Showing papers on "Monte Carlo molecular modeling published in 1986"

The rendering equation

Abstract: We present an integral equation which generalizes a variety of known rendering algorithms. In the course of discussing a monte carlo solution we also present a new form of variance reduction, called Hierarchical sampling and give a number of elaborations shows that it may be an efficient new technique for a wide variety of monte carlo procedures. The resulting rendering algorithm extends the range of optical phenomena which can be effectively simulated.

Replica Monte Carlo simulation of spin glasses.

Abstract: A new Monte Carlo method is presented for simulations of systems with quenched random interactions. The approach greatly reduces the long correlation times characteristic of standard methods, allowing the investigation of lower temperatures with less computer time than previously necessary.

Gap of the Linear Spin-1 Heisenberg Antiferromagnet: A Monte Carlo Calculation

Abstract: We have performed Monte Carlo calculations of the energies of several low-lying energy states of one-dimensional, spin-1 Heisenberg antiferromagnets with linear sizes up to n=32. Our results support Haldane's prediction that a gap exists in the excitation spectrum for n\ensuremath{\rightarrow}\ensuremath{\infty}. .AE

Computational statistical mechanics methodology, applications and supercomputing

Abstract: Computer simulation is adding a new dimension to scientific investigation, establishing a role of equal importance with the traditional approaches of experiment and theory. In this paper, we provide a text for understanding the computer simulation methodology of classical statistical mechanics. After developing the theoretical basis of the simulation techniques, the Monte Carlo and Langevin methods and various molecular dynamics methods are described. A very limited discussion is provided on interatomic potential functions, numerical integration schemes, and general simulation procedures for modelling different physical situations and for circumventing excessive computational burdens. The simulation methods are then illustrated using a variety of physical problems studied over the last several years at our laboratory. They include spinodal decomposition of a two-dimensional (2D) fluid, the melting of 2D and quasi-2D films, the structure and energetics of an incommensurate physisorbed film, and th...

Stochastic approximation for Monte Carlo optimization (1986)

Abstract: In this paper, we introduce two convergent Monte Carlo algorithms for optimizing complex stochastic systems. The first algorithm, which is applicable to regenerative processes, operates by estimating finite differences. The second method is of Robbins-Monro type and is applicable to Markov chains. The algorithm is driven by derivative estimates obtained via a likelihood ratio argument.

Quantum statistical monte carlo methods and applications to spin systems

Abstract: A short review is given concerning the quantum statistical Monte Carlo method based on the equivalence theorem(1) thatd-dimensional quantum systems are mapped onto (d+1)-dimensional classical systems. The convergence property of this approximate tansformation is discussed in detail. Some applications of this geneal appoach to quantum spin systems are reviewed. A new Monte Carlo method, “thermo field Monte Carlo method,” is presented, which is an extension of the projection Monte Carlo method at zero temperature to that at finite temperatures.

Monte Carlo investigation of a kinetic Ising model of the glass transition

Abstract: A detailed Monte Carlo study of the equilibrium and dynamical properties of the two‐spin facilitated kinetic Ising model proposed by Fredrickson and Andersen (FA) is presented. The model Hamiltonian is that of a spin‐1/2 Ising model in an external magnetic field and, in the present study, contains no interactions between spins. The kinetic properties of the model are described by a master equation with single‐spin‐flip dynamics and highly cooperative flip rates. In particular, the rate at which a spin flips is chosen to be zero unless at least two of its neighbors are spin up. Monte Carlo simulations of the model on a square lattice demonstrate that although there is no evidence for a kinetic singularity (as predicted by FA), the model has dynamical properties much like those of viscous liquids. We find non‐Arrhenius temperature dependence of the average relaxation time and highly nonexponential decay of various relaxation functions. The expression derived by Adam and Gibbs is found to describe the relationship between the average relaxation time and the entropy of the spin model. It is shown that the equilibrium time correlation functions can be accurately fit to the Kohlrausch–Williams–Watts (KWW) expression. The exponent in the KWW function is found to decrease as the temperature is lowered. Studies of multiple‐spin correlation functions demonstrate how spatial correlations develop in the model as it is perturbed from equilibrium and how these relax as the system equilibrates.

Comparison of the molecular dynamics method and the direct simulation Monte Carlo technique for flows around simple geometries

Abstract: The molecular dynamics method (MD) and the direct simulation Monte Carlo technique (DSMC) are compared with respect to their capability of simulating vorticity distributions. The statistical assumptions underlying the evaluation of the collision term by the DSMC are analyzed. They lead to the nonconservation of angular momentum for the interaction of particles. Both methods yield equally good results for the Rayleigh–Stokes flow. Using the present parameters, however, only the MD simulation shows the generation of vortices for the flow past an inclined flat plate. This might indicate an effect on the computation of vortical flows. It is suggested that further systematic studies of the effect of the cell size and particle dimensions be carried out.

A grand canonical Monte Carlo simulation study of polyelectrolyte solutions

Abstract: We present the results of grand canonical Monte Carlo simulations on a model of ‘‘rod‐like’’ polyelectrolyte solutions. The model is approximate, but well studied by a variety of techniques. The parameters in the model are chosen to mimic DNA and polystyrenesulfonate solutions. We find that the Poisson–Boltzmann equation retains its semiquantitative utility in this model if 1:1 electrolyte is present, and that integral equation theories are measurably even more accurate. By comparison with experimental results, we argue that there are limitations in the present model. Finally, a simulation of polyions surrounded by divalent mobile ions provides additional evidence for charge inversion under certain thermodynamic conditions. This feature is not predicted by the Poisson–Boltzmann equation.

Introduction: Theory and “Technical” Aspects of Monte Carlo Simulations

Abstract: An outline is given of the physical problems which can be treated by Monte Carlo sampling and which are described in the later chapters of this book. Then the theoretical background is described for the application of this technique to calculate statistical ensemble averages of classical interacting many-body systems. The practical realization of the method is discussed, as well as its limitations due to finite time averaging, finite size and boundary effects, etc. It is shown how to extract meaningful information from the “raw data” of such a “computer experiment”. The stochastic simulation of kinetic processes is also treated, with particular emphasis on the interpretation of the results near phase transitions in the system. Finally some approximative variants of the technique are discussed which might become useful to simulate critical phenomena.

On the implementation of the heat bath algorithms for Monte Carlo simulations of classical Heisenberg spin systems

Abstract: The Monte Carlo simulations based on the 'heat bath' algorithms are implemented for the following classical spin systems: (i) the continuous-spin Ising model; (ii) the XY model and (iii) the Heisenberg model.

Random tempering of Gaussian-type geminals. I. Atomic systems

Abstract: We use a method inspired by Monte Carlo quadrature formulas to create a basis set of Gaussian‐type geminals for the calculation of the second‐order energy of the beryllium atom. This technique matches results obtained by the full optimization of all nonlinear parameters but requires considerably less computational effort. For calculations involving microhartree accuracy this reduction may be as much as a factor of 1000.

Computations of mixtures of dirichlet processes

Abstract: The computation of Bayes estimators based on mixtures of Dirichlet processes is treated in this article. These estimators may be written as ratios of two multidimensional integrals, each of which may be decomposed into a weighted average of products of one-dimensional integrals. An importance sampling Monte Carlo method is proposed to approximate each of the weighted averages. A prior error bound for each of the Monte Carlo estimators and a posterior error bound for the ratio are developed to measure the efficiency of the Monte Carlo method. Jackknife and random group error estimates are also considered. Two examples are given which illustrate the computation of the Bayes estimators.

Equation of state for athermal lattice chains

Abstract: We report results of Monte Carlo simulations of athermal chains in the square lattice, and present a detailed comparison between Flory and Flory–Huggins theories and the numerical results.

Quantum simulation of systems with nodal surfaces

Abstract: A modification of the diffusion Monte Carlo algorithm that enables the direct simulation of wave functions containing nodal surfaces is described. The use of orthogonality constraints during the simulation enables the properties of excited state systems to be calculated. For Fermi systems, spin variables and exchange operators are also included in the algorithm. The effectiveness of the methods is demonstrated using applications to several simple models.

Monte Carlo simulation of adhesive disks

Abstract: A new method has been developed that permits the Monte Carlo simulation of systems in which the intermolecular potential contains a well which is both infinitely deep and infinitesimally wide. Adhesive potentials of this type are analytically tractable and have been used in a number of applications. The simulation algorithm combines the generation and acceptance steps of the conventional Metropolis method to overcome the effect of the singularity in the potential. The method is applied to a two‐dimensional system of adhesive disks. Results are reported for the equation of state and the radial distribution function, which has delta function peaks not present in the three‐dimensional Percus–Yevick solution. We also present an exact solution for one‐dimensional adhesive rods.

Molecular physics and chemistry applications of quantum Monte Carlo

Abstract: We discuss recent work with the diffusion quantum Monte Carlo (QMC) method in its application to molecular systems. The formal correspondence of the imaginary-time Schrodinger equation to a diffusion equation allows one to calculate quantum mechanical expectation values as Monte Carlo averages over an ensemble of random walks. We report work on atomic and molecular total energies, as well as properties including electron affinities, binding energies, reaction barriers, and moments of the electronic charge distribution. A brief discussion is given on how standard QMC must be modified for calculating properties. Calculated energies and properties are presented for a number of molecular systems, including He, F, F−, H2, N, and N2. Recent progress in extending the basic QMC approach to the calculation of “analytic” (as opposed to finite-difference) derivatives of the energy is presented, together with an H2 potential-energy curve obtained using analytic derivatives.

Nuclear spin relaxation by translational diffusion in solids: X. Monte Carlo calculation for the simple hopping model

Abstract: The spectral density functions J(p)( omega ) relevant to nuclear spin relaxation rates due to magnetic dipole coupling between diffusing spins in cubic crystals are calculated, for the simple hopping model, by a Monte Carlo method. The analysis makes use of known exact results in various limits. The statistical fluctuations in the Monte Carlo calculations become more significant at high frequencies but accurate analytic results are known in this regime. Numerical results are therefore obtained over the entire frequency range for all spin concentrations except the monovacancy limit.

A cluster Monte Carlo method for the simulation of anisotropic systems

Abstract: A Monte Carlo method for studying anisotropic systems with a new type of boundary conditions is proposed. The missing interactions at the sample box surface are replaced by interactions with ghost molecules. The orientations of these ghost particles are sampled from a ‘‘least biased’’ singlet distribution obtained self‐consistently from the order parameter inside the sample. The method is tested on the Lebwohl–Lasher model with 125 and 1000 particles. Results for the transition temperature and order parameters are in good agreement with those obtained from simulation of much larger systems. The method is fairly general and should be applicable in a variety of simulations. Here we show that it can also be used to study director fluctuations in nematogen models.