Showing papers on "Monte Carlo method published in 1988"
TL;DR: In this paper, a new method for using the data from Monte Carlo simulations that can increase the efficiency by 2 or more orders of magnitude is presented. But the method is not applicable to statistical models and lattice-gauge theories.
Abstract: We present a new method for using the data from Monte Carlo simulations that can increase the efficiency by 2 or more orders of magnitude. A single Monte Carlo simulation is sufficient to obtain complete thermodynamic information over the entire scaling region near a phase transition. The accuracy of the method is demonstrated by comparison with exact results for the d=2 Ising model. New results for d=2 eight-state Potts model are also presented. The method is generally applicable to statistical models and lattice-gauge theories.
2,219 citations
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TL;DR: In particular, the tests developed by Phillips and Perron (1988) seem more sensitive to model misspeciflcation than the high order autoregressive approximation suggested by Said and Diekey(1984) as mentioned in this paper.
Abstract: Recent work by Said and Dickey (1984 ,1985) , Phillips (1987), and Phillips and Perron(1988) examines tests for unit roots in the autoregressive part of mixed autoregressive-integrated-moving average (ARIHA) models (tests for stationarity). Monte Carlo experiments show that these unit root tests have different finite sample distributions than the unit root tests developed by Fuller(1976) and Dickey and Fuller (1979, l981) for autoregressive processes. In particular, the tests developed by Philllps (1987) and Phillips and Perron (1988) seem more sensitive to model misspeciflcation than the high order autoregressive approximation suggested by Said and Diekey(1984).
1,495 citations
TL;DR: In this paper, a new technique based on the standard Monte Carlo simulation method with Markov chain sampling is developed, in which a set of three dimensional particle configurations are generated that are consistent with the experimentally measured structure factor.
Abstract: We have developed a new technique, based on the standard Monte Carlo simulation method with Markov chain sampling, in which a set of three dimensional particle configurations are generated that are consistent with the experimentally measured structure factor. A(Q), and radial distribution function, g(r), of a liquid or other disordered system. Consistency is determined by a standard χ2 test using the experimental errors. No input potential is required, we present initial results for liquid argon. Since the technique can work directly from the structure factor it promises to be useful for modelling the structures of glasses or amorphous materials. It also has other advantages in multicomponent systems and as a tool for experimental data analysis.
1,394 citations
TL;DR: A Monte Carlo optimization technique called “simulated annealing” is a descent algorithm modified by random ascent moves in order to escape local minima which are not global minima.
Abstract: A Monte Carlo optimization technique called “simulated annealing” is a descent algorithm modified by random ascent moves in order to escape local minima which are not global minima. The level of randomization is determined by a control parameter T, called temperature, which tends to zero according to a deterministic “cooling schedule.” We give a simple necessary and sufficient condition on the cooling schedule for the algorithm state to converge in probability to the set of globally minimum cost states. In the special case that the cooling schedule has parametric form Tt = c/log1 + t, the condition for convergence is that c be greater than or equal to the depth, suitably defined, of the deepest local minimum which is not a global minimum state.
1,282 citations
TL;DR: In this article, the authors studied the distribution function P L ( s ) of the local order parameters in finite blocks of linear dimension L for Ising lattices of dimension d = 2,3 and 4.
Abstract: The distribution function P L ( s ) of the local order parameters in finite blocks of linear dimension L is studied for Ising lattices of dimensionality d = 2,3 and 4. Apart from the case where the block is a subsystem of an infinite lattice, also the distribution in finite systems with free [ P L ( f ) ( s )] and periodic [ P L ( p ) ( s )] boundary conditions is treated. Above the critical point T c , these distributions tend for large L towards the same gaussian distribution centered around zero block magnetization, while below T c these distributions tend towards two gaussians centered at ± M , where M is the spontaneous magnetization appearing in the infinite systems. However, below T c the wings of the distribution at small | s | are distinctly nongaussian, reflecting two-phase coexistence. Hence the distribution functions can be used to obtain the interface tension between ordered phases. At criticality, the distribution functions tend for large L towards scaled universal forms, though dependent on the boundary conditions. These scaling functions are estimated from Monte Carlo simulations. For subsystem-blocks, good agreement with previous renormalization group work of Bruce is obtained. As an application, it is shown that Monte Carlo studies of critical phenomena can be improved in several ways using these distribution functions: ( i ) standard estimates of order parameter, susceptibility, interface tension are improved ( ii ) T c can be estimated independent of critical exponent estimates ( iii ) A Monte Carlo “renormalization group” similar to Nightingale's phenomenological renormalization is proposed, which yields fairly accurate exponent estimates with rather moderate effort ( iv ) Information on coarse-grained hamiltonians can be gained, which is particularly interesting if the method is extended to more general Hamiltonians.
1,259 citations
TL;DR: In this article, the Gibbs-ensemble Monte Carlo simulation methodology for phase equilibrium calculations proposed by Panagiotopoulos is generalized and applied to mixture and membrane equilibria, and an alternative derivation of the Gibbs simulation criteria based on the limiting distributions for the appropriate statistical mechanical ensembles is presented.
Abstract: The Gibbs-ensemble Monte Carlo simulation methodology for phase equilibrium calculations proposed by Panagiotopoulos [1] is generalized and applied to mixture and membrane equilibria. An alternative derivation of the Gibbs simulation criteria based on the limiting distributions for the appropriate statistical mechanical ensembles is presented. The method is then generalized for the calculation of phase equilibria of mixtures by simulation in a constantpressure Gibbs ensemble and the calculation of equilibria across semipermeable membranes with an imposed osmotic pressure difference. The method is used to calculate phase equilibria for binary mixtures of Lennard-Jones molecules. Good agreement is found with published results obtained using other simulation techniques. The computer time required for the Gibbs method is only a small fraction of the corresponding requirement for previously available simulation techniques. Calculations for simple osmotic systems are performed for the first time by simulation, ...
1,049 citations
Journal Article•
987 citations
TL;DR: In this paper, the authors argue that the quadratic assignment procedure (QAP) is superior to OLS for testing hypothesis in both simple and multiple regression models based on dyadic data, such as found in network analysis.
946 citations
IBM1
TL;DR: In the systems considered, the inclusion of the full band structure has the effect of reducing the amount of velocity overshoot via electron transfer to upper conduction valleys, particularly at large biases and low temperatures.
Abstract: The physics of electron transport in Si and GaAs is investigated with use of a Monte Carlo technique which improves the "state-of-the-art" treatment of high-energy carrier dynamics. (1) The semiconductor is modeled beyond the effective-mass approximation by using the band structure obtained from empirical-pseudopotential calculations. (2) The electron-phonon, electron-impurity, and electron-electron scattering rates are computed in a way consistent with the full band structure of the solid, thus accounting for density-of-states and matrix-element effects more accurately than previous transport formulations. (3) The long-range carrier-carrier interaction and space-charge effects are included by coupling the Monte Carlo simulation to a self-consistent two-dimensional Poisson solution updated at a frequency large enough to resolve the plasma oscillations in highly doped regions. The technique is employed to study experimental submicrometer Si field-effect transistors with channel lengths as small as 60 nm operating at 77 and 300 K. Velocity overshoot and highly nonlocal, off-equilibrium phenomena are investigated together with the role of electron-electron interaction in these ultrasmall structures. In the systems considered, the inclusion of the full band structure has the effect of reducing the amount of velocity overshoot via electron transfer to upper conduction valleys, particularly at large biases and low temperatures. The reasonableness of the physical picture is supported by the close agreement of the results of the simulation to available experimental data.
906 citations
TL;DR: This paper finds that the pivot algorithm is extraordinarily efficient: one “effectively independent” sample can be produced in a computer time of orderN, and presents a rigorous proof of ergodicity and numerical results on self-avoiding walks in two and three dimensions.
Abstract: The pivot algorithm is a dynamic Monte Carlo algorithm, first invented by Lal, which generates self-avoiding walks (SAWs) in a canonical (fixed-N) ensemble with free endpoints (hereN is the number of steps in the walk). We find that the pivot algorithm is extraordinarily efficient: one “effectively independent” sample can be produced in a computer time of orderN. This paper is a comprehensive study of the pivot algorithm, including: a heuristic and numerical analysis of the acceptance fraction and autocorrelation time; an exact analysis of the pivot algorithm for ordinary random walk; a discussion of data structures and computational complexity; a rigorous proof of ergodicity; and numerical results on self-avoiding walks in two and three dimensions. Our estimates for critical exponents areυ=0.7496±0.0007 ind=2 andυ= 0.592±0.003 ind=3 (95% confidence limits), based on SAWs of lengths 200⩽N⩽10000 and 200⩽N⩽ 3000, respectively.
793 citations
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TL;DR: The Hybrid Monte Carlo (HMC) algorithm for lattice gauge theory calculations as discussed by the authors is a large step method which has none of the discrete step size errors usually associated with the Molecular Dynamics, Langevin, or Hybrid algorithms.
Abstract: I discuss the Hybrid Monte Carlo algorithm for performing lattice gauge theory calculations. This is a large step method which has none of the discrete step size errors usually associated with the Molecular Dynamics, Langevin, or Hybrid algorithms. The method allows the inclusion of dynamical fermion fields in a straightforward way.
TL;DR: In this paper, the authors extended their previous work on the simulation of coherent soft-gluon radiation to hard collisions that involve incoming as well as outgoing coloured partons, and proposed a new Monte Carlo program which incorporates this procedure, together with other new features such as azimuthal correlations due to gluon polarization and interference.
TL;DR: A simple explanation of the Swendsen-Wang algorithm for Potts models in terms of a joint model of Potts spin variables interacting with bond occupation variables is given and how to generalize this representation to arbitrary models is shown.
Abstract: We give a simple explanation of the Swendsen-Wang algorithm for Potts models in terms of a joint model of Potts spin variables interacting with bond occupation variables. We then show how to generalize this representation, as well as the corresponding Monte Carlo algorithm, to arbitrary models. We give initial results of tests of the new algorithm on the two-dimensional XY model.
TL;DR: This work presents a procedure for obtaining optimized trial wave functions for use in quantum Monte Carlo calculations that have both smaller statistical errors and improved expectation values, compared to commonly used functions.
Abstract: We present a procedure for obtaining optimized trial wave functions for use in quantum Monte Carlo calculations that have both smaller statistical errors and improved expectation values, compared to commonly used functions. Results are presented for several two-electron atoms and ions (including some excited states) and for the Be atom.
TL;DR: In this paper, the problem of structural response variability resulting from the spatial variability of material properties of structures, when they are subjected to static loads of a deterministic nature, is dealt with with the aid of the finite element method.
Abstract: With the aid of the finite element method, the present paper deals with the problem of structural response variability resulting from the spatial variability of material properties of structures, when they are subjected to static loads of a deterministic nature. The spatial variabilities are modeled as two‐dimensional stochastic fields. The finite element discretization is performed in such a way that the size of each element is sufficiently small. Then, the present paper takes advantage of the Neumann expansion technique in deriving the finite element solution for the response variability within the framework of the Monte Carlo method. The Neumann expansion technique permits more detailed comparison between the perturbation and Monte Carlo solutions for accuracy, convergence, and computational efficiency. The result from such a Monte Carlo method is also compared with that based on the commonly used perturbation method. The comparison shows that the validity of the perturbation method is limited to the c...
TL;DR: In this article, an iterative Monte-Carlo simulation procedure for structural analysis is proposed, which utilizes results from simulation to adapt the importance sampling density to the specific problem, and a significant reduction of the statistical error of the estimated failure probability is achieved.
TL;DR: In this paper, the number of electron-like single-prong events is in good agreement with the predictions of a Monte Carlo calculation based on atmospheric neutrino interactions in the KAMIOKANDE detector.
TL;DR: In this paper, a review of feature selection for multidimensional pattern classification is presented, and the potential benefits of Monte Carlo approaches such as simulated annealing and genetic algorithms are compared.
Abstract: We review recent research on methods for selecting features for multidimensional pattern classification. These methods include nonmonotonicity-tolerant branch-and-bound search and beam search. We describe the potential benefits of Monte Carlo approaches such as simulated annealing and genetic algorithms. We compare these methods to facilitate the planning of future research on feature selection.
01 Jan 1988
TL;DR: The simulation of electron and photon transport by Monte Carlo techniques was discussed at a conference in 1987 as discussed by the authors, which brought together in one place a large collection of information on this subject, which was normally spread over a large area of applications.
Abstract: This book is a report on a conference held in September, 1987, to discuss the simulation of electron and photon transport by Monte Carlo techniques. The book brings together in one place a large collection of information on this subject, which is normally spread over a large area of applications. Authors present papers on several of the most popular codes in use at this time, discussing applications, operation, and limitations of the codes. Applications range from radiation therapy to high energy physics, from modeling dosimetry and dosimeters to planning radiation applications for cancer patients. There is also discussion on the basic physics which goes into these codes, cross sections, multiple scattering, energy loss straggling, as well as cautions on how to avoid erronious results by blindly applying the codes to problems. Separate abstracts have been prepared for each chapter in the book.
TL;DR: L'etat fondamental d'antiferromagnetiques d'Heisenberg a spin 1/2 a reseaux carre et triangulaire est determine par une extension de la methode variationnelle de Kasteleijn et Marshall.
Abstract: We generalize a type of variational wave function introduced by Kasteleijn and Marshall, to include long-range correlations and nonbipartite lattices. We find the lowest-energy wave function in a three-parameter space for both the square- and triangular-lattice spin-\textonehalf{} Heisenberg antiferromagnets. This produces useful upper bounds on the ground-state energies of these systems. The wave functions are completely explicit, so that precise estimates of expectation values are readily obtained by Monte Carlo techniques. It appears that the antiferromagnet has long-range magnetic order on the triangular lattice, as well as on the square lattice.
TL;DR: This article reviews various methods for the Monte Carlo simulation of models for long flexible polymer chains, namely self-avoiding random walks at various lattices, and discusses the basic ideas on which the various algorithms are based as well as their limitations.
TL;DR: In this paper, the free energy of binding for two methane-like particles at their contact separation of 4 A has been computed in TIP4P water using Monte Carlo simulations with statistical perturbation theory.
Abstract: An efficient procedure is noted for computing absolute free energies of binding for complexes in solution. Two series of computer simulations are required in which the substrate is annihilated in the solvent by itself and in the solvated complex. For illustration, the free energy of binding for two methane‐like particles at their contact separation of 4 A has been computed in TIP4P water. Though several alternatives are possible, in this case, Monte Carlo simulations were employed with statistical perturbation theory in the NPT ensemble at 25 °C and 1 atm. The results for the free energy of binding as well as for the potential of mean force are consistent with prior findings from the integral equation theory of Pratt and Chandler.
TL;DR: In this paper, a new Monte Carlo method suitable for simulations of chain molecules over a wide range of densities was introduced, and results for the equation of state of chains composed of 4, 8 and 16 freely joined hard spheres were compared with the predictions of several theories.
Abstract: We introduce a new Monte Carlo method suitable for simulations of chain molecules over a wide range of densities. Results for the equation of state of chains composed of 4, 8, and 16 freely joined hard spheres are compared with the predictions of several theories. The density profile of the fluid in the vicinity of the wall, and the scaling of the pressure with chain length are also discussed.
TL;DR: The EGS Monte Carlo code was used to generate photon energy deposition kernels which describe the energy deposited by charged particles set in motion by primary, first scattered, second scattered, multiple scattered and bremsstrahlung plus annihilation photons.
Abstract: The EGS Monte Carlo code was used to generate photon energy deposition kernels which describe the energy deposited by charged particles set in motion by primary, first scattered, second scattered, multiple scattered and bremsstrahlung plus annihilation photons. These were calculated for a water medium irradiated with monoenergetic photons with energies in the range 0.1-50 MeV. In addition to the primary energy deposition kernels, primary charged particle transport was further characterised by computing the effective centre of the voxels, and the effective penetration depth, effective radius and effective lateral distance travelled by these particles. The dose per unit collision kerma for parallel monoenergetic primary photons beta ' was calculated. Additional applications of the energy deposition kernels are discussed.
TL;DR: In this paper, a general formalism and methodology are presented for the Monte Carlo simulation of equilibria in multicomponent systems, and are applied to the study of phase equilibrium in a model binary mixture, and to phase and chemical equilibrium in the ternary mixture Br2−Cl2−BrCl.
Abstract: A general formalism and methodology are presented for the Monte Carlo simulation of equilibria in multicomponent systems, and are applied to the study of phase equilibrium in a model binary mixture, and to phase and chemical equilibrium in the ternary mixture Br2−Cl2−BrCl. Very good agreement with available experimental data is obtained. The formalism is based upon an ensemble in which the ratios of all fugacities to a reference fugacity are imposed. Simulations of mixtures performed in this ensemble fluctuate in composition while keeping constant the total number of particles. The reference fugacity is computed by integration of simulation averages of the composition for varying values of the fugacity ratios. Several features of the approach are: (1) it can be readily applied to mixtures of any number of components, even to polydisperse systems, with little additional computational effort; (2) the chemical potential of only one species at one state need be evaluated by conventional techniques, regardless...
TL;DR: In this paper, the authors proposed to sample antithetically rather than randomly from the posterior density in Bayesian inference using Monte Carlo integration and established conditions under which the number of replications required with antithetic sampling relative to the number required with random sampling is inversely proportional to sample size.
TL;DR: The results of Monte Carlo simulations of the static properties of polymer melts confined between hard walls are presented in this article. But the results of these simulations are restricted to the case where the beads are assumed to interact with an empirical 6-12 Lennard-Jones potential which has parameters chosen to simulate polyethylene melt at 400 K.
Abstract: In this paper, we present the results of Monte Carlo simulations of the static properties of polymer melts confined between hard walls. The simulations are conducted in the canonical ensemble with a method that is a combination of reptation and crankshaft motions. 1250 polymer chains each comprising of 100 connected beads are placed in a box which allows for the simulation of a typical polymer melt confined between two hard plates at a separation of 51 bead diameters. Noncovalently bonded beads are assumed to interact with an empirical 6‐12 Lennard‐Jones potential which has parameters chosen to simulate a polyethylene melt at 400 K. From the analysis of the simulation results we show the existence of two relevant length scales in the problem. Single‐chain statistics are perturbed by the wall, and this effect is screened out only after one proceeds to a distance comparable to twice the unperturbed radius of gyration of the polymer chain. However, many‐chain statistics, i.e., packing and orientation of chain segments, are screened out as soon as one proceeds about three times the bead size from the wall. The simulation also allows for the study of the conformations of chains near the wall, and we observe that chains near the surface are flattened into nearly two‐dimensional structures. The interface therefore corresponds to a region where chain configurations gradually evolve from this nearly two‐dimensional structure to the unperturbed, three‐dimensional Gaussian configurations in the bulk.
TL;DR: In this article, a simple intermolecular potential function has been devised to yield good thermodynamic and structural results for liquid acetonitrile The function was tested in Monte Carlo statistical mechanics simulations for the liquid at temperatures of 25°C and 70°C at 1 atm.
Abstract: A simple intermolecular potential function has been devised to yield good thermodynamic and structural results for liquid acetonitrile The function was tested in Monte Carlo statistical mechanics simulations for the liquid at temperatures of 25°C and 70°C at 1 atm. The average errors in the computed densities and heats of vaporization are 1–2 per cent. The structural results are presented by means of radial distribution functions and dipole-dipole correlation functions, and compared with prior findings. In addition, the importance of the electrostatic interactions in determining the liquid's structure is illustrated by the results of a simulation at 25°C with the partial charges set to zero.
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TL;DR: In this paper, the authors examined the finite sample properties of the variance ratio test of the random walk hypothesis via Monte Carlo simulations under two null and three alternative hypotheses, and compared the performance of the Dickey-Fuller t and the Box-Pierce Q statistics.
Abstract: We examine the finite sample properties of the variance ratio test of the random walk hypothesis via Monte Carlo simulations under two null and three alternative hypotheses. These results are compared to the performance of the Dickey-Fuller t and the Box-Pierce Q statistics. Under the null hypothesis of a random walk with independent and identically distributed Gaussian increments, the empirical size of all three tests are comparable. Under a heteroscedastic random walk null, the variance ratio test is more reliable than either the Dickey-Fuller or Box-Pierce tests. We compute the power of these three tests against three alternatives of recent empirical interest: a stationary AR(1), the sum of this AR(1) and a random walk, and an integrated AR( 1). By choosing the sampling frequency appropriately, the variance ratio test is shown to be as powerful as the Dickey-Fuller and Box-Pierce tests against the stationary alternative, and is more powerful than either of the two tests against the two unit-root alternatives.
TL;DR: In this paper, the cross section for single hard photon bremsstrahlung in Bhabha scattering is presented, and its main qualitative features are reviewed, including all one-loop electroweak corrections.