the static local field correction. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations require barostats to be performed at a constant pressure. The usual recipe is to employ the Berendsen barostat first, which displays a first-order volume relaxation efficient in equilibration but results in incorrect volume fluctuations, followed by a second-order or a Monte Carlo barostat for production runs. In this paper, we introduce stochastic cell rescaling, a first-order barostat that samples the correct volume fluctuations by including a suitable noise term. The algorithm is shown to report volume fluctuations compatible with the isobaric ensemble and its anisotropic variant is tested on a membrane simulation. Stochastic cell rescaling can be straightforwardly implemented in the existing codes and can be used effectively in both equilibration and production phases. [ABSTRACT FROM AUTHOR]

In the present study, variational path integral molecular dynamics and associated hybrid Monte Carlo (HMC) methods have been developed on the basis of a fourth order approximation of a density operator. To reveal various parameter dependence of physical quantities, we analytically solve one dimensional harmonic oscillators by the variational path integral; as a byproduct, we obtain the analytical expression of the discretized density matrix using the fourth order approximation for the oscillators. Then, we apply our methods to realistic systems like a water molecule and a para-hydrogen cluster. In the HMC, we adopt two level description to avoid the time consuming Hessian evaluation. For the systems examined in this paper, the HMC method is found to be about three times more efficient than the molecular dynamics method if appropriate HMC parameters are adopted; the advantage of the HMC method is suggested to be more evident for systems described by many body interaction. [ABSTRACT FROM AUTHOR]

The weighted stochastic simulation algorithm (wSSA) recently introduced by Kuwahara and Mura [J. Chem. Phys. 129, 165101 (2008)] is an innovative variation on the stochastic simulation algorithm (SSA). It enables one to estimate, with much less computational effort than was previously thought possible using a Monte Carlo simulation procedure, the probability that a specified event will occur in a chemically reacting system within a specified time when that probability is very small. This paper presents some procedural extensions to the wSSA that enhance its effectiveness in practical applications. The paper also attempts to clarify some theoretical issues connected with the wSSA, including its connection to first passage time theory and its relation to the SSA. [ABSTRACT FROM AUTHOR]

Of growing concern for the security of many nations are numerous incidents of lost or stolen radioactive sources or materials. The detection of and search for these abnormal radioactive sources plays an important role in monitoring nuclear safety and disposal of nuclear waste. In this paper, a method for autonomously searching for radioactive sources in a flat open rectangular-shaped field through mobile platforms was proposed. In this method, by using the possibility particle filter, the search for radioactive sources was realized according to a series of radiation information measured by the mobile platform carrying a Geiger–Müller counter. According to the inverse square law and the radiation counting governed by Poisson distribution, a radioactive source localization model was constructed. Then, a mobile platform controlled by an information entropy strategy constantly moved within the search area and detected radiation at specific points. The possibility filter algorithm, implemented via the sequential Monte Carlo method, is used to update posterior probability distributions of the source parameters. The performance of the proposed search algorithm, including a comparison with a standard particle filter algorithm, is studied by simulations. The simulation experiment proves that the possibility particle filter algorithm has good robustness. The successful application of the experimental dataset collected in the simulations verifies the measurement model and theoretical consideration. [ABSTRACT FROM AUTHOR]

In this paper, a new path integration algorithm is proposed for the non-autonomous vibro-impact system. It can be used to obtain the stochastic response of the system at the impact instant. The innovation of this algorithm is that the fixed excitation phase at the impact instant is introduced. The fixed excitation phase and the impact surface are combined as the special impact surface, and the algorithm sets up the different evolution methods of the probability density function and the impact completion condition. It can directly capture the stochastic response of the system at the impact instant without any non-smooth approximations. The non-smooth characteristics of the impact can be well preserved. This new path integration algorithm has good applicability. It has no limitation on the restitution coefficient. The design idea of this algorithm may provide a framework for the non-smooth system subject to the periodic excitation. In the end, a linear vibro-impact system and a nonlinear vibro-impact system excited by the external periodic force are used as examples to show how our method could be implemented. The stochastic P-bifurcation phenomena induced by parameters also are considered. The Monte Carlo simulations verify the effectiveness and accuracy of the proposed path integration algorithm. [ABSTRACT FROM AUTHOR]

Computer simulations of structure formation in network forming materials (such as amorphous semiconductors, glasses, or fluids containing hydrogen bonds) are challenging. The problem is that large structural changes in the network topology are rare events, making it very difficult to equilibrate these systems. To overcome this problem, Wooten, Winer, and Weaire [Phys. Rev. Lett. 54, 1392 (1985)] proposed a Monte Carlo bond-switch move, constructed to alter the network topology at every step. The resulting algorithm is well suited to study networks at zero temperature. However, since thermal fluctuations are ignored, it cannot be used to probe the phase behavior at finite temperature. In this paper, a modification of the original bond-switch move is proposed, in which detailed balance and ergodicity are both obeyed, thereby facilitating a correct sampling of the Boltzmann distribution for these systems at any finite temperature. The merits of the modified algorithm are demonstrated in a detailed investigation of the melting transition in a two-dimensional 3-fold coordinated network. [ABSTRACT FROM AUTHOR]

Stochastic Brownian dynamics is an extremely powerful way to simulate the polymer dynamics in solutions and melts. Mathematically, these models are described by stochastic differential equations. The most challenging problems are the Monte Carlo algorithm, which simulates the motion of a large number of model particles and hence requires an enormous amount of computer time. It is therefore necessary to develop an efficient numerical method in operational emergency response applications. In this paper, we give an improved multilevel Monte Carlo (improved-MLMC) method based on equilibrium control variables at each level to calculate the propagation of polymers. The improved-MLMC method can be shown to result in asymptotically optimal random errors and reduce total cost when compared to the standard Monte Carlo and MLMC methods. Finally, the effect of the Wi number (dimensionless parameter) on the total cost of the presented MLMC method is also discussed in detail. [ABSTRACT FROM AUTHOR]

In this paper, we describe the way to set up the floppy-box Monte Carlo (FBMC) method [L. Filion, M. Marechal, B. van Oorschot, D. Pelt, F. Smallenburg, and M. Dijkstra, Phys. Rev. Lett. 103, 188302 (2009)] to predict crystal-structure candidates for colloidal particles. The algorithm is explained in detail to ensure that it can be straightforwardly implemented on the basis of this text. The handling of hard-particle interactions in the FBMC algorithm is given special attention, as (soft) short-range and semi-long-range interactions can be treated in an analogous way. We also discuss two types of algorithms for checking for overlaps between polyhedra, the method of separating axes and a triangular-tessellation based technique. These can be combined with the FBMC method to enable crystal-structure prediction for systems composed of highly shape-anisotropic particles. Moreover, we present the results for the dense crystal structures predicted using the FBMC method for 159 (non)convex faceted particles, on which the findings in [J. de Graaf, R. van Roij, and M. Dijkstra, Phys. Rev. Lett. 107, 155501 (2011)] were based. Finally, we comment on the process of crystal-structure prediction itself and the choices that can be made in these simulations. [ABSTRACT FROM AUTHOR]

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule. [ABSTRACT FROM AUTHOR]

This paper describes the use of a Monte Carlo model incorporating a finite-element method computing the electrostatic fields inside and outside a semiconductor, plus a ray-tracing algorithm for determining the doping contrast observed in a scanning electron microscope (SEM). This combined numerical method also enables the effects on the doping contrast of surface band-bending to be distinguished from those of external patch fields outside the specimen, as well as any applied macroscopic external fields from the detection system in the SEM. Good agreement of our new theory with experiment is obtained. The contrast characteristics in energy-filtered secondary electron images are also explained. The results of this work lead to a more advanced understanding of the doping contrast mechanisms, thereby enabling quantitative dopant profiling using the SEM. [ABSTRACT FROM AUTHOR]

Two iterative procedures have been proposed recently to calculate the chemical potentials corresponding to prescribed concentrations from grand canonical Monte Carlo (GCMC) simulations. Both are based on repeated GCMC simulations with updated excess chemical potentials until the desired concentrations are established. In this paper, we propose combining our robust and fast converging iteration algorithm [Malasics, Gillespie, and Boda, J. Chem. Phys. 128, 124102 (2008)] with the suggestion of Lamperski [Mol. Simul. 33, 1193 (2007)] to average the chemical potentials in the iterations (instead of just using the chemical potentials obtained in the last iteration). We apply the unified method for various electrolyte solutions and show that our algorithm is more efficient if we use the averaging procedure. We discuss the convergence problems arising from violation of charge neutrality when inserting/deleting individual ions instead of neutral groups of ions (salts). We suggest a correction term to the iteration procedure that makes the algorithm efficient to determine the chemical potentials of individual ions too. [ABSTRACT FROM AUTHOR]

Density functional theory as proposed by Rosenfeld [Phys. Rev. Lett. 63, 980 (1989)] is used to study hard sphere mixture exposed by cylindrically symmetric external field. Exploiting the symmetry of the system, explicit formulas for the weighted densities are derived. The resulting density profiles are compared with new grand canonical Monte Carlo simulations. The comparison reveals very good agreement between the predicted and simulated results even at high densities and very narrow pores. Finally, simple algorithms for computing complete elliptic functions of the first and second kinds that occur in the derived formulae are presented to make the paper self-contained. [ABSTRACT FROM AUTHOR]

In this paper, we present a path integral hybrid Monte Carlo (PIHMC) method for rotating molecules in quantum fluids. This is an extension of our PIHMC for correlated Bose fluids [S. Miura and J. Tanaka, J. Chem. Phys. 120, 2160 (2004)] to handle the molecular rotation quantum mechanically. A novel technique referred to be an effective potential of quantum rotation is introduced to incorporate the rotational degree of freedom in the path integral molecular dynamics or hybrid Monte Carlo algorithm. For a permutation move to satisfy Bose statistics, we devise a multilevel Metropolis method combined with a configurational-bias technique for efficiently sampling the permutation and the associated atomic coordinates. Then, we have applied the PIHMC to a helium-4 cluster doped with a carbonyl sulfide molecule. The effects of the quantum rotation on the solvation structure and energetics were examined. Translational and rotational fluctuations of the dopant in the superfluid cluster were also analyzed. [ABSTRACT FROM AUTHOR]

In this paper a new algorithm is presented that improves the efficiency of Wang and Landau algorithm or density of states (DOS) Monte Carlo simulations by employing rejected states. The algorithm is shown to have a performance superior to that of the original Wang-Landau [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)] algorithm and the more recent configurational temperature DOS algorithm. The performance of the method is illustrated in the context of results for the Lennard-Jones fluid. [ABSTRACT FROM AUTHOR]

A local method is developed for estimating the effective conductivity for materials with varying deterministic or random conductivity on domains with mixed boundary conditions. The effective conductivity is the conductivity of a virtual homogeneous material which behaves globally as the original heterogeneous material. It is shown that the effective conductivity can be calculated from the values of the potential at a relatively small number of points in the specimen. A method is developed for calculating the potential at an arbitrary point in the specimen directly, rather than extracting its value from a field solution. The method is based on some technical concepts related to properties of diffusion processes and an extension of Itô’s formula for continuous semimartingales to the case of reflected diffusion processes. However, the application of the method is intuitive and uses elementary Monte Carlo simulation algorithms. The paper presents essential facts proving the validity of the proposed method and two numerical examples illustrating the calculation of the effective conductivity for specimens with deterministic and random conductivity fields. [ABSTRACT FROM AUTHOR]

This paper formulates a hybrid Monte Carlo implementation of the Fourier path integral (FPI-HMC) approach with partial averaging. Such a hybrid Monte Carlo approach allows one to generate collective moves through configuration space using molecular dynamics while retaining the computational advantages associated with the Fourier path integral Monte Carlo method. In comparison with the earlier Metropolis Monte Carlo implementations of the FPI algorithm, the present HMC method is shown to be significantly more efficient for quantum Lennard-Jones solids and suggests that such algorithms may prove useful for efficient simulations of a range of atomic and molecular systems. [ABSTRACT FROM AUTHOR]

This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential V to be computed using a Monte Carlo simulation for a system with a possibly less complex stochastically altered potential V. By proper choices of the stochastic switching and transition probabilities, it is shown that detailed balance can be strictly maintained with respect to the original potential V. The validity of the method is illustrated with a simple one-dimensional example. The method is then generalized to multidimensional systems with any additive potential, providing a framework for the design of more efficient algorithms to simulate complex systems. A near-critical Lennard-Jones fluid with more than 20 000 particles is used to illustrate the method. The new algorithm produced a much smaller dynamic scaling exponent compared to the Metropolis method and improved sampling efficiency by over an order of magnitude. [ABSTRACT FROM AUTHOR]

In Paper I of this series the formulations of the replica-exchange multicanonical algorithm and the multicanonical replica-exchange method for Monte Carlo versions have been presented. The effectiveness of these algorithms were then tested with the system of a penta peptide, Met-enkephalin, in the gas phase. In this article the detailed comparisons of performances of these algorithms together with the regular replica-exchange method are made, taking a more complex system of a 17-residue helical peptide. It is shown that these two new algorithms are more efficient than the regular replica-exchange method. [ABSTRACT FROM AUTHOR]

The replica-exchange multicanonical algorithm and the multicanonical replica-exchange method for molecular dynamics simulations have recently been developed. In the former method the multicanonical weight factor is determined from a short replica-exchange simulation with the multiple-histogram reweighting techniques. A long multicanonical production run with high statistics is then performed with this weight factor. In this method, the process of determining the multicanonical weight factor is faster and simpler than that in the usual iterative determination. The multicanonical replica-exchange method is a further extension of the first in which a replica-exchange multicanonical simulation is performed with a small number of replicas. In this paper, we give the formulations of these two methods for Monte Carlo simulations and demonstrate the effectiveness of these algorithms for a penta peptide in the gas phase. [ABSTRACT FROM AUTHOR]

A "figure-8" sensor is so labeled because its spatial pattern resembles the character "8" with regard to the sensor's axis. This figure-8 pattern narrows as the sensor's order increases. Using two such figure-8 directional sensors of higher order, oriented perpendicularly to each other—this paper pioneers closed-form signal-processing algorithms to estimate an incident signal's azimuth-elevation bivariate direction-of-arrival. Monte Carlo simulations verify these proposed algorithms' efficacy and statistical closeness to the corresponding Cramér-Rao bounds. [ABSTRACT FROM AUTHOR]

The efficient measurement of the threshold and slope of the psychometric function (PF) is an important objective in psychoacoustics. This paper proposes a procedure that combines a Bayesian estimate of the PF with either a look one-ahead or a look two-ahead method of selecting the next stimulus presentation. The procedure differs from previously proposed algorithms in two respects: (i) it does not require the range of possible PF parameters to be specified in advance and (ii) the sequence of probe signal-to-noise ratios optimizes the threshold and slope estimates at a performance level, ɸ, that can be chosen by the experimenter. Simulation results show that the proposed procedure is robust and that the estimates of both threshold and slope have a consistently low bias. Over a wide range of listener PF parameters, the root-mean-square errors after 50 trials were ~1.2 dB in threshold and 0.14 in log-slope. It was found that the performance differences between the look one-ahead and look two-ahead methods were negligible and that an entropy-based criterion for selecting the next stimulus was preferred to a variance-based criterion. [ABSTRACT FROM AUTHOR]

Quantitative measures of acoustic similarity can reveal patterns of shared vocal behavior in social species. Many methods for computing similarity have been developed, but their performance has not been extensively characterized in noisy environments and with vocalizations characterized by complex frequency modulations. This paper describes methods of bioacoustic comparison based on dynamic time warping (DTW) of the fundamental frequency or spectrogram. Fundamental frequency is estimated using a Bayesian particle filter adaptation of harmonic template matching. The methods were tested on field recordings of flight calls from superb starlings, Lamprotornis superbus, for how well they could separate distinct categories of call elements (motifs). The fundamental-frequency-based method performed best, but the spectrogram-based method was less sensitive to noise. Both DTW methods provided better separation of categories than spectrographic cross correlation, likely due to substantial variability in the duration of superb starling flight call motifs. [ABSTRACT FROM AUTHOR]

A method based on motion vectors of feature points and particle filter has been proposed and developed for an active/moving camera for object detection and tracking purposes. The object is detected by histogram of motion vectors first, and then, on the basis of particle filter algorithm, the weighing factors are obtained via color information. In addition, re-sampling strategy and surf feature points are used to remedy the drawback of particle degeneration. Experimental results demonstrate the practicability and accuracy of the new method and are presented in the paper. [ABSTRACT FROM AUTHOR]

This paper develops a sequential trans-dimensional Monte Carlo algorithm for geoacoustic inversion in a strongly range-dependent environment. The algorithm applies advanced Markov chain Monte Carlo methods in combination with sequential techniques (particle filters) to carry out geoacoustic inversions for consecutive data sets acquired along a track. Changes in model parametrization along the track (e.g., number of sediment layers) are accounted for with trans-dimensional partition modeling, which intrinsically determines the amount of structure supported by the data information content. Challenging issues of rapid environmental change between consecutive data sets and high information content (peaked likelihood) are addressed by bridging distributions implemented using annealed importance sampling. This provides an efficient method to locate high-likelihood regions for new data which are distant and/or disjoint from previous high-likelihood regions. The algorithm is applied to simulated reflection-coefficient data along a track, such as can be collected using a towed array close to the seabed. The simulated environment varies rapidly along the track, with changes in the number of layers, layer thicknesses, and geoacoustic parameters within layers. In addition, the seabed contains a geologic fault, where all layers are offset abruptly, and an erosional channel. Changes in noise level are also considered. [ABSTRACT FROM AUTHOR]

The 1953 publication, “Equation of State Calculations by Very Fast Computing Machines” by N. Metropolis, A. W. Rosenbluth and M. N. Rosenbluth, and M. Teller and E. Teller [J. Chem. Phys. 21, 1087 (1953)] marked the beginning of the use of the Monte Carlo method for solving problems in the physical sciences. The method described in this publication subsequently became known as the Metropolis algorithm, undoubtedly the most famous and most widely used Monte Carlo algorithm ever published. As none of the authors made subsequent use of the algorithm, they became unknown to the large simulation physics community that grew from this publication and their roles in its development became the subject of mystery and legend. At a conference marking the 50th anniversary of the 1953 publication, Marshall Rosenbluth gave his recollections of the algorithm’s development. The present paper describes the algorithm, reconstructs the historical context in which it was developed, and summarizes Marshall’s recollections. [ABSTRACT FROM AUTHOR]