Showing papers on "Dynamic Monte Carlo method published in 1989"
TL;DR: In this article, the authors present a method for optimizing the analysis of data from multiple Monte Carlo computer simulations over wide ranges of parameter values, which is applicable to simulations in lattice gauge theories, chemistry, and biology, as well as statistical mechanics.
Abstract: We present a new method for optimizing the analysis of data from multiple Monte Carlo computer simulations over wide ranges of parameter values. Explicit error estimates allow objective planning of the lengths of runs and the parameter values to be simulated. The method is applicable to simulations in lattice gauge theories, chemistry, and biology, as well as statistical mechanics.
2,198 citations
TL;DR: This paper provides all the details necessary for implementation of a Monte Carlo program andVariance reduction schemes that improve the effiency of the Monte Carlo method are discussed.
Abstract: The Monte Carlo method is rapidly becoming the model of choice for simulating light transport in tissue. This paper provides all the details necessary for implementation of a Monte Carlo program. Variance reduction schemes that improve the eciency of the Monte Carlo method are discussed. Analytic expressions facilitating convolution calculations for finite flat and Gaussian beams are included. Useful validation benchmarks are presented.
691 citations
357 citations
TL;DR: In this article, simple Monte Carlo significance testing has many applications, particularly in the preliminary analysis of spatial data, where the value of the test statistic is ranked among a random sample of values generated according to the null hypothesis.
Abstract: SUMMARY Simple Monte Carlo significance testing has many applications, particularly in the preliminary analysis of spatial data. The method requires the value of the test statistic to be ranked among a random sample of values generated according to the null hypothesis. However, there are situations in which a sample of values can only be conveniently generated using a Markov chain, initiated by the observed data, so that independence is violated. This paper describes two methods that overcome the problem of dependence and allow exact tests to be carried out. The methods are applied to the Rasch model, to the finite lattice Ising model and to the testing of association between spatial processes. Power is discussed in a simple case.
301 citations
TL;DR: In this paper, the authors present a method for optimizing the analysis of data from multiple Monte Carlo computer simulations over wide ranges of parameter values, which is applicable to simulations in lattice gauge theories, chemistry, and biology, as well as statistical mechanics.
Abstract: We present a new method for optimizing the analysis of data from multiple Monte Carlo computer simulations over wide ranges of parameter values. Explicit error estimates allow objective planning of the lengths of runs and the parameter values to be simulated. The method is applicable to simulations in lattice gauge theories, chemistry, and biology, as well as statistical mechanics.
279 citations
TL;DR: In this article, a new model is presented and discussed that allows Monte Carlo simulations to be carried out with a proper energy barrier crossing, and results are presented for the surface diffusion coefficient and the growth exponent of domain ordering of a half-monolayer of adatoms experiencing nearest-and next-nearest-neighbor repulsive lateral interactions (equal in magnitude), both on a square lattice.
Abstract: A new model is presented and discussed that allows Monte Carlo simulations to be carried out with a proper energy barrier crossing. Results are presented for the surface diffusion coefficient and the growth exponent of domain ordering of a half-monolayer of adatoms experiencing nearest- and next-nearest-neighbor repulsive lateral interactions (equal in magnitude), both on a square lattice. The results are compared with those derived using both Kawasaki dynamics and a Metropolis walk. The reasons why neither of the latter methods can be expected, in general, to describe thermally excited, time-dependent phenomena are explained and discussed.
198 citations
TL;DR: A simple recursive iteration of the leapfrog discretization of Newton's equations leads to a removal of the finite-step-size error to any desired order in a manner that preserves phase-space areas and reversibility.
Abstract: We present a simple recursive iteration of the leapfrog discretization of Newton's equations which leads to a removal of the finite-step-size error to any desired order. This is done in a manner that preserves phase-space areas and reversibility, as required for use in the hybrid Monte Carlo method for simulating fermionic fields. The resulting asymptotic volume dependence is exp((ln/ital V/)/sup 1/2/). We test the scheme on the (2+1)-dimensional Hubbard model.
164 citations
TL;DR: A new method for the numerical integration of very high dimensional functions is introduced and implemented based on the Metropolis' Monte Carlo algorithm, and the improvement in accuracy is found to be substantial comparing to the conventional crude Monte Carlo integration.
Abstract: A new method for the numerical integration of very high dimensional functions is introduced and implemented based on the Metropolis' Monte Carlo algorithm. The logarithm of the high dimensional integral is reduced to a 1-dimensional integration of a certain statistical function with respect to a scale parameter over the range of the unit interval. The improvement in accuracy is found to be substantial comparing to the conventional crude Monte Carlo integration. Several numerical demonstrations are made, and variability of the estimates are shown.
140 citations
TL;DR: In this paper, a Monte Carlo simulation of a model heterogeneous catalytic chemical reaction which is deterministically monostable was performed and it was shown that the behavior of this system is a consequence of the interaction of noise with the spatial degrees of freedom on the model catalytic surface.
Abstract: We find a noise-induced transition to bistability in a Monte Carlo simulation of a model heterogeneous catalytic chemical reaction which is deterministically monostable. Analysis of the probability density function and the correlation integral of time series of this model indicates the existence and central role of noise in this transition. We find that the behavior of this system is a consequence of the interaction of noise with the spatial degrees of freedom on the model catalytic surface.
123 citations
TL;DR: In this article, a self-consistent decoupling of the associated hierarchy of kinetic equations for time-dependent correlation functions is employed for non-tracer coefficients in a simple cubic binary random lattice gas.
Abstract: Linear response formulae for the phenomenological atomic transport coefficients LXY of non-equilibrium thermodynamics are analysed for the randomlattice-gas model in which all configurations have the same energy. A new self-consistent decoupling of the associated hierarchy of kinetic equations for time-dependent correlation functions is employed. For a binary system with an atom jump-rate ratio of ten to one for the two components the agreement with Monte Carlo simulations is generally good for both tracer and non-tracer coefficients and is more complete than for earlier theories. New Monte Carlo simulation results for non-tracer coefficients in a simple cubic binary random lattice gas are presented.
TL;DR: In this article, the effect of simulation order on the level accuracy and power of Monte Carlo tests has been discussed, and it is shown that if the level of a Monte Carlo test is known only nominally, not precisely, then the level error of the test is an order of magnitude less than that of the corresponding asymptotic test.
Abstract: We discuss the effect of simulation order on level accuracy and power of Monte Carlo tests, in a very general setting. Both parametric problems, with or without nuisance parameters, and nonparametric problems are treated by a single unifying argument. It is shown that if the level of a Monte Carlo test is known only nominally, not precisely, then the level error of a Monte Carlo test is an order of magnitude less than that of the corresponding asymptotic test. This result is available whenever the test statistic is asymptotically pivotal, even if the number of simulations is held fixed as the sample size n increases. It implies that Monte Carlo methods are a real alternative to asymptotic methods. We also show that, even if the number of simulations is held fixed, a Monte Carlo test is able to distinguish between the null hypothesis and alternative hypotheses distant n-'12 from the null.
TL;DR: A method for calculating the production of direct photons beyond the leading-logarithm approximation has been developed, utilizing a combination of analytic and Monte Carlo integration methods.
Abstract: A method for calculating the production of direct photons beyond the leading-logarithm approximation has been developed, utilizing a combination of analytic and Monte Carlo integration methods. The method is described and examples are given, including a comparison with experimental results for the inclusive single-photon invariant cross section and the photon-plus-jet cross section. The flexibility of the Monte Carlo technique makes it straightforward to calculate a variety of observables and to take into account experimental cuts while still retaining the next-to-leading-logarithm terms.
TL;DR: In this article, an efficient projector Monte Carlo method is proposed to calculate the elementary excitation spectrum of quantum systems, which is applied to the spin-1/2 and -1 Heisenberg antiferromagnetic chain with length 32.
Abstract: An efficient Monte Carlo method is proposed to calculate the elementary excitation spectrum of quantum systems. The lowest energy with arbitrary momentum is obtained by the projector Monte Carlo method. This is applied to the spin-(1/2 and -1 Heisenberg antiferromagnetic chain with length 32. For the S=(1/2 case, the spectrum coincides completely with the spectrum of des Cloiseaux and Pearson. For the S=1 case, the spectrum has a gap at momentum \ensuremath{\pi} as was predicted by Haldane. The value of the gap coincides with the calculation of Nightingale and Blote. The spectrum satisfies a variational relation with the structure factor.
TL;DR: In this paper, the angular-momentum projection operator was used to transform nonlocal potentials based on angular momentum projection operators into local, yet angular momentum dependent, pseudo-heuristics by modifying the kinetic energy operator.
Abstract: Nonlocal potentials based on angular-momentum projection operators can be transformed into local, yet angular-momentum dependent, pseudo-Hamiltonians by modifying the kinetic energy operator. Ionic pseudo-Hamiltonians of this type can replace core electrons in atomic calculations. Their use in Green's-Function Monte Carlo simulations gives accurate electron affinities, ionization, and binding energies for second-row atoms and diatomics. This opens the way to quantum simulations of many condensed-matter systems.
TL;DR: In this paper, the utility of deterministic nonstationary models of charge transport in GaAs is studied, including energy and momentum conserving, energy conserving and electron-temperature formulations.
Abstract: A study of the utility of deterministic nonstationary models of charge transport in GaAs is presented. The models considered include energy and momentum conserving, energy conserving, and electron-temperature formulations. Predictions of the models are compared with results calculated using a more detailed Monte Carlo-based scattering-process-level simulation. The basis of the comparison is calculated trajectories in velocity-energy-field space for a range of time-dependent electric field forcing functions. All the nonstationary transport models considered are found to be in reasonable agreement with Monte Carlo results for all but the most extreme circumstances considered and to be greatly superior to the drift-diffusion approximation. Strengths, weaknesses, and applicability of individual models are discussed. >
01 Jan 1989
TL;DR: In this article, a general method of calculating the substrate current for n-MOSFETs, using a two-dimensional conventional device simulator coupled with a full-band-structure Monte Carlo simulation, has been enhanced through the use of efficient estimators and statistical weighting of the high-energy electrons.
Abstract: A general method of calculating the substrate current for n-MOSFETs, using a two-dimensional conventional device simulator coupled with a full-band-structure Monte Carlo simulation, has been enhanced through the use of efficient estimators and statistical weighting of the high-energy electrons. The detailed physics of hot-electron effects in MOSFETs is explained on the basis of the energy distribution as a function of the spatial variables. Monte Carlo results show that the distribution function in the region of the device that makes the largest contribution to the substrate current does not fit a Maxwell-Boltzmann function. The effective cooling of the distribution, due in part to energy loss to impact ionization, is shown clearly. The results of the Monte Carlo calculation are used to evaluate the validity of the assumption of a constant mean path for inelastic scattering used in various analytic treatments. The calculated values of substrate current are compared to experimental results. >
TL;DR: Through an application of the quantum Monte Carlo technique, the thermal equilibrium properties of the one-dimensional model proposed by Davydov for the description of energy transport processes in the α-helix are investigated.
Abstract: Through an application of the quantum Monte Carlo technique, we investigate the thermal equilibrium properties of the one-dimensional model proposed by Davydov for the description of energy transport processes in the α-helix. The calculations in this paper are free from uncontrollable approximations. The deformation of the lattice about a single (mobile) excitation is computed at a number of temperatures for a variety of coupling strengths. Broad and smooth coherent localized quasi-particle units are observed at low temperatures for some parameters of the system. For the “standard” α-helix data, the quasi-particle is embedded in strong fluctuations and is very localized. At temperatures greater than a few Kelvins, the quasi-particle attains its most localized form. We also considered scenarios in which several excitations are present in the system simultaneously; some preliminary results for the density-density correlation are calculated. The structure of polaron clusters is found, and their implication for biological systems is discussed.
TL;DR: In this paper, the authors reexamine the behavior of weakly first-order systems by performing extensive Monte Carlo simulations, and demonstrate that the ''novel'' states previously observed in internal energy distribution histograms tend to disappear when runs of sufficient length are used.
Abstract: A new kind of finite-size phenomenon in the five-state Potts model in two dimensions, a ``false'' ground state, was recently reported by Katznelson and Lauwers based on Monte Carlo studies of large lattices. We reexamine the behavior of this weakly first-order system by performing extensive Monte Carlo simulations, and demonstrate that the ``novel'' states previously observed in internal-energy-distribution histograms tend to disappear when runs of sufficient length are used. We present evidence that very strong critical slowing down and a pseudodivergent correlation length are responsible for the observed effects. Our additional analysis of finite-size effects in the ten-state Potts model on small lattices (L\ensuremath{\le}10) shows a crossover of scaling from ${L}^{\mathrm{\ensuremath{-}}d}$ behavior (observed earlier on larger lattices) to a nonanalytic form. This result is used to discuss the observed nonanalytic scaling of thermodynamic quantities in the five-state Potts model.
TL;DR: In this article, the interdependence of surface morphology and the dissolution kinetics of minerals is studied by means of Monte Carlo simulations, and the results indicate that steady-state surface morphologies are formed after a few lattice layers have been dissolved.
TL;DR: The three-dimensional conformation of Met-enkephalin, corresponding to the lowest minimum of the empirical potential energy function ECEPP/2 (empirical conformational energy program for peptides), has been determined using a new algorithm, viz. the Electrostatically Driven Monte Carlo Method.
Abstract: The three-dimensional conformation of Met-enkephalin, corresponding to the lowest minimum of the empirical potential energy function ECEPP/2 (empirical conformational energy program for peptides), has been determined using a new algorithm, viz. the Electrostatically Driven Monte Carlo Method. This methodology assumes that a polypeptide or protein molecule is driven toward the native structure by the combined action of electrostatic interactions and stochastic conformational changes associated with thermal movements. These features are included in the algorithm that produces a Monte Carlo search in the conformational hyperspace of the polypeptide, using electrostatic predictions and a random sampling technique to locate low-energy conformations. In addition, we have incorporated an alternative mechanism that allows the structure to escape from some conformational regions representing metastable local energy minima and even from regions of the conformational space with great stability. In 33 test calculations on Met-enkephalin, starting from arbitrary or completely random conformations, the structure corresponding to the global energy minimum was found inall the cases analyzed, with a relatively small search of the conformational space. Some of these starting conformations wereright orleft-handed α-helices, characterized by good electrostatic interactions involving their backbone peptide dipoles; nevertheless, the procedure was able to convert such locally stable structures to the global-minimum conformation.
TL;DR: In this paper, a simple extension of the Carnahan-Starling equation of state to symmetric mixtures of hard spheres with positively or negatively non-additive diameters is presented.
TL;DR: The first mirror potential GFMC calculations in a many-fermion problem are reported, comparing them with transient estimation and fixed-node studies to illustrate the strengths and weaknesses of each.
Abstract: Variational Monte Carlo and several many-fermion Green's-function Monte Carlo (GFMC) algorithms are used to study the ground state of liquid /sup 3/He. We report the first mirror potential GFMC calculations in a many-fermion problem, comparing them with transient estimation and fixed-node studies to illustrate the strengths and weaknesses of each. GFMC results with the Aziz HFDHE2 interaction are in good agreement with experiment, yielding energies within approximately 0.1 K per particle. In addition, each of these calculations predict a kinetic energy per particle of between 12 and 12.5 K.
TL;DR: A new method is introduced for analytically continuing imaginary-time data from quantum Monte Carlo calculations to the real-frequency axis based on a least-squares-fitting procedure with constraints of positivity and smoothness on theReal-frequency quantities.
Abstract: A new method is introduced for analytically continuing imaginary-time data from quantum Monte Carlo calculations to the real-frequency axis. The method is based on a least-squares fitting procedure with constraints of positivity and smoothness on the real-frequency quantities. Results are shown for the single-particle spectral-weight function and density of states for the half-filled two-dimensional Hubbard model.
TL;DR: In this article, the authors show that hysteresis is a non-equilibrium phenomenon that cannot be properly treated by equilibrium statistical-mechanical methods, and that the degree of hystresis can be diminished by increasing the surface area of the pore wall and by extending the Markov chain.
Abstract: The grand-canonical ensemble Monte Carlo method has been used to study sorption isotherms (plots of density versus chemical potential) for a rare-gas fluid in a slit-pore whose plane-parallel walls comprise rigidly fixed rare-gas atoms. Hysteresis in the vicinity of the capillary-condensation transition is evinced by fluctuations between liquid and vapour phases as the length of the Markov chain increases (at fixed chemical potential). The degree of hysteresis, which reflects the non-ergodic behaviour of the Markov chain, can be diminished by increasing the surface area of the pore wall and by extending the Markov chain. It is concluded that hysteresis is a non-equilibrium phenomenon that cannot be properly treated by equilibrium statistical-mechanical methods.