Showing papers on "Dynamic Monte Carlo method published in 1995"
TL;DR: In this article, a Monte Carlo collision (MCC) package including the null collision method has been developed, as an addition to the usual PIC charged particle scheme which will be discussed here.
881 citations
Book•
01 Jan 1995
TL;DR: In this article, Monte Carlo Methods for the Self-Avoiding Walk and Monte Carlo Simulation of Neutral and Charged Polymer Solutions: Effects of Long-range Interactions are presented.
Abstract: 1. Introduction. General Aspects of Computer Simulation Techniques and Their Applicaitons in Polymer Physics 2. Monte Carlo Methods for the Self-Avoiding Walk 3. Structure and Dynamics of Neutral and Charged Polymer Solutions: Effects of Long-Range Interactions 4. Entanglement Effects in Polymer Melts 5. Molecular Dynamics of Glassy Polymers 6. Monte Carlo Simulations of the Glass Transition of Polymers 7. Monte Carlo Studies of Polymer Blends and Block Copolymer Thermodynamics 9. Computer Simulations of Tethered Chains
870 citations
TL;DR: In this article, an approach is presented to solve the reverse problem of statistical mechanics: reconstruction of interaction potentials from radial distribution functions, consisting of the iterative adjustment of the interaction potential to known radial distribution function using a Monte Carlo simulation technique and statistical-mechanics relations to connect deviations of canonical averages with Hamiltonian parameters.
Abstract: An approach is presented to solve the reverse problem of statistical mechanics: reconstruction of interaction potentials from radial distribution functions. The method consists of the iterative adjustment of the interaction potential to known radial distribution functions using a Monte Carlo simulation technique and statistical-mechanics relations to connect deviations of canonical averages with Hamiltonian parameters. The method is applied to calculate the effective interaction potentials between the ions in aqueous NaCl solutions at two different concentrations. The reference ion-ion radial distribution functions, calculated in separate molecular dynamics simulations with water molecules, are reproduced in Monte Carlo simulations, using the effective interaction potentials for the hydrated ions. Application of the present method should provide an effective and economical way to simulate equilibrium properties for very large molecular systems (e.g., polyelectrolytes) in the presence of hydrated ions, as well as to offer an approach to reduce a complexity in studies of various associated and aggregated systems in solution.
772 citations
15 Sep 1995
TL;DR: This work presents a powerful alternative for constructing robust Monte Carlo estimators, by combining samples from several distributions in a way that is provably good, and can reduce variance significantly at little additional cost.
Abstract: Monte Carlo integration is a powerful technique for the evaluation of difficult integrals. Applications in rendering include distribution ray tracing, Monte Carlo path tracing, and form-factor computation for radiosity methods. In these cases variance can often be significantly reduced by drawing samples from several distributions, each designed to sample well some difficult aspect of the integrand. Normally this is done by explicitly partitioning the integration domain into regions that are sampled differently. We present a powerful alternative for constructing robust Monte Carlo estimators, by combining samples from several distributions in a way that is provably good. These estimators are unbiased, and can reduce variance significantly at little additional cost. We present experiments and measurements from several areas in rendering: calculation of glossy highlights from area light sources, the “final gather” pass of some radiosity algorithms, and direct solution of the rendering equation using bidirectional path tracing. CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism; I.3.3 [Computer Graphics]: Picture/Image Generation; G.1.9 [Numerical Analysis]: Integral Equations— Fredholm equations. Additional
633 citations
TL;DR: In this paper, the authors compared the performance of quasi-random and random Monte Carlo methods for multidimensional integrals with respect to variance, variation, smoothness, and dimension.
492 citations
01 Jan 1995
TL;DR: The book is mainly concerned with the mathematical foundations of Bayesian image analysis and its algorithms, which amounts to the study of Markov random fields and dynamic Monte Carlo algorithms like sampling, simulated annealing and stochastic gradient algorithms.
486 citations
Book•
13 Apr 1995
TL;DR: In this paper, the authors introduce Monte Carlo Methods and their application in the field of X-ray production and micro-analysis, including charge collection microscopy and Cathodoluminescence.
Abstract: Preface 1. An Introducton to Monte Carlo Methods 2. Constructing a Simulation 3. The Single Scattering Model 4. The Plural Scattering Model 5. Practical Applications of Monte Carlo Models 6. Backscattered Electrons 7. Charge Collection Microscopy and Cathodoluminescence 8. Secondary Electrons and Imaging 9. X-ray Production and Micro-Analysis 10. What Next in Monte Carlo Simulations?
480 citations
03 Apr 1995
TL;DR: If the authority ascribed to Monte Carlo models of devices at 1/spl mu/m feature size is to be maintained, modelling of the fundamental physics must be further improved, and the device model must be made more realistic.
Abstract: There can be little doubt that the Monte Carlo method for semiconductor device simulation has enormous power as a research tool. It represents a detailed physical model of the semiconductor material(s), and provides a high degree of insight into the microscopic transport processes. However, if the authority ascribed to Monte Carlo models of devices at 1/spl mu/m feature size is to be maintained for devices below O.1/spl mu/m, modelling of the fundamental physics must be further improved. And if the Monte Carlo method is to be successful as a semiconductor device design tool, the device model must be made more realistic. Success in the industrial sector depends on this, but also on achieving fast run-times optimisation - where the scope and need for ingenuity is now greatest.
436 citations
TL;DR: A simple model for biological aging is presented through computer simulations and it is finted to reflect some features of real populations to reflect the changes in real populations.
Abstract: We present a simple model for biological aging. We study it through computer simulations and fint it to reflect some features of real populations.
289 citations
TL;DR: In this article, a new Monte Carlo algorithm for the simulation of atomistically detailed polymer melts is presented, where the connectivity of the polymer is altered in Monte Carlo moves that satisfy the detailed constraints of molecular geometry.
Abstract: A new Monte Carlo algorithm for the simulation of atomistically detailed polymer melts is presented. The method introduces connectivity relationships as variables in the description of the polymer. The connectivity of the polymer is altered in Monte Carlo moves that satisfy the detailed constraints of molecular geometry. Connectivity-altering moves are seen to induce large jumps in the configuration space of the bulk polymer, thereby greatly enhancing the efficiency with which molecular configurations are sampled. Simulations are carried out in a semigrand ensemble in which the chain length distribution is controlled by a spectrum of chemical potentials. Limiting chain length distributions are derived and compared with simulation results. Volumetric and structural predictions of the method are found to be in agreement with previous work.
TL;DR: In this article, the authors investigated three Ising models on the simple cubic lattice by means of Monte Carlo methods and finite-size scaling, and found that the correction-to-scaling amplitudes are strongly dependent on the introduction of further-neighbour interactions or a third spin state.
Abstract: We investigate three Ising models on the simple cubic lattice by means of Monte Carlo methods and finite-size scaling. These models are the spin-1/2 Ising model with nearest-neighbour interactions, a spin-1/2 model with nearest-neighbour and third-neighbour interactions, and a spin-1 model with nearest-neighbour interactions. The results are in accurate agreement with the hypothesis of universality. Analysis of the finite-size scaling behaviour reveals corrections beyond those caused by the leading irrelevant scaling field. We find that the correction-to-scaling amplitudes are strongly dependent on the introduction of further-neighbour interactions or a third spin state. In a spin-1 Ising model, these corrections appear to be very small. This is very helpful for the determination of the universal constants of the Ising model. The renormalization exponents of the Ising model are determined as yt=1.587 (2), yh=2.4815 (15) and yi=-0.82 (6). The universal ratio Q=(m2)2/(m4) is equal to 0.6233 (4) for periodic systems with cubic symmetry. The critical point of the nearest-neighbour spin-1/2 model is Kc=0.2216546 (10).
TL;DR: In this paper, Woźniakowski et al. presented a program committee for the International Journal of Distributed Sensor Networks (GanIzerS) with the following members: Piotr krzyżanowski, Marek kwas, leszek Plaskota, and Grzegorz Wasilkowski.
Abstract: loCal orGanIzerS • Piotr krzyżanowski • Marek kwas • leszek Plaskota • Henryk Woźniakowski (chair) PROGRAM COMMITTEE • William Chen (australia) • ronald Cools (Belgium) • Josef dick (australia) • Henri Faure (France) • alan Genz (USa) • Paul Glasserman (USa) • Stefan Heinrich (Germany) • Fred J. Hickernell (USa) • Stephen Joe (new zealand) • aneta karaivanova (Bulgaria) • alexander keller (Germany) • Frances kuo (australia) • Gerhard larcher (austria) • Pierre l’ecuyer (Canada) • Christiane lemieux (Canada) • Makoto Matsumoto (Japan) • Peter Mathé (Germany) • thomas Müller-Gronbach (Germany) • Harald niederreiter (austria) • erich novak (Germany) • art B. owen (USa) • Friedrich Pillichshammer (austria) • leszek Plaskota (Poland) • klaus ritter (Germany) • Wolfgang Ch. Schmid (austria) • nikolai Simonov (russia) • Ian H. Sloan (australia) • Ilya M. Sobol’ (russia) • Jerome Spanier (USa) • Shu tezuka (Japan) • Xiaoqun Wang (China) • Grzegorz Wasilkowski (USa) • Henryk Woźniakowski (chair) (Poland/USa)
TL;DR: In this paper, the spectral properties such as the energy spectrum, the eigenmodes, and the density of states of a classical finite system of two-dimensional charged particles which are confined by a quadratic potential were studied.
Abstract: We present a study of the spectral properties such as the energy spectrum, the eigenmodes, and the density of states of a classical finite system of two-dimensional charged particles which are confined by a quadratic potential. Using the method of Newton optimization we obtain the ground state and the metastable states. For a given configuration the eigenvectors and eigenfrequencies for the normal modes are obtained using the Householder diagonalization technique for the dynamical matrix whose elements are the second derivative of the potential energy. For small clusters the lowest excitation corresponds to an intershell rotation. The energy barrier for such rotations is calculated. For large clusters the lowest excitation consists of a vortex/antivortex pair. The Lindeman melting criterion is used to calculate the order-disorder transition temperature for intershell rotation and intershell diffusion. The value of the transition temperature at which intershell rotation becomes possible depends very much on the configuration of the cluster, i.e., the distribution of the particles between the different shells. Magic numbers are associated with clusters which are most stable against intershell rotation. The specific heat of the cluster is also calculated using the Monte Carlo technique, which we compare with an analytical calculation where effects due to anharmonicity are incorporated.
TL;DR: In this article, an asymptotically efficient algorithm for the allocation of computing resources to the problem of Monte Carlo integration of continuous-time security prices is presented, where the tradeoff between increasing the number of time intervals per unit of time and increasing the simulation time is investigated.
Abstract: This paper provides an asymptotically efficient algorithm for the allocation of computing resources to the problem of Monte Carlo integration of continuous-time security prices The tradeoff between increasing the number of time intervals per unit of time and increasing the number of simulations, given a limited budget of computer time, is resolved for first-order discretization schemes (such as Euler) as well as second- and higher-order schemes (such as those of Milshtein or Talay)
TL;DR: In this paper, the authors examined the thermodynamic properties of 27 monomer lattice copolymer copolymers and found two independent transitions: a collapse transition to compact states and a folding transition from compact states to the native state.
Abstract: Using Monte Carlo dynamics and the Monte Carlo histogram method, the simple three‐dimensional 27 monomer lattice copolymer is examined in depth. The thermodynamic properties of various sequences are examined contrasting the behavior of good and poor folding sequences. The good (fast folding) sequences have sharp well‐defined thermodynamic transitions while the slow folding sequences have broad ones. We find two independent transitions: a collapse transition to compact states and a folding transition from compact states to the native state. The collapse transition is second‐order‐like, while folding is first‐order‐like. The system is also studied as a function of the energy parameters. In particular, as the average energetic drive toward compactness is reduced, the two transitions approach each other. At zero average drive, collapse and folding occur almost simultaneously; i.e., the chain collapses directly into the native state. At a specific value of this energy drive the folding temperature falls below ...
TL;DR: In this article, it was shown that the recently developed configurational-bias Monte Carlo technique can be used in a grand canonical Monte Carlo simulation to make the insertion of chain molecules possible, and the use of this technique is illustrated by calculations of the adsorption isotherms of butane and hexane in the zeolite silicate.
Abstract: Simulations of open systems are performed conveniently in the grand canonical ensemble. For chain molecules simulations of this type converge very poorly because of the very low probability of a successful insertion in the exchange step. Here, it is shown that the recently developed configurational-bias Monte Carlo technique can be used in a grand canonical Monte Carlo simulation to make the insertion of chain molecules possible. The use of this technique is illustrated by calculations of the adsorption isotherms of butane and hexane in the zeolite silicate.
TL;DR: The phase diagram is determined for the first time for a lattice system of biaxial particles interacting with a second rank anisotropic potential using Monte Carlo simulations for a number of values of the molecular biaXiality.
Abstract: We have determined the phase diagram for a lattice system of biaxial particles interacting with a second rank anisotropic potential using Monte Carlo simulations for a number of values of the molecular biaxiality. We find increasing differences from mean field theory as the biaxiality increases. We have also calculated for the first time the full set of second rank biaxial and uniaxial order parameters and their temperature dependence, and on this basis we comment on the difficulties of measuring phase biaxiality by NMR.
TL;DR: In this article, a theory for nonuniform polymer melts is presented, which combines density functional theory with Monte Carlo methods, treating the ideal gas functional exactly via a single chain simulation and using the weighted density approximation for the excess free energy functional.
Abstract: A theory for nonuniform polymer melts is presented, which combines density functional theory with Monte Carlo methods. The theory treats the ideal gas functional exactly via a single chain simulation and uses the weighted density approximation for the excess free energy functional. The bulk fluid properties required in the theory are obtained from a generalized Flory equation of state. The predictions of the theory are compared to Monte Carlo simulations for the density profiles of semiflexible polymer melts confined between flat plates. Good agreement between theory and simulation is found for 3mers and 20mers and for several densities and molecular stiffnesses.
TL;DR: In this paper, the authors present Monte Carlo methods with a correct real-time dependence for simulating chemical reactions on a surface that have reaction-rate constants that may vary in time.
TL;DR: A new ensemble for Monte Carlo simulations, in which each state is assigned a statistical weight $1/k$, where $k$ is the number of states with smaller or equal energy, which has robust ergodicity properties and gives significant weight to the ground state.
Abstract: We propose a new ensemble for Monte Carlo simulations, in which each state is assigned a statistical weight $1/k$, where $k$ is the number of states with smaller or equal energy. This ensemble has robust ergodicity properties and gives significant weight to the ground state, making it effective for hard optimization problems. It can be used to find free energies at all temperatures and picks up aspects of critical behaviour (if present) without any parameter tuning. We test it on the travelling salesperson problem, the Edwards-Anderson spin glass and the triangular antiferromagnet.
TL;DR: In this paper, a multi-canonical Monte Carlo method is proposed to sample across an extended space of macro-states, showing that a good approximation to this distribution may be generated efficiently by exploiting measurements of the transition rate between macro states, in simulations launched from sub-dominant macro states.
Abstract: We present a study of the multi-canonical Monte Carlo method which constructs and exploits Monte Carlo procedures that sample across an extended space of macrostates. We examine the strategies by which the sampling distribution can be constructed, showing, in particular, that a good approximation to this distribution may be generated efficiently by exploiting measurements of the transition rate between macrostates, in simulations launched from sub-dominant macrostates. We explore the utility of the method in the measurement of absolute free energies, and how it compares with traditional methods based on path integration. We present new results revealing the behaviour of the magnetization distribution of a critical finite-sized magnet, for magnetization values extending from the scaling region all the way to saturation.
TL;DR: In this article, the continuum configurational bias (CCB) Monte Carlo method has been extended to perform elementary moves that involve the rearrangement of inner segments of flexible chains, where the continuity with the rest of the chain is ensured by disregarding those configurations that would imply an unrealistic elongation of the bonds once the chain was reconstructed.
Abstract: The continuum configurational bias (CCB) Monte Carlo method has been extended to perform elementary moves that involve the rearrangement of inner segments of flexible chains. When regrowing inner sites, the continuity with the rest of the chain is ensured by disregarding those configurations that would imply an unrealistic elongation of the bonds once the chain is reconstructed. The formalism presented here also allows the simulation of branched chains and crosslinked‐network structures. The Monte Carlo elementary moves proposed in this work are used in conjunction with an alternative method of preferential sampling in which the segments to be rearranged are chosen from a preselected region of space. The performance and capabilities of the new moves are compared to those of standard CCB and crank‐shaft algorithms for simulation of melts and solutions of hard‐sphere chains at high densities. Our results indicate that the methods presented here provide a fast relaxation of the bond orientation and the end‐to‐end orientation autocorrelation functions. Our isobaric simulations for homopolymer chains of up to 51 sites and for concentrated solutions of chain molecules in the monomer are consistent with previously reported data obtained by approximate molecular dynamics methods and by conventional Monte Carlo methods. However, small disagreements with existing data are identified at high densities. These PV results are also compared to the predictions of two recent equations of state. This comparison shows the presence of some small but systematic deviations.
TL;DR: In this paper, a class of Monte Carlo algorithms incorporating absorbing Markov chains is presented to study the escape from the metastable state in the two-dimensional square-lattice nearest-neighbor Ising ferromagnet in an unfavorable applied field.
Abstract: A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest order of these algorithms reduces to the $n$-fold way algorithm. These algorithms are applied to study the escape from the metastable state in the two-dimensional square-lattice nearest-neighbor Ising ferromagnet in an unfavorable applied field, and the agreement with theoretical predictions is very good. It is demonstrated that the higher-order algorithms can be many orders of magnitude faster than either the traditional Monte Carlo or $n$-fold way algorithms.
12 Jun 1995
TL;DR: A 5D tree structure to cache illumination information gained during Monte Carlo ray tracing is presented and it is adaptive and makes abstraction of the complexity of the input scene automatically.
Abstract: In this paper we present a 5D tree structure to cache illumination information gained during Monte Carlo ray tracing. The structure is elegant and simple to use. It is adaptive and makes abstraction of the complexity of the input scene automatically.
TL;DR: This work proposes a method which allows the parallel generation of MC moves, and which is especially useful for simulations with unavoidably low acceptance rates, such as for long chain molecules.
Abstract: The Monte Carlo (MC) method is an important tool in sampling the state space of a chosen statistical ensemble. It allows the study of thermodynamic averages of configurational properties by generating ``moves'' in a system and accepting or rejecting the thus generated new state depending on the energy of the new system and/or a random choice. These moves are intrinsically sequential and complicate parallel implementation. We propose a method which allows the parallel generation of MC moves, and which is especially useful for simulations with unavoidably low acceptance rates, such as for long chain molecules.
TL;DR: The proposed algorithm yields accurate results when it is applied to test problems such as the hydrogen atom and the hydrogen molecule and an excellent description of several properties of a fully many-body problem such as liquid $^{4}\mathrm{He}$ at zero temperature is achieved.
Abstract: A Monte Carlo algorithm for computing quantum-mechanical expectation values of coordinate operators in many-body problems is presented The algorithm, which relies on the forward walking method, fits naturally in a Green's function Monte Carlo calculation, ie, it does not require side walks or a bilinear sampling method Our method evidences stability regions large enough to accurately sample unbiased pure expectation values The proposed algorithm yields accurate results when it is applied to test problems such as the hydrogen atom and the hydrogen molecule An excellent description of several properties of a fully many-body problem such as liquid $^{4}\mathrm{He}$ at zero temperature is achieved
TL;DR: The structural properties of binary silicon-germanium alloys are investigated by means of large-scale constant-pressure Monte Carlo simulations of the Stillinger-Weber model and it is found that Vegard's law is valid at temperatures above the critical point.
Abstract: The structural properties of binary silicon-germanium alloys are investigated by means of large-scale constant-pressure Monte Carlo simulations of the Stillinger-Weber model. At low temperatures, the binary-mixture phase separates into Si-rich and Ge-rich phases. The two-phase coexistence region is terminated by a critical point that belongs to the mean-field universality class. We also studied the structural properties of pure Si and Ge as well as the binary mixture. In particular, we found that the linear thermal expansions for both Si and Ge are in agreement with experiments, and that V\'egard's law is valid at temperatures above the critical point. Finally, we compare the bond-length and bond-angle distributions with earlier analytical and numerical calculations based on the Kirkwood potential.
01 Mar 1995-Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms
TL;DR: Two-dimensional implanted dopant distributions at mask edges are studied using the Monte Carlo code IMSIL in this paper, and the simulation results show that the penetration below the mask is larger than expected and that a Gaussian function is inappropriate to describe the lateral distribution function.
Abstract: Two-dimensional implanted dopant distributions at mask edges are studied using the Monte Carlo code IMSIL. The models implemented in the program are reviewed. An empirical model of electronic stopping describes correctly the range of channeled B, P, and As ions in a wide energy range. The damage model takes defect recombination into account but does not require the simulation of recoil cascades. Two-dimensional dopant distributions are calculated by randomly selecting the starting points of the ions between two positions defining a mask opening. The simulation results show that the penetration below the mask is larger than expected and that a Gaussian function is inappropriate to describe the lateral distribution function. The discrepancy increases with decreasing implantation energy. The dependence of the two-dimensional profiles on mask edge orientation, tilt angle, and ion species, and the influence of a screening oxide are investigated.