Showing papers on "Dynamic 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
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
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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.
722 citations
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.
529 citations
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.
297 citations
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.
288 citations
TL;DR: In this paper, an analysis of the known numerical direct Monte Carlo simulation technique is presented, where an effective numerical realization of the direct statistical modelling (the majorant frequency scheme) is suggested.
Abstract: An analysis of the known numerical direct Monte Carlo simulation technique is presented. Effective numerical realization of the direct statistical modelling—the majorant frequency scheme—is suggested. The nonlinear kinetic Boltzmann equation for a one-particle distribution function /(i, x, v) is the fundamental one in the rarefied gas dynamics, which can be written in the form 7\\ Α Γ (0.1) where b and ε are collision parameters. Velocities (ν',ϋ\\) and (ν,ϋ^ satisfy the momentum and energy conservation laws Difficulties involved in the numerical solution of this equation are well known. They are raised by the high dimension and the complicated structure of the nonlinear collision integral J(/,/). A constructive numerical method for solving this equation is that of splitting according to the physical processes for a time interval Δί. This means that a spatially homogeneous relaxation problem is solved first, and the free molecular flow is evaluated next. In particular, a conservative splitting scheme for equation (0.1) is suggested in [1] where the collision integral for the time interval Δί is calculated by the Monte Carlo method. To evaluate the distribution function, a finite-difference scheme with correction was used such that the conservation laws were satisfied. Nowadays the Monte Carlo methods based on splitting the process of evolution of a gas system into two stages are widely used in the rarefied gas dynamics. In the numerical realization of this method, the flow region is divided into a network of cells of extent Δχ. According to the initial distribution function, Ν model particles are placed into each cell. Next, a spatially homogeneous relaxation and free molecular flows are consecutively simulated in all cells. The free molecular flow is simulated using standard schemes [2,4] and does not raise additional difficulties. The numerical realization of the stage of spatially homogeneous relaxation is of a particular importance. We mention two approaches to construct a random process of collision relaxation. The first one is based on a direct derivation of the Monte Carlo algorithms from the nonlinear homogeneous Boltzmann equation. In [9], using the theory of branching 454 M. S. Ivanov and S. V. Rogasinsky random processes, an exact algorithm for solving the Boltzmann equation was constructed. However, this method is too costly. Using the Euler scheme and its corresponding randomization for the spatially homogeneous Boltzmann equation, a random process for the approximate solution of the Boltzmann equation was constructed in [18]. The second approach is based on a direct statistical modelling (DSM) of the evolution of a system of N particles. Nowadays numerical techniques for simulating a spatially homogeneous relaxation suggested in [2, 4, 7, 15] are widely used. All these schemes are obtained using heuristic arguments on the basis of physical ideas about the relaxation processes in a realistic gas. Therefore, these schemes are not directly related to the kinetic Boltzmann equation. The heuristic character of these schemes permits only a qualitative comparison using a Boltzmann collision frequency as a main criterion (see, for example, [5, 19, 20]). However, a relation between the trajectory simulation of the whole system of N particles in a 3N-dimensional space of velocities and the master kinetic equation [12] was already mentioned in [8]. A detailed investigation of the relation between the numerical algorithm and the kinetic equation is given in [3] where a probabilistic model of a system of N particles is constructed such that a Markov property holds. Next, a difference scheme for the master kinetic equation written for the N-particle distribution function is derived from the evolution of the model described. This difference counterpart is known to transform into the Boltzmann equation, as N -> oo, provided that the chaotic property holds [12, 13, 21]. It seems necessary to investigate known numerical schemes of statistical modelling of rarefied gas flows from the standpoint of general theory of Monte Carlo methods [10]. This general consideration enables us to compare various schemes, to study relations between known methods and to apply correctly different weight Monte Carlo techniques [17]. According to the general idea of Monte Carlo methods [10], we use the following approach. We pass from the integro-differential kinetic equation to the integral equation for the N-particle distribution function. Probabilistic interpretation of this equation leads to the construction of the corresponding random process of direct simulation. Note that we shall consider relaxation in a simple one-atom gas. 1. DIRECT SIMULATION ALGORITHMS In the spatially homogeneous case, the master kinetic equation for the Af-particle distribution function has the form [13]: =Tt Σ Γ ^ Ui<;
278 citations
TL;DR: The model described herein is applied to the study of laser-excited carriers in a quantum-well system and to the response of such a system to high parallel electric fields.
Abstract: We model nonequilibrium transport in a GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As quantum-well structure using an ensemble Monte Carlo simulation of the full multisubband system in which we include electron-electron (e-e) scattering explicitly into the calculation. The e-e scattering cross section is calculated using the Born approximation and introduced into the transient Monte Carlo simulation via a self-scattering technique. This interaction is found to be especially effective in transferring energy between different subbands, thus thermalizing the carriers within a picosecond. The model described herein is applied to the study of laser-excited carriers in a quantum-well system and to the response of such a system to high parallel electric fields. In the case of laser excitation, e-e interaction may dominate the initial evolution, reducing the cascade of carriers via optical-phonon emission.
230 citations
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.
216 citations
TL;DR: In this paper, the Monte Carlo-minimization procedure has been applied to determine the structure of a pentapeptide Met-enkephalin, leading consistently to a stable β-bend structure, starting from random initial conformations.
Abstract: Biological systems are intrinsically complex, involving many degrees of freedom, heterogeneity, and strong interactions among components. For the simplest of biological substances, e.g., biomolecules, which obey the laws of thermodynamics, we may try to investigate them by means of a statistical mechanical approach. Even for these simplest many-body systems, assuming all microscopic interactions are completely known, current physical and chemical methods of characterizing the overall structure and free energy face the fundamental challenge of an exponential amount of computations as the number of degrees of freedom of these systems increases. As a response to this problem, two general procedures have been developed to compute the structure (Monte Carlo-minimization method) and free energy (Monte Carlo recursion method) of a complex thermodynamic system. The Monte Carlo-minimization procedure has been applied to determine the structure of a pentapeptide Met-enkephalin, leading consistently to a stable β-bend structure, starting from random initial conformations. The Monte Carlo recursion method has been applied to a Lennard-Jones fluid, with results in agreement with previously published values of the free energy obtained from other procedures.
190 citations
TL;DR: It is shown that the algorithm is capable of modelling layer by layer growth of AsGa, and based on using conditional probabilities to select the sites at which events occur, this has the advantage of being economic on computer time.
Abstract: A new algorithm is proposed for Monte Carlo simulation of MBE growth. The algorithm is based on using conditional probabilities to select the sites at which events occur. This has the advantage of being economic on computer time, the time per event scaling as the square root of the number of sites in the system. It is shown that the algorithm is capable of modelling layer by layer growth of AsGa.
TL;DR: In this paper, the authors presented results obtained from extensive Monte Carlo simulations of domain growth in the two-dimensional spin-exchange kinetic Ising model with equal numbers of up and down spins.
Abstract: Results obtained from extensive Monte Carlo simulations of domain growth in the two-dimensional spin-exchange kinetic Ising model with equal numbers of up and down spins are presented. Using different measures of domain size---including the pair-correlation function, the energy, and circularly-averaged structure factor---the domain size is determined (at T=0.5${T}_{c}$) as a function of time for times up to ${10}^{6}$ Monte Carlo steps. The growth law R(t)=A+${\mathrm{Bt}}^{1/3}$ is found to provide an excellent fit (within 0.3%) to the data, thus indicating that at long times the classical value of (1/3 for the exponent is correct. It is pointed out that this growth law is equivalent to an effective exponent for all times (as given by Huse) ${n}_{\mathrm{eff}}$(t)=(1/3-1)/3 C/R(t). No evidence for logarithmic behavior is seen. The self-averaging properties of the various measures of domain size and the variation of the constants A and B with temperature are also discussed. In addition, the scaling of the structure factor and anisotropy effects due to the lattice are examined.
TL;DR: The critical temperature for the two-dimensional XY model on a square lattice is determined to within a few tenths of a percent by combining Monte Carlo simulations with a lattice size scaling relation.
Abstract: The critical temperature for the two-dimensional XY model on a square lattice is determined to within a few tenths of a percent by combining Monte Carlo simulations with a lattice size scaling relation.
TL;DR: In this article, a modified Monte Carlo algorithm has been developed which makes it possible to explore the phase diagram for a large region of both the packing fraction and the stickiness parameter τ.
Abstract: Monte Carlo simulations of the three-dimensional sticky-hard-sphere system are presented. A new modified Monte Carlo algorithm has been developed which makes it possible to explore the phase diagram for a large region of both the packing fraction and the stickiness parameter τ. The phase diagram is calculated, as well as pair distribution functions and structure factors. Cluster percolation has been studied and its relation to the phase diagram. The simulation results are compared with predictions, obtained from the Percus-Yevick approximation, which can be solved analytically for this model. The potential relevance of the present simulation results for experiments on clustering in neutral colloids is discussed.
TL;DR: In this paper, test particle methods were used to calculate chemical potentials in uniform and non-uniform electrolytes using computer simulations, and the results were compared with similar Grand Canonical Monte Carlo simulations for 1:1, 2:1 and 2:2 uniform electrolytes.
Abstract: We develop and apply test particle methods to calculate chemical potentials in uniform and non-uniform electrolytes using computer simulations. Our techniques are based on the well-known Widom method, but account for non-electroneutral particle fluctuations, implicitly suppressed in a usual Canonical Ensemble Monte Carlo simulation. These fluctuations are shown to contribute greatly to the Widom average for a single ionic species. We compare our results with similar Grand Canonical Monte Carlo simulations for 1:1, 2:1 and 2:2 uniform electrolytes, and 1:1 electrolytes at a charged planar interface. In general, we find good agreement between the methods, all within the statistical fluctuations. The advantages of using the test particle approaches are discussed.
TL;DR: A new method of calculating total energies of solids using nonlocal pseudopotentials in conjunction with the variational quantum Monte Carlo approach is presented, which avoids the large fluctuations of the energies in the core region of the atoms which occur in Quantum Monte Carlo all-electron calculations.
Abstract: A new method of calculating total energies of solids using nonlocal pseudopotentials in conjunction with the variational quantum Monte Carlo approach is presented. By use of pseudopotentials, the large fluctuations of the energies in the core region of the atoms which occur in quantum Monte Carlo all-electron calculations are avoided. The method is applied to calculate the binding energy and structural properties of diamond. The results are in excellent agreement with experiment.
TL;DR: In this paper, a method for incorporating the complete quantum-mechanical effect of spin correlations is proposed for Monte Carlo event generators, where spin correlations are normally ignored since the event generators treat the decays as completely independent.
01 Jan 1988
TL;DR: A hybrid Monte Carlo/zonal approach is presented, which allows visual details to be captured more efficiently than with a pure zonal approach, and is presented as a toolbox of techniques.
Abstract: Using computer graphics techniques, realistic synthetic images are constructed of visual scenes containing radiatively participating media, such as smoke, fog, and clouds. A new suite of methods for generating such images is introduced. In all, six methods are described, which employ two separate avenues of approach borrowed from radiation heat transfer.
The first avenue of approach uses radiosity-based enclosure theory. When extended to participating media, the result is known as the zonal method. The zonal method applies to isotropically scattering, possibly spatially varying, media. When extended to anisotropically scattering media with a low scattering albedo (and/or to optically thin media) the result is known as the modified zonal method. Both the zonal method and the modified zonal method are used to generate synthetic images of visual scenes. The derivation of the methods from the general equations of radiative transport is outlined, and new algorithms for generating the required geometric form factors are introduced.
The second avenue of approach employs Monte Carlo methods to calculate the radiant energy exchange in an environment. Monte Carlo formulations are separately outlined for isotropic and anisotropic directional scattering media, with arbitrary spatial variations in the media. The two Monte Carlo methods are derived from the general equations of radiative transport. Care is taken to illustrate how the various terms in the equations are simulated. Efficient and accurate algorithms are presented for sampling light source intensities and determining the number of significant reflection/scattering events.
The two Monte Carlo methods (i.e., for isotropic and anisotropic scattering) are computationally expensive. To reduce computational times, a novel preprocessing step is introduced. The preprocessing step uses the aforementioned radiosity-based zonal and/or modified zonal solutions. The result is a hybrid Monte Carlo/zonal approach, which allows visual details to be captured more efficiently than with a pure zonal approach. Using the Monte Carlo and Monte Carlo/zonal methods, example images are presented. Both isotropic and anisotropic participating media are illustrated.
The zonal, Monte Carlo, and Monte Carlo/zonal methods are presented as a toolbox of techniques. Each method has isotropic and anisotropic formulations.
TL;DR: In this paper, a kinetic lattice gas model is applied to study collective surface diffusion of adsorbates on inhomogeneous surfaces, and the diffusion coefficient is extracted from Monte Carlo (MC) simulations by observing the decay of the autocorrelation functions for density fluctuations.
Abstract: A kinetic lattice gas model is applied to study collective surface diffusion of adsorbates on inhomogeneous surfaces. The diffusion coefficient is extracted from Monte Carlo (MC) simulations by observing the decay of the autocorrelation functions for density fluctuations. Calculations are presented for diffusion on a surface with various different coverages of randomly placed blocks and to diffusion on a surface with various distributions of traps of different binding energies. In the cases where analytical expressions for the collective diffusion coefficient can be derived, the MC results show excellent agreement with analytical predictions.
TL;DR: In this article, the authors systematically studied the spin 1/2 quantum XXZ model on the square lattice using a quantum Monte Carlo method, and the temperature dependence of the energy, specific heat and order parameter was calculated for the systems of sizes up to 16×16.
Abstract: We systematically study the spin 1/2 quantum XXZ model on the square lattice using a quantum Monte Carlo method. The temperature dependence of the energy, specific heat and order parameter is calculated for the systems of sizes up to 16×16. Investigating the size dependence carefully, we exarnine the ground-state energy and the existence of the long-range order.
TL;DR: In this article, the authors present a numerically exact procedure for the calculation of an important class of finite temperature quantum mechanical time correlation functions, based around the stationary phase Monte Carlo (SPMC) method, a general mathematical tool for calculation of high dimensional averages of oscillatory integrands.
Abstract: We present a numerically exact procedure for the calculation of an important class of finite temperature quantum mechanical time correlation functions. The present approach is based around the stationary phase Monte Carlo (SPMC) method, a general mathematical tool for the calculation of high dimensional averages of oscillatory integrands. In the present context the method makes possible the direct numerical path integral calculation of real‐time quantum dynamical quantities for times appreciably greater than the thermal time (βℏ). Illustrative applications involving finite temperature anharmonic motion are presented. Issues of importance with respect to future applications are identified and discussed.
TL;DR: The Green's function Monte Carlo and variational methods have been used to calculate the properties of the ground state of two-dimensional liquid and solid /sup 4/He described by the HFDHE2 potential.
Abstract: The Green's function Monte Carlo and variational methods have been used to calculate the properties of the ground state of two-dimensional liquid and solid /sup 4/He described by the HFDHE2 potential. The equation of state, melting freezing transition, radial distribution functions in the liquid and solid, and the momentum distribution in the liquid are all presented. Comparisons are made with three-dimensional /sup 4/He and two-dimensional classical systems.
TL;DR: Methods of generating pseudorandom number sequences that might have predetermined spectral and probability distribution functions are discussed and are of potential value in Monte Carlo simulation of communication, radar, and allied systems.
Abstract: Methods of generating pseudorandom number sequences that might have predetermined spectral and probability distribution functions are discussed. Such sequences are of potential value in Monte Carlo simulation of communication, radar, and allied systems. The methods described are particularly suited to implementation on microcomputers, are machine portable, and have been subjected to exhaustive investigation by means of both statistical and theoretical tests. >
TL;DR: In this article, the absolute binding energies of an excess electron to small clusters of xenon atoms (n≤19) were determined using path integral Monte Carlo simulations and the ground state wave function of the excess electron and the decomposition of the binding energy of the electron into kinetic and potential parts were determined for a number of small clusters.
Abstract: Diffusion Monte Carlo simulations were performed to determine the absolute binding energies of an excess electron to small clusters of xenon atoms (n≤19). It was found that clusters as small as Xe6 could bind the electron. The ground state wave function of the excess electron and the decomposition of the binding energy of the electron into kinetic and potential parts were determined for a number of small clusters. Large (n>50) and small clusters anions were then studied at finite temperatures using path integral Monte Carlo. In all cases the excess electron in small clusters was found to exist in very diffuse state extending well beyond the radius of the cluster. However, in large clusters the electron was localized within the bulk of the cluster. Various properties are presented to characterize the electron in Xe−n as function of cluster size and the results compared to an electron solvated in fluid xenon.
TL;DR: This work parametrizes the general behavior of the symmetric Anderson-impurity model, determining the approach towards universality and establishing the range of validity of various approximations.
Abstract: Using a recently proposed quantum Monte Carlo technique, we consider moment formation and magnetic properties of the symmetric Anderson-impurity model for a wide range of parameters and temperatures. We parametrize the general behavior, determining the approach towards universality and establishing the range of validity of various approximations.
TL;DR: In this paper, the authors use a leading-order analysis of the energy of sample curves to show how static properties of finite samples become ensemble dependent in Gaussian ensembles.
Abstract: The recently introduced Gaussian ensemble involves a sample (of size N) thermally connected to a finite heat bath (of size N') with specific properties. Treating N' as a parameter, we use a leading-order analysis of the \ensuremath{\beta} (inverse temperature) -versus-E (energy of sample) curves to show how static properties of finite samples become ensemble dependent. Inflection points in \ensuremath{\beta}(E) at phase transitions, however, appear as nontrivial fixed points with respect to N' and are defined as the transition temperature of the sample. By developing a fluctuation relation for the heat capacity C we show that, for small N', states with Cl0 are accessible at first-order transitions resulting in van der Waals loops in \ensuremath{\beta}(E). Monte Carlo studies of phase transitions in Potts models on two- and three-dimensional lattices confirm the finite-N' and finite-N effects. We find that the method significantly reduces computer time (sometimes by a factor of 100) compared with canonical-ensemble simulations and is effective in diagnosing the order of phase transition. Specific-heat data at second-order transitions reveal a new phenomenon; the peak in C sharpens as N' becomes smaller, leading us to speculate on sharp transitions in finite samples.
TL;DR: An analytical model based on extensive Monte Carlo simulations of ion-implantation-induced damage profiles based on the binary collision approximation, the assumption of a random target, and the validity of the linear collision cascade theory is presented.
Abstract: An analytical model for the description of ion-implantation-induced damage profiles is presented. The model is based on extensive Monte Carlo simulations of B-, P-, As-, and Sb-implantations in Si. One-dimensional profiles are described by a Gaussian function and an exponential function joined together continuously with continuous first derivatives. The two-dimensional model has previously been developed by the authors for dopant profiles and is demonstrated to apply well to point defect distributions. Parameters have been obtained for the four ions by fitting the model to the Monte Carlo results, and they are provided in the form of tables for the energy range of 10-300 keV (for the 1D model 1-300 keV). The Monte Carlo simulations are based on the binary collision approximation, the assumption of a random target, and the validity of the linear collision cascade theory. The importance of energy transport by recoils is pointed out. >
01 Jan 1988
TL;DR: The TIGER series of time-independent coupled electron-photon Monte Carlo transport codes is a group of multimaterial and multidimensional codes designed to provide a state-of-the-art description of the production and transport of the electronphoton cascade by combining microscopic photon transport with a macroscopic random walk as mentioned in this paper.
Abstract: The TIGER series of time-independent coupled electron-photon Monte Carlo transport codes is a group of multimaterial and multidimensional codes designed to provide a state-of-the-art description of the production and transport of the electron-photon cascade by combining microscopic photon transport with a macroscopic random walk1 for electron transport. Major contributors to its evolution are listed in Table 10.1.