Showing papers on "Dynamic Monte Carlo method published in 1997"

Robust Monte Carlo methods for light transport simulation

Abstract: Light transport algorithms generate realistic images by simulating the emission and scattering of light in an artificial environment. Applications include lighting design, architecture, and computer animation, while related engineering disciplines include neutron transport and radiative heat transfer. The main challenge with these algorithms is the high complexity of the geometric, scattering, and illumination models that are typically used. In this dissertation, we develop new Monte Carlo techniques that greatly extend the range of input models for which light transport simulations are practical. Our contributions include new theoretical models, statistical methods, and rendering algorithms. We start by developing a rigorous theoretical basis for bidirectional light transport algorithms (those that combine direct and adjoint techniques). First, we propose a linear operator formulation that does not depend on any assumptions about the physical validity of the input scene. We show how to obtain mathematically correct results using a variety of bidirectional techniques. Next we derive a different formulation, such that for any physically valid input scene, the transport operators are symmetric. This symmetry is important for both theory and implementations, and is based on a new reciprocity condition that we derive for transmissive materials. Finally, we show how light transport can be formulated as an integral over a space of paths. This framework allows new sampling and integration techniques to be applied, such as the Metropolis sampling algorithm. We also use this model to investigate the limitations of unbiased Monte Carlo methods, and to show that certain kinds of paths cannot be sampled. Our statistical contributions include a new technique called multiple importance sampling, which can greatly increase the robustness of Monte Carlo integration. It uses more than one sampling technique to evaluate an integral, and then combines these samples in a

An algorithm for Monte Carlo simulation of coupled electron-photon transport

Abstract: An algorithm for Monte Carlo simulation of coupled electron-photon transport is described. Electron and positron tracks are generated by means of PENELOPE, a mixed procedure developed by Baro et al. [Nucl. Instr. and Meth. B 100 (1995) 31]. The simulation of photon transport follows the conventional, detailed method. Photons are assumed to interact via coherent and incoherent scattering, photoelectric absorption and electron-positron pair production. Photon interactions are simulated through analytical differential cross sections, derived from simple physical models and renormalized to reproduce accurate attenuation coefficients available from the literature. The combined algorithm has been implemented in a FORTRAN 77 computer code that generates electron-photon showers in arbitrary materials for the energy range from ∼1 GeV down to 1 keV or the binding energy of the L-shell of the heaviest element in the medium, whichever is the largest. The code is capable of following secondary particles that are generated within this energy range. The reliability of the algorithm and computer code is demonstrated by comparing simulation results with experimental data and with results from other Monte Carlo codes.

Thermodynamic behaviour of homonuclear and heteronuclear lennard-jones chains with association sites from simulation and theory

Abstract: Monte Carlo simulation and theoretical results are presented for mixtures of associating and non-associating Lennard-Jones chains. The molecular model accounts explicitly for repulsive, dispersive, chain, and association interactions. A modified statistical associating fluid theory for Lennard-Jones chains is used to compare with the NPT and Gibbs ensemble Monte Carlo simulation results. The equation is extended to describe heteronuclear Lennard-Jones chains, and results are compared with those obtained by Monte Carlo simulations. The influence of several variables, such as chain length, segment size and dispersive energy, polydispersity, etc., on the supercritical properties and the phase equilibria behaviour of these systems is discussed here. The theory seems to predict more accurately the behaviour of long chains rather than of those of intermediate length, due to the approximations made in the radial distribution function of the fluid.

Monte Carlo Simulation

Abstract: Introduction Generating Individual Samples from a Pseudo-Population Using the Pseudo-Population in Monte Carlo Simulation Using Monte Carlo Simulation in the Social Sciences Conclusion

Molecular dynamics, Langevin, and hybrid Monte Carlo simulations in multicanonical ensemble

Abstract: We demonstrate that the multicanonical approach is not restricted to Monte Carlo simulations, but can also be applied to simulation techniques such as molecular dynamics, Langevin, and hybrid Monte Carlo algorithms. The effectiveness of the methods are tested with an energy function for the protein folding problem. Simulations in the multicanonical ensemble by the three methods are performed for a penta peptide, Met-enkephalin. For each algorithm, it is shown that from only one simulation run one can not only find the global-minimum-energy conformation but also obtain probability distributions in canonical ensemble at any temperature, which allows the calculation of any thermodynamic quantity as a function of temperature.

The direct simulation Monte Carlo method

Abstract: Numerical simulation of the hydrodynamics of gas flow and fluid flow is described using the Direct Simulation Monte Carlo method. (AIP) © 1997 American Institute of Physics.

Theory of cumulative small-angle collisions in plasmas

Abstract: A succession of small-angle binary collisions can be grouped into a unique binary collision with a large scattering angle. The latter is called a cumulative collision. This makes it possible to treat the cumulative collision like a collision between neutral molecules. A significant feature of the cumulative collision is that the probability density function for a deflection angle depends on the time spent by a charged particle while engaged in the cumulative collision. Here a simple analytic expression for the function is proposed which is easy to use together with the Monte Carlo method. The validity of the present theory is ascertained by calculating various relaxation phenomena in plasmas. The theory is best suited to particle simulation of plasmas.

An accurate potential energy curve for helium based on ab initio calculations

Abstract: Korona, Williams, Bukowski, Jeziorski, and Szalewicz [J. Chem. Phys. 106, 1 (1997)] constructed a completely ab initio potential for He2 by fitting their calculations using infinite order symmetry adapted perturbation theory at intermediate range, existing Green’s function Monte Carlo calculations at short range and accurate dispersion coefficients at long range to a modified Tang–Toennies potential form. The potential with retardation added to the dipole-dipole dispersion is found to predict accurately a large set of microscopic and macroscopic experimental data. The potential with a significantly larger well depth than other recent potentials is judged to be the most accurate characterization of the helium interaction yet proposed.

Dissipative dynamics for hard spheres

Abstract: The dynamics for a system of hard spheres with dissipative collisions is described at the levels of statistical mechanics, kinetic theory, and simulation. The Liouville operator(s) and associated binary scattering operators are defined as the generators for time evolution in phase space. The BBGKY hierarchy for reduced distribution functions is given, and an approximate kinetic equation is obtained that extends the revised Enskog theory to dissipative dynamics. A Monte Carlo simulation method to solve this equation is described, extending the Bird method to the dense, dissipative hard-sphere system. A practical kinetic model for theoretical analysis of this equation also is proposed. As an illustration of these results, the kinetic theory and the Monte Carlo simulations are applied to the homogeneous cooling state of rapid granular flow.

Free energy of crystalline solids: A lattice-switch Monte Carlo method

Abstract: We present a Monte Carlo method for evaluating the difference between the free energies of two crystal structures. The method uses a biased sampling of atomic displacements to favor configurations of one structure that can be replaced by corresponding configurations of the other through a Monte Carlo switch of the lattice. The configurations of both structures can be sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. The method is applied to the free energies of the fcc and hcp phases of hard spheres.

Electrostatic Attraction between Two Charged Surfaces: A (N,V,T) Monte Carlo Simulation

Abstract: We have performed (N,V,T) Monte Carlo simulations in order to study the stability of two parallel charged surfaces (lamellae) neutralized by exchangeable counterions. By varying each parameter characterizing the interface, i.e., the interlamellar separation, the surface charge density of the lamellae, the dielectric constant of the solvent, and the radius and charge of the counterions, we have determined the stability of a wide class of physical situations. The ion−ion, lamella−ion, and lamella−lamella interactions are described within the context of the “primitive model”. We give evidence that, despite the intrinsic simplicity of the primitive model, the phase diagram of such a system exhibits complex patterns. We have determined 2D contour maps of the equation of state in order to localize attracto/repulsive domains and optimize adhesive properties of the interface. This study concerns a large variety of lamellar materials, including hydrated cement and clays, and pillared and organo clays. At low diele...

Solvent Effects from a Sequential Monte Carlo - Quantum Mechanical Approach

Abstract: An approach based on the sequential use of Monte Carlo simulation and Quantum Mechanics is suggested for the treatment of solvent effects with special attention to solvatochromic shifts. The basic idea is to treat the solute, the solvent and its interaction by quantum mechanics. This is a totally discrete model that avoids the use of a dielectric continuum. Statistical analysis is used to obtain uncorrelated structures. The radial distribution function is used to determine the solvation shells. Quantum mechanical calculations are then performed in supermolecular structures and the spectral shifts are obtained using ensemble average. Attention is also given to the case of specific hydrogen bond between the solute and solvent.

Photon migration through a turbid slab described by a model based on diffusion approximation. II. Comparison with Monte Carlo results

Abstract: In our companion paper we presented a model to describe photon migration through a diffusing slab. The model, developed for a homogeneous slab, is based on the diffusion approximation and is able to take into account reflection at the boundaries resulting from the refractive index mismatch. In this paper the predictions of the model are compared with solutions of the radiative transfer equation obtained by Monte Carlo simulations in order to determine the applicability limits of the approximated theory in different physical conditions. A fitting procedure, carried out with the optical properties as fitting parameters, is used to check the application of the model to the inverse problem. The results show that significant errors can be made if the effect of the refractive index mismatch is not properly taken into account. Errors are more important when measurements of transmittance are used. The effects of using a receiver with a limited angular field of view and the angular distribution of the radiation that emerges from the slab have also been investigated.

Monte Carlo studies of the dynamics of an interacting monodispersive magnetic-particle system

Abstract: The influence of the dipole-dipole interaction on the dynamics of monodispersive ensembles of magnetic nanoparticles have been studied by Monte Carlo simulations. An increased interaction strength ...

Monte Carlo simulations of polymer dynamics: Recent advances

Abstract: A brief review is given of applications of Monte Carlo simulations to study the dynamical properties of coarse-grained models of polymer melts, emphasizing the crossover from the Rouse model toward reptation, and the glass transition. The extent to which Monte Carlo algorithms can mimic the actual chain dynamics is critically examined, and the need for the use of coarse-grained rather than fully atomistic models for such simulations is explained. It is shown that various lattice and continuum models yield qualitatively similar results, and the behavior agrees with the findings of corresponding molecular dynamics simulations and experiments, where available. It is argued that these simulations significantly enhance our understanding of the theoretical concepts on the dynamics of dense macromolecular systems. © 1997 John Wiley & Sons, Inc.

Grand canonical Brownian dynamics simulation of colloidal adsorption

Abstract: A dynamic simulation of colloidal adsorption has been developed to probe the effects of colloidal interactions on the kinetics and extent of adsorption. The simulation accounts for diffusion by Brownian dynamics to a homogeneous planar adsorption surface from a region of constant chemical potential. A grand canonical Monte Carlo routine is used periodically to re-equilibrate this region. Particle motion in the plane of the surface is subject to either unrestricted diffusion or zero diffusion. Deryaguin-Landau-Verwey-Overbeek pair potentials are used to characterize both particle–particle and particle–surface interactions. The pair potential parameters were chosen to mimic (separately) polystyrene latex microspheres and small globular proteins, two classes of charged colloidal particles for which experimental adsorption data exist. The simulation qualitatively captures the variation in adsorptive capacity with ionic strength distinct to each system: fractional coverage increases for polystyrene latex adsor...

Structure and energetics of small helium clusters: Quantum simulations using a recent perturbational pair potential

Abstract: We report accurate ground state energies and structural properties for small clusters of 4He computed with the diffusion quantum Monte Carlo (DMC) method combined with high quality trial wave functions and using the recent analytical pair potential of Tang, Toennies, and Yiu [Phys. Rev. Lett. 74, 1546 (1995)]. Calculations based on the older HFD-B(He) potential are reported for comparison. The clusters are found to be extremely floppy and to be characterized by very diffuse wave functions. The DMC results for 4He2 and 4He3 are in excellent agreement with other calculations using conventional methods. 4He3 is found to have a noticeable contribution from nearly linear geometries. The internal structure of the clusters is described by a three particle correlation function which reveals a significantly non-spherical internal cluster structure. The energies for all cluster sizes are found to be slightly higher than those obtained with the HFD-B(He) pair potential. Exploratory calculations on the helium trimer ...

Generalized-ensemble monte carlo method for systems with rough energy landscape

Abstract: We present a Monte Carlo algorithm which enhances equilibrization of low-temperature simulations and allows sampling of configurations over a large range of energies. The method is based on a non-Boltzmann probability weight factor and is another version of the so-called generalized-ensemble techniques. The effectiveness of the approach is demonstrated for the system of a small peptide, an example of the frustrated system with a rugged energy landscape.

Numerical Simulations of Spin Glass Systems

Abstract: We discuss the status of Monte Carlo simulations of (mainly finite dimensional) spin glass systems After a short historical note and a brief theoretical introduction we start by discussing the (crucial) 3D case: the warm phase, the critical point and the cold phase, the ultrametric structure and the out of equilibrium dynamics With the same style we discuss the cases of 4D and 2D In a few appendices we give some details about the definition of states and about the tempering Monte Carlo approach

On Monte Carlo and molecular dynamics methods inspired by Tsallis statistics: Methodology, optimization, and application to atomic clusters

Abstract: Generalized Monte Carlo and molecular dynamics algorithms which provide enhanced sampling of the phase space in the calculation of equilibrium thermodynamic properties is presented The algorithm samples trial moves from a generalized statistical distribution derived from a modification of the Gibbs–Shannon entropy proposed by Tsallis Results for a one-dimensional model potential demonstrate that the algorithm leads to a greatly enhanced rate of barrier crossing and convergence in the calculation of equilibrium averages Comparison is made with standard Metropolis Monte Carlo and the J-walking algorithm of Franz, Freeman and Doll Application to a 13-atom Lennard-Jones cluster demonstrates the ease with which the algorithm may be applied to complex molecular systems

Monte Carlo simulations of surface reactions

Abstract: Numerical simulations based on the Monte Carlo method offer a powerful approach for detailed studies of complex reaction sequences, such as those associated with heterogeneous catalysis. In this article, we summarize some of the recent work based on discrete models for irreversible surface reactions. Particular emphasis is placed on kinetic phase transition, bistability, and oscillatory (nonstationary) reactions. In addition to discussing some of the fundamental aspects of nonequilibrium kinetics, we show through specific examples that explicit Monte Carlo simulations can transcend traditional approaches based on rate-equation methods, in particular those invoking the mean-field approximation. This is particularly the case when local correlations and fluctuations among the reactants are important.

Monte Carlo PDF modelling of a turbulent natural-gas diffusion flame

Abstract: A piloted turbulent natural-gas diffusion flame is investigated numerically using a 2D elliptic Monte Carlo algorithm to solve for the joint probability density function (PDF) of velocity and composition. Results from simulations are compared to detailed experimental data: measurements of temperature statistics, data on mean velocity and turbulence characteristics and data on OH. Conserved-scalar/constrained-equilibrium chemistry calculations were performed using three different models for scalar micro-mixing: the interaction by exchange with the mean (IEM) model, a coalescence/dispersion (C/D) model and a mapping closure model. All three models yield good agreement with the experimental data for the mean temperature. Temperature standard deviation and PDF shapes are generally predicted well by the C/D and mapping closure models, whereas the IEM model gives qualitatively incorrect results in parts of the domain. It is concluded that the choice of micro-mixing model can have a strong influence on the quali...

Statistical delay calculation, a linear time method

Abstract: This paper discusses a statistical approach to static timing analysis. Delays of gates and wires are modeled by stochastic values instead of the triple best case, typical and worst case delay. This has the advantage of avoiding the overly pessimistic (optimistic) outcome of traditional worst (best) case calculations. The paper proposes a new approximate scheme to perform the delay calculations with stochastic delay values in linear time. The results are validated with Monte Carlo simulations. From a mathematical analysis some counter–intuitive properties of delays in the presence of uncertain delay values are shown. The results section shows that that traditional worst–case timing analysis is on average 21% too pessimistic for the set of IWLS ’91 combinational benchmark circuits for a given delay model. Also, it is shown that the traditional typical delay calculation underestimates the most likely circuit delay by 0 – 14%. Furthermore, due to the mathematical properties of the delay calculations, the uncertainty in the delay of a circuit is usually much smaller than the uncertainty in the delays of the individual delay elements.

Long range corrections to thermodynamic properties of inhomogeneous systems with planar interfaces

Abstract: Expressions for the long range corrections to configurational energy, normal pressure, surface tension, and chemical potential of an inhomogeneous system with two planar interfaces are developed. Applying the Euler forward difference scheme to correlate the density at any height to that of a central spatial element separates the corrections into two parts: one relates directly to the central local density, and another is due to the density differences between the central local value and those around the central spatial element. An analytical expression is obtained for the first part when the Lennard-Jones potential function is adopted in the evaluation. Variations of these properties along the normal direction are illustrated in terms of the equilibrium density profiles obtained from Monte Carlo simulations performed at T*=0.90 and T*=1.15.

On the size and shape of self-assembled micelles

Abstract: Equilibrium size and shape distributions of self-assembled micelles are investigated using lattice Monte Carlo simulation techniques. The micellar size distributions are shown to include a Gaussian peak of spherical micelles, in combination with an exponential tail of cylindrical micelles.

Smart walking: A new method for Boltzmann sampling of protein conformations

Abstract: A new Monte Carlo algorithm is presented for the efficient sampling of protein conformation space called the Smart-Walking (S-Walking) method. The method is implemented using a hybrid Monte Carlo protocol. The S-Walking method is closely related to the J-Walking method proposed by Frantz et al. (J. Chem. Phys. 93, 2769, 1990). Like the J-Walking method, the S-Walking method runs two walkers, one at the temperature of interest, the other at a higher temperature which more efficiently generates ergodic distributions. Instead of sampling from the Boltzmann distribution of the higher temperature walker as in J-Walking, S-Walking first approximately minimizes the structures being jumped into, and then uses the relaxed structures as the trial moves at the low temperature. By jumping into a relaxed structure, or a local minimum, the jump acceptance ratio increases dramatically, which makes the protein system easily undergo barrier-crossing events from one basin to another, thus greatly improving the ergodicity o...

On advanced Monte Carlo simulation procedures in stochastic structural dynamics

Abstract: As analytical methods to predict the response of MDOF-systems under stochastic loading are quite limited, numerical procedures, such as Monte Carlo simulation techniques, are frequently applied. Direct Monte Carlo simulation, however, particularly for reliability analyses, is not suitable for providing sufficient information on the tails of the distribution of the response. In this paper Monte Carlo methods, applicable to Markov processes are further advanced, i.e. by leading the generated samples towards the low probability range which is practically not accessible by direct Monte Carlo methods. In this context, notions as developed for variance reduction techniques are introduced and discussed. Based on criteria denoting those realizations which lead most likely to failure, a numerical procedure called “Double & Clump” (D&C) is discussed briefly. It is shown that the rather numerically involved D&C procedure can be simplified by a technique known as “Russian Roulette and Splitting” (RR&S). In two numerical examples, both procedures D&C and RR&S are compared with direct Monte Carlo simulation as well as the Response Surface Method (RSM) demonstrating comparable accuracy.