Showing papers on "Dynamic Monte Carlo method published in 1996"

Empirical potential Monte Carlo simulation of fluid structure

Abstract: It is shown that data on the site-site pair correlation functions for a fluid of molecules can be used to derive a set of empirical site-site potential energy functions. These potential functions reproduce the fluid structure accurately but at the present time do not reproduce thermodynamic information on the fluid, such as the internal energy or pressure. The method works in an iterative manner, starting from a reference fluid in which only Lennard-Jones interactions are included, and generates, by Monte Carlo simulation, successive corrections to those potentials which eventually lead to the correct site-site pair correlation functions. Using the approach the structure of water as determined from neuron scattering experiments is compared to the structure of water obtained from the simple point charge extended (SPCE) model of water interactions. The empirical potentials derived from both experiment and SPCE water show qualitative similarities with the true SPCE potential, although there are quantitative differences. The simulation is driven by a set of potential energy functions, with equilibration of the energy of the distribution, and not, as in the reverse Monte Carlo method, by equilibrating the value of χ2, which measures how closely the simulated site-site pair correlation functions fit a set of diffraction data. As a result the simulation proceeds on a true random walk and samples a wide range of possible molecular configurations.

Diffusive dynamics of the reaction coordinate for protein folding funnels

Abstract: The quantitative description of model protein folding kinetics using a diffusive collective reaction coordinate is examined. Direct folding kinetics, diffusional coefficients and free energy profiles are determined from Monte Carlo simulations of a 27‐mer, 3 letter code lattice model, which corresponds roughly to a small helical protein. Analytic folding calculations, using simple diffusive rate theory, agree extremely well with the full simulation results. Folding in this system is best seen as a diffusive, funnel‐like process.

3D electron dose calculation using a Voxel based Monte Carlo algorithm (VMC)

Abstract: A new model for calculating electron beam dose has been developed The algorithm is based on a two- or three-dimensional geometry defined by computerized tomography (CT) images The Monte Carlo technique was used to solve the electron transport equation However, in contrast to conventional Monte Carlo models (EGS4) several approximations and simplifications in the description of elementary electron processes were introduced reducing in this manner the computational time by a factor of about 35 without significant loss in accuracy The Monte Carlo computer program does not need any precalculated data The random access memory required is about 16 Mbytes for a 128(2) X 50 matrix, depending on the resolution of the CT cube The Voxel Monte Carlo model (VMC) was tested in comparison to calculations by EGS4 and the "Hogstrom algorithm" (MDAH) using several fictive phantoms In all cases a good coincidence has been found between EGS4 and VMC, especially near tissue inhomogeneities, whereas the MDAH algorithm has produced dose underestimations of up to 40%

Monte carlo study of the interacting self-avoiding walk model in three dimensions

Abstract: We consider self-avoiding walks on the simple cubic lattice in which neighboring pairs of vertices of the walk (not connected by an edge) have an associated pair-wise additive energy. If the associated force is attractive, then the walk can collapse from a coil to a compact ball. We describe two Monte Carlo algorithms which we used to investigate this collapse process, and the properties of the walk as a function of the energy or temperature. We report results about the thermodynamic and configurational properties of the walks and estimate the location of the collapse transition.

Monte Carlo techniques for direct lighting calculations

Abstract: In a distributed ray tracer, the sampling strategy is the crucial part of the direct lighting calculation. Monte Carlo integration with importance sampling is used to carry out this calculation. Importance sampling involves the design of integrand-specific probability density functions that are used to generate sample points for the numerical quadrature. Probability density functions are presented that aid in the direct lighting calculation from luminaires of various simple shapes. A method for defining a probability density function over a set of luminaires is presented that allows the direct lighting calculation to be carried out with a number of sample points that is independent of the number of luminaires.

Finite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions

Abstract: Quantum Monte Carlo (QMC) calculations are only possible in finite systems and so solids and liquids must be modeled using small simulation cells subject to periodic boundary conditions. The resulting finite-size errors are often corrected using data from local-density functional or Hartree-Fock calculations, but systematic errors remain after these corrections have been applied. The results of our jellium QMC calculations for simulation cells containing more than 600 electrons confirm that the residual errors are significant and decay very slowly as the system size increases. We show that they are sensitive to the form of the model Coulomb interaction used in the simulation cell Hamiltonian and that the usual choice, exemplified by the Ewald summation technique, is not the best. The finite-size errors can be greatly reduced and the speed of the calculations increased by a factor of 20 if a better choice is made. Finite-size effects plague most methods used for extended Coulomb systems and many of the ideas in this paper are quite general: they may be applied to any type of quantum or classical Monte Carlo simulation, to other many-body approaches such as the GW method, and to Hartree-Fock and density-functional calculations.

Multiconfiguration wave functions for quantum Monte Carlo calculations of first‐row diatomic molecules

Abstract: We use the variance minimization method to determine accurate wave functions for first‐row homonuclear diatomic molecules. The form of the wave function is a product of a sum of determinants and a generalized Jastrow factor. One of the important features of the calculation is that we are including low‐lying determinants corresponding to single and double excitations from the Hartree–Fock configuration within the space of orbitals whose atomic principal quantum numbers do not exceed those occurring in the Hartree–Fock configuration. The idea is that near‐degeneracy correlation is most effectively described by a linear combination of low‐lying determinants whereas dynamic correlation is well described by the generalized Jastrow factor. All the parameters occurring in both the determinantal and the Jastrow parts of the wave function are optimized. The optimized wave functions recover 79%–94% of the correlation energy in variational Monte Carlo and 93%–99% of the correlation energy in diffusion Monte Carlo.

Determination of the optical properties of turbid media from a single Monte Carlo simulation

Abstract: We describe a fast, accurate method for determination of the optical coefficients of 'semi-infinite' and 'infinite' turbid media. For the particular case of time-resolved reflectance from a biological medium, we show that a single Monte Carlo simulation can be used to fit the data and to derive the absorption and reduced scattering coefficients. Tests with independent Monte Carlo simulations showed that the errors in the deduced absorption and reduced scattering coefficients are smaller than 1% and 2%, respectively.

Monte Carlo study of phase separation in aqueous protein solutions

Abstract: The binary liquid phase separation of aqueous solutions of γ‐crystallins is utilized to gain insight into the microscopic interactions between these proteins. The interactions are modeled by a square‐well potential with reduced range λ and depth e. A comparison is made between the experimentally determined phase diagram and the results of a modified Monte Carlo procedure which combines simulations with analytic techniques. The simplicity and economy of the procedure make it practical to investigate the effect on the phase diagram of an essentially continuous variation of λ in the domain 1.05≤λ≤2.40. The coexistence curves are calculated and are in good agreement with the information available from previous standard Monte Carlo simulations conducted at a few specific values of λ. Analysis of the experimental data for the critical volume fractions of the γ‐crystallins permits the determination of the actual range of interaction appropriate for these proteins. A comparison of the experimental and calculated ...

Henyey–Greenstein and Mie phase functions in Monte Carlo radiative transfer computations

Abstract: Monte Carlo radiative transfer simulation of light scattering in planetary atmospheres is not a simple problem, especially the study of angular distribution of light intensity. Approximate phase functions such as Henyey-Greenstein, modified Henyey-Greenstein, or Legendre polynomial decomposition are often used to simulate the Mie phase function. An alternative solution using an exact calculation alleviates these approximations.

Numerical Modeling of Micromechanical Devices Using the Direct Simulation Monte Carlo Method

Abstract: A direct simulation Monte Carlo (DSMC) investigation of flows related to microelectromechanical systems (MEMS) is detailed. This effort is intended to provide tools to facilitate the design and optimization of micro-devices as well as to probe the effects of rarefaction, especially in regimes not amenable to other means of analysis. The code written for this purpose employs an unstructured grid, a trajectory-tracing particle movement scheme, and an infinite channel boundary formulation. Its results for slip-flow and transition regime micro-channels and a micro-nozzle are presented to demonstrate its capabilities.

Combining ab initio computations, neural networks, and diffusion Monte Carlo: An efficient method to treat weakly bound molecules

Abstract: We describe a new method to calculate the vibrational ground state properties of weakly bound molecular systems and apply it to (HF)2 and HF–HCl A Bayesian Inference neural network is used to fit an analytic function to a set of ab initio data points, which may then be employed by the quantum diffusion Monte Carlo method to produce ground state vibrational wave functions and properties The method is general and relatively simple to implement and will be attractive for calculations on systems for which no analytic potential energy surface exists

Monte Carlo vs Molecular Dynamics for Conformational Sampling

Abstract: A comparison study has been carried out to test the relative efficiency of Metropolis Monte Carlo and molecular dynamics simulations for conformational sampling. The test case that has been examine...

Dynamic exponent of the two-dimensional ising model and Monte Carlo computation of the subdominant eigenvalue of the stochastic matrix

Abstract: We introduce a novel variance-reducing Monte Carlo algorithm for accurate determination of correlation times. We apply this method to two-dimensional Ising systems with sizes up to 15 3 15, using single-spin flip dynamics, random site selection, and transition probabilities according to the heat-bath method. From a finite-size scaling analysis of these correlation times, the dynamic critical exponent z is determined as z › 2.1665s12d. [S0031-9007(96)00379-1]

A coupled density functional‐molecular mechanics Monte Carlo simulation method: The water molecule in liquid water

Abstract: A theoretical model to investigate chemical processes in solution is described. It is based on the use of a coupled density functional/molecular mechanics Hamiltonian. The most interesting feature of the method is that it allows a detailed study of the solute's electronic distribution and of its fluctuations. We present the results for isothermal‐isobaric constant‐NPT Monte Carlo simulation of a water molecule in liquid water. The quantum subsystem is described using a double‐zeta quality basis set with polarization orbitals and nonlocal exchange‐correlation corrections. The classical system is constituted by 128 classical TIP3P or Simple Point Charge (SPC) water molecules. The atom‐atom radial distribution functions present a good agreement with the experimental curves. Differences with respect to the classical simulation are discussed. The instantaneous and the averaged polarization of the quantum molecule are also analyzed. © 1996 by John Wiley & Sons, Inc.

Introduction to the diffusion Monte Carlo method

Abstract: A self‐contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a numerical algorithm is formulated. The algorithm is applied to determine the ground state of the harmonic oscillator, the Morse oscillator, the hydrogen atom, and the electronic ground state of the H+2 ion and of the H2 molecule. A computer program on which the sample calculations are based is available upon request.

Chain length dependence of the polymer-solvent critical point parameters

Abstract: We report grand canonical Monte Carlo simulations of the critical point properties of homopolymers within the bond fluctuation model. By employing configurational bias Monte Carlo methods, chain lengths of up to N=60 monomers could be studied. For each chain length investigated, the critical point parameters were determined by matching the ordering operator distribution function to its universal fixed‐point Ising form. Histogram reweighting methods were employed to increase the efficiency of this procedure. The results indicate that the scaling of the critical temperature with chain length is relatively well described by Flory theory, i.e., Θ−Tc∼N−0.5. The critical volume fraction, on the other hand, was found to scale like φc∼N−0.37, in clear disagreement with the Flory theory prediction φc∼N−0.5, but in good agreement with experiment. Measurements of the chain length dependence of the end‐to‐end distance indicate that the chains are not collapsed at the critical point.

Monte Carlo wavefunctions in quantum optics

Abstract: In this paper we present a review of the Monte Carlo wavefunction method. We discuss some aspects of its application in numerical simulations, and we comment on some of its relations to the foundations of quantum physics. Finally, we investigate the generalization to problems that have so far not been considered tractable by this method - in particular, nonlinear master equations may become relevant, and we discuss the application of Monte Carlo wavefunctions to such problems.

Application of an extended ensemble method to spin glasses

Abstract: An efficient Monte Carlo algorithm for simulating hardly-relaxing systems is proposed. By using this algorithm the three-dimensional ± J Ising spin glass model is studied. The result shows that reasonable values of the critical temperature and of the critical exponents can be obtained within Monte Carlo steps much shorter than the observation time a conventional simulation usually requires.

On the calculation of dynamical properties of solvated electrons by maximum entropy analytic continuation of path integral Monte Carlo data

Abstract: The maximum entropy analytic continuation method, to determine the dynamical properties of a solvated electron from equilibrium path integral Monte Carlo data, is applied to the calculation of the optical absorption spectra, real time correlation functions, and transport coefficients of an excess electron in water, supercritical helium, and supercritical xenon. Comparisons with experiments and with analytical theories are presented.

Simulation and prediction of vapour-liquid equilibria for chain molecules

Abstract: Monte Carlo simulations of phase equilibria for Lennard-Jones chains of intermediate length are performed in the Gibbs ensemble using configurational bias sampling. Simulations of phase equilibria for square-well chains of up to 100 segments are performed using the NPT-μ method and newly proposed Monte Carlo moves. A two-reference-fluid equation of state is developed to describe the pressure-volume-temperature properties of square-well and Lennard-Jones chains. The phase envelopes predicted by such an equation are in good agreement with results of simulations. This equation is also shown to be superior to models derived from first-order thermodynamic perturbation theory (TPT1).