Showing papers on "Dynamic Monte Carlo method published in 1981"
TL;DR: This book provides the first simultaneous coverage of the statistical aspects of simulation and Monte Carlo methods, their commonalities and their differences for the solution of a wide spectrum of engineering and scientific problems.
Abstract: From the Publisher:
Provides the first simultaneous coverage of the statistical aspects of simulation and Monte Carlo methods, their commonalities and their differences for the solution of a wide spectrum of engineering and scientific problems. Contains standard material usually considered in Monte Carlo simulation as well as new material such as variance reduction techniques, regenerative simulation, and Monte Carlo optimization.
2,776 citations
TL;DR: In this paper, a formalism for carrying out Monte Carlo calculations of field theories with both boson and fermion degrees of freedom is presented, and the structure of the effective action for a wide class of theories is studied.
Abstract: We present a formalism for carrying out Monte Carlo calculations of field theories with both boson and fermion degrees of freedom. The basic approach is to integrate out the fermion degrees of freedom and obtain an effective action for the boson fields to which standard Monte Carlo techniques can be applied. We study the structure of the effective action for a wide class of theories. We develop a procedure for making rapid calculations of the variation in the effective action due to local changes in the boson fields, which is essential for practical numerical calculations.
833 citations
TL;DR: In this paper, a Monte Carlo method is presented which simulates the transport equations of joint probability density functions (pdf's) in turbulent flows, and the method can be used to solve the pdf equation for turbulent flows involving many chemical species and complex reaction kinetics.
Abstract: —A Monte Carlo method is presented which simulates the transport equations of joint probability density functions (pdf's) in turbulent flows. (Finite-difference solutions of the equations are impracticable, mainly because of the large dimensionality of the pdf's). Attention is focused on an equation for the joint pdf of chemical and thermodynamic properties in turbulent reactive flows. It is shown that the Monte Carlo method provides a true simulation of this equation, and that the amount of computation required increases only linearly with the number of properties considered. Consequently, the method can be used to solve the pdf equation for turbulent flows involving many chemical species and complex reaction kinetics. Test calculations are reported that demonstrate the method and determine the influence of the numerical parameters. The method is then used to calculate pdf's of temperature in a turbulent mixing layer, and the calculations are found to be in good agreement with the measurements o...
347 citations
TL;DR: In this paper, a method for evaluating transport coefficients in asymmetric geometries using the Monte Carlo method is developed for evaluating the transport coefficients of the stellarator, which is applied to the star.
Abstract: A method is developed for evaluating transport coefficients in asymmetric geometries using the Monte Carlo method. The method is applied to the stellarator.
339 citations
CERN1
TL;DR: In this paper, a possible extension of the Monte Carlo technique to systems with fermionic degrees of freedom is proposed. But the authors focus on the application to an elementary example.
215 citations
IBM1
TL;DR: In this article, a detailed study of the thermodynamics of the phase diagram for a two-dimensional system of molecules interacting with Lennard-Jones 6:12 potentials, which is a prototype for physisorbed systems, is presented.
Abstract: There has recently been extensive interest in the nature of the melting/freezing transition for a two-dimensional system of molecules interacting with Lennard-Jones 6:12 potentials, which is a prototype for physisorbed systems. We have therefore made a detailed study of the thermodynamics of the phase diagram for this system. We first made calculations using liquid-state perturbation theory for the fluid state and a self-consistent cell theory for the solid state to determine thermodynamic functions; these results led to ordinary first-order phase transitions between solid/fluid and liquid/gas phases, in agreement with the constant-pressure Monte Carlo results of Abraham. We refined the calculations by using constant-pressure and constant-density Monte Carlo results to improve the accuracy of the calculated free energies, and we determined the two-phase equilibria by making direct Monte Carlo calculations for two-phase systems. The results are internally consistent and lead to a phase diagram qualitatively similar to the three-dimensional Lennard-Jones system.
160 citations
TL;DR: In this paper, a method for carrying out Monte Carlo calculations for field theories with fermion degrees of freedom is presented, and results for a simple one-dimensional model are given.
Abstract: A method is presented for carrying out Monte Carlo calculations for field theories with fermion degrees of freedom. As an example of our technique, results for a simple one-dimensional model are given.
131 citations
TL;DR: In this article, a new Monte Carlo approach applicable to systems with fermion and boson degrees of freedom is proposed, which reduces to doing Monte Carlo computations on a two-dimensional classical system with local interactions.
Abstract: A new Monte Carlo approach applicable to systems with fermion and boson degrees of freedom is proposed. The main advantage of the method is its speed: For systems in one space and one time dimension (1 + 1) the calculation reduces to doing Monte Carlo computations on a two-dimensional classical system with local interactions. Here the potential of the method is illustrated by application to various (1 + 1)-dimensional systems.
122 citations
TL;DR: In this paper, a Monte Carlo study of SAW's on a diluted diamond lattice is presented, and it is shown that the exponent does not change by dilution,v≈0.59 as in the undiluted case.
Abstract: A Monte Carlo study of SAW's on a diluted diamond lattice is presented. We find that the exponentv does not change by dilution,v≈0.59 as in the undiluted case, in contrast to the original conclusion of Chakrabarti and Kertesz. This result cannot be understood by the Harris criterion. At the percolation concentrationp
c
of the lattice we find a higher exponentv
pc
≈2/3. A scaling form of the crossover between these exponents nearp
c
is proposed and found to be consistent with the Monte Carlo results.
110 citations
TL;DR: In this article, the sputtering of inhomogeneous multielement targets by medium-energy ions is simulated using the Monte Carlo method, where incident ions as well as the multiple recoil atoms of the cascade produced in the medium are followed until either they escape from the solid or their energy falls below a low cut-off value.
Abstract: The sputtering of inhomogeneous multielement targets by medium-energy ions is simulated using the Monte Carlo method. Incident ions as well as the multiple recoil atoms of the cascade produced in the medium are followed until either they escape from the solid or their energy falls below a low cut-off value. Two modes of simulation are demonstrated. In the first mode, the program deals with an undisturbed medium and no change takes place in the medium for the simulation of successive ions; a situation which corresponds to low-dose sputtering experiments. In contrast to previous Monte Carlo codes, the other mode of this program considers atomic-mixing of all species including the implanted beam ions in the medium during the simulation of ion bombardment. This simulation of time-dependent processes can help us to a better understanding of some sputtering phenomena of complicated nature such as the preferential sputtering of certain species within a multielement medium. Furthermore, this simulation d...
97 citations
TL;DR: In this article, Monte Carlo simulations on liquid water between two rigid walls have been performed and the results of these simulations have been compared with simulations on non-polar solutes in water.
TL;DR: In this article, a Monte Carlo method was developed to calculate the binding energy and density distribution of the 3 H and 4 He nuclei for a variational wave function written as a symmetrized product of correlation operators.
TL;DR: In this article, a reference system to test models for adsorption in molecular sieves has been developed, which takes into account both dispersion and electrostatic energies in zeolite cavities for the gas-solid potential energy.
Abstract: Adsorption isotherms, heats of adsorption and radial distribution functions for hard sphere and Lennard-Jones molecules in MS-13X have been generated by a Monte Carlo simulation of the grand canonical ensemble. A model which takes into consideration both dispersion and electrostatic energies in zeolite cavities was used for the gas-solid potential energy. Heterogeneity of the zeolite cavity and intermolecular forces between adsorbate molecules were found to be equally important in determining the adsorptive properties. A reference system to test models for adsorption in molecular sieves has been developed.
TL;DR: In this article, the precise mathematical complexity of distributed phase systems with population balances and Monte-Carlo simulation methods is established, and the exact mathematical complexity can be found in Table 1.
TL;DR: In this article, Monte Carlo calculations of the thermodynamic properties of a pseudopotential metal fluid, approximating lithium, were carried out over a wide range of temperatures and densities.
Abstract: Monte Carlo calculations of the thermodynamic properties of a pseudopotential metal fluid, approximating lithium, were carried out over a wide range of temperatures and densities. The calculations were compared with the predictions of variational perturbation theories employing the hard sphere, soft sphere, and the one component plasma (OCP) as reference systems. The OCP predictions are in better agreement with Monte Carlo pressures, but are comparable for energies. The OCP reference system has the lower Helmholtz free energy at all points studied.
TL;DR: The multi-spin-coding technique applied to the Monte Carlo simulation of the Ising model is presented in some detail, including a FORTRAN program, and its efficiency is confirmed.
TL;DR: In this article, the energy, specific heat, and the static density-density correlation functions for a one-dimensional lattice model at nonzero temperatures were calculated using a Monte Carlo technique.
Abstract: Starting from a genuine discrete version of the Feynman path-integral representation for the partition function, calculations have been made of the energy, specific heat, and the static density-density correlation functions for a one-dimensional lattice model at nonzero temperatures. A Monte Carlo technique has been used to calculate the temperature-dependent properties. The results are compared with exact calculations for short chains, the Hartree-Fock approximation, and a classical model.
TL;DR: In this article, Monte Carlo results for the chemical diffusivity in a lattice-gas model of an ordered adsorbate were presented, where the model employed is the square-planar lattice gas with nearest neighbor repulsive lateral interactions and next neighbor attractive lateral interactions at a temperature less than the critical temperature at 50% coverage.
Abstract: Monte Carlo results are presented for the chemical diffusivity in a lattice-gas model of an ordered adsorbate. The model employed is the square-planar lattice gas with nearest-neighbour repulsive lateral interactions and next-nearest-neighbour attractive lateral interactions at a temperature less than the critical temperature at 50% coverage. Use is made of the recently derived rigorous form of the Darken equation in order to gain insight into the behaviour of the diffusivity. Within the ordered c(2 × 2) phase, a strong maximum in the diffusivity is observed. This phenomenon is shown unequivocally to be a result of a rapid change in the adsorption isotherm within the ordered phase.
TL;DR: In this paper, the mean square radii of the conformations with a given N are found to vary with N as Nν, where ν?1.23 and ν 0.92 in two and three dimensions, respectively.
Abstract: As a simple model of randomly branched polymers, we consider the different ways that N‐bond trees may be self‐avoidingly embedded on a lattice. A general Monte Carlo approach is developed and applied. The mean square radii of gyration of the conformations with a given N are found to vary with N as Nν, where ν?1.23 and ν?0.92 in two and three dimensions. The critical importance of volume exclusion for branched structures is discussed.
TL;DR: In this article, a Monte Carlo algorithm was designed for studying the stochastic behavior of large reaction-diffusion systems and compared with those obtained by a standard method for a solvable model system for which they calculate the mean concentration, the variance, and the spatial autocorrelation function of concentration.
Abstract: We present a Monte Carlo algorithm which is specially designed for studying the stochastic behavior of large reaction–diffusion systems. We compare its performance and results to those obtained by a standard method for a solvable model system for which we calculate the mean concentration, the variance, and the spatial autocorrelation function of concentration.
CERN1
TL;DR: In this paper, the results of Monte Carlo simulations for the two-dimensional O(3) non-linear sigma model were reported, and the estimates based on the combined use of the renormalization group and of the high temperature expansion were found to be in agreement with the data.
TL;DR: In this paper, the authors developed a formalism for carrying out Monte Carlo calculations on systems with coupled boson-fermion degrees of freedom and presented the results obtained using these techniques on some specific systems.
Abstract: We have recently developed a formalism for carrying out Monte Carlo calculations on systems with coupled boson-fermion degrees of freedom. Here we present the results obtained using these techniques on some specific systems. First the quantum-mechanics problem of a single boson coordinate linearly coupled to a fermion is studied. The fermion Green's function and the boson coordinate displacement are calculated and compared with exact results. Extending this analysis to a one-dimensional array, a field theory in one space and one imaginary time dimension is investigated. The fermion and boson Green's functions are calculated and compared with analytic results obtained in the limit where the bare boson frequency is much larger or much smaller than the characteristic fermion energies.
TL;DR: In this paper, Monte Carlo calculations have been carried out with the Metropolis method for two systems each containing 63 ST 2 water and one Lennard Jones solute in NVT ensemble at 298.15 K and 18.07 cm3 mol−1.
Abstract: Monte Carlo calculations have been carried out with the Metropolis method for two systems each containing 63 ST‐2 water and one Lennard‐Jones solute in NVT ensemble at 298.15 K and 18.07 cm3 mol−1. The solutes chosen approximately simulate ethane and pentane. The internal energy and various distribution functions have been calculated and their results enable us, when combined with the previous study on methane and isobutane solutions, to examine the solute size dependence of hydrophobic hydration. Although energetic stabilization and structuration of water due to the introduction of a nonpolar solute have been shown to exist for all of the four solutions studied, they do not change monotonically with the size of solute. A long MC run has also been done for an aqueous methane solution to check the convergence characteristics of the present calculation.
TL;DR: In this paper, Bruns and Naghizadeh used the direct Monte Carlo method to generate ring polymers with any number of bonds, which can be used in future studies of ring polymer statistics.
Abstract: Ring polymers of the freely jointed model are efficiently obtained by joining two linear chains together (dimerization). The rings produced are equivalent to those obtained by the direct Monte Carlo method of Bruns and Naghizadeh, based on the radius of gyration and the various distribution functions. The method can be used to generate any number of ring polymers with any number of bonds and is therefore useful in future studies of ring polymer statistics.