Showing papers on "Dynamic Monte Carlo method published in 1986"
31 Aug 1986
TL;DR: An integral equation is presented which generalizes a variety of known rendering algorithms and a new form of variance reduction, called Hierarchical sampling, which may be an efficient new technique for a wide variety of monte carlo procedures.
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.
2,631 citations
TL;DR: A new Monte Carlo method is presented for simulations of systems with quenched random interactions, allowing the investigation of lower temperatures with less computer time than previously necessary.
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.
1,848 citations
01 Jan 1986-Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms
TL;DR: A new electron transport algorithm for use with electron Monte Carlo transport codes is presented which will allow the inexperienced user to obtain reliable results from the EGS Monte Carlo code without having to do a detailed study of the electron transport parameters.
Abstract: A new electron transport algorithm for use with electron Monte Carlo transport codes is presented. Its components are: a path-length correction (PLC) algorithm which is based on the multiple scattering theory of Moliere and which takes into account the differences between the straight path length and the total curved path length for each electron step; a lateral correlation algorithm (LCA) which takes into account lateral transport; and a boundary crossing algorithm (BCA) which ensures that electrons are transported accurately in the vicinity of interfaces. The algorithm has been implemented in the EGS4 code system and a variety of tests validating the algorithms are presented. In its standard configuration, use of this algorithm will allow the inexperienced user to obtain reliable results from the EGS Monte Carlo code without having to do a detailed study of the electron transport parameters. In many situations, substantial savings in computing time may be realized in comparison to the present EGS algorithm. The developments described in this report may be adapted to other electron transport codes where many of the same conclusions may be drawn.
451 citations
317 citations
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TL;DR: An outline of a random walk computational method for solving the Schr�dinger equation for many interacting particles is given, together with a survey of results achieved so far and of applications that remain to be explored.
Abstract: An outline of a random walk computational method for solving the Schrodinger equation for many interacting particles is given, together with a survey of results achieved so far and of applications that remain to be explored. Monte Carlo simulations can be used to calculate accurately the bulk properties of the light elements hydrogen, helium, and lithium as well as the properties of the isolated atoms and of molecules made up from these elements. It is now possible to make reliable predictions of the behavior of these substances under experimentally difficult conditions, such as high pressure, and of properties that are difficult to measure experimentally, such as the momentum distribution in superfluid helium. For chemical systems, the stochastic method has a number of advantages over the widely used variational approach to determine ground-state properties, namely fast convergence to the exact result within objectively established error bounds.
299 citations
TL;DR: In this article, 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 were performed.
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
233 citations
TL;DR: In this article, the null collision concept is introduced into the direct simulation Monte Carlo method in the rarefied gas dynamics and it is concluded that the null-collision technique is superior to any other existing techniques in the direct simulating Monte Carlo (DMMC) method.
Abstract: The null‐collision concept is introduced into the direct‐simulation Monte Carlo method in the rarefied gas dynamics. The null‐collision technique overcomes the principle fault in the time‐counter technique and the difficulties in the collision‐frequency technique. The computation time required for the null‐collision technique is comparable to that for the time‐counter technique. Therefore, it is concluded that the null‐collision technique is superior to any other existing techniques in the direct‐simulation Monte Carlo method.
170 citations
TL;DR: In this article, the Monte Carlo method is extended to evaluate the integrals of complex-valued functions, i.e. the Feynman path integrals representing the time-dependent Green function of the one-dimensional non-stationary Schrodinger equation.
149 citations
135 citations
TL;DR: In this article, the UK code monk is analysed and formulae for the biases are worked out and a new algorithm for the Monte Carlo simulation is devised which effectively gets rid of both biases and, as a bonus, reduces the true variance of the sampling for K eff.
TL;DR: A stochastic generalization of the multigrid method, which reduces critical slowing down in Monte Carlo computations of lattice field theories, is proposed, which shows a factor of roughly-equal10 reduction in the work needed to get a given accuracy (error-bar size).
Abstract: We propose a stochastic generalization of the multigrid method, which reduces critical slowing down in Monte Carlo computations of lattice field theories. For free fields, critical slowing down is completely eliminated. For a ${\ensuremath{\varphi}}^{4}$ model, numerical experiments show a factor of \ensuremath{\cong} 10 reduction, over a standard heat-bath algorithm, in the work needed to get a given accuracy (error-bar size).
TL;DR: In this article, the practicality of the Monte Carlo (MC) method developed for the analysis of the particle transport process in sputterdeposition was examined and the results showed that sufficient performance of the MC method can be obtained in the usual sputtering condition up to the argon pressure beyond which the majority of particles are transported by the thermal diffusion process.
Abstract: Practicality of the Monte Carlo (MC) method developed for the analysis of the particle transport process in sputter‐deposition was examined. Titanium film thickness distributions on both faces of a planar substrate facing and not facing a planar‐magnetron‐type target were compared with corresponding calculated profiles. The results show that sufficient performance of the MC method can be obtained in the usual sputtering condition up to the argon pressure beyond which the majority of particles are transported by the thermal diffusion process.
TL;DR: A short review of the quantum statistical Monte Carlo method based on the equivalence theorem that d-dimensional quantum systems are mapped onto (d+1)-dimensional classical systems is given in this article.
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.
TL;DR: 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 in this paper.
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.
01 Nov 1986-Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms
TL;DR: In this article, the theory of Monte Carlo computer calculations for ion shadowing and blocking experiments is discussed, and a new algorithm with which ion backscattering measurements from relaxed or reconstructed crystal surfaces, overlayer systems, interfaces, etc., can be accurately simulated.
Abstract: Monte Carlo computer calculations form an indispensable tool in the preparation and analysis of high-energy (50 keV–5 MeV) ion shadowing and blocking experiments. In this paper we discuss the theory of such calculations and describe a new algorithm, with which ion backscattering measurements from relaxed or reconstructed crystal surfaces, overlayer systems, interfaces, etc., can be accurately simulated. A comparison is made with other calculations, and some results are presented as illustration.
TL;DR: In this paper, the results of grand canonical Monte Carlo simulations on a model of "rod-like" polyelectrolyte solutions are presented, and they show that the Poisson-Boltzmann equation retains its semiquantitative utility in this model.
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.
01 Jan 1986
TL;DR: The theoretical background is described for the application of Monte Carlo sampling to calculate statistical ensemble averages of classical interacting many-body systems and some approximative variants of the technique are discussed which might become useful to simulate critical phenomena.
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.
TL;DR: In this paper, the computer method of Lattice Statics (HADES/CASCADE) was used to calculate anion migration energies for 30 unique local environments involving the distribution of Y 3+ ions in CeO 2.
TL;DR: In this article, the Monte Carlo simulations based on the heat bath algorithm are implemented for the following classical spin systems: (i) the continuous-spin Ising model; (ii) the XY model and (iii) the Heisenberg model.
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.
TL;DR: In this article, the phase diagram of the Blume-Capel model is investigated by using the technique of phenomenological finite-size scaling, and the location of the tricritical point and the values of the critical and trichethoric exponents are determined.
Abstract: The phase diagram of the two-dimensional Blume-Capel model is investigated by using the technique of phenomenological finite-size scaling. The location of the tricritical point and the values of the critical and tricritical exponents are determined. The location of the tricritical point (${T}_{t}$=0.610\ifmmode\pm\else\textpm\fi{}0.005, ${D}_{t}$=1.9655\ifmmode\pm\else\textpm\fi{}0.0010) is well outside the error bars for the value quoted in previous Monte Carlo simulations but in excellent agreement with more recent Monte Carlo renormalization-group results. The values of the critical and tricritical exponents, with the exception of the leading thermal tricritical exponent, are in excellent agreement with previous calculations, conjectured values, and Monte Carlo renormalization-group studies.
TL;DR: In this article, the results of a Monte Carlo simulation for the temporal evolution of a two-dimensional soap froth are reported, which is an alternative method to the previous technique used to model the froth by Weaire and Kermode (1983 b).
Abstract: The results of a Monte Carlo simulation for the temporal evolution of a two-dimensional soap froth are reported. The simulation was used, in particular, to study the asymptotic behaviour of the system, as t→∞. It is an alternative method to the previous technique used to model the froth by Weaire and Kermode (1983 b). In the Monte Carlo simulation the network of cells is mapped onto a discrete lattice of (200 × 200) points with periodic boundary conditions. The main quantities of interest are the rate of increase of average cell diameter and the behaviour of the distribution of numbers of sides f(n), characterized by its second moment, as a function of time.
TL;DR: In this paper, a method inspired by Monte Carlo quadrature formulas was used to create a basis set of Gaussian type geminals for the calculation of the second-order energy of the beryllium atom.
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.
TL;DR: In this paper, Monte Carlo simulations of athermal chains in the square lattice were performed, and a detailed comparison between Flory and Flory-Huggins theories and numerical results were presented.
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.
TL;DR: In this article, a modification of the diffusion Monte Carlo algorithm that enables the direct simulation of wave functions containing nodal surfaces is described, and the use of orthogonality constraints during the simulation enables the properties of excited state systems to be calculated.
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.
TL;DR: In this article, a discretization of the bosonic string through dynamically triangulated surfaces with weights depending on the internal curvature is studied analytically and by Monte Carlo simulations.
TL;DR: In this article, 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.
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.