Stochastic Variants of EM: Monte Carlo, Quasi-Monte Carlo and More Wolfgang Jank
Jank, Wolfgang
Stochastic Variants of EM: Monte Carlo, Quasi-Monte Carlo and More Wolfgang Jank Robert H. Smith School of Business University of Maryland KEY WORDS: Monte Carlo EM; Stochas- tic Approximation denotes an unknown parameter vector. The EM (Expectation-Maximization) algorithm naturally appeals
Monte Carlo Monte Carlo at Work by Gary D. Doolen and John Hendricks E very second nearly 10,000,000,000 "random" numbers are being generated on computers around the world for Monte Carlo solutions to problems hundreds of full-time careers invested in the fine art of generating Monte Carlo solutions--a livelihood
L'Ecuyer, Pierre
VARIANCE REDUCTION OF MONTE CARLO AND RANDOMIZED QUASIMONTE CARLO ESTIMATORS FOR STOCHASTIC and partial hedging strategies, with different models for the volatility process. For variance reduction, we improvement (e.g., via variance reduction) is therefore quite important in this con text. In this paper, we
Protein folding and phylogenetic tree reconstruction using stochastic approximation Monte Carlo
Cheon, Sooyoung
2007-09-17
Recently, the stochastic approximation Monte Carlo algorithm has been proposed by Liang et al. (2005) as a general-purpose stochastic optimization and simulation algorithm. An annealing version of this algorithm was developed for real small protein...
Franke, B. C. [Sandia National Laboratories, Albuquerque, NM 87185 (United States); Prinja, A. K. [Department of Chemical and Nuclear Engineering, University of New Mexico, Albuquerque, NM 87131 (United States)
2013-07-01
The stochastic Galerkin method (SGM) is an intrusive technique for propagating data uncertainty in physical models. The method reduces the random model to a system of coupled deterministic equations for the moments of stochastic spectral expansions of result quantities. We investigate solving these equations using the Monte Carlo technique. We compare the efficiency with brute-force Monte Carlo evaluation of uncertainty, the non-intrusive stochastic collocation method (SCM), and an intrusive Monte Carlo implementation of the stochastic collocation method. We also describe the stability limitations of our SGM implementation. (authors)
Del Moral , Pierre
Sequential Monte Carlo simulation for the estimation of small reachability probabilities for stochastic hybrid systems Jaroslav Krystul and Henk A.P. Blom Abstract-- The problem of estimating the probability that a system reaches a given set within some time horizon is considered. Standard Monte Carlo
Attard, Phil
Stochastic molecular dynamics: A combined Monte Carlo and molecular dynamics technique techniques--Monte Carlo and molecular dynamics--has their own advantage. The molecular dynamics method can to cover the important states of the system in an efficient manner. In recent years the molecular dynamics
Protein folding and phylogenetic tree reconstruction using stochastic approximation Monte Carlo
Cheon, Sooyoung
2007-09-17
folding problems. The numerical results indicate that it outperforms simulated annealing and conventional Monte Carlo algorithms as a stochastic optimization algorithm. We also propose one method for the use of secondary structures in protein folding...
Variance reduction for Monte Carlo simulation in a stochastic volatility environment
Jean-Pierre Fouque; Tracey Andrew Tullie
2002-01-01
We propose a variance reduction method for Monte Carlo computation of option prices in the context of stochastic volatility. This method is based on importance sampling using an approximation of the option price obtained by a fast mean-reversion expansion introduced in Fouque et al (2000 Derivatives in Financial Markets with Stochastic Volatility (Cambridge: Cambridge University Press)). We compare this with
O'Neill, Philip D
2002-01-01
Recent Bayesian methods for the analysis of infectious disease outbreak data using stochastic epidemic models are reviewed. These methods rely on Markov chain Monte Carlo methods. Both temporal and non-temporal data are considered. The methods are illustrated with a number of examples featuring different models and datasets. PMID:12387918
NSDL National Science Digital Library
David Joiner
Monte Carlo modeling refers to the solution of mathematical problems with the use of random numbers. This can include both function integration and the modeling of stochastic phenomena using random processes.
A Hybrid Monte Carlo-Deterministic Method for Global Binary Stochastic Medium Transport Problems
Keady, K P; Brantley, P
2010-03-04
Global deep-penetration transport problems are difficult to solve using traditional Monte Carlo techniques. In these problems, the scalar flux distribution is desired at all points in the spatial domain (global nature), and the scalar flux typically drops by several orders of magnitude across the problem (deep-penetration nature). As a result, few particle histories may reach certain regions of the domain, producing a relatively large variance in tallies in those regions. Implicit capture (also known as survival biasing or absorption suppression) can be used to increase the efficiency of the Monte Carlo transport algorithm to some degree. A hybrid Monte Carlo-deterministic technique has previously been developed by Cooper and Larsen to reduce variance in global problems by distributing particles more evenly throughout the spatial domain. This hybrid method uses an approximate deterministic estimate of the forward scalar flux distribution to automatically generate weight windows for the Monte Carlo transport simulation, avoiding the necessity for the code user to specify the weight window parameters. In a binary stochastic medium, the material properties at a given spatial location are known only statistically. The most common approach to solving particle transport problems involving binary stochastic media is to use the atomic mix (AM) approximation in which the transport problem is solved using ensemble-averaged material properties. The most ubiquitous deterministic model developed specifically for solving binary stochastic media transport problems is the Levermore-Pomraning (L-P) model. Zimmerman and Adams proposed a Monte Carlo algorithm (Algorithm A) that solves the Levermore-Pomraning equations and another Monte Carlo algorithm (Algorithm B) that is more accurate as a result of improved local material realization modeling. Recent benchmark studies have shown that Algorithm B is often significantly more accurate than Algorithm A (and therefore the L-P model) for deep penetration problems such as examined in this paper. In this research, we investigate the application of a variant of the hybrid Monte Carlo-deterministic method proposed by Cooper and Larsen to global deep penetration problems involving binary stochastic media. To our knowledge, hybrid Monte Carlo-deterministic methods have not previously been applied to problems involving a stochastic medium. We investigate two approaches for computing the approximate deterministic estimate of the forward scalar flux distribution used to automatically generate the weight windows. The first approach uses the atomic mix approximation to the binary stochastic medium transport problem and a low-order discrete ordinates angular approximation. The second approach uses the Levermore-Pomraning model for the binary stochastic medium transport problem and a low-order discrete ordinates angular approximation. In both cases, we use Monte Carlo Algorithm B with weight windows automatically generated from the approximate forward scalar flux distribution to obtain the solution of the transport problem.
Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application
NASA Astrophysics Data System (ADS)
Blunt, N. S.; Smart, Simon D.; Kersten, J. A. F.; Spencer, J. S.; Booth, George H.; Alavi, Ali
2015-05-01
We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable.
Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application.
Blunt, N S; Smart, Simon D; Kersten, J A F; Spencer, J S; Booth, George H; Alavi, Ali
2015-05-14
We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable. PMID:25978883
Empirical Analysis of Stochastic Volatility Model by Hybrid Monte Carlo Algorithm
NASA Astrophysics Data System (ADS)
Takaishi, Tetsuya
2013-04-01
The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is superior to other Markov Chain Monte Carlo methods in sampling volatility variables. We perform the HMC simulations of the SV model for two liquid stock returns traded on the Tokyo Stock Exchange and measure the volatilities of those stock returns. Then we calculate the accuracy of the volatility measurement using the realized volatility as a proxy of the true volatility and compare the SV model with the GARCH model which is one of other volatility models. Using the accuracy calculated with the realized volatility we find that empirically the SV model performs better than the GARCH model.
Wolfgang Wagner
1988-01-01
Variance–reducing estimators are derived for functionals of the solution of the general Ito stochastic differential equation. These estimators allow to apply variance reduction techniques known from the Monte Carlo theory. In particular, variance–reducing Euler estimators are constructed as well as variance–reducing unbiased estimators. Numerical examples are given. They show that the variance reduction techniques cause an enormous gain in efficiency,
Jean-Pierre Fouque; Chuan-Hsiang Han
2004-01-01
We present variance reduction methods for Monte Carlo simulations to evaluate European and Asian options in the context of multiscale stochastic volatility models. European option price approximations, obtained from singular and regular perturbation analysis [Fouque J P, Papanicolaou G, Sircar R and Solna K 2003 Multiscale stochastic volatility asymptotics, SIAM J. Multiscale Modeling and Simulation2], are used in importance sampling
Quasi-Monte Carlo Sampling to improve the Efficiency of Monte Carlo EM
Jank, Wolfgang
Quasi-Monte Carlo Sampling to improve the Efficiency of Monte Carlo EM Wolfgang Jank Department@rhsmith.umd.edu November 17, 2003 Abstract In this paper we investigate an efficient implementation of the Monte Carlo EM al- gorithm based on Quasi-Monte Carlo sampling. The Monte Carlo EM algorithm is a stochastic version
Monte Carlo methods Sequential Monte Carlo
Doucet, Arnaud
Monte Carlo methods Sequential Monte Carlo A. Doucet Carcans Sept. 2011 A. Doucet (MLSS Sept. 2011) Sequential Monte Carlo Sept. 2011 1 / 85 #12;Generic Problem Consider a sequence of probability distributions, Fn = Fn 1 F. A. Doucet (MLSS Sept. 2011) Sequential Monte Carlo Sept. 2011 2 / 85 #12;Generic Problem
Samant, A; Vlachos, D G
2005-10-01
In this paper the problem of stiffness in stochastic simulation of singularly perturbed systems is discussed. Such stiffness arises often from partial equilibrium or quasi-steady-state type of conditions. A multiscale Monte Carlo method is discussed that first assesses whether partial equilibrium is established using a simple criterion. The exact stochastic simulation algorithm (SSA) is next employed to sample among fast reactions over short time intervals (microscopic time steps) in order to compute numerically the proper probability distribution function for sampling the slow reactions. Subsequently, the SSA is used to sample among slow reactions and advance the time by large (macroscopic) time steps. Numerical examples indicate that not only long times can be simulated but also fluctuations are properly captured and substantial computational savings result. PMID:16238381
Asselineau, Charles-Alexis; Zapata, Jose; Pye, John
2015-06-01
A stochastic optimisation method adapted to illumination and radiative heat transfer problems involving Monte-Carlo ray-tracing is presented. A solar receiver shape optimisation case study illustrates the advantages of the method and its potential: efficient receivers are identified using a moderate computational cost. PMID:26072868
ERIC Educational Resources Information Center
Gold, Michael Steven; Bentler, Peter M.
2000-01-01
Describes a Monte Carlo investigation of four methods for treating incomplete data: (1) resemblance based hot-deck imputation (RBHDI); (2) iterated stochastic regression imputation; (3) structured model expectation maximization; and (4) saturated model expectation maximization. Results favored the expectation maximization methods. (SLD)
Combining Stochastics and Analytics for a Fast Monte Carlo Decay Chain Generator
Kareem Kazkaz; Nick Walsh
2011-04-14
Various Monte Carlo programs, developed either by small groups or widely available, have been used to calculate the effects of decays of radioactive chains, from the original parent nucleus to the final stable isotopes. These chains include uranium, thorium, radon, and others, and generally have long-lived parent nuclei. Generating decays within these chains requires a certain amount of computing overhead related to simulating unnecessary decays, time-ordering the final results in post-processing, or both. We present a combination analytic/stochastic algorithm for creating a time-ordered set of decays with position and time correlations, and starting with an arbitrary source age. Thus the simulation costs are greatly reduced, while at the same time avoiding chronological post-processing. We discuss optimization methods within the approach to minimize calculation time.
Combining Stochastics and Analytics for a Fast Monte Carlo Decay Chain Generator
Kazkaz, Kareem
2011-01-01
Various Monte Carlo programs, developed either by small groups or widely available, have been used to calculate the effects of decays of radioactive chains, from the original parent nucleus to the final stable isotopes. These chains include uranium, thorium, radon, and others, and generally have long-lived parent nuclei. Generating decays within these chains requires a certain amount of computing overhead related to simulating unnecessary decays, time-ordering the final results in post-processing, or both. We present a combination analytic/stochastic algorithm for creating a time-ordered set of decays with position and time correlations, and starting with an arbitrary source age. Thus the simulation costs are greatly reduced, while at the same time avoiding chronological post-processing. We discuss optimization methods within the approach to minimize calculation time.
Yukito Iba
2001-01-01
``Extended Ensemble Monte Carlo'' is a generic term that indicates a set of algorithms, which are now popular in a variety of fields in physics and statistical information processing. Exchange Monte Carlo (Metropolis-Coupled Chain, Parallel Tempering), Simulated Tempering (Expanded Ensemble Monte Carlo) and Multicanonical Monte Carlo (Adaptive Umbrella Sampling) are typical members of this family. Here, we give a cross-disciplinary
Graduiertenschule Hybrid Monte Carlo
Heermann, Dieter W.
Graduiertenschule Hybrid Monte Carlo SS 2005 Heermann - Universit¨at Heidelberg Seite 1 #12;Graduiertenschule · In conventional Monte-Carlo (MC) calculations of condensed matter systems, such as an N probability distribution, unlike Monte-Carlo calculations. · The Hybrid Monte-Carlo (HMC) method combines
Stochastic Monte-Carlo Markov Chain Inversions on Models Regionalized Using Receiver Functions
NASA Astrophysics Data System (ADS)
Larmat, C. S.; Maceira, M.; Kato, Y.; Bodin, T.; Calo, M.; Romanowicz, B. A.; Chai, C.; Ammon, C. J.
2014-12-01
There is currently a strong interest in stochastic approaches to seismic modeling - versus deterministic methods such as gradient methods - due to the ability of these methods to better deal with highly non-linear problems. Another advantage of stochastic methods is that they allow the estimation of the a posteriori probability distribution of the derived parameters, meaning the envisioned Bayesian inversion of Tarantola allowing the quantification of the solution error. The cost to pay of stochastic methods is that they require testing thousands of variations of each unknown parameter and their associated weights to ensure reliable probabilistic inferences. Even with the best High-Performance Computing resources available, 3D stochastic full waveform modeling at the regional scale still remains out-of-reach. We are exploring regionalization as one way to reduce the dimension of the parameter space, allowing the identification of areas in the models that can be treated as one block in a subsequent stochastic inversion. Regionalization is classically performed through the identification of tectonic or structural elements. Lekic & Romanowicz (2011) proposed a new approach with a cluster analysis of the tomographic velocity models instead. Here we present the results of a clustering analysis on the P-wave receiver-functions used in the subsequent inversion. Different clustering algorithms and quality of clustering are tested for different datasets of North America and China. Preliminary results with the kmean clustering algorithm show that an interpolated receiver function wavefield (Chai et al., GRL, in review) improve the agreement with the geological and tectonic regions of North America compared to the traditional approach of stacked receiver functions. After regionalization, 1D profile for each region is stochastically inferred using a parallelized code based on Monte-Carlo Markov Chains (MCMC), and modeling surfacewave-dispersion and receiver-functions observations. The parameters of the inversion are the elastic properties, the thickness and the number of isotropic layers. We will present preliminary results and compare them to results obtained from a different regionalizationbased on a tomographic model (Calo et al., 2013).
Practical Markov Chain Monte Carlo
Charles J. Geyer
1992-01-01
Markov chain Monte Carlo using the Metropolis-Hastings algorithm is a general method for the simulation of stochastic processes having probability densities known up to a constant of proportionality. Despite recent advances in its theory, the practice has remained controversial. This article makes the case for basing all inference on one long run of the Markov chain and estimating the Monte
NASA Astrophysics Data System (ADS)
Hassan, Ahmed E.; Cushman, John H.; Delleur, Jacques W.
1997-11-01
A Monte Carlo simulation of flow and transport is employed to study tracer migration in porous media with evolving scales of heterogeneity (fractal media). Transport is studied with both conservative and reactive chemicals in media that possess physical as well as chemical heterogeneity. Linear kinetic equations are assumed to relate the sorbed phase and the aqueous phase concentrations. The fluctuating log conductivity possesses the power law spectrum of a fractional Brownian motion (fBm). Chemical heterogeneity is represented as spatially varying reaction rates that also are assumed to obey fBm statistics and may be correlated to the conductivity field. The model is based on a finite difference approximation to the flow problem and a random walk particle-tracking approach for solving the solute transport equation. The model is used to make comparisons with the nonlocal transport equations recently developed by Deng et al. [1993], and Hu et al. [1995, 1997]. The results presented herein support these nonlocal models for a wide range of heterogeneous systems. However, the infinite integral scale associated with the fractal conductivity has a significant effect on the prediction of the nonlocal theories. This suggests that integral scale should play a role in stochastic Eulerian perturbation theories. The importance of the local-scale dispersion depends to a great extent on the magnitude of the local dispersivities. The effect of neglecting local dispersion decreases with the decrease in local dispersivity.
Bayrakci, Alp Arslan; Tasiran, Serdar
2008-01-01
In the nano era in integrated circuit fabrication technologies, the performance variability due to statistical process and circuit parameter variations is becoming more and more significant. Considerable effort has been expended in the EDA community during the past several years in trying to cope with the so-called statistical timing problem. Most of this effort has been aimed at generalizing the static timing analyzers to the statistical case. In this paper, we take a pragmatic approach in pursuit of making the Monte Carlo method for timing yield estimation practically feasible. The Monte Carlo method is widely used as a golden reference in assessing the accuracy of other timing yield estimation techniques. However, it is generally believed that it can not be used in practice for estimating timing yield as it requires too many costly full circuit simulations for acceptable accuracy. In this paper, we present a novel approach to constructing an improvedMonte Carlo estimator for timing yield which provides the...
Combining stochastics and analytics for a fast Monte Carlo decay chain generator
K. Kazkaz; N. Walsh
2011-01-01
Various Monte Carlo programs, developed either by small groups or widely available, have been used simulate decays of radioactive chains, from the original parent nucleus to the final stable isotopes. These chains include uranium, thorium, radon, and others, and generally have long-lived parent nuclei. Generating decays within these chains requires a certain amount of computing overhead related to simulating unnecessary
Ahmed E. Hassan; John H. Cushman; Jacques W. Delleur
1997-01-01
A Monte Carlo simulation of flow and transport is employed to study tracer migration in porous media with evolving scales of heterogeneity (fractal media). Transport is studied with both conservative and reactive chemicals in media that possess physical as well as chemical heterogeneity. Linear kinetic equations are assumed to relate the sorbed phase and the aqueous phase concentrations. The fluctuating
Brown, F.B.; Sutton, T.M.
1996-02-01
This report is composed of the lecture notes from the first half of a 32-hour graduate-level course on Monte Carlo methods offered at KAPL. These notes, prepared by two of the principle developers of KAPL`s RACER Monte Carlo code, cover the fundamental theory, concepts, and practices for Monte Carlo analysis. In particular, a thorough grounding in the basic fundamentals of Monte Carlo methods is presented, including random number generation, random sampling, the Monte Carlo approach to solving transport problems, computational geometry, collision physics, tallies, and eigenvalue calculations. Furthermore, modern computational algorithms for vector and parallel approaches to Monte Carlo calculations are covered in detail, including fundamental parallel and vector concepts, the event-based algorithm, master/slave schemes, parallel scaling laws, and portability issues.
A. M. Runov; D. Reiter; S. V. Kasilov; M. F. Heyn; W. Kernbichler
2001-01-01
The heat balance equation is derived and solved for fusion edge plasma conditions with (partially developed) ergodic magnetic-field structures. For this purpose, a three-dimensional (3D) Monte Carlo code, ``E3D,'' based upon the ``multiple local magnetic coordinate system approach'' has been developed. Parameters typical for the Dynamic Ergodic Divertor (DED) of TEXTOR-94 (Torus Experiment for the Technology Oriented Research) [K. H.
Thomas C. Henderson; Brandt Erickson; Travis Longoria; Edward Grant; Kyle Luthy; Leonardo Mattos; Matt Craver
2005-01-01
Biswas et al. (1) introduced a probabilistic approach to inference with limited information in sensor networks. They represented the sensor network as a Bayesian network and performed approximate inference using Markov Chain Monte Carlo (MCMC). The goal is to robustly answer queries even under noisy or partial information scenarios. We propose an alter- native method based on simple Monte Carlo
Monte-Carlo Tests Diplomarbeit
Monte-Carlo Tests Diplomarbeit Wiebke Werft Mathematisches Institut der Heinrich.2 Suffizienz und Vollständigkeit . . . . . . . . . . . . . . . . . . . . 5 2 Monte-Carlo Tests 8 2.1 Formulierung des Testproblems . . . . . . . . . . . . . . . . . . . 8 2.2 Definition des Monte-Carlo Tests
NASA Astrophysics Data System (ADS)
Chatterjee, Abhijit; Vlachos, Dionisios G.
2006-02-01
Monte Carlo (MC) simulation of most spatially distributed systems is plagued by several problems, namely, execution of one process at a time, large separation of time scales of various processes, and large length scales. Recently, a coarse-grained Monte Carlo (CGMC) method was introduced that can capture large length scales at reasonable computational times. An inherent assumption in this CGMC method revolves around a mean-field closure invoked in each coarse cell that is inaccurate for short-ranged interactions. Two new approaches are explored to improve upon this closure. The first employs the local quasichemical approximation, which is applicable to first nearest-neighbor interactions. The second, termed multiscale CGMC method, employs singular perturbation ideas on multiple grids to capture the entire cluster probability distribution function via short microscopic MC simulations on small, fine-grid lattices by taking advantage of the time scale separation of multiple processes. Computational strategies for coupling the fast process at small length scales (fine grid) with the slow processes at large length scales (coarse grid) are discussed. Finally, the binomial ?-leap method is combined with the multiscale CGMC method to execute multiple processes over the entire lattice and provide additional computational acceleration. Numerical simulations demonstrate that in the presence of fast diffusion and slow adsorption and desorption processes the two new approaches provide more accurate solutions in comparison to the previously introduced CGMC method.
Chatterjee, Abhijit; Vlachos, Dionisios G
2006-02-14
Monte Carlo (MC) simulation of most spatially distributed systems is plagued by several problems, namely, execution of one process at a time, large separation of time scales of various processes, and large length scales. Recently, a coarse-grained Monte Carlo (CGMC) method was introduced that can capture large length scales at reasonable computational times. An inherent assumption in this CGMC method revolves around a mean-field closure invoked in each coarse cell that is inaccurate for short-ranged interactions. Two new approaches are explored to improve upon this closure. The first employs the local quasichemical approximation, which is applicable to first nearest-neighbor interactions. The second, termed multiscale CGMC method, employs singular perturbation ideas on multiple grids to capture the entire cluster probability distribution function via short microscopic MC simulations on small, fine-grid lattices by taking advantage of the time scale separation of multiple processes. Computational strategies for coupling the fast process at small length scales (fine grid) with the slow processes at large length scales (coarse grid) are discussed. Finally, the binomial tau-leap method is combined with the multiscale CGMC method to execute multiple processes over the entire lattice and provide additional computational acceleration. Numerical simulations demonstrate that in the presence of fast diffusion and slow adsorption and desorption processes the two new approaches provide more accurate solutions in comparison to the previously introduced CGMC method. PMID:16483199
Cramer, S.N.
1984-01-01
The MORSE code is a large general-use multigroup Monte Carlo code system. Although no claims can be made regarding its superiority in either theoretical details or Monte Carlo techniques, MORSE has been, since its inception at ORNL in the late 1960s, the most widely used Monte Carlo radiation transport code. The principal reason for this popularity is that MORSE is relatively easy to use, independent of any installation or distribution center, and it can be easily customized to fit almost any specific need. Features of the MORSE code are described.
Monte Carlo methods Monte Carlo Principle and MCMC
Doucet, Arnaud
Monte Carlo methods Monte Carlo Principle and MCMC A. Doucet Carcans Sept. 2011 A. Doucet (MLSS Sept. 2011) MCMC Sept. 2011 1 / 91 #12;Overview of the Lectures 1 Monte Carlo Principles A. Doucet (MLSS Sept. 2011) MCMC Sept. 2011 2 / 91 #12;Overview of the Lectures 1 Monte Carlo Principles 2 Markov
Monte Carlo variance reduction
NASA Technical Reports Server (NTRS)
Byrn, N. R.
1980-01-01
Computer program incorporates technique that reduces variance of forward Monte Carlo method for given amount of computer time in determining radiation environment in complex organic and inorganic systems exposed to significant amounts of radiation.
NASA Astrophysics Data System (ADS)
Hosseini, Seyed Mahmoud; Shahabian, Farzad
2009-09-01
In this article, the dynamic responses of functionally graded thick hollow cylinders are studied from stochastic view using Monte Carlo method. The FG cylinder is subjected to mechanical shock loads applied to inner surface of cylinder. The FG cylinder is assumed to be in plane strain conditions and axisymmetry conditions. To obtain the radial displacement in each point, the Navier equation in displacement form is derived using isotropic elements. To solve the problem, the combined numerical method is used (Galerkin finite element and Newmark finite difference methods). The maximum, mean and minimum values of radial displacement also variance of variation in radial displacement are calculated in various points across thickness for different values of volume fraction exponent (in mechanical properties function of FG cylinder).
NASA Astrophysics Data System (ADS)
Runov, A. M.; Reiter, D.; Kasilov, S. V.; Heyn, M. F.; Kernbichler, W.
2001-03-01
The heat balance equation is derived and solved for fusion edge plasma conditions with (partially developed) ergodic magnetic-field structures. For this purpose, a three-dimensional (3D) Monte Carlo code, "E3D," based upon the "multiple local magnetic coordinate system approach" has been developed. Parameters typical for the Dynamic Ergodic Divertor (DED) of TEXTOR-94 (Torus Experiment for the Technology Oriented Research) [K. H. Finken et al., Fusion Eng. Des. 37, 1 (1997)] are chosen in the applications. The plasma temperature fields and the profiles of the radial component of heat flux due to the classical parallel and anomalous perpendicular diffusion are calculated. Because of magnetic-field ergodization and diversion of field lines, parallel conduction also can contribute to this radial flux. The results are compared with theoretical predictions for two limiting cases: With the Rechester-Rosenbluth model of ergodization-induced transport and with a "laminar flow model" proposed in the present paper. This latter model describes the effects of field line diversion. The diversion effect is shown to be dominant for TEXTOR-DED conditions.
A stochastic Markov chain approach for tennis: Monte Carlo simulation and modeling
NASA Astrophysics Data System (ADS)
Aslam, Kamran
This dissertation describes the computational formulation of probability density functions (pdfs) that facilitate head-to-head match simulations in tennis along with ranking systems developed from their use. A background on the statistical method used to develop the pdfs , the Monte Carlo method, and the resulting rankings are included along with a discussion on ranking methods currently being used both in professional sports and in other applications. Using an analytical theory developed by Newton and Keller in [34] that defines a tennis player's probability of winning a game, set, match and single elimination tournament, a computational simulation has been developed in Matlab that allows further modeling not previously possible with the analytical theory alone. Such experimentation consists of the exploration of non-iid effects, considers the concept the varying importance of points in a match and allows an unlimited number of matches to be simulated between unlikely opponents. The results of these studies have provided pdfs that accurately model an individual tennis player's ability along with a realistic, fair and mathematically sound platform for ranking them.
Shell model Monte Carlo methods
Koonin, S.E. [California Inst. of Tech., Pasadena, CA (United States). W.K. Kellogg Radiation Lab.; Dean, D.J. [Oak Ridge National Lab., TN (United States)
1996-10-01
We review quantum Monte Carlo methods for dealing with large shell model problems. These methods reduce the imaginary-time many-body evolution operator to a coherent superposition of one-body evolutions in fluctuating one-body fields; resultant path integral is evaluated stochastically. We first discuss the motivation, formalism, and implementation of such Shell Model Monte Carlo methods. There then follows a sampler of results and insights obtained from a number of applications. These include the ground state and thermal properties of pf-shell nuclei, thermal behavior of {gamma}-soft nuclei, and calculation of double beta-decay matrix elements. Finally, prospects for further progress in such calculations are discussed. 87 refs.
Monte Carlo Neutrino Oscillations
James P. Kneller; Gail C. McLaughlin
2005-09-29
We demonstrate that the effects of matter upon neutrino propagation may be recast as the scattering of the initial neutrino wavefunction. Exchanging the differential, Schrodinger equation for an integral equation for the scattering matrix S permits a Monte Carlo method for the computation of S that removes many of the numerical difficulties associated with direct integration techniques.
An ecien t Markov chain Monte Carlo simulation of a stochastic inverse radiation problem
Jingbo Wang; Nicholas Zabaras
A novel methodology that combines recent advances in computational statistics and reduced-order modeling is presented to explore the application of Bayesian statistical infer- ence to a stochastic inverse problem in radiative heat transfer. The underlying objective of this work is to reveal the potential of using statistical approaches, mainly Bayesian com- putational statistics and spatial statistics, to solve data-driven stochastic
Quantum Monte Carlo Helsinki 2011
Boyer, Edmond
Quantum Monte Carlo Helsinki 2011 Marius Lewerenz MSME/CT, UMR 8208 CNRS, Universit´e Paris Est? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 What is a Monte Carlo method? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 What are Monte Carlo methods good for? . . . . . . . . . . . . . . . . . . . . . . . 5 1
Inference for Levy Driven Stochastic Volatility Models Via Adaptive Sequential Monte Carlo
Stephens, David A.
of the posterior. Secondly, we investigate the effectiveness of the model in capturing the leverage effect in high-frequency to describe the behaviour of moderate and high frequency financial data. This is due to the inability, by the usage of simple results in stochastic calculus and by an auxiliary variable representation
Viral load and stochastic mutation in a Monte Carlo simulation of HIV
NASA Astrophysics Data System (ADS)
Ruskin, H. J.; Pandey, R. B.; Liu, Y.
2002-08-01
Viral load is examined, as a function of primary viral growth factor ( Pg) and mutation, through a computer simulation model for HIV immune response. Cell-mediated immune response is considered on a cubic lattice with four cell types: macrophage ( M), helper ( H), cytotoxic ( C), and virus ( V). Rule-based interactions are used with random sequential update of the binary cellular states. The relative viral load (the concentration of virus with respect to helper cells) is found to increase with the primary viral growth factor above a critical value ( Pc), leading to a phase transition from immuno-competent to immuno-deficient state. The critical growth factor ( Pc) seems to depend on mobility and mutation. The stochastic growth due to mutation is found to depend non-monotonically on the relative viral load, with a maximum at a characteristic load which is lower for stronger viral growth.
Chin, P.W. [Department of Medical Physics, Velindre Cancer Centre, Velindre Road, Cardiff CF14 2TL (United Kingdom)]. E-mail: mary.chin@physics.org
2005-10-15
This project developed a solution for verifying external photon beam radiotherapy. The solution is based on a calibration chain for deriving portal dose maps from acquired portal images, and a calculation framework for predicting portal dose maps. Quantitative comparison between acquired and predicted portal dose maps accomplishes both geometric (patient positioning with respect to the beam) and dosimetric (two-dimensional fluence distribution of the beam) verifications. A disagreement would indicate that beam delivery had not been according to plan. The solution addresses the clinical need for verifying radiotherapy both pretreatment (without the patient in the beam) and on treatment (with the patient in the beam). Medical linear accelerators mounted with electronic portal imaging devices (EPIDs) were used to acquire portal images. Two types of EPIDs were investigated: the amorphous silicon (a-Si) and the scanning liquid ion chamber (SLIC). The EGSnrc family of Monte Carlo codes were used to predict portal dose maps by computer simulation of radiation transport in the beam-phantom-EPID configuration. Monte Carlo simulations have been implemented on several levels of high throughput computing (HTC), including the grid, to reduce computation time. The solution has been tested across the entire clinical range of gantry angle, beam size (5 cmx5 cm to 20 cmx20 cm), and beam-patient and patient-EPID separations (4 to 38 cm). In these tests of known beam-phantom-EPID configurations, agreement between acquired and predicted portal dose profiles was consistently within 2% of the central axis value. This Monte Carlo portal dosimetry solution therefore achieved combined versatility, accuracy, and speed not readily achievable by other techniques.
Advanced Monte Carlo Methods: General Principles of the Monte
Mascagni, Michael
Advanced Monte Carlo Methods: General Principles of the Monte Carlo Method Prof. Dr. Michael of Monte CarloProf. Dr. Michael Mascagni: Advanced Monte Carlo Methods Slide 2 of 61 Numerical Integration: The Canonical Monte Carlo Application Numerical integration is a simple problem to explain and thoroughly
MONTE CARLO EXTENSION OF QUASIMONTE CARLO Art B. Owen
Owen, Art
MONTE CARLO EXTENSION OF QUASIMONTE CARLO Art B. Owen Department of Statistics Stanford University Stanford CA 94305, U.S.A. ABSTRACT This paper surveys recent research on using Monte Carlo techniques to improve quasiMonte Carlo tech niques. Randomized quasiMonte Carlo methods pro vide a basis for error
H. M. Elkamchouchi; M. A. El-Shimy
2006-01-01
Monte Carlo simulation is a stochastic technique used to solve a variety of physical problems. In all applications of the Monte Carlo method, a stochastic model is constructed in which the expected value of a certain random variable is equivalent to the value of a physical quantity to be determined. In this paper Monte Carlo simulations were carried out for
Interaction Picture Density Matrix Quantum Monte Carlo
Malone, Fionn D; Shepherd, James J; Lee, D K K; Spencer, J S; Foulkes, W M C
2015-01-01
The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N -body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.
Monte Carlo and Quasi-Monte Carlo algorithms for the Barker-Ferry equation with low
Whitlock, Paula
Monte Carlo and Quasi-Monte Carlo algorithms for the Barker-Ferry equation with low complexity ? T. The quasi-Monte Carlo (QMC) solutions obtained by QRNs are compared with the Monte Carlo (MC) solutions) converges [3] and the solution can be evaluated by a MC estimator. 2 Monte Carlo and Quasi-Monte Carlo
F. Einar Kruis; Jianming Wei; Till van der Zwaag; Stefan Haep
No method is currently available to combine stochastic, particle-based PBE modeling by means of Monte-Carlo simulation of individual particles and CFD. CFD is based on solving numerically partial differential equations, whereas Monte-Carlo simulation of the PBE bases on converting kinetic rate equations into probabilities and selecting the relevant events by means of random numbers. A joint mathematical framework is thus
Monte Carlo simulation of coherent effects in multiple scattering
Igor V. Meglinski; Vladimir L. Kuzmin; Dmitry Y. Churmakov
2005-01-01
Using a combination of the stochastic Monte Carlo technique and the iteration procedure of the solution to the Bethe-Salpeter equation, it has been shown that the simulation of the optical path of a photon packet undergoing an nth scattering event directly corresponds to the nth-order ladder diagram contribution. In this paper, the Monte Carlo technique is generalized for the simulation
Monte Carlo Eikonal Scattering
NASA Astrophysics Data System (ADS)
Gibbs, W. R.; Dedonder, J.-P.
2011-04-01
Eikonal multiple scattering theory in the form of the Glauber model is believed to be accurate for high-energy elastic scattering of heavy-ion systems. The evaluation of the full expression has only been done for the lightest systems with recourse often being made to an optical model model approximation. We evaluate the full expression without further approximation using a Monte Carlo representation of the nuclear density including the center-of-mass and Coulomb corrections. The center-of-mass correction remains very important for all nuclei investigated. The input to these calculations is the basic NN amplitude, characterized by four parameters, and the nuclear density. We have made calculations of a number of cases of elastic scattering using NN parameters taken from the VPI/GWU fits. Results of several calculations will be shown and compared with data.
Parallelizing Monte Carlo with PMC
Rathkopf, J.A.; Jones, T.R.; Nessett, D.M.; Stanberry, L.C.
1994-11-01
PMC (Parallel Monte Carlo) is a system of generic interface routines that allows easy porting of Monte Carlo packages of large-scale physics simulation codes to Massively Parallel Processor (MPP) computers. By loading various versions of PMC, simulation code developers can configure their codes to run in several modes: serial, Monte Carlo runs on the same processor as the rest of the code; parallel, Monte Carlo runs in parallel across many processors of the MPP with the rest of the code running on other MPP processor(s); distributed, Monte Carlo runs in parallel across many processors of the MPP with the rest of the code running on a different machine. This multi-mode approach allows maintenance of a single simulation code source regardless of the target machine. PMC handles passing of messages between nodes on the MPP, passing of messages between a different machine and the MPP, distributing work between nodes, and providing independent, reproducible sequences of random numbers. Several production codes have been parallelized under the PMC system. Excellent parallel efficiency in both the distributed and parallel modes results if sufficient workload is available per processor. Experiences with a Monte Carlo photonics demonstration code and a Monte Carlo neutronics package are described.
Quantum Gibbs ensemble Monte Carlo
Fantoni, Riccardo, E-mail: rfantoni@ts.infn.it [Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari Venezia, Calle Larga S. Marta DD2137, I-30123 Venezia (Italy); Moroni, Saverio, E-mail: moroni@democritos.it [DEMOCRITOS National Simulation Center, Istituto Officina dei Materiali del CNR and SISSA Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, I-34136 Trieste (Italy)
2014-09-21
We present a path integral Monte Carlo method which is the full quantum analogue of the Gibbs ensemble Monte Carlo method of Panagiotopoulos to study the gas-liquid coexistence line of a classical fluid. Unlike previous extensions of Gibbs ensemble Monte Carlo to include quantum effects, our scheme is viable even for systems with strong quantum delocalization in the degenerate regime of temperature. This is demonstrated by an illustrative application to the gas-superfluid transition of {sup 4}He in two dimensions.
Wormhole Hamiltonian Monte Carlo
Lan, Shiwei; Streets, Jeffrey; Shahbaba, Babak
2015-01-01
In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to another. To address this issue, we propose a novel Bayesian inference approach based on Markov Chain Monte Carlo. Our method can effectively sample from multimodal distributions, especially when the dimension is high and the modes are isolated. To this end, it exploits and modifies the Riemannian geometric properties of the target distribution to create wormholes connecting modes in order to facilitate moving between them. Further, our proposed method uses the regeneration technique in order to adapt the algorithm by identifying new modes and updating the network of wormholes without affecting the stationary distribution. To find new modes, as opposed to redis-covering those previously identified, we employ a novel mode searching algorithm that explores a residual energy function obtained by subtracting an approximate Gaussian mixture density (based on previously discovered modes) from the target density function. PMID:25861551
Raychaudhuri, Subhadip; Willgohs, Eric; Nguyen, Thuc-Nghi; Khan, Elaine M.; Goldkorn, Tzipora
2008-01-01
Apoptosis, or genetically programmed cell death, is a crucial cellular process that maintains the balance between life and death in cells. The precise molecular mechanism of apoptosis signaling and the manner in which type 1 and type 2 pathways of the apoptosis signaling network are differentially activated under distinct apoptotic stimuli is poorly understood. Based on Monte Carlo stochastic simulations, we show that the type 1 pathway becomes activated under strong apoptotic stimuli, whereas the type 2 mitochondrial pathway dominates apoptotic signaling in response to a weak death signal. Our results also show signaling in the type 2 pathway is stochastic; the population average over many cells does not capture the cell-to-cell fluctuations in the time course (?1–10 h) of downstream caspase-3 activation. On the contrary, the probability distribution of caspase-3 activation for the mitochondrial pathway shows a distinct bimodal behavior that can be used to characterize the stochastic signaling in type 2 apoptosis and other similar complex signaling processes. Interestingly, such stochastic fluctuations in apoptosis signaling occur even in the presence of large numbers of signaling molecules. PMID:18641073
Monte Carlo Methods for Inference and Learning
Hinton, Geoffrey E.
Monte Carlo Methods for Inference and Learning Guest Lecturer: Ryan Adams CSC 2535 http://www.cs.toronto.edu/~rpa #12;Overview ·Monte Carlo basics ·Rejection and Importance sampling ·Markov chain Monte Carlo ·Metropolis-Hastings and Gibbs sampling ·Slice sampling ·Hamiltonian Monte Carlo #12;Computing Expectations We
Monte Carlo and Quasi-Monte Carlo for Art B. Owen
Owen, Art
Monte Carlo and Quasi-Monte Carlo for Statistics Art B. Owen Abstract This article reports Monte Carlo methods can be used. There was a special emphasis on areas where Quasi-Monte Carlo ideas This survey is aimed at exposing good problems in statistics to researchers in Quasi- Monte Carlo. It has
Discrete Diffusion Monte Carlo for grey Implicit Monte Carlo simulations.
Densmore, J. D. (Jeffery D.); Urbatsch, T. J. (Todd J.); Evans, T. M. (Thomas M.); Buksas, M. W. (Michael W.)
2005-01-01
Discrete Diffusion Monte Carlo (DDMC) is a hybrid transport-diffusion method for Monte Carlo simulations in diffusive media. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Thus, DDMC produces accurate solutions while increasing the efficiency of the Monte Carlo calculation. In this paper, we extend previously developed DDMC techniques in several ways that improve the accuracy and utility of DDMC for grey Implicit Monte Carlo calculations. First, we employ a diffusion equation that is discretized in space but is continuous time. Not only is this methodology theoretically more accurate than temporally discretized DDMC techniques, but it also has the benefit that a particle's time is always known. Thus, there is no ambiguity regarding what time to assign a particle that leaves an optically thick region (where DDMC is used) and begins transporting by standard Monte Carlo in an optically thin region. In addition, we treat particles incident on an optically thick region using the asymptotic diffusion-limit boundary condition. This interface technique can produce accurate solutions even if the incident particles are distributed anisotropically in angle. Finally, we develop a method for estimating radiation momentum deposition during the DDMC simulation. With a set of numerical examples, we demonstrate the accuracy and efficiency of our improved DDMC method.
Monte Carlo Methods for Computation and Optimization (048715) Winter 2013/4
Shimkin, Nahum
Monte Carlo Methods for Computation and Optimization (048715) Winter 2013/4 Lecture Notes Nahum Shimkin i #12;PREFACE These lecture notes are intended for a first, graduate-level, course on Monte-Carlo, Simulation and the Monte Carlo Method, Wiley, 2008. (2) S. Asmussen and P. Glynn, Stochastic Simulation
Monte Carlo Simulation of Interacting Electron Models
Robinson, Robert W.
Monte Carlo Simulation of Interacting Electron Models by a New Determinant Approach by Mucheng discusses the calculation of determinants and Monte Carlo simulation of Hub- bard models by a new and a Monte Carlo summation algorithm to evaluate the relevant diagram determinant sums. Index words: Monte
Proton Upset Monte Carlo Simulation
NASA Technical Reports Server (NTRS)
O'Neill, Patrick M.; Kouba, Coy K.; Foster, Charles C.
2009-01-01
The Proton Upset Monte Carlo Simulation (PROPSET) program calculates the frequency of on-orbit upsets in computer chips (for given orbits such as Low Earth Orbit, Lunar Orbit, and the like) from proton bombardment based on the results of heavy ion testing alone. The software simulates the bombardment of modern microelectronic components (computer chips) with high-energy (.200 MeV) protons. The nuclear interaction of the proton with the silicon of the chip is modeled and nuclear fragments from this interaction are tracked using Monte Carlo techniques to produce statistically accurate predictions.
First principles quantum Monte Carlo
J. M. A. Figueiredo
2006-12-07
Present quantum Monte Carlo codes use statistical techniques adapted to find the amplitude of a quantum system or the associated eigenvalues. Thus, they do not use a true physical random source. It is demonstrated that, in fact, quantum probability admits a description based on a specific class of random process at least for the single particle case. Then a first principle Monte Carlo code that exactly simulates quantum dynamics can be constructed. The subtle question concerning how to map random choices in amplitude interferences is explained. Possible advantages of this code in simulating single hit experiments are discussed.
Monte Carlo simulation of coherent effects in mulitple scattering
Igor V. Meglinski; V. L. Kuzmin; Dmitry Y. Churmakov; Douglas A. Greenhalgh
2004-01-01
Based on the collation of the stochastic Monte Carlo technique and the iteration procedure of the solution of Bethe-Salpeter equation, it is shown that simulation of optical path of photons undergoing n-th scattering event is directly agreed with the n-th order ladder diagram calculation approach. In frame of this correspondence the Monte Carlo technique is generalised for simulation of coherent
Bieda, Bogus?aw
2014-05-15
The purpose of the paper is to present the results of application of stochastic approach based on Monte Carlo (MC) simulation for life cycle inventory (LCI) data of Mittal Steel Poland (MSP) complex in Kraków, Poland. In order to assess the uncertainty, the software CrystalBall® (CB), which is associated with Microsoft® Excel spreadsheet model, is used. The framework of the study was originally carried out for 2005. The total production of steel, coke, pig iron, sinter, slabs from continuous steel casting (CSC), sheets from hot rolling mill (HRM) and blast furnace gas, collected in 2005 from MSP was analyzed and used for MC simulation of the LCI model. In order to describe random nature of all main products used in this study, normal distribution has been applied. The results of the simulation (10,000 trials) performed with the use of CB consist of frequency charts and statistical reports. The results of this study can be used as the first step in performing a full LCA analysis in the steel industry. Further, it is concluded that the stochastic approach is a powerful method for quantifying parameter uncertainty in LCA/LCI studies and it can be applied to any steel industry. The results obtained from this study can help practitioners and decision-makers in the steel production management. PMID:24290145
NSDL National Science Digital Library
McGath, Gary
1996-01-01
This is the description and instructions for the Monte Carlo Estimation of Pi applet. It is a simulation of throwing darts at a figure of a circle inscribed in a square. It shows the relationship between the geometry of the figure and the statistical outcome of throwing the darts.
Is Monte Carlo embarrassingly parallel?
Hoogenboom, J. E. [Delft Univ. of Technology, Mekelweg 15, 2629 JB Delft (Netherlands); Delft Nuclear Consultancy, IJsselzoom 2, 2902 LB Capelle aan den IJssel (Netherlands)
2012-07-01
Monte Carlo is often stated as being embarrassingly parallel. However, running a Monte Carlo calculation, especially a reactor criticality calculation, in parallel using tens of processors shows a serious limitation in speedup and the execution time may even increase beyond a certain number of processors. In this paper the main causes of the loss of efficiency when using many processors are analyzed using a simple Monte Carlo program for criticality. The basic mechanism for parallel execution is MPI. One of the bottlenecks turn out to be the rendez-vous points in the parallel calculation used for synchronization and exchange of data between processors. This happens at least at the end of each cycle for fission source generation in order to collect the full fission source distribution for the next cycle and to estimate the effective multiplication factor, which is not only part of the requested results, but also input to the next cycle for population control. Basic improvements to overcome this limitation are suggested and tested. Also other time losses in the parallel calculation are identified. Moreover, the threading mechanism, which allows the parallel execution of tasks based on shared memory using OpenMP, is analyzed in detail. Recommendations are given to get the maximum efficiency out of a parallel Monte Carlo calculation. (authors)
EDDE Monte Carlo event generator
V. A. Petrov; R. A. Ryutin; A. E. Sobol; J. -P. Guillaud
2005-09-26
EDDE is a Monte Carlo event generator, under construction, for different Exclusive Double Diffractive Events. The program is based on the extended Regge-eikonal approach for "soft" processes. Standard Model and its extensions are used for "hard" fusion processes. An interface to PYTHIA, CMSJET and CMKIN is provided.
Michael H. Seymour
2010-08-17
I review the status of the general-purpose Monte Carlo event generators for the LHC, with emphasis on areas of recent physics developments. There has been great progress, especially in multi-jet simulation, but I mention some question marks that have recently arisen.
Introduction to Monte Carlo algorithms
NASA Astrophysics Data System (ADS)
Krauth, Werner
These lectures that I gave in the summer of 1996 at the Beg-Rohu (France) and Budapest summer schools discuss the fundamental principles of thermodynamic and dynamic Monte Carlo methods in a simple and light-weight fashion. The key-words are Markov chains, sampling, detailed balance, a priori probabilities, rejections, ergodicity, "Faster than the clock algorithms".
A Monte Carlo approach to water management
NASA Astrophysics Data System (ADS)
Koutsoyiannis, D.
2012-04-01
Common methods for making optimal decisions in water management problems are insufficient. Linear programming methods are inappropriate because hydrosystems are nonlinear with respect to their dynamics, operation constraints and objectives. Dynamic programming methods are inappropriate because water management problems cannot be divided into sequential stages. Also, these deterministic methods cannot properly deal with the uncertainty of future conditions (inflows, demands, etc.). Even stochastic extensions of these methods (e.g. linear-quadratic-Gaussian control) necessitate such drastic oversimplifications of hydrosystems that may make the obtained results irrelevant to the real world problems. However, a Monte Carlo approach is feasible and can form a general methodology applicable to any type of hydrosystem. This methodology uses stochastic simulation to generate system inputs, either unconditional or conditioned on a prediction, if available, and represents the operation of the entire system through a simulation model as faithful as possible, without demanding a specific mathematical form that would imply oversimplifications. Such representation fully respects the physical constraints, while at the same time it evaluates the system operation constraints and objectives in probabilistic terms, and derives their distribution functions and statistics through Monte Carlo simulation. As the performance criteria of a hydrosystem operation will generally be highly nonlinear and highly nonconvex functions of the control variables, a second Monte Carlo procedure, implementing stochastic optimization, is necessary to optimize system performance and evaluate the control variables of the system. The latter is facilitated if the entire representation is parsimonious, i.e. if the number of control variables is kept at a minimum by involving a suitable system parameterization. The approach is illustrated through three examples for (a) a hypothetical system of two reservoirs performing a variety of functions, (b) the water resource system of Athens comprising four reservoirs and many aqueducts, and (c) a human-modified inadequately measured basin in which the parameter fitting of a hydrological model is sought.
Population Monte Carlo Methods/OFPR/CREST/May 5, 2003 1 Population Monte Carlo Methods
Robert, Christian P.
Population Monte Carlo Methods/OFPR/CREST/May 5, 2003 1 Population Monte Carlo Methods Christian P. Robert Universit´e Paris Dauphine #12;Population Monte Carlo Methods/OFPR/CREST/May 5, 2003 2 1 A Benchmark example #12;Population Monte Carlo Methods/OFPR/CREST/May 5, 2003 3 Even simple models may lead
Population Monte Carlo and adaptive sampling schemes Population Monte Carlo and adaptive sampling
Robert, Christian P.
Population Monte Carlo and adaptive sampling schemes Population Monte Carlo and adaptive sampling://www.ceremade.dauphine.fr/~xian Joint work with O. Capp´e, R. Douc, A. Guillin, J.M. Marin Population Monte Carlo and adaptive sampling schemes Outline 1 Crash course in simulation 2 Population Monte Carlo Algorithm 3 Illustrations 4 Further
Washington at Seattle, University of - Department of Physics, Electroweak Interaction Research Group
Towards Monte Carlo Simulations on Large Nuclei Â· August 2014 Towards Monte Carlo Simulations published method to compute properties on neutron matter using variational Monte Carlo simulations published a method of performing variational Monte Carlo calculations on neutron matter comprised of up
Monte Carlo Experiments: Design and Implementation.
ERIC Educational Resources Information Center
Paxton, Pamela; Curran, Patrick J.; Bollen, Kenneth A.; Kirby, Jim; Chen, Feinian
2001-01-01
Illustrates the design and planning of Monte Carlo simulations, presenting nine steps in planning and performing a Monte Carlo analysis from developing a theoretically derived question of interest through summarizing the results. Uses a Monte Carlo simulation to illustrate many of the relevant points. (SLD)
Monte Carlo Integration Lecture 2 The Problem
Liang, Faming
Monte Carlo Integration Lecture 2 The Problem Let be a probability measure over the Borel -field X S and h(x) = 0 otherwise. #12;Monte Carlo Integration Lecture 2 When the problem appears to be intractable, Press et al (1992) and reference therein). For high dimensional problems, Monte Carlo methods have
Monte Carlo Methods in Statistics Christian Robert
Boyer, Edmond
Monte Carlo Methods in Statistics Christian Robert Universit´e Paris Dauphine and CREST, INSEE September 2, 2009 Monte Carlo methods are now an essential part of the statistician's toolbox, to the point! We recall in this note some of the advances made in the design of Monte Carlo techniques towards
A Monte Carlo Study of Titrating Polyelectrolytes
Peterson, Carsten
A Monte Carlo Study of Titrating Polyelectrolytes Magnus Ullner y and Bo J¨onsson z Physical, Sweden Journal of Chemical Physics 104, 30483057 (1996) Monte Carlo simulations have been used to study of the polymer more difficult and biases the conformations towards more extended structures. In the Monte Carlo
Monte Carlo Simulations of Model Nonionic Surfactants
Monte Carlo Simulations of Model Nonionic Surfactants A.P. Chatterjee and A.Z. Panagiotopoulos was studied by histogram reweight- ing grand canonical Monte Carlo simulations. Two di erent sets of site volume fractions using lattice Monte Carlo simulations performed in the canonical constant NV T ensemble
A Monte Carlo Study of Titrating Polyelectrolytes
Peterson, Carsten
A Monte Carlo Study of Titrating Polyelectrolytes Magnus Ullnery and Bo Jonssonz Physical Chemistry Journal of Chemical Physics 104, 3048-3057 (1996) Monte Carlo simulations have been used to study three di the conformations towards more extended structures. In the Monte Carlo simulations presented here, focus
MONTE CARLO METHOD AND SENSITIVITY ESTIMATIONS
Dufresne, Jean-Louis
MONTE CARLO METHOD AND SENSITIVITY ESTIMATIONS A. de Lataillade a;#3; , S. Blanco b , Y. Clergent b on a formal basis and simple radiative transfer examples are used for illustration. Key words: Monte Carlo submitted to Elsevier Science 18 February 2002 #12; 1 Introduction Monte Carlo methods are commonly used
Monte Carlo techniques for real-time quantum dynamics
Mark R. Dowling; Matthew J. Davis; Peter D. Drummond; Joel F. Corney
2005-07-01
The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the "weight", and its magnitude is related to the importance of the stochastic trajectory. We investigate the use of Monte Carlo algorithms to improve the sampling of the weighted trajectories and thus reduce sampling error in a simulation of quantum dynamics. The method can be applied to calculations in real time, as well as imaginary time for which Monte Carlo algorithms are more-commonly used. The method is applicable when the weight is guaranteed to be real, and we demonstrate how to ensure this is the case. Examples are given for the anharmonic oscillator, where large improvements over stochastic sampling are observed.
Parallel Monte Carlo Simulation for control system design
NASA Technical Reports Server (NTRS)
Schubert, Wolfgang M.
1995-01-01
The research during the 1993/94 academic year addressed the design of parallel algorithms for stochastic robustness synthesis (SRS). SRS uses Monte Carlo simulation to compute probabilities of system instability and other design-metric violations. The probabilities form a cost function which is used by a genetic algorithm (GA). The GA searches for the stochastic optimal controller. The existing sequential algorithm was analyzed and modified to execute in a distributed environment. For this, parallel approaches to Monte Carlo simulation and genetic algorithms were investigated. Initial empirical results are available for the KSR1.
Monte Carlo Methods for Uncertainty Quantification Mathematical Institute, University of Oxford
Giles, Mike
In computational finance, stochastic differential equations are used to model the behaviour of stocks interest Carlo Mike Giles (Oxford) Monte Carlo methods May 3031, 2013 2 / 33 #12;SDEs in Finance Carlo methods May 3031, 2013 3 / 33 #12;SDEs in Finance Stochastic differential equations are just
Hofer, Markus
Motivation Monte Carlo Methoden Quasi-Monte Carlo Methoden Folgen kleiner Diskrepanz Simulationstechniken in Finanz- und Versicherungsmathematik #12;Motivation Monte Carlo Methoden Quasi-Monte Carlo Methoden Folgen kleiner Diskrepanz 1 Motivation 2 Monte Carlo Methoden 3 Quasi-Monte Carlo Methoden 4
Zimmerman, G.B.
1997-06-24
Monte Carlo methods appropriate to simulate the transport of x-rays, neutrons, ion and electrons in Inertial Confinement Fusion targets are described and analyzed. The Implicit Monte Carlo method of x-ray transport handles symmetry within indirect drive ICF hohlraums well, but can be improved 50X in efficiency by angular biasing the x-rays towards the fuel capsule. Accurate simulation of thermonuclear burns nd burn diagnostics involves detailed particle source spectra, charged particle ranges, inflight reaction kinematics, corrections for bulk and thermal Doppler effects and variance reduction to obtain adequate statistics for rare events. It is found that the effects of angular Coulomb scattering must be included in models of charged particle transport through heterogeneous materials.
Bacteria Allocation Using Monte Carlo
NSDL National Science Digital Library
Hill, David R.
This applet, created by David Hill and Lila Roberts, uses the Monte Carlo technique to simulate a count of bacteria that are present as a result of a certain sampling process. This simulation could be modified to perform other experiments. This experiment is geared towards high school calculus students or probability courses for mathematics majors in college. Students must possess a basic understanding of probability concepts before performing this experiment. Overall, it is a nice activity for a mathematics classroom.
Efficient Monte Carlo device modeling
F. M. Bufler; A. Schenk; Wolfgang Fichtner
2000-01-01
A single-particle approach to full-band Monte Carlo device simulation is presented which allows an efficient computation of drain, substrate and gate currents in deep submicron MOSFETs. In this approach, phase-space elements are visited according to the distribution of real electrons. This scheme is well adapted to a test-function evaluation of the drain current, which emphasizes regions with large drift velocities
An Introduction to Multilevel Monte Carlo for Option Valuation
Higham, Desmond J
2015-01-01
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation. In 2008, Giles proposed a remarkable improvement to the approach of discretizing with a numerical method and applying standard Monte Carlo. His multilevel Monte Carlo method offers an order of speed up given by the inverse of epsilon, where epsilon is the required accuracy. So computations can run 100 times more quickly when two digits of accuracy are required. The multilevel philosophy has since been adopted by a range of researchers and a wealth of practically significant results has arisen, most of which have yet to make their way into the expository literature. In this work, we give a brief, accessible, introduction to multilevel Monte Carlo and summarize recent results applicable to the task of option evaluation.
The path forward: Monte Carlo Convergence discussion
Andreopoulos, Costas [Rutherford Appleton Laboratory, STFC Oxfordshire OX11 0QX (United Kingdom); Gallagher, Hugh [Tufts University, Medford, Massachusetts (United States); Hayato, Yoshinari [Kamioka Observatory, ICRR, University of Tokyo Higashi-Mozumi 456, Kamioka-cho, Hida-city Gifu 506-1205 (Japan); Sobczyk, Jan T. [Institute of Theoretical Physics, Wroclaw, University Poland (Poland); Walter, Chris [Department of Physics, Duke University, Durham, NC 27708 (United States); Zeller, Sam [Los Alamos National Laboratory, Los Alamos, NM (United States)
2009-11-25
This is a summary of 'the path forward' discussion session of the NuInt09 workshop which focused on Monte Carlo event generators. The main questions raised as part of this discussion are: how to make Monte Carlo generators more reliable and how important it is to work on a universal Monte Carlo generator of events? In this contribution, several experts in the field summarize their views, as presented at the workshop.
Monte-Carlo Go Reinforcement Learning Experiments
Bruno Bouzy; Guillaume Chaslot
2006-01-01
Abstractó This paper describes experiments using reinforcement learning techniques to compute pattern urgencies used during simulations performed in a Monte-Carlo Go architecture. Currently, Monte-Carlo is a popular technique for computer Go. In a previous study, Monte-Carlo was associated with domain-dependent knowledge in the Go-playing program Indigo. In 2003, a 3x3 pattern database was built manually. This paper explores the possibility
NSDL National Science Digital Library
AMPS GK-12 Program,
At its core, the LEGO® MINDSTORMS® NXT product provides a programmable microprocessor. Students use the NXT processor to simulate an experiment involving thousands of uniformly random points placed within a unit square. Using the underlying geometry of the experimental model, as well as the geometric definition of the constant ? (pi), students form an empirical ratio of areas to estimate a numerical value of ?. Although typically used for numerical integration of irregular shapes, in this activity, students use a Monte Carlo simulation to estimate a common but rather complex analytical form—the numerical value of the most famous irrational number, ?.
Block, Louis
Rome Monte Carlo Barcelona Marseille Palma de Mallorca Florence Pisa Porto no La Spezia/ Cinque Barcelona, Spain Embark 1:00 p.m. 7:00 p.m. Day 3 Palma de Mallorca, Spain 8:00 a.m. 4:00 p.m. Day 4,399 PENTHOUSE SUITE $11,198 PH3 $5,099 $11,598 PH2 $5,299 $12,198 PH1 $5,599 #12;PORTS OF CALL PALMA DE MALLORCA
Multivariate Monte Carlo Model Fitting
NASA Astrophysics Data System (ADS)
Peterson, J. R.; Jernigan, J. G.; Kahn, S. M.
2000-05-01
We present a new method for analyzing multi-dimensional data. The method uses an astrophysical and instrument response Monte Carlo to simulate photons and then iteratively analyze the data. The simulated photons are then compared directly with the measured values for the data with a new multivariate generalization of the Cramér-von Mises and Kolmogorov-Smirnov statistic. Techniques for model fitting, error estimation, and deconvolution using this method are discussed. Examples of this approach using Chandra observations of X-ray clusters of galaxies and XMM-Newton Reflection Grating Spectrometer data are presented.
The PHOBOS Glauber Monte Carlo
B. Alver; M. Baker; C. Loizides; P. Steinberg
2008-05-28
``Glauber'' models are used to calculate geometric quantities in the initial state of heavy ion collisions, such as impact parameter, number of participating nucleons and initial eccentricity. The four RHIC experiments have different methods for Glauber Model calculations, leading to similar results for various geometric observables. In this document, we describe an implementation of the Monte Carlo based Glauber Model calculation used by the PHOBOS experiment. The assumptions that go in the calculation are described. A user's guide is provided for running various calculations.
Alavi, Ali
Fermion Monte Carlo without fixed nodes: A Game of Life, death and annihilation in Slater Monte Carlo method for the simulation of correlated many- electron systems in Full Configuration of many- electron systems via stochastic methods such as Diffusion quantum Monte Carlo (DMC) [1
1-D EQUILIBRIUM DISCRETE DIFFUSION MONTE CARLO
T. EVANS; ET AL
2000-08-01
We present a new hybrid Monte Carlo method for 1-D equilibrium diffusion problems in which the radiation field coexists with matter in local thermodynamic equilibrium. This method, the Equilibrium Discrete Diffusion Monte Carlo (EqDDMC) method, combines Monte Carlo particles with spatially discrete diffusion solutions. We verify the EqDDMC method with computational results from three slab problems. The EqDDMC method represents an incremental step toward applying this hybrid methodology to non-equilibrium diffusion, where it could be simultaneously coupled to Monte Carlo transport.
NASA Technical Reports Server (NTRS)
Parrish, R. V.; Dieudonne, J. E.; Filippas, T. A.
1971-01-01
An algorithm employing a modified sequential random perturbation, or creeping random search, was applied to the problem of optimizing the parameters of a high-energy beam transport system. The stochastic solution of the mathematical model for first-order magnetic-field expansion allows the inclusion of state-variable constraints, and the inclusion of parameter constraints allowed by the method of algorithm application eliminates the possibility of infeasible solutions. The mathematical model and the algorithm were programmed for a real-time simulation facility; thus, two important features are provided to the beam designer: (1) a strong degree of man-machine communication (even to the extent of bypassing the algorithm and applying analog-matching techniques), and (2) extensive graphics for displaying information concerning both algorithm operation and transport-system behavior. Chromatic aberration was also included in the mathematical model and in the optimization process. Results presented show this method as yielding better solutions (in terms of resolutions) to the particular problem than those of a standard analog program as well as demonstrating flexibility, in terms of elements, constraints, and chromatic aberration, allowed by user interaction with both the algorithm and the stochastic model. Example of slit usage and a limited comparison of predicted results and actual results obtained with a 600 MeV cyclotron are given.
Density-matrix quantum Monte Carlo method
NASA Astrophysics Data System (ADS)
Blunt, N. S.; Rogers, T. W.; Spencer, J. S.; Foulkes, W. M. C.
2014-06-01
We present a quantum Monte Carlo method capable of sampling the full density matrix of a many-particle system at finite temperature. This allows arbitrary reduced density matrix elements and expectation values of complicated nonlocal observables to be evaluated easily. The method resembles full configuration interaction quantum Monte Carlo but works in the space of many-particle operators instead of the space of many-particle wave functions. One simulation provides the density matrix at all temperatures simultaneously, from T =? to T =0, allowing the temperature dependence of expectation values to be studied. The direct sampling of the density matrix also allows the calculation of some previously inaccessible entanglement measures. We explain the theory underlying the method, describe the algorithm, and introduce an importance-sampling procedure to improve the stochastic efficiency. To demonstrate the potential of our approach, the energy and staggered magnetization of the isotropic antiferromagnetic Heisenberg model on small lattices, the concurrence of one-dimensional spin rings, and the Renyi S2 entanglement entropy of various sublattices of the 6×6 Heisenberg model are calculated. The nature of the sign problem in the method is also investigated.
Monte Carlo Methods for Uncertainty Quantification Mathematical Institute, University of Oxford
Giles, Mike
finance, stochastic differential equations are used to model the behaviour of stocks interest rates Carlo Mike Giles (Oxford) Monte Carlo methods May 3031, 2013 2 / 33 SDEs in Finance In computational methods May 3031, 2013 3 / 33 SDEs in Finance Stochastic differential equations are just ordinary
Monte Carlo Application ToolKit (MCATK)
NASA Astrophysics Data System (ADS)
Adams, Terry; Nolen, Steve; Sweezy, Jeremy; Zukaitis, Anthony; Campbell, Joann; Goorley, Tim; Greene, Simon; Aulwes, Rob
2014-06-01
The Monte Carlo Application ToolKit (MCATK) is a component-based software library designed to build specialized applications and to provide new functionality for existing general purpose Monte Carlo radiation transport codes. We will describe MCATK and its capabilities along with presenting some verification and validations results.
Sequential Monte Carlo for Bayesian Computation
Pierre Del Moral; Arnaud Doucet; Ajay Jasra
Summary Sequential Monte Carlo (SMC) methods are a class of importance sampling and resampling techniques designed to simulate from a sequence of probability distributions. These approaches have become very popular over the last few years to solve sequential Bayesian inference problems (e.g. Doucet et al. 2001). However, in comparison to Markov chain Monte Carlo (MCMC), the applica- tion of SMC
Monte Carlo results for the hydrogen Hugoniot
V. Bezkrovniy; V. S. Filinov; D. Kremp; M. Bonitz; M. Schlanges; W. D. Kraeft; P. R. Levashov; V. E. Fortov
2004-01-01
We propose a theoretical Hugoniot relation obtained by combining results for the equation of state from the direct path integral Monte Carlo technique (DPIMC) and those from reaction ensemble Monte Carlo (REMC) simulations. The main idea of this proposal is based on the fact that the DPMIC technique provides first-principle results for a wide range of densities and temperatures including
Monte Carlo methods for security pricing
Phelim Boyle; Mark Broadie; Paul Glasserman
1997-01-01
The Monte Carlo approach has proved to be a valuable and flexible computational tool in modern finance. This paper discusses some of the recent applications of the Monte Carlo method to security pricing problems, with emphasis on improvements in efficiency. We first review some variance reduction methods that have proved useful in finance. Then we describe the use of deterministic
Leon E. Smith; Christopher J. Gesh; Richard T. Pagh; Erin A. Miller; Mark W. Shaver; Eric D. Ashbaker; Michael T. Batdorf; J. Edward Ellis; William R. Kaye; Ronald J. McConn; George H. Meriwether; Jennifer J. Ressler; Andrei B. Valsan; Todd A. Wareing
2008-01-01
Simulation is often used to predict the response of gamma-ray spectrometers in technology viability and comparative studies for homeland and national security scenarios. Candidate radiation transport methods generally fall into one of two broad categories: stochastic (Monte Carlo) and deterministic. Monte Carlo methods are the most heavily used in the detection community and are particularly effective for calculating pulse-height spectra
Parallel Monte Carlo Ion Recombination Simulation in Orca
Seinstra, Frank J.
Parallel Monte Carlo Ion Recombination Simulation in Orca Frank J. Seinstra Department. This report describes the implementation in Orca of a realistic Monte Carlo simulation of the recombinations. Keywords: Parallel computing, Orca, Ethernet, Myrinet, Monte Carlo sim ulation, ion recombination
Variance Reduction for Monte Carlo Implementation of Adaptive Sensor
Vo, Ba-Ngu
Variance Reduction for Monte Carlo Implementation of Adaptive Sensor Management Sumeetpal Singh horizon POMDP and implemented using sequential Monte Carlo. In Monte Carlo, variance reduction. Keywords: Tracking, sensor management, filtering, particle filter, variance reduction, control variate. 1
MONTE CARLO METHODS IN GEOPHYSICAL INVERSE Malcolm Sambridge
Sambridge, Malcolm
MONTE CARLO METHODS IN GEOPHYSICAL INVERSE PROBLEMS Malcolm Sambridge Research School Earth 27 2000; revised 15 December 2001; accepted 9 September published 5 December Monte Carlo inversion encountered in exploration seismology. traces development application Monte Carlo methods inverse problems
Fission Matrix Capability for MCNP Monte Carlo
Carney, Sean E. [Los Alamos National Laboratory; Brown, Forrest B. [Los Alamos National Laboratory; Kiedrowski, Brian C. [Los Alamos National Laboratory; Martin, William R. [Los Alamos National Laboratory
2012-09-05
In a Monte Carlo criticality calculation, before the tallying of quantities can begin, a converged fission source (the fundamental eigenvector of the fission kernel) is required. Tallies of interest may include powers, absorption rates, leakage rates, or the multiplication factor (the fundamental eigenvalue of the fission kernel, k{sub eff}). Just as in the power iteration method of linear algebra, if the dominance ratio (the ratio of the first and zeroth eigenvalues) is high, many iterations of neutron history simulations are required to isolate the fundamental mode of the problem. Optically large systems have large dominance ratios, and systems containing poor neutron communication between regions are also slow to converge. The fission matrix method, implemented into MCNP[1], addresses these problems. When Monte Carlo random walk from a source is executed, the fission kernel is stochastically applied to the source. Random numbers are used for: distances to collision, reaction types, scattering physics, fission reactions, etc. This method is used because the fission kernel is a complex, 7-dimensional operator that is not explicitly known. Deterministic methods use approximations/discretization in energy, space, and direction to the kernel. Consequently, they are faster. Monte Carlo directly simulates the physics, which necessitates the use of random sampling. Because of this statistical noise, common convergence acceleration methods used in deterministic methods do not work. In the fission matrix method, we are using the random walk information not only to build the next-iteration fission source, but also a spatially-averaged fission kernel. Just like in deterministic methods, this involves approximation and discretization. The approximation is the tallying of the spatially-discretized fission kernel with an incorrect fission source. We address this by making the spatial mesh fine enough that this error is negligible. As a consequence of discretization we get a spatially low-order kernel, the fundamental eigenvector of which should converge faster than that of continuous kernel. We can then redistribute the fission bank to match the fundamental fission matrix eigenvector, effectively eliminating all higher modes. For all computations here biasing is not used, with the intention of comparing the unaltered, conventional Monte Carlo process with the fission matrix results. The source convergence of standard Monte Carlo criticality calculations are, to some extent, always subject to the characteristics of the problem. This method seeks to partially eliminate this problem-dependence by directly calculating the spatial coupling. The primary cost of this, which has prevented widespread use since its inception [2,3,4], is the extra storage required. To account for the coupling of all N spatial regions to every other region requires storing N{sup 2} values. For realistic problems, where a fine resolution is required for the suppression of discretization error, the storage becomes inordinate. Two factors lead to a renewed interest here: the larger memory available on modern computers and the development of a better storage scheme based on physical intuition. When the distance between source and fission events is short compared with the size of the entire system, saving memory by accounting for only local coupling introduces little extra error. We can gain other information from directly tallying the fission kernel: higher eigenmodes and eigenvalues. Conventional Monte Carlo cannot calculate this data - here we have a way to get new information for multiplying systems. In Ref. [5], higher mode eigenfunctions are analyzed for a three-region 1-dimensional problem and 2-dimensional homogenous problem. We analyze higher modes for more realistic problems. There is also the question of practical use of this information; here we examine a way of using eigenmode information to address the negative confidence interval bias due to inter-cycle correlation. We apply this method mainly to four problems: 2D pressurized water reactor (PWR) [6],
Configuration Path Integral Monte Carlo
NASA Astrophysics Data System (ADS)
Bonitz, Michael; Schoof, Tim; Groth, Simon; Filinov, Alexei; Hochstuhl, David
2011-10-01
A novel path integral Monte Carlo (PIMC) approach for correlated many-particle systems with arbitrary pair interaction in continuous space at low temperatures is presented. It is based on a representation of the N-particle density operator in a basis of (anti-)symmetrized N-particle states (``configurations'' of occupation numbers). The path integral is transformed into a sum over trajectories with the same topology and, finally, the limit of M to infinity, (M is the number of high-temperature factors), is analytically performed. This yields exact expressions for the thermodynamic quantities and allows to perform efficient simulations for fermions at low temperature and weak to moderate coupling. Our method is applicable to dense quantum plasmas in the regime of strong degeneracy where conventional PIMC, e.g., fails due to the fermion sign problem. This work is supported by the Deutsche Forschungsgemeinschaft.
Physics-based Predictive Time Propagation Method for Monte Carlo Coupled Depletion Simulations
Johns, Jesse Merlin
2014-12-18
calculation. In 16 the stochastic Monte Carlo simulation, the neutron transport process is simulated similarly to the real physical process. This leads to a pseudo-physical/numerical noise that can be amplified if the simulation is not appropriately converged...
Fluctuating hydrodynamics and direct simulation Monte Carlo
NASA Astrophysics Data System (ADS)
Balakrishnan, Kaushik; Bell, John B.; Donev, Aleksandar; Garcia, Alejandro L.
2012-11-01
Thermodynamic fluctuations are significant at microscopic scales even when hydrodynamic transport models (i.e., Navier-Stokes equations) are still accurate; a well-known example is Rayleigh scattering, which makes the sky blue. Interesting phenomena also appear in non-equilibrium systems, such as the enhancement of diffusion during mixing due to the correlation of velocity and concentration fluctuations. Direct Simulation Monte Carlo (DSMC) simulations are useful in the study of hydrodynamic fluctuations due to their computational efficiency and ability to model molecular detail, such as internal energy and chemical reactions. More recently, finite volume schemes based on the fluctuating hydrodynamic equations of Landau and Lifshitz have been formulated and validated by comparisons with DSMC simulations. This paper discusses some of the relevant numerical issues and physical effects investigated using DSMC and stochastic Navier-Stokes simulations. This paper also presents the multi-component fluctuating hydrodynamic equations, including chemical reactions, and illustrates their numerical solutions in the study of Turing patterns. We find that behind a propagating reaction front, labyrinth patterns are produced due to the coupling of reactions and species diffusion. In general, fluctuations accelerate the propagation speed of the leading front but differences are observed in the Turing patterns depending on the origin of the fluctuations (stochastic hydrodynamic fluxes versus Langevin chemistry).
Variational Monte Carlo and Markov Chains for Computational Physics
NASA Astrophysics Data System (ADS)
Sorella, Sandro
In this chapter the basic concepts of Markov-processes and Monte Carlo methods, as well as a detailed description of the variational Monte Carlo technique will be presented. Particular emphasis will be devoted to the apparent mistery of Monte Carlo techniques that allows us to sample a correlated many electron wave function defined in an Hilbert space that is exponentially large with the number N of electrons, in an affordable computational time, namely scaling with a modest power of N. This is a direct consequence of two key properties that are not common to all Monte Carlo techniques: (i) the possibility to define a Markov process and appropriate stochastic variables with a finite correlation time and variance, respectively; (ii) both these quantities should increase at most polynomially with N. In principle, the above properties should be proven a priori, because their numerical validations could be very difficult in practice. It will be shown that this is the case for the simplest variational Monte Carlo technique for quite generic wave functions and model Hamiltonians.
Monte Carlo approaches to light nuclei
Carlson, J.
1990-01-01
Significant progress has been made recently in the application of Monte Carlo methods to the study of light nuclei. We review new Green's function Monte Carlo results for the alpha particle, Variational Monte Carlo studies of {sup 16}O, and methods for low-energy scattering and transitions. Through these calculations, a coherent picture of the structure and electromagnetic properties of light nuclei has arisen. In particular, we examine the effect of the three-nucleon interaction and the importance of exchange currents in a variety of experimentally measured properties, including form factors and capture cross sections. 29 refs., 7 figs.
Importance iteration in MORSE Monte Carlo calculations
Kloosterman, J.L.; Hoogenboom, J.E. (Delft Univ. of Technology (Netherlands). Interfaculty Reactor Institute)
1994-05-01
an expression to calculate point values (the expected detector response of a particle emerging from a collision or the source) is derived and implemented in the MORSE-SGC/S Monte Carlo code. It is outlined how these point values can be smoothed as a function of energy and as a function of the optical thickness between the detector and the source. The smoothed point values are subsequently used to calculate the biasing parameters of the Monte Carlo runs to follow. The method is illustrated by an example that shows that the obtained biasing parameters lead to a more efficient Monte Carlo calculation.
Monte Carlo Simulations for VLBI2010
NASA Astrophysics Data System (ADS)
Wresnik, J.; Böhm, J.; Schuh, H.
2007-07-01
Monte Carlo simulations are carried out at the Institute of Geodesy and Geophysics (IGG), Vienna, and at Goddard Space Flight Center (GSFC), Greenbelt (USA), with the goal to design a new geodetic Very Long Baseline Interferometry (VLBI) system. Influences of the schedule, the network geometry and the main stochastic processes on the geodetic results are investigated. Therefore schedules are prepared with the software package SKED (Vandenberg 1999), and different strategies are applied to produce temporally very dense schedules which are compared in terms of baseline length repeatabilities. For the simulation of VLBI observations a Monte Carlo Simulator was set up which creates artificial observations by randomly simulating wet zenith delay and clock values as well as additive white noise representing the antenna errors. For the simulation at IGG the VLBI analysis software OCCAM (Titov et al. 2004) was adapted. Random walk processes with power spectrum densities of 0.7 and 0.1 psec2/sec are used for the simulation of wet zenith delays. The clocks are simulated with Allan Standard Deviations of 1*10^-14 @ 50 min and 2*10^-15 @ 15 min and three levels of white noise, 4 psec, 8 psec and, 16 psec, are added to the artificial observations. The variations of the power spectrum densities of the clocks and wet zenith delays, and the application of different white noise levels show clearly that the wet delay is the critical factor for the improvement of the geodetic VLBI system. At GSFC the software CalcSolve is used for the VLBI analysis, therefore a comparison between the software packages OCCAM and CalcSolve was done with simulated data. For further simulations the wet zenith delay was modeled by a turbulence model. This data was provided by Nilsson T. and was added to the simulation work. Different schedules have been run.
Coherent multiple scattering effects and Monte Carlo method
V. L. Kuzmin; I. V. Meglinski
2004-01-01
Based on the comparison of the iteration procedure of solving the Bethe-Salpeter equation and the Monte Carlo method, we developed\\u000a a method for simulating coherent multiple-scattering effects within the framework of a unified stochastic approach. The time\\u000a correlation function and the interference component were calculated for the coherent backscattering from a multiply scattering\\u000a medium.
Monte Carlo Shower Counter Studies
NASA Technical Reports Server (NTRS)
Snyder, H. David
1991-01-01
Activities and accomplishments related to the Monte Carlo shower counter studies are summarized. A tape of the VMS version of the GEANT software was obtained and installed on the central computer at Gallaudet University. Due to difficulties encountered in updating this VMS version, a decision was made to switch to the UNIX version of the package. This version was installed and used to generate the set of data files currently accessed by various analysis programs. The GEANT software was used to write files of data for positron and proton showers. Showers were simulated for a detector consisting of 50 alternating layers of lead and scintillator. Each file consisted of 1000 events at each of the following energies: 0.1, 0.5, 2.0, 10, 44, and 200 GeV. Data analysis activities related to clustering, chi square, and likelihood analyses are summarized. Source code for the GEANT user subprograms and data analysis programs are provided along with example data plots.
Area Estimates by Monte Carlo Simulation
NSDL National Science Digital Library
Roberts, Lila F.
2001-06-02
This demo estimates the area of a circle or triangle using a probability experiment employing the Monte Carlo technique. We also indicate how to use our approach to estimate the area of a polygonal region.
A comparison of Monte Carlo generators
NASA Astrophysics Data System (ADS)
Golan, Tomasz
2015-05-01
A comparison of GENIE, NEUT, NUANCE, and NuWro Monte Carlo neutrino event generators is presented using a set of four observables: protons multiplicity, total visible energy, most energetic proton momentum, and ?+ two-dimensional energy vs cosine distribution.
Quantum Monte Carlo Calculations of Light Nuclei
Steven C. Pieper
2007-11-09
During the last 15 years, there has been much progress in defining the nuclear Hamiltonian and applying quantum Monte Carlo methods to the calculation of light nuclei. I describe both aspects of this work and some recent results.
Monte Carlo techniques in statistical physics
NASA Astrophysics Data System (ADS)
Murthy, K. P. N.
2006-11-01
In this paper we shall briefly review a few Markov Chain Monte Carlo methods for simulating closed systems described by canonical ensembles. We cover both Boltzmann and non-Boltzmann sampling techniques. The Metropolis algorithm is a typical example of Boltzmann Monte Carlo method. We discuss the time-symmetry of the Markov chain generated by Metropolis like algo- rithms that obey detailed balance. The non-Boltzmann Monte Carlo techniques reviewed include the multicanonical and Wang-Landau sampling. We list what we consider as milestones in the historical development of Monte Carlo methods in statistical physics. We dedicate this article to Prof. Dr. G. Ananthakrishna and wish him the very best in the coming years
Frontiers of quantum Monte Carlo workshop: preface
Gubernatis, J.E.
1985-01-01
The introductory remarks, table of contents, and list of attendees are presented from the proceedings of the conference, Frontiers of Quantum Monte Carlo, which appeared in the Journal of Statistical Physics. (GHT)
Extra Chance Hybrid Monte Carlo$ Cdric M. Campos
Sanz-Serna , J M
Extra Chance Hybrid Monte Carlo$ CÃ©dric M. Campos , J. M. Sanz-Serna Dept. MatemÃ¡tica Aplicada e Chance Generalized Hybrid Monte Carlo) to avoid rejections in the Hybrid Monte Carlo (HMC) method of the quality of the samples generated. Keywords: sampling methods, hybrid Monte Carlo, detailed balance
Monte Carlo data association for multiple target tracking Rickard Karlsson
Gustafsson, Fredrik
Monte Carlo data association for multiple target tracking Rickard Karlsson Dept. of Electrical, these estimation methods may lead to non-optimal solutions. The sequential Monte Carlo methods, or particle filters chose the number of particles. 2 Sequential Monte Carlo methods Monte Carlo techniques have been
Monte Carlo methods for fissured porous media: gridless approaches
Paris-Sud XI, UniversitÃ© de
Monte Carlo methods for fissured porous media: gridless approaches Antoine Lejay1, -- Projet OMEGA (INRIA / Institut Â´Elie Cartan, Nancy) Abstract: In this article, we present two Monte Carlo methods) Published in Monte Carlo Methods and Applications. Proc. of the IV IMACS Seminar on Monte Carlo Methods
Monte Carlo data association for multiple target tracking Rickard Karlsson
Gustafsson, Fredrik
Monte Carlo data association for multiple target tracking Rickard Karlsson Dept. of Electrical, these estimation methods may lead to nonoptimal solutions. The sequential Monte Carlo methods, or particle filters chose the number of particles. 2 Sequential Monte Carlo methods Monte Carlo techniques have been
Monte-Carlo vs. Bulk Conductivity Modeling of RF
Kaganovich, Igor
Monte-Carlo vs. Bulk Conductivity Modeling of RF Breakdown of Helium* Carsten Thoma, Thomas Hughes distribution function can be quite non-Maxwellian #12;2 approaches to simulating weakly- ionized plasma · Monte-Carlo with He at STP. #12;Monte Carlo Scattering Algorithm* · Implemented a Monte Carlo scattering algorithm
The Monte Carlo Method and Software Reliability Theory
Pratt, Vaughan
1 The Monte Carlo Method and Software Reliability Theory Brian Korver1 briank@cs.pdx.edu TR 94-1. February 18, 1994 1.0 Abstract The Monte Carlo method of reliability prediction is useful when system for valid, nontrivial input data and an external oracle. 2.0 The Monte Carlo Method The Monte Carlo method
A Monte Carlo method for solving unsteady adjoint equations
Wang, Qiqi
A Monte Carlo method for solving unsteady adjoint equations Qiqi Wang a,*, David Gleich a , Amin on this technique and uses a Monte Carlo linear solver. The Monte Carlo solver yields a forward-time algorithm' equation, the Monte Carlo approach is faster for a large class of problems while preserving sufficient
Monte Carlo radiative transfer in protoplanetary disks
Christophe Pinte; Francois Menard; Gaspard Duchene; Pierre Bastien
2006-01-01
We present a new continuum 3D radiative transfer code, MCFOST, based on a\\u000aMonte-Carlo method. MCFOST can be used to calculate (i) monochromatic images in\\u000ascattered light and\\/or thermal emission, (ii) polarisation maps, (iii)\\u000ainterferometric visibilities, (iv) spectral energy distributions and (v) dust\\u000atemperature distributions of protoplanetary disks. Several improvements to the\\u000astandard Monte Carlo method are implemented in MCFOST
Monte Carlo radiative transfer in protoplanetary disks
C. Pinte; F. Ménard; G. Duchêne; P. Bastien
2006-01-01
Aims.We present a new continuum 3D radiative transfer code, MCFOST, based on a Monte-Carlo method. MCFOST can be used to calculate (i) monochromatic images in scattered light and\\/or thermal emission; (ii) polarisation maps; (iii) interferometric visibilities; (iv) spectral energy distributions; and (v) dust temperature distributions of protoplanetary disks. Methods: .Several improvements to the standard Monte Carlo method are implemented in
Bandit based Monte-Carlo Planning
Levente Kocsis; Csaba Szepesvari
2006-01-01
For large state-space Markovian Decision Problems Monte- Carlo planning is one of the few viable approaches to flnd near-optimal solutions. In this paper we introduce a new algorithm, UCT, that ap- plies bandit ideas to guide Monte-Carlo planning. In flnite-horizon or discounted MDPs the algorithm is shown to be consistent and flnite sample bounds are derived on the estimation error
A Guide to Monte Carlo Simulations in Statistical Physics
NASA Astrophysics Data System (ADS)
Landau, David P.; Binder, Kurt
2014-11-01
1. Introduction; 2. Some necessary background; 3. Simple sampling Monte Carlo methods; 4. Importance sampling Monte Carlo methods; 5. More on importance sampling Monte Carlo methods for lattice systems; 6. Off-lattice models; 7. Reweighting methods; 8. Quantum Monte Carlo methods; 9. Monte Carlo renormalization group methods; 10. Non-equilibrium and irreversible processes; 11. Lattice gauge models: a brief introduction; 12. A brief review of other methods of computer simulation; 13. Monte Carlo simulations at the periphery of physics and beyond; 14. Monte Carlo studies of biological molecules; 15. Outlook; Appendix: listing of programs mentioned in the text; Index.
Monte Carlo analysis of inverse problems
Klaus Mosegaard; Malcolm Sambridge
2002-01-01
Monte Carlo methods have become important in analysis of nonlinear inverse problems where no analytical expression for the forward relation between data and model parameters is available, and where linearization is unsuccessful. In such cases a direct mathematical treatment is impossible, but the forward relation materializes itself as an algorithm allowing data to be calculated for any given model. Monte
Stanford University
Chapter 2 Monte Carlo Integration This chapter gives an introduction to Monte Carlo integration useful in computer graphics. Good references on Monte Carlo methods include Kalos & Whitlock [1986 for Monte Carlo applications to neutron transport problems; Lewis & Miller [1984] is a good source
NASA Astrophysics Data System (ADS)
Morales-Casique, E.; Briseño-Ruiz, J. V.; Hernández, A. F.; Herrera, G. S.; Escolero-Fuentes, O.
2014-12-01
We present a comparison of three stochastic approaches for estimating log hydraulic conductivity (Y) and predicting steady-state groundwater flow. Two of the approaches are based on the data assimilation technique known as ensemble Kalman filter (EnKF) and differ in the way prior statistical moment estimates (PSME) (required to build the Kalman gain matrix) are obtained. In the first approach, the Monte Carlo method is employed to compute PSME of the variables and parameters; we denote this approach by EnKFMC. In the second approach PSME are computed through the direct solution of approximate nonlocal (integrodifferential) equations that govern the spatial conditional ensemble means (statistical expectations) and covariances of hydraulic head (h) and fluxes; we denote this approach by EnKFME. The third approach consists of geostatistical stochastic inversion of the same nonlocal moment equations; we denote this approach by IME. In addition to testing the EnKFMC and EnKFME methods in the traditional manner that estimate Y over the entire grid, we propose novel corresponding algorithms that estimate Y at a few selected locations and then interpolate over all grid elements via kriging as done in the IME method. We tested these methods to estimate Y and h in steady-state groundwater flow in a synthetic two-dimensional domain with a well pumping at a constant rate, located at the center of the domain. In addition, to evaluate the performance of the estimation methods, we generated four unconditional different realizations that served as "true" fields. The results of our numerical experiments indicate that the three methods were effective in estimating h, reaching at least 80% of predictive coverage, although both EnKF were superior to the IME method. With respect to estimating Y, the three methods reached similar accuracy in terms of the mean absolute value error. Coupling the EnKF methods with kriging to estimate Y reduces to one fourth the CPU time required for data assimilation while both estimation accuracy and uncertainty do not deteriorate significantly.
FPGA-driven pseudorandom number generators aimed at accelerating Monte Carlo methods
Tarek Ould Bachir; Jean-Jules Brault
2009-01-01
Hardware acceleration in high performance computing (HPC) context is of growing interest, particularly in the field of Monte Carlo methods where the resort to field programmable gate array (FPGA) technology has been proven as an effective media, capable of enhancing by several orders the speed execution of stochastic processes. The spread-use of reconfigurable hardware for stochastic simulation gathered a significant
The Monte-Carlo Revolution in Go Remi Coulom
Coulom, Rémi - Groupe de Recherche sur l'Apprentissage Automatique, Université Charles de Gaulle
The Monte-Carlo Revolution in Go R´emi Coulom Universit´e Charles de Gaulle, INRIA, CNRS, Lille, France January, 2009 JFFoS'2008: Japanese-French Frontiers of Science Symposium #12;Introduction Monte configurations R´emi Coulom The Monte Carlo Revolution in Go 2 / 12 #12;Introduction Monte-Carlo Tree Search
Minimum variance importance sampling via Population Monte Carlo
Douc, Randal
Variance reduction has always been a central issue in Monte Carlo experiments. Population Monte Carlo can Carlo, variance reduction, AMS Classification: 60F05, 62L12, 65-04, 65C05, 65C40, 65C60. 1 #12Minimum variance importance sampling via Population Monte Carlo R. Douc1 , A. Guillin2 , J
Quantum speedup of Monte Carlo methods
Ashley Montanaro
2015-04-27
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomised or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.
Shell model the Monte Carlo way
Ormand, W.E.
1995-03-01
The formalism for the auxiliary-field Monte Carlo approach to the nuclear shell model is presented. The method is based on a linearization of the two-body part of the Hamiltonian in an imaginary-time propagator using the Hubbard-Stratonovich transformation. The foundation of the method, as applied to the nuclear many-body problem, is discussed. Topics presented in detail include: (1) the density-density formulation of the method, (2) computation of the overlaps, (3) the sign of the Monte Carlo weight function, (4) techniques for performing Monte Carlo sampling, and (5) the reconstruction of response functions from an imaginary-time auto-correlation function using MaxEnt techniques. Results obtained using schematic interactions, which have no sign problem, are presented to demonstrate the feasibility of the method, while an extrapolation method for realistic Hamiltonians is presented. In addition, applications at finite temperature are outlined.
Monte Carlo simulation of launchsite winds at Kennedy Space Center
NASA Technical Reports Server (NTRS)
Queen, Eric M.; Moerder, Daniel D.; Warner, Michael S.
1991-01-01
This paper develops and validates an easily implemented model for simulating random horizontal wind profiles over the Kennedy Space Center (KSC) at Cape Canaveral, Florida. The model is intended for use in Monte Carlo launch vehicle simulations of the type employed in mission planning, where the large number of profiles needed for statistical fidelity of such simulation experiments makes the use of actual wind measurements impractical. The model is based on measurements made at KSC and represents vertical correlations by a decaying exponential model which is parameterized via least-squares parameter optimization against the sample data. The validity of the model is evaluated by comparing two Monte Carlo simulations of an asymmetric, heavy-lift launch vehicle. In the first simulation, the measured wind profiles are used, while in the second, the wind profiles are generated using the stochastic model. The simulations indicate that the use of either the measured or simulated wind field results in similar launch vehicle performance.
Advanced interacting sequential Monte Carlo sampling for inverse scattering
NASA Astrophysics Data System (ADS)
Giraud, F.; Minvielle, P.; Del Moral, P.
2013-09-01
The following electromagnetism (EM) inverse problem is addressed. It consists in estimating the local radioelectric properties of materials recovering an object from global EM scattering measurements, at various incidences and wave frequencies. This large scale ill-posed inverse problem is explored by an intensive exploitation of an efficient 2D Maxwell solver, distributed on high performance computing machines. Applied to a large training data set, a statistical analysis reduces the problem to a simpler probabilistic metamodel, from which Bayesian inference can be performed. Considering the radioelectric properties as a hidden dynamic stochastic process that evolves according to the frequency, it is shown how advanced Markov chain Monte Carlo methods—called sequential Monte Carlo or interacting particles—can take benefit of the structure and provide local EM property estimates.
Nuclear pairing within a configuration-space Monte Carlo approach
NASA Astrophysics Data System (ADS)
Lingle, Mark; Volya, Alexander
2015-06-01
Pairing correlations in nuclei play a decisive role in determining nuclear drip lines, binding energies, and many collective properties. In this work a new configuration-space Monte Carlo (CSMC) method for treating nuclear pairing correlations is developed, implemented, and demonstrated. In CSMC the Hamiltonian matrix is stochastically generated in Krylov subspace, resulting in the Monte Carlo version of Lanczos-like diagonalization. The advantages of this approach over other techniques are discussed; the absence of the fermionic sign problem, probabilistic interpretation of quantum-mechanical amplitudes, and ability to handle truly large-scale problems with defined precision and error control are noteworthy merits of CSMC. The features of our CSMC approach are shown using models and realistic examples. Special attention is given to difficult limits: situations with nonconstant pairing strengths, cases with nearly degenerate excited states, limits when pairing correlations in finite systems are weak, and problems when the relevant configuration space is large.
Geodesic Monte Carlo on Embedded Manifolds
Byrne, Simon; Girolami, Mark
2013-01-01
Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton–Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices. PMID:25309024
The Rational Hybrid Monte Carlo Algorithm
M. A. Clark
2006-10-06
The past few years have seen considerable progress in algorithmic development for the generation of gauge fields including the effects of dynamical fermions. The Rational Hybrid Monte Carlo (RHMC) algorithm, where Hybrid Monte Carlo is performed using a rational approximation in place the usual inverse quark matrix kernel is one of these developments. This algorithm has been found to be extremely beneficial in many areas of lattice QCD (chiral fermions, finite temperature, Wilson fermions etc.). We review the algorithm and some of these benefits, and we compare against other recent algorithm developements. We conclude with an update of the Berlin wall plot comparing costs of all popular fermion formulations.
Kinetic Monte Carlo theory of sliding friction
NASA Astrophysics Data System (ADS)
Furlong, Octavio Javier; Manzi, Sergio Javier; Pereyra, Victor Daniel; Bustos, Victor; Tysoe, Wilfred T.
2009-10-01
The sliding friction as a function of scanning velocity at the nanometer scale was simulated based on a modified one-dimensional Tomlinson model. Monte Carlo theory was exploited to describe the thermally activated hopping of the contact atoms, where both backward and forward jumps were allowed to occur. By comparing with the Monte Carlo results, improvements to current semiempirical solutions [E. Riedo , Phys. Rev. Lett. 91, 084502 (2003)] were made. Finally, experimental results of sliding friction on a NaCl(100) as a function of normal load and scanning velocity [E. Gnecco , Phys. Rev. Lett. 84, 1172 (2000)] where successfully simulated.
Monte Carlo simulation of scenario probability distributions
Glaser, R.
1996-10-23
Suppose a scenario of interest can be represented as a series of events. A final result R may be viewed then as the intersection of three events, A, B, and C. The probability of the result P(R) in this case is the product P(R) = P(A) P(B {vert_bar} A) P(C {vert_bar} A {intersection} B). An expert may be reluctant to estimate P(R) as a whole yet agree to supply his notions of the component probabilities in the form of prior distributions. Each component prior distribution may be viewed as the stochastic characterization of the expert`s uncertainty regarding the true value of the component probability. Mathematically, the component probabilities are treated as independent random variables and P(R) as their product; the induced prior distribution for P(R) is determined which characterizes the expert`s uncertainty regarding P(R). It may be both convenient and adequate to approximate the desired distribution by Monte Carlo simulation. Software has been written for this task that allows a variety of component priors that experts with good engineering judgment might feel comfortable with. The priors are mostly based on so-called likelihood classes. The software permits an expert to choose for a given component event probability one of six types of prior distributions, and the expert specifies the parameter value(s) for that prior. Each prior is unimodal. The expert essentially decides where the mode is, how the probability is distributed in the vicinity of the mode, and how rapidly it attenuates away. Limiting and degenerate applications allow the expert to be vague or precise.
Monte-Carlo Integration Using Cryptographically Secure Pseudorandom Generator
Hiroshi Sugita
2002-01-01
The drastic reduction of randomness by random Weyl sampling enables us to use cryptographically secure pseudo-random generators\\u000a for Monte-Carlo integration as well as for parallel Monte-Carlo integration.
Non-Linear Monte-Carlo Search in Civilization II
Branavan, Satchuthanan R.
This paper presents a new Monte-Carlo search algorithm for very large sequential decision-making problems. Our approach builds on the recent success of Monte-Carlo tree search algorithms, which estimate the value of states ...
Monte Carlo event reconstruction implemented with artificial neural networks
Tolley, Emma Elizabeth
2011-01-01
I implemented event reconstruction of a Monte Carlo simulation using neural networks. The OLYMPUS Collaboration is using a Monte Carlo simulation of the OLYMPUS particle detector to evaluate systematics and reconstruct ...
Monte Carlo techniques for direct lighting calculations
Peter Shirley; Changyaw Wang; Kurt Zimmerman
1996-01-01
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 by Monte Carlo Integration
Peter Shirley Changyaw Wang
1991-01-01
The details of doing a Monte Carlo direct lighting calculation are presented. For directlighting from multiple luminaires, a method of sending one shadow ray per viewing ray ispresented, and it is argued that this is preferable for scenes with many luminaires. Someissues of the design of probability densities on unions of luminaire surfaces are discussed.1 IntroductionMany rendering algorithms separately calculate
Exploring Probability and the Monte Carlo Method
NSDL National Science Digital Library
2003-01-01
This multimedia mathematics resource examines probability. A video illustrates how math is used to evaluate the danger of avalanches in the mountains of Alberta. An interactive component allows students to compare theoretical and experimental probabilities, as well as explore the Monte Carlo method. A probability print activity is also included.
Monte Carlo dose calculations in advanced radiotherapy
Karl Kenneth Bush
2009-01-01
The remarkable accuracy of Monte Carlo (MC) dose calculation algorithms has led to the widely accepted view that these methods should and will play a central role in the radiotherapy treatment verification and planning of the future. The advantages of using MC clinically are particularly evident for radiation fields passing through inhomogeneities, such as lung and air cavities, and for
Structural Reliability and Monte Carlo Simulation.
ERIC Educational Resources Information Center
Laumakis, P. J.; Harlow, G.
2002-01-01
Analyzes a simple boom structure and assesses its reliability using elementary engineering mechanics. Demonstrates the power and utility of Monte-Carlo simulation by showing that such a simulation can be implemented more readily with results that compare favorably to the theoretical calculations. (Author/MM)
Monte Carlo simulations of lattice gauge theories
Rebbi, C
1980-02-01
Monte Carlo simulations done for four-dimensional lattice gauge systems are described, where the gauge group is one of the following: U(1); SU(2); Z/sub N/, i.e., the subgroup of U(1) consisting of the elements e 2..pi..in/N with integer n and N; the eight-element group of quaternions, Q; the 24- and 48-element subgroups of SU(2), denoted by T and O, which reduce to the rotation groups of the tetrahedron and the octahedron when their centers Z/sub 2/, are factored out. All of these groups can be considered subgroups of SU(2) and a common normalization was used for the action. The following types of Monte Carlo experiments are considered: simulations of a thermal cycle, where the temperature of the system is varied slightly every few Monte Carlo iterations and the internal energy is measured; mixed-phase runs, where several Monte Carlo iterations are done at a few temperatures near a phase transition starting with a lattice which is half ordered and half disordered; measurements of averages of Wilson factors for loops of different shape. 5 figures, 1 table. (RWR)
MONTE-CARLO METHODS IN GLOBAL ILLUMINATION
Frey, Pascal
MONTE-CARLO METHODS IN GLOBAL ILLUMINATION Script written by Szirmay-Kalos LÂ´aszlÂ´o in WS of 1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Global illumination problem 5 2.1 The rendering equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4 Solution strategies for the global illumination problem 28 4.1 Inversion
Parallel processing Monte Carlo radiation transport codes
McKinney, G.W.
1994-02-01
Issues related to distributed-memory multiprocessing as applied to Monte Carlo radiation transport are discussed. Measurements of communication overhead are presented for the radiation transport code MCNP which employs the communication software package PVM, and average efficiency curves are provided for a homogeneous virtual machine.
Non-Hermitian Polynomial Hybrid Monte Carlo
Oliver Witzel
2008-09-05
We report on a new variant of the hybrid Monte Carlo algorithm employing a polynomial approximation of the inverse of the non-Hermitian Dirac-Wilson operator. Our approximation relies on simple and stable recurrence relations of complex Chebyshev polynomials. First performance figures are presented.
MIMO detection employing Markov Chain Monte Carlo
V. Sundaram; K. P. N. Murthy
2007-05-05
We propose a soft-output detection scheme for Multiple-Input-Multiple-Output (MIMO) systems. The detector employs Markov Chain Monte Carlo method to compute bit reliabilities from the signals received and is thus suited for coded MIMO systems. It offers a good trade-off between achievable performance and algorithmic complexity.
Markov Chain Monte Carlo with People
Adam Sanborn; Thomas L. Griffiths
2007-01-01
Many formal models of cognition implicitly use subjective probability distribu- tions to capture the assumptions of human learners. Most applications of these models determine these distributions indirectly. We propose a method for directly determining the assumptions of human learners by sampling from subjective prob- ability distributions. Using a correspondence between a model of human choice and Markov chain Monte Carlo
Monte Carlo approach to Dark Matter Mapping
Suzanne Lorenz; J. R. Peterson
2011-01-01
We present an an analysis method of constructing dark matter maps based on weak lensing using a Markov Chain Monte Carlo technique. The dark matter in a cluster can be modeled as a collection of massive blobs that bend light according to gravitational lensing. We move these dark matter blobs in RA, Dec and redshift and as a result perturb
Monte Carlo transition dynamics and variance reduction
Fitzgerald, M.; Picard, R.R.; Silver, R.N.
2000-01-01
For Metropolis Monte Carlo simulations in statistical physics, efficient, easy-to-implement, and unbiased statistical estimators of thermodynamic properties are based on the transition dynamics. Using an Ising model example, they demonstrate (problem-specific) variance reductions compared to conventional histogram estimators. A proof of variance reduction in a microstate limit is presented.
An Introduction to Monte Carlo Methods
ERIC Educational Resources Information Center
Raeside, D. E.
1974-01-01
Reviews the principles of Monte Carlo calculation and random number generation in an attempt to introduce the direct and the rejection method of sampling techniques as well as the variance-reduction procedures. Indicates that the increasing availability of computers makes it possible for a wider audience to learn about these powerful methods. (CC)
Precision Localization in Monte Carlo Sensor Networks
Thomas C. Henderson; Edward Grant; Kyle Luthy; Leonardo Mattos; Matt Craver
2005-01-01
We have proposed Monte Carlo Sensor Networks as a method to solve certain sensor queries in the presence of noise and partial information. In that work we used very coarse position estimates for enemy agents. Here we propose methods to (1) improve the posterior probability estimates by using a more precise analysis of the sensor range geometry, and (2) help
Monte Carlo Experiments on Bootstrap DEA
Panagiotis Tziogkidis
2012-01-01
Since the introduction of bootstrap DEA there is a growing literature on applications which use this method, mainly for hypothesis testing. It is therefore important to establish the consistency and evaluate the performance of bootstrap DEA. The few Monte Carlo experiments in the literature perform this exercise on the basis of coverage probabilities, using a certain population assumption and usually
Monte Carlo Tools for Jet Quenching
Korinna Zapp
2011-09-07
A thorough understanding of jet quenching on the basis of multi-particle final states and jet observables requires new theoretical tools. This talk summarises the status and propects of the theoretical description of jet quenching in terms of Monte Carlo generators.
Monte Carlo simulation for radiative kaon decays
C. Gatti
2005-07-26
For high precision measurements of K decays, the presence of radiated photons cannot be neglected. The Monte Carlo simulations must include the radiative corrections in order to compute the correct event counting and efficiency calculations. In this paper we briefly describe a method for simulating such decays.
Monte Carlo analysis of CLAS data
L. Del Debbio; A. Guffanti; A. Piccione
2008-06-30
We present a fit of the virtual-photon scattering asymmetry of polarized Deep Inelastic Scattering which combines a Monte Carlo technique with the use of a redundant parametrization based on Neural Networks. We apply the result to the analysis of CLAS data on a polarized proton target.
Sequential Monte Carlo Methods for Dynamic Systems
Jun S. Liu; Rong Chen
1998-01-01
We provide a general framework for using Monte Carlo methods in dynamic systems and discuss its wide applications. Under this framework, several currently available techniques are studied and generalized to accommodate more complex features. All of these methods are partial combinations of three ingredients: importance sampling and resampling, rejection sampling, and Markov chain iterations. We provide guidelines on how they
Nonuniversal critical dynamics in Monte Carlo simulations
Robert H. Swendsen; Jian-Sheng Wang
1987-01-01
A new approach to Monte Carlo simulations is presented, giving a highly efficient method of simulation for large systems near criticality. The algorithm violates dynamic universality at second-order phase transitions, producing unusually small values of the dynamical critical exponent.
Improved Monte Carlo Renormalization Group Method
Gupta, R.; Wilson, K.G.; Umrigar, C.
1985-01-01
An extensive program to analyse critical systems using an Improved Monte Carlo Renormalization Group Method (IMCRG) being undertaken at LANL and Cornell is described. Here we first briefly review the method and then list some of the topics being investigated. 9 refs.
Landon, Colin Donald
2010-01-01
Direct Simulation Monte Carlo (DSMC)-the prevalent stochastic particle method for high-speed rarefied gas flows-simulates the Boltzmann equation using distributions of representative particles. Although very efficient in ...
Advanced topics 5.1 Hybrid Monte Carlo
Schofield, Jeremy
5 Advanced topics 5.1 Hybrid Monte Carlo 5.1.1 The Method One drawback of traditional Monte-Carlo in a Monte-Carlo procedure. See S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Phys. Lett. B 45, 216;5.1. HYBRID MONTE CARLO 89 · Claim: The transition probability Eq. (5.3) satisfies the stationarity condition
Parallel Monte Carlo Approach for Integration of the Rendering Equation
Dimov, Ivan
Parallel Monte Carlo Approach for Integration of the Rendering Equation Ivan T. Dimov1 , Anton A are the Monte Carlo methods for solving the rendering equation in order to create photorealistic images. In this work we consider the Monte Carlo solving of the render- ing equation in the context of the parallel
Bayesian Monte Carlo Carl Edward Rasmussen and Zoubin Ghahramani
Ghahramani, Zoubin
Bayesian Monte Carlo Carl Edward Rasmussen and Zoubin Ghahramani Gatsby Computational Neuroscience,zoubin@gatsby.ucl.ac.uk http://www.gatsby.ucl.ac.uk Abstract We investigate Bayesian alternatives to classical Monte Carlo methods for evaluating integrals. Bayesian Monte Carlo (BMC) allows the in- corporation of prior knowledge
TECHNICAL MATERIAL New Hybrid Monte Carlo Methods for Efficient Sampling
Reich, Sebastian
TECHNICAL MATERIAL New Hybrid Monte Carlo Methods for Efficient Sampling: from Physics to Biology in physics, biology, materials science and statistics. These generalized shadow Hybrid Monte Carlo (GSHMC known methods in sampling efficiency by an order of magnitude4) . KEYWORDS: Hybrid, Monte Carlo
TOWARDS A HYBRID MONTE CARLO METHOD FOR RAREFIED GAS DYNAMICS
Pareschi, Lorenzo
TOWARDS A HYBRID MONTE CARLO METHOD FOR RAREFIED GAS DYNAMICS RUSSEL E. CAFLISCH #3; AND LORENZO PARESCHI y Abstract. For the Boltzmann equation, we present a hybrid Monte Carlo method that is robust-equilibrium particle distribution and a Maxwellian. The hybrid distribution is then evolved by Monte Carlo
John von Neumann Institute for Computing Monte Carlo Protein Folding
Hsu, Hsiao-Ping
John von Neumann Institute for Computing Monte Carlo Protein Folding: Simulations of Met://www.fz-juelich.de/nic-series/volume20 #12;#12;Monte Carlo Protein Folding: Simulations of Met-Enkephalin with Solvent-Accessible Area difficulties in applying Monte Carlo methods to protein folding. The solvent-accessible area method, a popular
Multigroup cross section generation via Monte Carlo methods
Everett Lee Redmond II
1997-01-01
Monte Carlo methods of performing radiation transport calculations are heavily used in many different applications. However, despite their prevalence, Monte Carlo codes do not eliminate the need for other methods of analysis like discrete ordinates transport codes or even diffusion theory codes. For example: current Monte Carlo codes are not capable of performing transient analysis or continuous energy adjoint calculations.
Parallel computing and Monte Carlo algorithms Je rey S. Rosenthal*
Rosenthal, Jeffrey S.
Parallel computing and Monte Carlo algorithms by Je#11;rey S. Rosenthal* [Far East Journal to parallel computing, and that \\parallel Monte Carlo" should be more widely used. We consider a number of parallel Markov chain Monte Carlo. We illustrate our results with actual computer experiments. Keywords
Biopolymer structure simulation and optimization via fragment regrowth Monte Carlo
McQuade, D. Tyler
Biopolymer structure simulation and optimization via fragment regrowth Monte Carlo Jinfeng Zhang, S. In this study, the authors propose a new Monte Carlo method, fragment regrowth via energy-guided sequential sampling FRESS , which incorporates the idea of multigrid Monte Carlo into the framework of configurational
Sequential Monte Carlo Methods for Statistical Analysis of Tables
Liu, Jun
Sequential Monte Carlo Methods for Statistical Analysis of Tables Yuguo CHEN, Persi DIACONIS, Susan- butions. Our method produces Monte Carlo samples that are remarkably close to the uniform distribution. Our method compares favorably with other existing Monte Carlo- based algorithms, and sometimes
Markov Chain Monte Carlo and Related Topics Department of Statistics
Liu, Jun
Markov Chain Monte Carlo and Related Topics Jun S. Liu Department of Statistics Stanford University review of recent developments in Markov chain Monte Carlo methodology. The methods discussed include.g., simulated tempering, paral lel tempering, parameter expansion, dynamic weighting, and multigrid Monte Carlo
FPGA-based Monte Carlo simulation for fault tree analysis
Alireza Ejlali; Seyed Ghassem Miremadi
2004-01-01
The reliability analysis of critical systems is often performed using fault-tree analysis. Fault trees are analyzed using analytic approaches or Monte Carlo simulation. The usage of the analytic approaches is limited in few models and certain kinds of distributions. In contrast to the analytic approaches, Monte Carlo simulation can be broadly used. However, Monte Carlo simulation is time-consuming because of
Generalised linear mixed model analysis via sequential Monte Carlo sampling
Y. Fan; D. S. Leslie; M. P. Wand
2008-01-01
We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely difficult, even when using the Bayesian approach combined with Markov chain Monte Carlo (MCMC). The Sequential Monte Carlo sampler (SMC) is a new and general method for
Monte Carlo variance reduction with deterministic importance functions
John C. Wagner
2003-01-01
Recent trends in Monte Carlo code development have reflected a recognition of the benefits of using deterministic importance functions for Monte Carlo variance reduction. This paper offers a review of the use of deterministic importance functions for variance reduction of Monte Carlo simulations. Adjoint methodology and the concept of “importance” are presented, along with an explanation of their use for
Lecture 15 Monte Carlo integration Weinan E1,2
Li, Tiejun
@pku.edu.cn No.1 Science Building, 1575 #12;Monte Carlo methods: basics Variance reduction methods An introduction to Markov chain Outline Monte Carlo methods: basics Variance reduction methods An introduction to Markov chain #12;Monte Carlo methods: basics Variance reduction methods An introduction to Markov chain
Monte Carlo Reliability Model for Microwave Monolithic Integrated Circuits
Rubloff, Gary W.
Monte Carlo Reliability Model for Microwave Monolithic Integrated Circuits Aris Christou Materials of the failure rate of each component due to interaction effects of the failed components. The Monte Carlo failure rates become nonconstant. The Monte Carlo technique is an appropriate methodology used to treat
MONTE CARLO METHODS IN GEOPHYSICAL INVERSE Malcolm Sambridge
Sambridge, Malcolm
MONTE CARLO METHODS IN GEOPHYSICAL INVERSE PROBLEMS Malcolm Sambridge Research School of Earth 2002. [1] Monte Carlo inversion techniques were first used by Earth scientists more than 30 years ago in exploration seismology. This pa- per traces the development and application of Monte Carlo methods for inverse
MONTE CARLO ANALYSIS: ESTIMATING GPP WITH THE CANOPY CONDUCTANCE METHOD
DeLucia, Evan H.
MONTE CARLO ANALYSIS: ESTIMATING GPP WITH THE CANOPY CONDUCTANCE METHOD 1. Overview A novel method performed a Monte Carlo Analysis to investigate the power of our statistical approach: i.e. what and Assumptions The Monte Carlo Analysis was performed as follows: · Natural variation. The only study to date
Monte Carlo Evaluation of Resampling-Based Hypothesis Tests
Boos, Dennis
Monte Carlo Evaluation of Resampling-Based Hypothesis Tests Dennis D. Boos and Ji Zhang October 1998 Abstract Monte Carlo estimation of the power of tests that require resampling can be very com in correcting for bias and thus reduces computation time in Monte Carlo power studies. KEY WORDS: Bootstrap
Monte Carlo Algorithms for the Partition Function and Information Rates
Loeliger, Hans-Andrea
1 Monte Carlo Algorithms for the Partition Function and Information Rates of Two Monte Carlo algorithms for the computation of the information rate of two-dimensional source / channel, of such channels has so far remained largely unsolved. Both problems can be reduced to computing a Monte Carlo
MONTE CARLO LIKELIHOOD INFERENCE FOR MISSING DATA MODELS
Jiang, Tiefeng
MONTE CARLO LIKELIHOOD INFERENCE FOR MISSING DATA MODELS By Yun Ju Sung and Charles J. Geyer University of Washington and University of Minnesota Abbreviated title: Monte Carlo Likelihood Asymptotics We describe a Monte Carlo method to approximate the maximum likeli- hood estimate (MLE), when
MONTE CARLO SIMULATION FOR AMERICAN Russel E. Caflisch
Caflisch, Russel
#12;Chapter 1 MONTE CARLO SIMULATION FOR AMERICAN OPTIONS Russel E. Caflisch Mathematics Department This paper reviews the basic properties of American options and the difficulties of applying Monte Carlo of Monte Carlo to American options is described including the following: Branching processes have been con
Monte-Carlo Tree Search in Crazy Stone Remi Coulom
Coulom, Rémi - Groupe de Recherche sur l'Apprentissage Automatique, Université Charles de Gaulle
Monte-Carlo Tree Search in Crazy Stone R´emi Coulom Universit´e Charles de Gaulle, INRIA, CNRS Introduction 2 Crazy Stone's Algorithm Principles of Monte-Carlo Evaluation Tree Search Patterns 3 Playing global understanding The Monte-Carlo Approach random playouts dynamic evaluation with global
Monte Carlo procedure for protein design Anders Irback,* Carsten Peterson,
Irbäck, Anders
Monte Carlo procedure for protein design Anders Irba¨ck,* Carsten Peterson, Frank Potthast functions, is based upon a different and very efficient multisequence Monte Carlo scheme. By construction a practical Monte Carlo MC procedure for perform- ing the maximization of P(r0 ). Thermodynamical
Monte Carlo simulations and option by Bingqian Lu
Mazzucato, Anna
Monte Carlo simulations and option pricing by Bingqian Lu Undergraduate Mathematics Department #12;Abstract Monte Carlo simulation is a legitimate and widely used technique for dealing of this technique to the stock volality and to test its accuracy by comparing the result computed by Monte Carlo
A Monte Carlo Approach for Finding More than One Eigenpair
Karaivanova, Aneta
A Monte Carlo Approach for Finding More than One Eigenpair Michael Mascagni1 and Aneta Karaivanova1. 25A, 1113 Sofia, Bulgaria, aneta@csit.fsu.edu, http://parallel.bas.bg/anet/ Abstract. The Monte Carlo) eigenvalues of matrices. In this paper we study computing eigenvectors as well with the Monte Carlo approach
Monte Carlo Ray Tracing Siggraph 2003 Course 44
Li, Yaohang
Monte Carlo Ray Tracing Siggraph 2003 Course 44 Tuesday, July 29, 2003 Organizer Henrik Wann Jensen;Abstract This full day course will provide a detailed overview of state of the art in Monte Carlo ray tracing. Recent advances in algorithms and available compute power have made Monte Carlo ray tracing based
Monte Carlo modeling of optical coherence tomography systems
Monte Carlo modeling of optical coherence tomography systems Peter E. Andersen Optics and Fluid 2003 Outline · Motivation · Monte Carlo OCT use MC to model interference? · Results comparison Dynamics Department SFM'03 7-10 October 2003 Motivation · Monte Carlo (MC) modeling of light propagation
Lattice kinetic Monte Carlo simulations of convective-diffusive systems.
Flamm, Matthew H; Diamond, Scott L; Sinno, Talid
2009-03-01
Diverse phenomena in physical, chemical, and biological systems exhibit significant stochasticity and therefore require appropriate simulations that incorporate noise explicitly into the dynamics. We present a lattice kinetic Monte Carlo approach to simulate the trajectories of tracer particles within a system in which both diffusive and convective transports are operational. While diffusive transport is readily accounted for in a kinetic Monte Carlo simulation, we demonstrate that the inclusion of bulk convection by simply biasing the rate of diffusion with the rate of convection creates unphysical, shocklike behavior in concentrated systems due to particle pile up. We report that elimination of shocklike behavior requires the proper passing of blocked convective rates along nearest-neighbor chains to the first available particle in the direction of flow. The resulting algorithm was validated for the Taylor-Aris dispersion in parallel plate flow and multidimensional flows. This is the first generally applicable lattice kinetic Monte Carlo simulation for convection-diffusion and will allow simulations of field-driven phenomena in which drift is present in addition to diffusion. PMID:19275421
Mengkuo Wang
2006-01-01
In particle transport computations, the Monte Carlo simulation method is a widely used algorithm. There are several Monte Carlo codes available that perform particle transport simulations. However the geometry packages and geometric modeling capability of Monte Carlo codes are limited as they can not handle complicated geometries made up of complex surfaces. Previous research exists that take advantage of the
Path integral Monte Carlo and the electron gas
NASA Astrophysics Data System (ADS)
Brown, Ethan W.
Path integral Monte Carlo is a proven method for accurately simulating quantum mechanical systems at finite-temperature. By stochastically sampling Feynman's path integral representation of the quantum many-body density matrix, path integral Monte Carlo includes non-perturbative effects like thermal fluctuations and particle correlations in a natural way. Over the past 30 years, path integral Monte Carlo has been successfully employed to study the low density electron gas, high-pressure hydrogen, and superfluid helium. For systems where the role of Fermi statistics is important, however, traditional path integral Monte Carlo simulations have an exponentially decreasing efficiency with decreased temperature and increased system size. In this thesis, we work towards improving this efficiency, both through approximate and exact methods, as specifically applied to the homogeneous electron gas. We begin with a brief overview of the current state of atomic simulations at finite-temperature before we delve into a pedagogical review of the path integral Monte Carlo method. We then spend some time discussing the one major issue preventing exact simulation of Fermi systems, the sign problem. Afterwards, we introduce a way to circumvent the sign problem in PIMC simulations through a fixed-node constraint. We then apply this method to the homogeneous electron gas at a large swatch of densities and temperatures in order to map out the warm-dense matter regime. The electron gas can be a representative model for a host of real systems, from simple medals to stellar interiors. However, its most common use is as input into density functional theory. To this end, we aim to build an accurate representation of the electron gas from the ground state to the classical limit and examine its use in finite-temperature density functional formulations. The latter half of this thesis focuses on possible routes beyond the fixed-node approximation. As a first step, we utilize the variational principle inherent in the path integral Monte Carlo method to optimize the nodal surface. By using a ansatz resembling a free particle density matrix, we make a unique connection between a nodal effective mass and the traditional effective mass of many-body quantum theory. We then propose and test several alternate nodal ansatzes and apply them to single atomic systems. Finally, we propose a method to tackle the sign problem head on, by leveraging the relatively simple structure of permutation space. Using this method, we find we can perform exact simulations this of the electron gas and 3He that were previously impossible.
Markov Chain Monte-Carlo Models of Starburst Clusters
NASA Astrophysics Data System (ADS)
Melnick, Jorge
2015-01-01
There are a number of stochastic effects that must be considered when comparing models to observations of starburst clusters: the IMF is never fully populated; the stars can never be strictly coeval; stars rotate and their photometric properties depend on orientation; a significant fraction of massive stars are in interacting binaries; and the extinction varies from star to star. The probability distributions of each of these effects are not a priori known, but must be extracted from the observations. Markov Chain Monte-Carlo methods appear to provide the best statistical approach. Here I present an example of stochastic age effects upon the upper mass limit of the IMF of the Arches cluster as derived from near-IR photometry.
Boltzmann bias grand canonical Monte Carlo
NASA Astrophysics Data System (ADS)
Garberoglio, G.
2008-04-01
We derive an efficient method for the insertion of structured particles in grand canonical Monte Carlo simulations of adsorption in very confining geometries. We extend this method to path integral simulations and use it to calculate the isotherm of adsorption of hydrogen isotopes in narrow carbon nanotubes (two-dimensional confinement) and slit pores (one-dimensional confinement) at the temperatures of 20 and 77 K, discussing its efficiency by comparison to the standard path integral grand canonical Monte Carlo algorithm. We use this algorithm to perform multicomponent simulations in order to calculate the hydrogen isotope selectivity for adsorption in narrow carbon nanotubes and slit pores at finite pressures. The algorithm described here can be applied to the study of adsorption of real oligomers and polymers in narrow pores and channels.
Status of Monte Carlo at Los Alamos
Thompson, W.L.; Cashwell, E.D.
1980-01-01
At Los Alamos the early work of Fermi, von Neumann, and Ulam has been developed and supplemented by many followers, notably Cashwell and Everett, and the main product today is the continuous-energy, general-purpose, generalized-geometry, time-dependent, coupled neutron-photon transport code called MCNP. The Los Alamos Monte Carlo research and development effort is concentrated in Group X-6. MCNP treats an arbitrary three-dimensional configuration of arbitrary materials in geometric cells bounded by first- and second-degree surfaces and some fourth-degree surfaces (elliptical tori). Monte Carlo has evolved into perhaps the main method for radiation transport calculations at Los Alamos. MCNP is used in every technical division at the Laboratory by over 130 users about 600 times a month accounting for nearly 200 hours of CDC-7600 time.
Monte Carlo Simulation of THz Multipliers
NASA Technical Reports Server (NTRS)
East, J.; Blakey, P.
1997-01-01
Schottky Barrier diode frequency multipliers are critical components in submillimeter and Thz space based earth observation systems. As the operating frequency of these multipliers has increased, the agreement between design predictions and experimental results has become poorer. The multiplier design is usually based on a nonlinear model using a form of harmonic balance and a model for the Schottky barrier diode. Conventional voltage dependent lumped element models do a poor job of predicting THz frequency performance. This paper will describe a large signal Monte Carlo simulation of Schottky barrier multipliers. The simulation is a time dependent particle field Monte Carlo simulation with ohmic and Schottky barrier boundary conditions included that has been combined with a fixed point solution for the nonlinear circuit interaction. The results in the paper will point out some important time constants in varactor operation and will describe the effects of current saturation and nonlinear resistances on multiplier operation.
Monte Carlo radiative transfer in protoplanetary disks
Pinte, C; Duchêne, G; Bastien, P; Pinte, Christophe; Menard, Francois; Duchene, Gaspard; Bastien, Pierre
2006-01-01
We present a new continuum 3D radiative transfer code, MCFOST, based on a Monte-Carlo method. MCFOST can be used to calculate (i) monochromatic images in scattered light and/or thermal emission, (ii) polarisation maps, (iii) interferometric visibilities, (iv) spectral energy distributions and (v) dust temperature distributions of protoplanetary disks. Several improvements to the standard Monte Carlo method are implemented in MCFOST to increase efficiency and reduce convergence time, including wavelength distribution adjustments, mean intensity calculations and an adaptive sampling of the radiation field. The reliability and efficiency of the code are tested against a previously defined benchmark, using a 2D disk configuration. No significant difference (no more than 10%, and generally much less) is found between the temperatures and SEDs calculated by MCFOST and by other codes included in the benchmark. A study of the lowest disk mass detectable by Spitzer, around young stars, is presented and the colours of ...
Monte Carlo simulations of fluid vesicles
NASA Astrophysics Data System (ADS)
Sreeja, K. K.; Ipsen, John H.; Kumar, P. B. Sunil
2015-07-01
Lipid vesicles are closed two dimensional fluid surfaces that are studied extensively as model systems for understanding the physical properties of biological membranes. Here we review the recent developments in the Monte Carlo techniques for simulating fluid vesicles and discuss some of their applications. The technique, which treats the membrane as an elastic sheet, is most suitable for the study of large scale conformations of membranes. The model can be used to study vesicles with fixed and varying topologies. Here we focus on the case of multi-component membranes with the local lipid and protein composition coupled to the membrane curvature leading to a variety of shapes. The phase diagram is more intriguing in the case of fluid vesicles having an in-plane orientational order that induce anisotropic directional curvatures. Methods to explore the steady state morphological structures due to active flux of materials have also been described in the context of Monte Carlo simulations.
Monte Carlo results for the hydrogen Hugoniot.
Bezkrovniy, V; Filinov, V S; Kremp, D; Bonitz, M; Schlanges, M; Kraeft, W D; Levashov, P R; Fortov, V E
2004-11-01
We propose a theoretical Hugoniot relation obtained by combining results for the equation of state from the direct path integral Monte Carlo technique (DPIMC) and those from reaction ensemble Monte Carlo (REMC) simulations. The main idea of this proposal is based on the fact that the DPMIC technique provides first-principle results for a wide range of densities and temperatures including the region of partially ionized plasmas. On the other hand, for lower temperatures where the formation of molecules becomes dominant, DPIMC simulations become cumbersome and inefficient. For this region it is possible to use accurate REMC simulations where bound states (molecules) are treated on the Born-Oppenheimer level. The remaining interaction is then reduced to the scattering between neutral particles which is reliably treated classically by applying effective potentials. The resulting Hugoniot is located between the experimental values of Knudson et al. [Phys. Rev. Lett. 87, 225501 (2001)] and Collins et al. [Science 281, 1178 (1998)]. PMID:15600800
Monte Carlo simulations of fluid vesicles.
Sreeja, K K; Ipsen, John H; Sunil Kumar, P B
2015-07-15
Lipid vesicles are closed two dimensional fluid surfaces that are studied extensively as model systems for understanding the physical properties of biological membranes. Here we review the recent developments in the Monte Carlo techniques for simulating fluid vesicles and discuss some of their applications. The technique, which treats the membrane as an elastic sheet, is most suitable for the study of large scale conformations of membranes. The model can be used to study vesicles with fixed and varying topologies. Here we focus on the case of multi-component membranes with the local lipid and protein composition coupled to the membrane curvature leading to a variety of shapes. The phase diagram is more intriguing in the case of fluid vesicles having an in-plane orientational order that induce anisotropic directional curvatures. Methods to explore the steady state morphological structures due to active flux of materials have also been described in the context of Monte Carlo simulations. PMID:26087479
Ex Post Facto Monte Carlo Variance Reduction
Booth, Thomas E. [Los Alamos National Laboratory (United States)
2004-11-15
The variance in Monte Carlo particle transport calculations is often dominated by a few particles whose importance increases manyfold on a single transport step. This paper describes a novel variance reduction method that uses a large importance change as a trigger to resample the offending transport step. That is, the method is employed only after (ex post facto) a random walk attempts a transport step that would otherwise introduce a large variance in the calculation.Improvements in two Monte Carlo transport calculations are demonstrated empirically using an ex post facto method. First, the method is shown to reduce the variance in a penetration problem with a cross-section window. Second, the method empirically appears to modify a point detector estimator from an infinite variance estimator to a finite variance estimator.
Status of Monte Carlo at Los Alamos
Thompson, W.L.; Cashwell, E.D.; Godfrey, T.N.K.; Schrandt, R.G.; Deutsch, O.L.; Booth, T.E.
1980-05-01
Four papers were presented by Group X-6 on April 22, 1980, at the Oak Ridge Radiation Shielding Information Center (RSIC) Seminar-Workshop on Theory and Applications of Monte Carlo Methods. These papers are combined into one report for convenience and because they are related to each other. The first paper (by Thompson and Cashwell) is a general survey about X-6 and MCNP and is an introduction to the other three papers. It can also serve as a resume of X-6. The second paper (by Godfrey) explains some of the details of geometry specification in MCNP. The third paper (by Cashwell and Schrandt) illustrates calculating flux at a point with MCNP; in particular, the once-more-collided flux estimator is demonstrated. Finally, the fourth paper (by Thompson, Deutsch, and Booth) is a tutorial on some variance-reduction techniques. It should be required for a fledging Monte Carlo practitioner.
Monte Carlo methods for pricing financial options
N. Bolia; S. Juneja
2005-01-01
Pricing financial options is amongst the most important and challenging problems in the modern financial industry. Except\\u000a in the simplest cases, the prices of options do not have a simple closed form solution and efficient computational methods\\u000a are needed to determine them. Monte Carlo methods have increasingly become a popular computational tool to price complex financial\\u000a options, especially when the
Monte Carlo simulations of supported bimetallic catalysts
J. K. Strohl; T. S. King
1989-01-01
Supported bimetallic catalysts are modeled with a Monte Carlo simulation technique that uses a coordination-dependent potential model. Cubo-octahedral particles with dispersions ranging from 30 to 60% are studied as well as particles that have irregular shapes. Systems modeled include the Pt-Ib (Ib = Cu, Ag, Au), Ag-Ru, and Pt-Rh bimetallics. In the Pt-Ib systems, the Ib element segregates to the
Inhomogeneous Monte Carlo simulations of dermoscopic spectroscopy
NASA Astrophysics Data System (ADS)
Gareau, Daniel S.; Li, Ting; Jacques, Steven; Krueger, James
2012-03-01
Clinical skin-lesion diagnosis uses dermoscopy: 10X epiluminescence microscopy. Skin appearance ranges from black to white with shades of blue, red, gray and orange. Color is an important diagnostic criteria for diseases including melanoma. Melanin and blood content and distribution impact the diffuse spectral remittance (300-1000nm). Skin layers: immersion medium, stratum corneum, spinous epidermis, basal epidermis and dermis as well as laterally asymmetric features (eg. melanocytic invasion) were modeled in an inhomogeneous Monte Carlo model.
Topological Zero Modes in Monte Carlo Simulations
Dilger, H
2015-01-01
We present an improvement of global Metropolis updating steps, the instanton hits, used in a hybrid Monte Carlo simulation of the two-flavor Schwinger model with staggered fermions. These hits are designed to change the topological sector of the gauge field. In order to match these hits to an unquenched simulation with pseudofermions, the approximate zero mode structure of the lattice Dirac operator has to be considered explicitly.
Monte-Carlo simulations of proton aurora
S. a. Synnes; F. Søraas; J. P. Hansen
1998-01-01
The spreading of a proton beam in the upper atmosphere is calculated based onMonte-Carlo simulations. The transport of the atoms is modelled in a magnetic field with dipolestrength. Neuralisation, ionisation and excitation mechanisms of the incoming particles areincluded from collision cross-sections of protons and hydrogen with an effective N2atmosphere. Assuming an isotropic pitch angle distribution for the incoming protons, theirspreading
Applications of Maxent to quantum Monte Carlo
Silver, R.N.; Sivia, D.S.; Gubernatis, J.E. (Los Alamos National Lab., NM (USA)); Jarrell, M. (Ohio State Univ., Columbus, OH (USA). Dept. of Physics)
1990-01-01
We consider the application of maximum entropy methods to the analysis of data produced by computer simulations. The focus is the calculation of the dynamical properties of quantum many-body systems by Monte Carlo methods, which is termed the Analytical Continuation Problem.'' For the Anderson model of dilute magnetic impurities in metals, we obtain spectral functions and transport coefficients which obey Kondo Universality.'' 24 refs., 7 figs.
Monte-Carlo Tree Search Solver
Mark H. M. Winands; Yngvi Björnsson; Jahn-takeshi Saito
2008-01-01
Recently, Monte-Carlo Tree Search (MCTS) has advanced the fleld of computer Go substantially. In this article we investigate the application of MCTS for the game Lines of Action (LOA). A new MCTS variant, called MCTS-Solver, has been designed to play narrow tacti- cal lines better in sudden-death games such as LOA. The variant difiers from the traditional MCTS in respect
Linear-scaling quantum Monte Carlo calculations.
Williamson, A J; Hood, R Q; Grossman, J C
2001-12-10
A method is presented for using truncated, maximally localized Wannier functions to introduce sparsity into the Slater determinant part of the trial wave function in quantum Monte Carlo calculations. When combined with an efficient numerical evaluation of these localized orbitals, the dominant cost in the calculation, namely, the evaluation of the Slater determinant, scales linearly with system size. This technique is applied to accurate total energy calculation of hydrogenated silicon clusters and carbon fullerenes containing 20-1000 valence electrons. PMID:11736525
Hybrid Radiosity\\/Monte Carlo Methods
Peter Shirley
1994-01-01
this document said that absorb and reemit wasasymptotically equivalent to the photon tracking model.8 Hybrid Radiosity\\/Monte Carlo MethodsRadiositySolutionGather fromsolution for smallarea zonesFinal (corrected)solutionFigure 4: Zones with small areas have their radiance recalculated more accurately in a postprocess.iteration (each ray carries approximately the same amount of power). The other is that, unlike in[7], the zone with the most power is not
Monte Carlo simulations of nonclassical nucleation
L. Monette; W. Klein; M. Zuckermann; A. Khadir; R. Harris
1988-01-01
We report results of Monte Carlo simulations of Ising-like systems with long-range interactions undergoing nucleation and growth near the classical spinodal. The simulations were performed in two dimensions with use of the Creutz algorithm. Results were obtained which differ significantly from those found for systems with short-range interactions. However, they are consistent with the theoretical predictions for nucleation in long-range-interaction
Monte-Carlo\\/PIC Simulations in VASIMR
A. V. Ilin; F. R. Chang Díaz; J. P. Squire; M. D. Carter; A. A. Chan
1998-01-01
The reported Monte-Carlo\\/Particle-In-Cell simulations in a Variable Specific Impulse Magnetoplasma Rocket (VASIMR) include: 1) Magnetostatic computation of initial magnetic fields, 2) Self-consistent plasma - electric field - magnetic field modeling, 3) Ion-Cyclotron Radio-Frequency heating, 4) Implementation of collision, radiation, scattering. Of particular importance is the effect of a magnetic nozzle in enhancing the axial momentum of the exhaust. The magnetic
Monte Carlo Simulations of Ultrathin Magnetic Dots
M. Rapini; R. A. Dias; D. P. Landau; B. V. Costa
2006-04-10
In this work we study the thermodynamic properties of ultrathin ferromagnetic dots using Monte Carlo simulations. We investigate the vortex density as a function of the temperature and the vortex structure in monolayer dots with perpendicular anisotropy and long-range dipole interaction. The interplay between these two terms in the hamiltonian leads to an interesting behavior of the thermodynamic quantities as well as the vortex density.
Monte Carlo simulation of ice models
Barkema, G.T. [HLRZ, Forschungszentrum Juelich, 52425 Juelich (Germany)] [HLRZ, Forschungszentrum Juelich, 52425 Juelich (Germany); Newman, M.E. [Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501 (United States)] [Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501 (United States)
1998-01-01
We study a number of Monte Carlo algorithms for the simulation of ice models, and compare their efficiency. One of them, a cluster algorithm for the equivalent three-color model, appears to have a dynamic exponent close to zero, making it particularly useful for simulations of critical ice models. We have performed extensive simulations using our algorithms to determine a number of critical exponents for the square ice and F models. {copyright} {ital 1998} {ital The American Physical Society}
Monte Carlo simulation of Touschek effect.
Xiao, A.; Borland, M.; Accelerator Systems Division (APS)
2010-07-30
We present a Monte Carlo method implementation in the code elegant for simulating Touschek scattering effects in a linac beam. The local scattering rate and the distribution of scattered electrons can be obtained from the code either for a Gaussian-distributed beam or for a general beam whose distribution function is given. In addition, scattered electrons can be tracked through the beam line and the local beam-loss rate and beam halo information recorded.
A Ballistic Monte Carlo Approximation of {\\pi}
Dumoulin, Vincent
2014-01-01
We compute a Monte Carlo approximation of {\\pi} using importance sampling with shots coming out of a Mossberg 500 pump-action shotgun as the proposal distribution. An approximated value of 3.136 is obtained, corresponding to a 0.17% error on the exact value of {\\pi}. To our knowledge, this represents the first attempt at estimating {\\pi} using such method, thus opening up new perspectives towards computing mathematical constants using everyday tools.
Path Integral Monte Carlo Methods for Fermions
NASA Astrophysics Data System (ADS)
Ethan, Ethan; Dubois, Jonathan; Ceperley, David
2014-03-01
In general, Quantum Monte Carlo methods suffer from a sign problem when simulating fermionic systems. This causes the efficiency of a simulation to decrease exponentially with the number of particles and inverse temperature. To circumvent this issue, a nodal constraint is often implemented, restricting the Monte Carlo procedure from sampling paths that cause the many-body density matrix to change sign. Unfortunately, this high-dimensional nodal surface is not a priori known unless the system is exactly solvable, resulting in uncontrolled errors. We will discuss two possible routes to extend the applicability of finite-temperatue path integral Monte Carlo. First we extend the regime where signful simulations are possible through a novel permutation sampling scheme. Afterwards, we discuss a method to variationally improve the nodal surface by minimizing a free energy during simulation. Applications of these methods will include both free and interacting electron gases, concluding with discussion concerning extension to inhomogeneous systems. Support from DOE DE-FG52-09NA29456, DE-AC52-07NA27344, LLNL LDRD 10- ERD-058, and the Lawrence Scholar program.
An introduction to Monte Carlo methods
NASA Astrophysics Data System (ADS)
Walter, J.-C.; Barkema, G. T.
2015-01-01
Monte Carlo simulations are methods for simulating statistical systems. The aim is to generate a representative ensemble of configurations to access thermodynamical quantities without the need to solve the system analytically or to perform an exact enumeration. The main principles of Monte Carlo simulations are ergodicity and detailed balance. The Ising model is a lattice spin system with nearest neighbor interactions that is appropriate to illustrate different examples of Monte Carlo simulations. It displays a second order phase transition between disordered (high temperature) and ordered (low temperature) phases, leading to different strategies of simulations. The Metropolis algorithm and the Glauber dynamics are efficient at high temperature. Close to the critical temperature, where the spins display long range correlations, cluster algorithms are more efficient. We introduce the rejection free (or continuous time) algorithm and describe in details an interesting alternative representation of the Ising model using graphs instead of spins with the so-called Worm algorithm. We conclude with an important discussion of the dynamical effects such as thermalization and correlation time.
Numerical reproducibility for implicit Monte Carlo simulations
Cleveland, M.; Brunner, T.; Gentile, N. [Lawrence Livermore National Laboratory, P. O. Box 808, Livermore CA 94550 (United States)
2013-07-01
We describe and compare different approaches for achieving numerical reproducibility in photon Monte Carlo simulations. Reproducibility is desirable for code verification, testing, and debugging. Parallelism creates a unique problem for achieving reproducibility in Monte Carlo simulations because it changes the order in which values are summed. This is a numerical problem because double precision arithmetic is not associative. In [1], a way of eliminating this roundoff error using integer tallies was described. This approach successfully achieves reproducibility at the cost of lost accuracy by rounding double precision numbers to fewer significant digits. This integer approach, and other extended reproducibility techniques, are described and compared in this work. Increased precision alone is not enough to ensure reproducibility of photon Monte Carlo simulations. A non-arbitrary precision approaches required a varying degree of rounding to achieve reproducibility. For the problems investigated in this work double precision global accuracy was achievable by using 100 bits of precision or greater on all unordered sums which where subsequently rounded to double precision at the end of every time-step. (authors)
NASA Astrophysics Data System (ADS)
Xu, Zuwei; Zhao, Haibo; Zheng, Chuguang
2015-01-01
This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance-rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are demonstrated in a physically realistic Brownian coagulation case. The computational accuracy is validated with benchmark solution of discrete-sectional method. The simulation results show that the comprehensive approach can attain very favorable improvement in cost without sacrificing computational accuracy.
Filippone, W.L.; Baker, R.S. [Arizona Univ., Tucson, AZ (United States)
1990-12-31
The neutron transport equation is solved by a hybrid method that iteratively couples regions where deterministic (S{sub N}) and stochastic (Monte Carlo) methods are applied. Unlike previous hybrid methods, the Monte Carlo and S{sub N} regions are fully coupled in the sense that no assumption is made about geometrical separation or decoupling. The hybrid method provides a new means of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor S{sub N} is well suited for by themselves. The fully coupled Monte Carlo/S{sub N} technique consists of defining spatial and/or energy regions of a problem in which either a Monte Carlo calculation or an S{sub N} calculation is to be performed. The Monte Carlo region may comprise the entire spatial region for selected energy groups, or may consist of a rectangular area that is either completely or partially embedded in an arbitrary S{sub N} region. The Monte Carlo and S{sub N} regions are then connected through the common angular boundary fluxes, which are determined iteratively using the response matrix technique, and volumetric sources. The hybrid method has been implemented in the S{sub N} code TWODANT by adding special-purpose Monte Carlo subroutines to calculate the response matrices and volumetric sources, and linkage subrountines to carry out the interface flux iterations. The common angular boundary fluxes are included in the S{sub N} code as interior boundary sources, leaving the logic for the solution of the transport flux unchanged, while, with minor modifications, the diffusion synthetic accelerator remains effective in accelerating S{sub N} calculations. The special-purpose Monte Carlo routines used are essentially analog, with few variance reduction techniques employed. However, the routines have been successfully vectorized, with approximately a factor of five increase in speed over the non-vectorized version.
Replica exchange with Smart Monte Carlo and Hybrid Monte Carlo in manifolds
NASA Astrophysics Data System (ADS)
Jenkins, R.; Curotto, E.; Mella, Massimo
2013-12-01
Several Smart Monte Carlo (SMC) and Hybrid Monte Carlo (HMC) simulations coupled with the Replica Exchange (RE) strategy are compared in multidimensional flat and curved manifolds characterized by extremely rugged potential energy surfaces, to quantify their convergence properties with respect to walk length and overall cost. We learn that the HMC coupled with a sampling enhancing method is much more efficient in manifolds mapped with unconventional coordinates than SMC. This is due to an inherent difficulty in conserving energy in curved spaces directly mapped, and the lack of such strict requirement for HMC.
Recent developments in quantum Monte Carlo methods for electronic structure of atomic clusters
Lubos Mitas
2004-01-01
Recent developments of quantum Monte Carlo (QMC) for electronic structure calculations of clusters, other nanomaterials and quantum systems will be reviewed. QMC methodology is based on a combination of analytical insights about properties of exact wavefunctions, explicit treatment of electron-electron correlation and robustness of computational stochastic techniques. In the course of QMC development for calculations of real materials, small and
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Mark Jerrum; Alistair Sinclair
1996-01-01
In the area of statistical physics, Monte Carlo algorithms based on Markov chain simulation have been in use for many years. The validity of these algorithms depends cru- cially on the rate of convergence to equilibrium of the Markov chain being simulated. Unfortunately, the classical theory of stochastic processes hardly touches on the sort of non-asymptotic analysis required in this
Sabelfeld, Karl
2015-01-01
A stochastic algorithm for simulation of fluctuation-induced kinetics of H$_2$ formation on grain surfaces is suggested as a generalization of the technique developed in our recent studies where this method was developed to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. The stochastic model is based on the spatially inhomogeneous, nonlinear integro-differential Smoluchowski equations with random source term. In this paper we derive the general system of Smoluchowski type equations for the formation of H$_2$ from two hydrogen atoms on the surface of interstellar dust grains with physisorption and chemisorption sites. We focus in this study on the spatial distribution, and numerically investigate the segregation in the case of a source with a continuous generation in time and randomly distributed in space. The stochastic particle method presented is based on a probabilistic interpretation of the underlying process as a stochastic Markov process of interacting ...
Status of Monte-Carlo Event Generators
Hoeche, Stefan; /SLAC
2011-08-11
Recent progress on general-purpose Monte-Carlo event generators is reviewed with emphasis on the simulation of hard QCD processes and subsequent parton cascades. Describing full final states of high-energy particle collisions in contemporary experiments is an intricate task. Hundreds of particles are typically produced, and the reactions involve both large and small momentum transfer. The high-dimensional phase space makes an exact solution of the problem impossible. Instead, one typically resorts to regarding events as factorized into different steps, ordered descending in the mass scales or invariant momentum transfers which are involved. In this picture, a hard interaction, described through fixed-order perturbation theory, is followed by multiple Bremsstrahlung emissions off initial- and final-state and, finally, by the hadronization process, which binds QCD partons into color-neutral hadrons. Each of these steps can be treated independently, which is the basic concept inherent to general-purpose event generators. Their development is nowadays often focused on an improved description of radiative corrections to hard processes through perturbative QCD. In this context, the concept of jets is introduced, which allows to relate sprays of hadronic particles in detectors to the partons in perturbation theory. In this talk, we briefly review recent progress on perturbative QCD in event generation. The main focus lies on the general-purpose Monte-Carlo programs HERWIG, PYTHIA and SHERPA, which will be the workhorses for LHC phenomenology. A detailed description of the physics models included in these generators can be found in [8]. We also discuss matrix-element generators, which provide the parton-level input for general-purpose Monte Carlo.
Discrete diffusion Monte Carlo for frequency-dependent radiative transfer
Densmore, Jeffrey D [Los Alamos National Laboratory; Kelly, Thompson G [Los Alamos National Laboratory; Urbatish, Todd J [Los Alamos National Laboratory
2010-11-17
Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations. In this paper, we develop an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold. Above this threshold we employ standard Monte Carlo. With a frequency-dependent test problem, we confirm the increased efficiency of our new DDMC technique.
MECA: a multiprocessor concept specialized to Monte Carlo
Solem, J.C.
1985-01-01
Discrete-ordinates and Monte Carlo techniques are compared for solving integrodifferential equations and compare their relative adaptability to vector processors. The author discusses the utility of multiprocessors for Monte Carlo calculations and describes a simple architecture (the monodirectional edge-coupled array or MECA) that seems ideally suited to Monte Carlo and overcomes many of the packaging problems associated with more general multiprocessors. 18 refs., 3 figs., 1 tab.
A Monte Carlo algorithm for degenerate plasmas
Turrell, A.E., E-mail: a.turrell09@imperial.ac.uk; Sherlock, M.; Rose, S.J.
2013-09-15
A procedure for performing Monte Carlo calculations of plasmas with an arbitrary level of degeneracy is outlined. It has possible applications in inertial confinement fusion and astrophysics. Degenerate particles are initialised according to the Fermi–Dirac distribution function, and scattering is via a Pauli blocked binary collision approximation. The algorithm is tested against degenerate electron–ion equilibration, and the degenerate resistivity transport coefficient from unmagnetised first order transport theory. The code is applied to the cold fuel shell and alpha particle equilibration problem of inertial confinement fusion.
Spectral functions from Quantum Monte Carlo
Silver, R.N.
1989-01-01
In his review, D. Scalapino identified two serious limitations on the application of Quantum Monte Carlo (QMC) methods to the models of interest in High {Tc} Superconductivity (HTS). One is the sign problem''. The other is the analytic continuation problem'', which is how to extract electron spectral functions from QMC calculations of the imaginary time Green's functions. Through-out this Symposium on HTS, the spectral functions have been the focus for the discussion of normal state properties including the applicability of band theory, Fermi liquid theory, marginal Fermi liquids, and novel non-perturbative states. 5 refs., 1 fig.
Variance minimization variational Monte Carlo method
Khan, I; Gao, Bo; Khan, Imran
2007-01-01
We present a variational Monte Carlo (VMC) method that works equally well for the ground and the excited states of a quantum system. The method is based on the minimization of the variance of energy, as opposed to the energy itself in standard methods. As a test, it is applied to the investigation of the universal spectrum at the van der Waals length scale for two identical Bose atoms in a symmetric harmonic trap, with results compared to the basically exact results obtained from a multiscale quantum-defect theory.
Monte Carlo simulation for the transport beamline
Romano, F.; Cuttone, G.; Jia, S. B.; Varisano, A. [INFN, Laboratori Nazionali del Sud, Via Santa Sofia 62, Catania (Italy)] [INFN, Laboratori Nazionali del Sud, Via Santa Sofia 62, Catania (Italy); Attili, A.; Marchetto, F.; Russo, G. [INFN, Sezione di Torino, Via P.Giuria, 1 10125 Torino (Italy)] [INFN, Sezione di Torino, Via P.Giuria, 1 10125 Torino (Italy); Cirrone, G. A. P.; Schillaci, F.; Scuderi, V. [INFN, Laboratori Nazionali del Sud, Via Santa Sofia 62, Catania, Italy and Institute of Physics Czech Academy of Science, ELI-Beamlines project, Na Slovance 2, Prague (Czech Republic)] [INFN, Laboratori Nazionali del Sud, Via Santa Sofia 62, Catania, Italy and Institute of Physics Czech Academy of Science, ELI-Beamlines project, Na Slovance 2, Prague (Czech Republic); Carpinelli, M. [INFN Sezione di Cagliari, c/o Dipartimento di Fisica, Università di Cagliari, Cagliari (Italy)] [INFN Sezione di Cagliari, c/o Dipartimento di Fisica, Università di Cagliari, Cagliari (Italy); Tramontana, A. [INFN, Laboratori Nazionali del Sud, Via Santa Sofia 62, Catania, Italy and Università di Catania, Dipartimento di Fisica e Astronomia, Via S. Sofia 64, Catania (Italy)] [INFN, Laboratori Nazionali del Sud, Via Santa Sofia 62, Catania, Italy and Università di Catania, Dipartimento di Fisica e Astronomia, Via S. Sofia 64, Catania (Italy)
2013-07-26
In the framework of the ELIMED project, Monte Carlo (MC) simulations are widely used to study the physical transport of charged particles generated by laser-target interactions and to preliminarily evaluate fluence and dose distributions. An energy selection system and the experimental setup for the TARANIS laser facility in Belfast (UK) have been already simulated with the GEANT4 (GEometry ANd Tracking) MC toolkit. Preliminary results are reported here. Future developments are planned to implement a MC based 3D treatment planning in order to optimize shots number and dose delivery.
Monte Carlo methods to calculate impact probabilities
NASA Astrophysics Data System (ADS)
Rickman, H.; Wi?niowski, T.; Wajer, P.; Gabryszewski, R.; Valsecchi, G. B.
2014-09-01
Context. Unraveling the events that took place in the solar system during the period known as the late heavy bombardment requires the interpretation of the cratered surfaces of the Moon and terrestrial planets. This, in turn, requires good estimates of the statistical impact probabilities for different source populations of projectiles, a subject that has received relatively little attention, since the works of Öpik (1951, Proc. R. Irish Acad. Sect. A, 54, 165) and Wetherill (1967, J. Geophys. Res., 72, 2429). Aims: We aim to work around the limitations of the Öpik and Wetherill formulae, which are caused by singularities due to zero denominators under special circumstances. Using modern computers, it is possible to make good estimates of impact probabilities by means of Monte Carlo simulations, and in this work, we explore the available options. Methods: We describe three basic methods to derive the average impact probability for a projectile with a given semi-major axis, eccentricity, and inclination with respect to a target planet on an elliptic orbit. One is a numerical averaging of the Wetherill formula; the next is a Monte Carlo super-sizing method using the target's Hill sphere. The third uses extensive minimum orbit intersection distance (MOID) calculations for a Monte Carlo sampling of potentially impacting orbits, along with calculations of the relevant interval for the timing of the encounter allowing collision. Numerical experiments are carried out for an intercomparison of the methods and to scrutinize their behavior near the singularities (zero relative inclination and equal perihelion distances). Results: We find an excellent agreement between all methods in the general case, while there appear large differences in the immediate vicinity of the singularities. With respect to the MOID method, which is the only one that does not involve simplifying assumptions and approximations, the Wetherill averaging impact probability departs by diverging toward infinity, while the Hill sphere method results in a severely underestimated probability. We provide a discussion of the reasons for these differences, and we finally present the results of the MOID method in the form of probability maps for the Earth and Mars on their current orbits. These maps show a relatively flat probability distribution, except for the occurrence of two ridges found at small inclinations and for coinciding projectile/target perihelion distances. Conclusions: Our results verify the standard formulae in the general case, away from the singularities. In fact, severe shortcomings are limited to the immediate vicinity of those extreme orbits. On the other hand, the new Monte Carlo methods can be used without excessive consumption of computer time, and the MOID method avoids the problems associated with the other methods. Appendices are available in electronic form at http://www.aanda.org
Diffusion quantum Monte Carlo for molecules
Lester, W.A. Jr.
1986-07-01
A quantum mechanical Monte Carlo method has been used for the treatment of molecular problems. The imaginary-time Schroedinger equation written with a shift in zero energy (E/sub T/ - V(R)) can be interpreted as a generalized diffusion equation with a position-dependent rate or branching term. Since diffusion is the continuum limit of a random walk, one may simulate the Schroedinger equation with a function psi (note, not psi/sup 2/) as a density of ''walks.'' The walks undergo an exponential birth and death as given by the rate term. 16 refs., 2 tabs.
Monte Carlo errors with less errors
NASA Astrophysics Data System (ADS)
Wolff, Ulli; Alpha Collaboration
2004-01-01
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is argued to produce more certain error estimates than binning techniques and hence to help toward a better exploitation of expensive simulations. An effective integrated autocorrelation time is computed which is suitable to benchmark efficiencies of simulation algorithms with regard to specific observables of interest. A Matlab code is offered for download that implements the method. It can also combine independent runs (replica) allowing to judge their consistency.
Monte Carlo study of disorder in HMTA
NASA Astrophysics Data System (ADS)
Goossens, D. J.; Welberry, T. R.
2001-12-01
We investigate disordered solids by automated fitting of a Monte Carlo simulation of a crystal to observed single-crystal diffuse X-ray scattering. This method has been extended to the study of crystals of relatively large organic molecules by using a z-matrix to describe the molecules. This allows exploration of motions within molecules. We refer to the correlated thermal motion observed in benzil, and to the occupational and thermal disorder in the 1:1 adduct of hexamethylenetetramine and azelaic acid, HMTA. The technique is capable of giving insight into modes of vibration within molecules and correlated motions between molecules.
Monte Carlo simulation of the enantioseparation process
NASA Astrophysics Data System (ADS)
Bustos, V. A.; Acosta, G.; Gomez, M. R.; Pereyra, V. D.
2012-09-01
By means of Monte Carlo simulation, a study of enantioseparation by capillary electrophoresis has been carried out. A simplified system consisting of two enantiomers S (R) and a selector chiral C, which reacts with the enantiomers to form complexes RC (SC), has been considered. The dependence of ?? (enantioseparation) with the concentration of chiral selector and with temperature have been analyzed by simulation. The effect of the binding constant and the charge of the complexes are also analyzed. The results are qualitatively satisfactory, despite the simplicity of the model.
Monte Carlo radiation transport¶llelism
Cox, L. J. (Lawrence J.); Post, S. E. (Susan E.)
2002-01-01
This talk summarizes the main aspects of the LANL ASCI Eolus project and its major unclassified code project, MCNP. The MCNP code provide a state-of-the-art Monte Carlo radiation transport to approximately 3000 users world-wide. Almost all hardware platforms are supported because we strictly adhere to the FORTRAN-90/95 standard. For parallel processing, MCNP uses a mixture of OpenMp combined with either MPI or PVM (shared and distributed memory). This talk summarizes our experiences on various platforms using MPI with and without OpenMP. These platforms include PC-Windows, Intel-LINUX, BlueMountain, Frost, ASCI-Q and others.
Marcus, Ryan C. [Los Alamos National Laboratory
2012-07-24
Overview of this presentation is (1) Exascale computing - different technologies, getting there; (2) high-performance proof-of-concept MCMini - features and results; and (3) OpenCL toolkit - Oatmeal (OpenCL Automatic Memory Allocation Library) - purpose and features. Despite driver issues, OpenCL seems like a good, hardware agnostic tool. MCMini demonstrates the possibility for GPGPU-based Monte Carlo methods - it shows great scaling for HPC application and algorithmic equivalence. Oatmeal provides a flexible framework to aid in the development of scientific OpenCL codes.
MBR Monte Carlo Simulation in PYTHIA8
R. Ciesielski; K. Goulianos
2012-08-06
We present the MBR (Minimum Bias Rockefeller) Monte Carlo simulation of (anti)proton-proton interactions and its implementation in the PYTHIA8 event generator. We discuss the total, elastic, and total-inelastic cross sections, and three contributions from diffraction dissociation processes that contribute to the latter: single diffraction, double diffraction, and central diffraction or double-Pomeron exchange. The event generation follows a renormalized-Regge-theory model, successfully tested using CDF data. Based on the MBR-enhanced PYTHIA8 simulation, we present cross-section predictions for the LHC and beyond, up to collision energies of 50 TeV.
Monte Carlo Generation of Bohmian Trajectories
T. M. Coffey; R. E. Wyatt; W. C. Schieve
2008-07-01
We report on a Monte Carlo method that generates one-dimensional trajectories for Bohm's formulation of quantum mechanics that doesn't involve differentiation or integration of any equations of motion. At each time, t=n\\delta t (n=1,2,3,...), N particle positions are randomly sampled from the quantum probability density. Trajectories are built from the sorted N sampled positions at each time. These trajectories become the exact Bohm solutions in the limits N->\\infty and \\delta t -> 0. Higher dimensional problems can be solved by this method for separable wave functions. Several examples are given, including the two-slit experiment.
Introduction to Cluster Monte Carlo Algorithms
NASA Astrophysics Data System (ADS)
Luijten, E.
This chapter provides an introduction to cluster Monte Carlo algorithms for classical statistical-mechanical systems. A brief review of the conventional Metropolis algorithm is given, followed by a detailed discussion of the lattice cluster algorithm developed by Swendsen and Wang and the single-cluster variant introduced by Wolff. For continuum systems, the geometric cluster algorithm of Dress and Krauth is described. It is shown how their geometric approach can be generalized to incorporate particle interactions beyond hardcore repulsions, thus forging a connection between the lattice and continuum approaches. Several illustrative examples are discussed.
Ming-hua Hsieh
2002-01-01
We review two types of adaptive Monte Carlo methods for rare event simulations. These methods are based on importance sampling. The first approach selects importance sampling distributions by minimizing the variance of importance sampling estimator. The second approach selects importance sampling distributions by minimizing the cross entropy to the optimal importance sampling distribution. We also review the basic concepts of
Quantum Monte Carlo methods for nuclear physics
Carlson, Joseph A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gandolfi, Stefano [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Pederiva, Francesco [Univ. of Trento (Italy); Pieper, Steven C. [Argonne National Lab. (ANL), Argonne, IL (United States); Schiavilla, Rocco [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States); Schmidt, K. E, [Arizona State Univ., Tempe, AZ (United States); Wiringa, Robert B. [Argonne National Lab. (ANL), Argonne, IL (United States)
2012-01-01
Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.
High performance computing&Monte Carlo
Brown, F. B. (Forrest B.); Martin, W. R. (William R.)
2004-01-01
High performance computing (HPC), used for the most demanding computational problems, has evolved from single processor custom systems in the 1960s and 1970s, to vector processors in the 1980s, to parallel processors in the 1990s, to clusters of commodity processors in the 2000s. Performance/price has increased by a factor of more than I million over that time, so that today's desktop PC is more powerful than yesterday's supercomputer. With the introduction of inexpensive Linux clusters and the standardization of parallel software through MPI and OpenMP, parallel computing is now widespread and available to everyone. Monte Carlo codes for particle transport are especially well-positioned to take advantage of accessible parallel computing, due to the inherently parallel nature of the computational algorithm. We review Monte Carlo particle parallelism, including the basic algorithm, load-balancing, fault tolerance, and scaling, using MCNP5 as an example. Due to memory limitations, especially on single nodes of Linux clusters, domain decomposition has been tried, with partial success. We conclude with a new scheme, data decomposition, which holds promise for very large problems.
Geometrical Monte Carlo simulation of atmospheric turbulence
NASA Astrophysics Data System (ADS)
Yuksel, Demet; Yuksel, Heba
2013-09-01
Atmospheric turbulence has a significant impact on the quality of a laser beam propagating through the atmosphere over long distances. Turbulence causes intensity scintillation and beam wander from propagation through turbulent eddies of varying sizes and refractive index. This can severely impair the operation of target designation and Free-Space Optical (FSO) communications systems. In addition, experimenting on an FSO communication system is rather tedious and difficult. The interferences of plentiful elements affect the result and cause the experimental outcomes to have bigger error variance margins than they are supposed to have. Especially when we go into the stronger turbulence regimes the simulation and analysis of the turbulence induced beams require delicate attention. We propose a new geometrical model to assess the phase shift of a laser beam propagating through turbulence. The atmosphere along the laser beam propagation path will be modeled as a spatial distribution of spherical bubbles with refractive index discontinuity calculated from a Gaussian distribution with the mean value being the index of air. For each statistical representation of the atmosphere, the path of rays will be analyzed using geometrical optics. These Monte Carlo techniques will assess the phase shift as a summation of the phases that arrive at the same point at the receiver. Accordingly, there would be dark and bright spots at the receiver that give an idea regarding the intensity pattern without having to solve the wave equation. The Monte Carlo analysis will be compared with the predictions of wave theory.
Enhanced Neoclassical Polarization: Monte Carlo Simulation
NASA Astrophysics Data System (ADS)
Xiao, Yong; Molvig, Kim; Ernst, Darin; Hallatschek, Klaus
2003-10-01
The theoretical prediction of enhanced neoclassical polarization (K. Molvig, Yong Xiao, D. R. Ernst, K. Hallatschek, Sherwood Fusion Theory Conference, 2003.) in a tokamak plasma is investigated numerically using a Monte Carlo approach to combine the effects of collisions with guiding center tokamak orbits. The collisionless, kinematic contribution to the polarization first calculated by Rosenbluth and Hinton (M.N. Rosenbluth and F.L. Hinton, Phys. Rev. Lett. 80), 724 (1998). is reproduced from the orbits directly. A fifth order Runge-Kutta orbit integrator is used to give extremely high orbit accuracy. The cancellation of opposite trapped and circulating particle radial flows is verified explicitly in this simulation. The Monte Carlo representation of pitch angle scattering collisions (X.Q. Xu and M.N. Rosenbluth, Phys. Fluids B 3), 627 (1991) is used to compute the collisional processes. The numerical simulation determines the generalized Fokker-Planck coefficients used as the basis for transport in the Lagrangian formulation (I.B. Bernstein and K. Molvig, Phys. Fluids, 26), 1488 (1983). of transport theory. The computation generates the banana diffusion coefficient, < ? ? ^2/? t>, and the correlated cross process, < ? ? ? ? /? t>, responsible for the enhanced polarization. The numerical procedure generates smooth coefficients and resolves the analytic singularity that occurs at the trapped-circulating boundary.
Quantum Monte Carlo methods for nuclear physics
J. Carlson; S. Gandolfi; F. Pederiva; Steven C. Pieper; R. Schiavilla; K. E. Schmidt; R. B. Wiringa
2015-04-29
Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.
Monte Carlo radiative transfer in protoplanetary disks
Christophe Pinte; Francois Menard; Gaspard Duchene; Pierre Bastien
2006-06-22
We present a new continuum 3D radiative transfer code, MCFOST, based on a Monte-Carlo method. MCFOST can be used to calculate (i) monochromatic images in scattered light and/or thermal emission, (ii) polarisation maps, (iii) interferometric visibilities, (iv) spectral energy distributions and (v) dust temperature distributions of protoplanetary disks. Several improvements to the standard Monte Carlo method are implemented in MCFOST to increase efficiency and reduce convergence time, including wavelength distribution adjustments, mean intensity calculations and an adaptive sampling of the radiation field. The reliability and efficiency of the code are tested against a previously defined benchmark, using a 2D disk configuration. No significant difference (no more than 10%, and generally much less) is found between the temperatures and SEDs calculated by MCFOST and by other codes included in the benchmark. A study of the lowest disk mass detectable by Spitzer, around young stars, is presented and the colours of ``representative'' parametric disks are compared to recent IRAC and MIPS Spitzer colours of solar-like young stars located in nearby star forming regions.
Reverse Monte Carlo modeling in confined systems
Sánchez-Gil, V.; Noya, E. G.; Lomba, E. [Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid (Spain)] [Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid (Spain)
2014-01-14
An extension of the well established Reverse Monte Carlo (RMC) method for modeling systems under close confinement has been developed. The method overcomes limitations induced by close confinement in systems such as fluids adsorbed in microporous materials. As a test of the method, we investigate a model system of {sup 36}Ar adsorbed into two zeolites with significantly different pore sizes: Silicalite-I (a pure silica form of ZSM-5 zeolite, characterized by relatively narrow channels forming a 3D network) at partial and full loadings and siliceous Faujasite (which exhibits relatively wide channels and large cavities). The model systems are simulated using grand canonical Monte Carlo and, in each case, its structure factor is used as input for the proposed method, which shows a rapid convergence and yields an adsorbate microscopic structure in good agreement with that of the model system, even to the level of three body correlations, when these are induced by the confining media. The application to experimental systems is straightforward incorporating factors such as the experimental resolution and appropriate q-sampling, along the lines of previous experiences of RMC modeling of powder diffraction data including Bragg and diffuse scattering.
Quantum Monte Carlo methods for nuclear physics
Carlson, Joseph A.; Gandolfi, Stefano; Pederiva, Francesco; Pieper, Steven C.; Schiavilla, Rocco; Schmidt, K. E,; Wiringa, Robert B.
2012-01-01
Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-bodymore »interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.« less
Quantum Monte Carlo methods for nuclear physics
Carlson, Joseph A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gandolfi, Stefano [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Pederiva, Francesco [Univ. of Trento (Italy); Pieper, Steven C. [Argonne National Lab. (ANL), Argonne, IL (United States); Schiavilla, Rocco [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States); Schmidt, K. E, [Arizona State Univ., Tempe, AZ (United States); Wiringa, Robert B. [Argonne National Lab. (ANL), Argonne, IL (United States)
2012-01-01
Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.
Monte Carlo parameter studies and uncertainty analyses with MCNP5
Brown, F. B. (Forrest B.); Sweezy, J. E. (Jeremy E.); Hayes, R. B. (Robert B.)
2004-01-01
A software tool called mcnp-pstudy has been developed to automate the setup, execution, and collection of results from a series of MCNPS Monte Carlo calculations. This tool provides a convenient means of performing parameter studies, total uncertainty analyses, parallel job execution on clusters, stochastic geometry modeling, and other types of calculations where a series of MCNPS jobs must be performed with varying problem input specifications. Monte Carlo codes are being used for a wide variety of applications today due to their accurate physical modeling and the speed of today's computers. In most applications for design work, experiment analysis, and benchmark calculations, it is common to run many calculations, not just one, to examine the effects of design tolerances, experimental uncertainties, or variations in modeling features. We have developed a software tool for use with MCNP5 to automate this process. The tool, mcnp-pstudy, is used to automate the operations of preparing a series of MCNP5 input files, running the calculations, and collecting the results. Using this tool, parameter studies, total uncertainty analyses, or repeated (possibly parallel) calculations with MCNP5 can be performed easily. Essentially no extra user setup time is required beyond that of preparing a single MCNP5 input file.
Monte Carlo source convergence and the Whitesides problem
Blomquist, R. N.
2000-02-25
The issue of fission source convergence in Monte Carlo eigenvalue calculations is of interest because of the potential consequences of erroneous criticality safety calculations. In this work, the authors compare two different techniques to improve the source convergence behavior of standard Monte Carlo calculations applied to challenging source convergence problems. The first method, super-history powering, attempts to avoid discarding important fission sites between generations by delaying stochastic sampling of the fission site bank until after several generations of multiplication. The second method, stratified sampling of the fission site bank, explicitly keeps the important sites even if conventional sampling would have eliminated them. The test problems are variants of Whitesides' Criticality of the World problem in which the fission site phase space was intentionally undersampled in order to induce marginally intolerable variability in local fission site populations. Three variants of the problem were studied, each with a different degree of coupling between fissionable pieces. Both the superhistory powering method and the stratified sampling method were shown to improve convergence behavior, although stratified sampling is more robust for the extreme case of no coupling. Neither algorithm completely eliminates the loss of the most important fissionable piece, and if coupling is absent, the lost piece cannot be recovered unless its sites from earlier generations have been retained. Finally, criteria for measuring source convergence reliability are proposed and applied to the test problems.
Quantum Monte Carlo Endstation for Petascale Computing
Lubos Mitas
2011-01-26
NCSU research group has been focused on accomplising the key goals of this initiative: establishing new generation of quantum Monte Carlo (QMC) computational tools as a part of Endstation petaflop initiative for use at the DOE ORNL computational facilities and for use by computational electronic structure community at large; carrying out high accuracy quantum Monte Carlo demonstration projects in application of these tools to the forefront electronic structure problems in molecular and solid systems; expanding the impact of QMC methods and approaches; explaining and enhancing the impact of these advanced computational approaches. In particular, we have developed quantum Monte Carlo code (QWalk, www.qwalk.org) which was significantly expanded and optimized using funds from this support and at present became an actively used tool in the petascale regime by ORNL researchers and beyond. These developments have been built upon efforts undertaken by the PI's group and collaborators over the period of the last decade. The code was optimized and tested extensively on a number of parallel architectures including petaflop ORNL Jaguar machine. We have developed and redesigned a number of code modules such as evaluation of wave functions and orbitals, calculations of pfaffians and introduction of backflow coordinates together with overall organization of the code and random walker distribution over multicore architectures. We have addressed several bottlenecks such as load balancing and verified efficiency and accuracy of the calculations with the other groups of the Endstation team. The QWalk package contains about 50,000 lines of high quality object-oriented C++ and includes also interfaces to data files from other conventional electronic structure codes such as Gamess, Gaussian, Crystal and others. This grant supported PI for one month during summers, a full-time postdoc and partially three graduate students over the period of the grant duration, it has resulted in 13 published papers, 15 invited talks and lectures nationally and internationally. My former graduate student and postdoc Dr. Michal Bajdich, who was supported byt this grant, is currently a postdoc with ORNL in the group of Dr. F. Reboredo and Dr. P. Kent and is using the developed tools in a number of DOE projects. The QWalk package has become a truly important research tool used by the electronic structure community and has attracted several new developers in other research groups. Our tools use several types of correlated wavefunction approaches, variational, diffusion and reptation methods, large-scale optimization methods for wavefunctions and enables to calculate energy differences such as cohesion, electronic gaps, but also densities and other properties, using multiple runs one can obtain equations of state for given structures and beyond. Our codes use efficient numerical and Monte Carlo strategies (high accuracy numerical orbitals, multi-reference wave functions, highly accurate correlation factors, pairing orbitals, force biased and correlated sampling Monte Carlo), are robustly parallelized and enable to run on tens of thousands cores very efficiently. Our demonstration applications were focused on the challenging research problems in several fields of materials science such as transition metal solids. We note that our study of FeO solid was the first QMC calculation of transition metal oxides at high pressures.
Reduced Density Matrices in Full Configuration Interaction Quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Overy, Catherine; Cleland, Deidre; Booth, George H.; Shepherd, James J.; Alavi, Ali
2013-03-01
Reduced density matrices are a powerful construct in quantum chemistry, providing a compact representation of highly multi-determinantal wavefunctions, from which the expectation values of important physical properties can be extracted, including multipole moments, polarizabilities and nuclear forces1,2. Full configuration interaction quantum Monte Carlo (FCIQMC)3 and its initiator extension (i-FCIQMC)4 perform a stochastic propagation of signed walkers within a space of Slater determinants to achieve FCI-quality energies without the need to store the complete wavefunction. We present here a method for a stochastic calculation of the 1- and 2-body reduced density matrices within the framework of (i)-FCIQMC, and apply this formulation to a range of archetypal molecular systems. Consideration is also given to the source and nature of systematic and stochastic error, and regimes to effectively alleviate these errors are discussed5. 1 P.-O. Löwdin, Phys. Rev. 97, 1474 (1955). 2 C. A. Coulson, Rev. Mod. Phys. 32, 170 (1960). 3 G. H. Booth, A. Thom, and A. Alavi, J. Chem. Phys. 131, 054106 (2009). 4 D. Cleland, G. H. Booth, and A. Alavi, J. Chem. Phys. 132, 041103 (2010). 5 D. Cleland, PhD thesis, University of Cambridge, 2012.
Normality of Monte Carlo criticality eigenfunction decomposition coefficients
Toth, B. E.; Martin, W. R. [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109 (United States); Griesheimer, D. P. [Bechtel Bettis, Inc., P.O. Box 79, West Mifflin, PA 15122 (United States)
2013-07-01
A proof is presented, which shows that after a single Monte Carlo (MC) neutron transport power method iteration without normalization, the coefficients of an eigenfunction decomposition of the fission source density are normally distributed when using analog or implicit capture MC. Using a Pearson correlation coefficient test, the proof is corroborated by results from a uniform slab reactor problem, and those results also suggest that the coefficients are normally distributed with normalization. The proof and numerical test results support the application of earlier work on the convergence of eigenfunctions under stochastic operators. Knowledge of the Gaussian shape of decomposition coefficients allows researchers to determine an appropriate level of confidence in the distribution of fission sites taken from a MC simulation. This knowledge of the shape of the probability distributions of decomposition coefficients encourages the creation of new predictive convergence diagnostics. (authors)
Monte Carlo simulations of two-dimensional fermion systems with string-bond states
NASA Astrophysics Data System (ADS)
Song, J.-P.; Clay, R. T.
2014-02-01
We describe an application of variational Monte Carlo to two-dimensional fermionic systems within the recently developed tensor-network string-bond state ansatz. We use a combination of variational Monte Carlo and stochastic optimization to optimize the matrix-product state matrices representing the ground state. We present results for a two-dimensional spinless fermion model including nearest-neighbor Coulomb interactions and determine using finite-size scaling the phase boundary between charge-ordered insulating and metallic phases. This approach can treat frustrated systems and be easily extended to fermion models with spin.
Liang, Y. Daniel
Case Study: Monte Carlo Simulation Monte Carlo simulation uses random numbers and probability, chemistry, and finance. This section gives an example of using Monte Carlo simulation for estimating . To estimate using the Monte Carlo method, draw a circle with its bounding square as shown below. x y 1-1 1 -1
Systematic improvement of variational Monte Carlo using Lanczos iterations
E. S. Heeb; T. M. Rice
1993-01-01
We present a new numerical technique which combines the variational Monte Carlo and the Lanczos methods without suffering from the fermion sign problem. Lanczos iterations allow systematic improvement of trial wavefunctions while Monte Carlo sampling permits treatment of large lattices. As in the usual Lanczos method we find it useful to symmetrize the starting wavefunction in order to accelerate convergence.
Monte Carlo simulation in PET and SPECT instrumentation using GATE
Karine Assi; Christian Morele; Martin Reye; Giovanni Santine; Luc Simone; Steven Staelensf; Jean-Marc Vieirae; Rik Van de Wallef
Monte Carlo simulation is an essential tool to assist in the design of new medical imaging devices for emission tomography. On one hand, dedicated Monte Carlo codes have been developed for PET and SPECT. However, they suffer from a variety of drawbacks and limitations in terms of validation, accuracy, and\\/or support. On the other hand, accurate and versatile simulation codes
A Primer in Monte Carlo Integration Using Mathcad
ERIC Educational Resources Information Center
Hoyer, Chad E.; Kegerreis, Jeb S.
2013-01-01
The essentials of Monte Carlo integration are presented for use in an upper-level physical chemistry setting. A Mathcad document that aids in the dissemination and utilization of this information is described and is available in the Supporting Information. A brief outline of Monte Carlo integration is given, along with ideas and pedagogy for…
HISTORY AND TERRITORY HEURISTICS FOR MONTE CARLO GO
BRUNO BOUZY
2006-01-01
Recently, the Monte Carlo approach has been applied to computer go with promising success. INDIGO uses such an approach which can be enhanced with specific heuristics. This paper assesses two heuristics within the 19 × 19 Monte Carlo go framework of INDIGO: the territory heuristic and the history heuristic, both in their internal and external versions. The external territory heuristic
Molecular physics and chemistry applications of quantum Monte Carlo
P. J. Reynolds; R. N. Barnett; B. L. Hammond; W. A. Lester
1986-01-01
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 Schrödinger 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
RADIATIVE HEAT TRANSFER WITH QUASI-MONTE CARLO METHODS
RADIATIVE HEAT TRANSFER WITH QUASI-MONTE CARLO METHODS A. Kersch1 W. Moroko2 A. Schuster1 1Siemens of Quasi-Monte Carlo to this problem. 1.1 Radiative Heat Transfer Reactors In the manufacturing of the problems which can be solved by such a simulation is high accuracy modeling of the radiative heat transfer
abcpmc: Approximate Bayesian Computation for Population Monte-Carlo code
NASA Astrophysics Data System (ADS)
Akeret, Joel
2015-04-01
abcpmc is a Python Approximate Bayesian Computing (ABC) Population Monte Carlo (PMC) implementation based on Sequential Monte Carlo (SMC) with Particle Filtering techniques. It is extendable with k-nearest neighbour (KNN) or optimal local covariance matrix (OLCM) pertubation kernels and has built-in support for massively parallelized sampling on a cluster using MPI.
Monte Carlo Methods for the Linearized Poisson-Boltzmann Equation
Simonov, Nikolai Aleksandrovich
algo- rithm, another, related, Monte Carlo algorithm is presented. This modified Monte Carlo method- timating certain Gaussian path integrals without the need for simulating Brownian trajectories in detail. We then similarly interpret the exponential weight in the Feynman-Kac formula as a survival
Monte Carlo mean-field method for spin systems
NASA Astrophysics Data System (ADS)
Henriques, Eduardo F.; Henriques, Vera B.; Salinas, S. R.
1995-04-01
We use a Monte Carlo mean-field method proposed by Netz and Berker to analyze the critical behavior of an Ising square lattice. We show that this method demands longer sampling times as compared with the conventional Monte Carlo simulations. Also, similar mean-field results can be obtained from self-consistent analytic calculations for small clusters of spins.
Monte Carlo Methods: A Computational Pattern for Our Pattern Language
California at Berkeley, University of
Monte Carlo Methods: A Computational Pattern for Our Pattern Language Jike Chong University The Monte Carlo Methods pattern is a computational software programming pattern in Our Pattern Language (OPL tacit knowledge about software design. One can construct a pattern language using a set of related
A New Adaptive Sampling Technique for Monte Carlo Global Illumination
Qing Xu; M. Feixas; M. Sbert; Jizhou Sun
2007-01-01
Monte Carlo is the only choice of physically correct method to compute the problem of global illumination in the field of realistic image synthesis. Adaptive sampling is an appealing tool to eliminate noise, which is one of the main problems of Monte Carlo based global illumination algorithms. In this paper, we investigate the use of entropy in the domain of
Multiple Overlapping Tiles for Contextual Monte Carlo Tree Search
Paris-Sud XI, Université de
Multiple Overlapping Tiles for Contextual Monte Carlo Tree Search Arpad Rimmel and Fabien Teytaud only a small relevant part of the whole problem, this allows it to ob- tain good performance to be automatically modified depending on the context: Contextual Monte Carlo (CMC) simulations. We show
Multiple Overlapping Tiles for Contextual Monte Carlo Tree Search
on the context: Contextual Monte Carlo (CMC) simulations. We show that it improves the performance for the gameMultiple Overlapping Tiles for Contextual Monte Carlo Tree Search Arpad Rimmel1 and Fabien Teytaud1 relevant part of the whole problem, this allows it to ob- tain good performance in such situations
Image Segmentation by Data-Driven Markov Chain Monte Carlo
Zhu, Song Chun
Image Segmentation by Data-Driven Markov Chain Monte Carlo Zhuowen Tu and Song-Chun Zhu AbstractÐThis paper presents a computational paradigm called Data-Driven Markov Chain Monte Carlo (DDMCMC) for image segmentation in the Bayesian statistical framework. The paper contributes to image segmentation in four aspects
Markov Chains Monte Carlo Algorithms University of Toronto
Rosenthal, Jeffrey S.
and MCMC algorithms. We will start by an introduction to MCMC in chapter 1 followed by topics in optimalMarkov Chains Monte Carlo Algorithms Kai Yang University of Toronto STA496H Readings in Statistics: Markov Chains Monte Carlo Algorithms Fall 2010 Supervisor: Prof. Jeffrey S. Rosenthal December 23, 2010
Monte Carlo simulation of thermoelectric properties in nanocomposites
Ming-Shan Jeng; Ronggui Yang; Gang Chen
2005-01-01
This paper presents a Monte Carlo simulation scheme to study the thermoelectric properties of nanocomposites with special attention paid to the implementation of periodic boundary condition in Monte Carlo simulation. The scheme is applied to study the thermal conductivity of silicon germanium (Si-Ge) nanocomposites, which are of great interest for high efficiency thermoelectric material development. The size effects of phonon
Using Monte-Carlo variance reduction in statistical tolerance synthesis
Victor J. Skowronski; Joshua U. Turner
1997-01-01
A statistical tolerance synthesis must analyse many sets of tolerances, each of which has a unique probability distribution. The Monte-Carlo technique that is typically used to evaluate the probability distribution must analyse large numbers of individual cases. The result is a huge number of individual analyses, which is computationally expensive. This paper examines two Monte-Carlo variance reduction techniques, importance sampling
Monte Carlo Methods for Portfolio Credit Risk Tim J. Brereton
Kroese, Dirk P.
Monte Carlo Methods for Portfolio Credit Risk Tim J. Brereton Dirk P. Kroese School of Mathematics of this chapter is to survey the Monte Carlo techniques that are used in portfolio credit risk modeling. We discuss various approaches for modeling the dependencies between individual components of a portfolio
Monte Carlo query processing of uncertain multidimensional array data
Tingjian Ge; David Grabiner
2011-01-01
Array database systems are architected for scientific and engineering applications. In these applications, the value of a cell is often imprecise and uncertain. There are at least two reasons that a Monte Carlo query processing algorithm is usually required for such uncertain data. Firstly, a probabilistic graphical model must often be used to model correlation, which requires a Monte Carlo
Monte Carlo Test Assembly for Item Pool Analysis and Extension
ERIC Educational Resources Information Center
Belov, Dmitry I.; Armstrong, Ronald D.
2005-01-01
A new test assembly algorithm based on a Monte Carlo random search is presented in this article. A major advantage of the Monte Carlo test assembly over other approaches (integer programming or enumerative heuristics) is that it performs a uniform sampling from the item pool, which provides every feasible item combination (test) with an equal…
Inverse Monte Carlo: a unified reconstruction algorithm for SPECT
Carey E. Floyd; R. E. Coleman; R. J. Jaszczak
1985-01-01
Inverse Monte Carlo (IMOC) is presented as a unified reconstruction algorithm for Emission Computed Tomography (ECT) providing simultaneous compensation for scatter, attenuation, and the variation of collimator resolution with depth. The technique of inverse Monte Carlo is used to find an inverse solution to the photon transport equation (an integral equation for photon flux from a specified source) for a
Economic Risk Analysis: Using Analytical and Monte Carlo Techniques.
ERIC Educational Resources Information Center
O'Donnell, Brendan R.; Hickner, Michael A.; Barna, Bruce A.
2002-01-01
Describes the development and instructional use of a Microsoft Excel spreadsheet template that facilitates analytical and Monte Carlo risk analysis of investment decisions. Discusses a variety of risk assessment methods followed by applications of the analytical and Monte Carlo methods. Uses a case study to illustrate use of the spreadsheet tool…
Monte Carlo Study of Melting of a Model Bulk Ice
Kyu-Kwang Han
1989-01-01
The methods of NVT (constant number, volume and temperature) and NPT (constant number, pressure and temperature) Monte Carlo computer simulations are used to examine the melting of a periodic hexagonal ice (ice Ih) sample with a unit cell of 192 (rigid) water molecules interacting via the revised central force potentials of Stillinger and Rahman (RSL2). In NVT Monte Carlo simulation
Popel, Aleksander S.
Monte Carlo simulations of VEGF binding to cell surface receptors in vitro Feilim Mac Gabhann The vascular endothelial growth factor (VEGF) family binds multiple endothelial cell surface receptors. Our interactions may be necessary. Here, we compare Monte Carlo simulations of the stochastic binding of VEGF
Monte Carlo simulations of protein folding
NASA Astrophysics Data System (ADS)
Dinner, Aaron Reuven
Monte Carlo simulations are employed to study how a protein folds from a random coil to its native state. In Part I, we investigate the kinetics and thermodynamics of a polypeptide modeled as a chain of 125 beads restricted to a lattice. The behavior of the model is found to be more complex than that of smaller systems. The diverse trajectories that lead to the native state can be classified into a small number of average pathways: a ``fast track'' in which the chain forms a stable core that folds directly to the native state and several ``slow tracks'' in which particular contacts form before the core is complete and direct the chain to misfolded intermediates. Rearrangement to the native state is slow because it requires breaking stable contacts that involve primarily surface residues. Increases in temperature destabilize the intermediates and shift the transition state in a Hammond manner. The mechanism is mapped to two coordinates that are based on a comparison of folding and non-folding trajectories. The free energy in terms of those variables is in good agreement with the observed kinetics, which indicates that they provide an adequate description of the folding reaction. The generality of the results is confirmed by statistical analysis of a 200 sequence database. In Part II, the study is extended to higher resolution (all-atom) models. We generalize a procedure for local deformation of a polymer by concerted rotation of several sequential rotatable main chain dihedral angles and evaluate its usefulness as an elementary move. A Monte Carlo module that includes this move is implemented for the program CHARMM and is applied to sampling the accessible configuration space of a 16-residue peptide that has been shown experimentally to adopt a hairpin structure in solution. A non-canonical weighting scheme is employed to accelerate the escape from local free energy minima. Overall, there is only a relatively small number of distinct conformations. The results suggest that Monte Carlo methods will be capable of finding the native states not only of peptides but also of proteins in the relatively near future.
Robust Monte Carlo Algorithms Centre for Advanced Computing and Emerging Technologies
Dimov, Ivan
Robust Monte Carlo Algorithms Ivan Dimov Centre for Advanced Computing and Emerging Technologies Remarks Areas of Application in Science and Technologies · Robust Monte Carlo Algorithms Basic Linear Algebra Problems Evaluation of Matrix Polynomials Robust Monte Carlo Algorithms Interpolation
A MONTE CARLO SEQUENTIAL ESTIMATION OF POINT PROCESS OPTIMUM FILTERING FOR BRAIN MACHINE INTERFACES
Slatton, Clint
1 A MONTE CARLO SEQUENTIAL ESTIMATION OF POINT PROCESS OPTIMUM FILTERING FOR BRAIN MACHINE Monte Carlo Sequential Estimation for Point Processes.................................................29 Simulation of Monte Carlo Sequential Estimation on Neural Spike Train Decoding............32 Interpretation
Monte Carlo technique in modeling ground motion coherence in sedimentary filled valleys
Cerveny, Vlastislav
Monte Carlo technique in modeling ground motion coherence in sedimentary filled valleys Arrigo propagation Monte Carlo numerical simulations Site effects a b s t r a c t Using a Monte Carlo method based
Vectorized Monte Carlo methods for reactor lattice analysis
Brown, F.B.
1984-03-01
Some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-energy Monte Carlo code for use on the CYBER-205 computer are discussed. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. For background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed.
Vectorized Monte Carlo methods for reactor lattice analysis
NASA Technical Reports Server (NTRS)
Brown, F. B.
1984-01-01
Some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-enery Monte Carlo code for use on the CYBER-205 computer are discussed. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. For background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed.
Total Monte Carlo evaluation for dose calculations.
Sjöstrand, H; Alhassan, E; Conroy, S; Duan, J; Hellesen, C; Pomp, S; Österlund, M; Koning, A; Rochman, D
2014-10-01
Total Monte Carlo (TMC) is a method to propagate nuclear data (ND) uncertainties in transport codes, by using a large set of ND files, which covers the ND uncertainty. The transport code is run multiple times, each time with a unique ND file, and the result is a distribution of the investigated parameter, e.g. dose, where the width of the distribution is interpreted as the uncertainty due to ND. Until recently, this was computer intensive, but with a new development, fast TMC, more applications are accessible. The aim of this work is to test the fast TMC methodology on a dosimetry application and to propagate the (56)Fe uncertainties on the predictions of the dose outside a proposed 14-MeV neutron facility. The uncertainty was found to be 4.2 %. This can be considered small; however, this cannot be generalised to all dosimetry applications and so ND uncertainties should routinely be included in most dosimetry modelling. PMID:24277871
Monte-Carlo simulations of proton aurora
NASA Astrophysics Data System (ADS)
Synnes, S. a.; Søraas, F.; Hansen, J. P.
1998-11-01
The spreading of a proton beam in the upper atmosphere is calculated based onMonte-Carlo simulations. The transport of the atoms is modelled in a magnetic field with dipolestrength. Neuralisation, ionisation and excitation mechanisms of the incoming particles areincluded from collision cross-sections of protons and hydrogen with an effective N2atmosphere. Assuming an isotropic pitch angle distribution for the incoming protons, theirspreading in the upper atmosphere and the return flux of the charged and neutral component ofthe hydrogen beam has been calculated. Depending on energy and the tilt angle of the magneticfield about 10% of the incoming particles return from the atmosphere as ENA (Energetic NeutralAtoms). The ENA returning from the atmosphere show a source region below 500 km for theincoming high energy protons. For low energy protons, the ENA originate mainly from twodifferent regions, one around 700 km and the other at 400 km altitude, reflecting their sensitivityto several charge exchange processes.
Monte Carlo simulations of medical imaging modalities
Estes, G.P. [Los Alamos National Lab., NM (United States)
1998-09-01
Because continuous-energy Monte Carlo radiation transport calculations can be nearly exact simulations of physical reality (within data limitations, geometric approximations, transport algorithms, etc.), it follows that one should be able to closely approximate the results of many experiments from first-principles computations. This line of reasoning has led to various MCNP studies that involve simulations of medical imaging modalities and other visualization methods such as radiography, Anger camera, computerized tomography (CT) scans, and SABRINA particle track visualization. It is the intent of this paper to summarize some of these imaging simulations in the hope of stimulating further work, especially as computer power increases. Improved interpretation and prediction of medical images should ultimately lead to enhanced medical treatments. It is also reasonable to assume that such computations could be used to design new or more effective imaging instruments.
Monte Carlo Simulation of Endlinking Oligomers
NASA Technical Reports Server (NTRS)
Hinkley, Jeffrey A.; Young, Jennifer A.
1998-01-01
This report describes initial efforts to model the endlinking reaction of phenylethynyl-terminated oligomers. Several different molecular weights were simulated using the Bond Fluctuation Monte Carlo technique on a 20 x 20 x 20 unit lattice with periodic boundary conditions. After a monodisperse "melt" was equilibrated, chain ends were linked whenever they came within the allowed bond distance. Ends remained reactive throughout, so that multiple links were permitted. Even under these very liberal crosslinking assumptions, geometrical factors limited the degree of crosslinking. Average crosslink functionalities were 2.3 to 2.6; surprisingly, they did not depend strongly on the chain length. These results agreed well with the degrees of crosslinking inferred from experiment in a cured phenylethynyl-terminated polyimide oligomer.
Monte Carlo simulation of radiating reentry flows
NASA Technical Reports Server (NTRS)
Taylor, Jeff C.; Carlson, Ann B.; Hassan, H. A.
1993-01-01
The Direct Simulation Monte Carlo (DSMC) method is applied to a radiating, hypersonic, axisymmetric flow over a blunt body in the near continuum regime. The ability of the method to predict the flowfield radiation and the radiative heating is investigated for flow over the Project Fire II configuration at 11.36 kilometers per second at an altitude of 76.42 kilometers. Two methods that differ in the manner in which they treat ionization and estimate electronic excitation are employed. The calculated results are presented and compared with both experimental data and solutions where radiation effects were not included. Differences in the results are discussed. Both methods ignore self absorption and, as a result, overpredict measured radiative heating.
Monte Carlo simulations in Nuclear Medicine
Loudos, George K. [Department of Medical Instrumentation Technology, Technological Educational Institute of Athens (Greece)
2007-11-26
Molecular imaging technologies provide unique abilities to localise signs of disease before symptoms appear, assist in drug testing, optimize and personalize therapy, and assess the efficacy of treatment regimes for different types of cancer. Monte Carlo simulation packages are used as an important tool for the optimal design of detector systems. In addition they have demonstrated potential to improve image quality and acquisition protocols. Many general purpose (MCNP, Geant4, etc) or dedicated codes (SimSET etc) have been developed aiming to provide accurate and fast results. Special emphasis will be given to GATE toolkit. The GATE code currently under development by the OpenGATE collaboration is the most accurate and promising code for performing realistic simulations. The purpose of this article is to introduce the non expert reader to the current status of MC simulations in nuclear medicine and briefly provide examples of current simulated systems, and present future challenges that include simulation of clinical studies and dosimetry applications.
Exploring Theory Space with Monte Carlo Reweighting
James S. Gainer; Joseph Lykken; Konstantin T. Matchev; Stephen Mrenna; Myeonghun Park
2014-12-25
Theories of new physics often involve a large number of unknown parameters which need to be scanned. Additionally, a putative signal in a particular channel may be due to a variety of distinct models of new physics. This makes experimental attempts to constrain the parameter space of motivated new physics models with a high degree of generality quite challenging. We describe how the reweighting of events may allow this challenge to be met, as fully simulated Monte Carlo samples generated for arbitrary benchmark models can be effectively re-used. In particular, we suggest procedures that allow more efficient collaboration between theorists and experimentalists in exploring large theory parameter spaces in a rigorous way at the LHC.
Hybrid algorithms in quantum Monte Carlo
Esler, Kenneth P [ORNL] [ORNL; Mcminis, Jeremy [University of Illinois, Urbana-Champaign] [University of Illinois, Urbana-Champaign; Morales, Miguel A [Lawrence Livermore National Laboratory (LLNL)] [Lawrence Livermore National Laboratory (LLNL); Clark, Bryan K. [Princeton University] [Princeton University; Shulenburger, Luke [Sandia National Laboratory (SNL)] [Sandia National Laboratory (SNL); Ceperley, David M [ORNL] [ORNL
2012-01-01
With advances in algorithms and growing computing powers, quantum Monte Carlo (QMC) methods have become a leading contender for high accuracy calculations for the electronic structure of realistic systems. The performance gain on recent HPC systems is largely driven by increasing parallelism: the number of compute cores of a SMP and the number of SMPs have been going up, as the Top500 list attests. However, the available memory as well as the communication and memory bandwidth per element has not kept pace with the increasing parallelism. This severely limits the applicability of QMC and the problem size it can handle. OpenMP/MPI hybrid programming provides applications with simple but effective solutions to overcome efficiency and scalability bottlenecks on large-scale clusters based on multi/many-core SMPs. We discuss the design and implementation of hybrid methods in QMCPACK and analyze its performance on current HPC platforms characterized by various memory and communication hierarchies.
Accuracy control in Monte Carlo radiative calculations
NASA Technical Reports Server (NTRS)
Almazan, P. Planas
1993-01-01
The general accuracy law that rules the Monte Carlo, ray-tracing algorithms used commonly for the calculation of the radiative entities in the thermal analysis of spacecraft are presented. These entities involve transfer of radiative energy either from a single source to a target (e.g., the configuration factors). or from several sources to a target (e.g., the absorbed heat fluxes). In fact, the former is just a particular case of the latter. The accuracy model is later applied to the calculation of some specific radiative entities. Furthermore, some issues related to the implementation of such a model in a software tool are discussed. Although only the relative error is considered through the discussion, similar results can be derived for the absolute error.
Monte Carlo modeling and meteor showers
NASA Technical Reports Server (NTRS)
Kulikova, N. V.
1987-01-01
Prediction of short lived increases in the cosmic dust influx, the concentration in lower thermosphere of atoms and ions of meteor origin and the determination of the frequency of micrometeor impacts on spacecraft are all of scientific and practical interest and all require adequate models of meteor showers at an early stage of their existence. A Monte Carlo model of meteor matter ejection from a parent body at any point of space was worked out by other researchers. This scheme is described. According to the scheme, the formation of ten well known meteor streams was simulated and the possibility of genetic affinity of each of them with the most probable parent comet was analyzed. Some of the results are presented.
Optimized Fermion Path Integral Monte Carlo
NASA Astrophysics Data System (ADS)
Khairallah, Saad; Draeger, Erik; Shumway, John
2011-03-01
We present the latest developments in a new path integral Monte Carlo method for continuum fermions. The new formalism uses the maximum entropy principle to map the approximated density matrix to an effective bosonic problem. Verification and performance results are presented for both free electrons and compressed hydrogen, showing accurate results with a substantial performance gain over reference slice fPIMC, particularly at lower temperatures where ergodicity issues can significantly impact sampling efficiency. The limiting approximations in the method are identified and discussed, and suggest the need for improved nodal models. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Correlations in the Monte Carlo Glauber model
NASA Astrophysics Data System (ADS)
Blaizot, Jean-Paul; Broniowski, Wojciech; Ollitrault, Jean-Yves
2014-09-01
Event-by-event fluctuations of observables are often modeled using the Monte Carlo Glauber model, in which the energy is initially deposited in sources associated with wounded nucleons. In this paper, we analyze in detail the correlations between these sources in proton-nucleus and nucleus-nucleus collisions. There are correlations arising from nucleon-nucleon correlations within each nucleus, and correlations due to the collision mechanism, which we dub twin correlations. We investigate this new phenomenon in detail. At the Brookhaven Relativistic Heavy Ion Collider and CERN Large Hadron Collider energies, correlations are found to have modest effects on size and eccentricity fluctuations, such that the Glauber model produces to a good approximation a collection of independent sources.
Monte Carlo simulation of modulated phases
Srolovitz, D.J.; Hassold, G.N.; Gayda, J.
1987-01-01
This paper presents Monte Carlo simulation results for the formation of modulated phases in the framework of the two dimensional ANNNI model with a nonconserved order parameter. This work complements the earlier studies of Kaski, et al. by examining a different, wider area of parameter space and temperature. Like Kaski, et al., it is found that for certain temperatures and values of the frustration parameter, kappa, ordered domains form quickly and the correlation length grows as the square root of time. However, there exists a range of kappa for which a quench from high to low temperature results in the formation of a metastable glassy phase. In addition to the ANNNI model study, preliminary results are presented on a newly developed model which exhibits phase modulation due to the presence of elastic interactions between the different phase and with an externally applied stress. 12 refs., 12 figs.
Quasicontinuum Monte Carlo Simulation of Surface Growth
NASA Astrophysics Data System (ADS)
Devita, Jason P.; Sander, Leonard M.; Smereka, Peter
2004-03-01
We present a new algorithm for simulating surface growth, which utilizes both continuum and Kinetic Monte-Carlo (KMC) methods. Atoms which are part of an island are treated as discrete particles (with dynamics governed by KMC), while lone adatoms are treated as a probability density. Using the adatom probability density and the geometry of the island edges, we calculate the adatom density at a later time. Then discrete particles are added to or removed from the island edges according to the probability density in the sites adjacent to the edges. Results from our method compare favorably to standard KMC (and to experiment) for both sub-monolayer and multilayer growth, including Schwoebel barrier-induced mounding and equilibrium island shapes.
Monte Carlo simulation of discrete ?-ray detectors
NASA Astrophysics Data System (ADS)
Bakkali, A.; Tamda, N.; Parmentier, M.; Chavanelle, J.; Pousse, A.; Kastler, B.
2005-06-01
Needs in medical diagnosis, especially for early and reliable breast cancer detection, lead us to consider developments in scintillation crystals and position sensitive photomultiplier tubes (PSPMT) in order to develop a high-resolution medium field ?-ray imaging device. However the ideal detector for ?-rays represents a compromise between many conflicting requirements. In order to optimize different parameters involved in the detection process, we have developed a Monte Carlo simulation software. Its aim was to study the light distribution produced by a gamma photon interacting with a pixellated scintillation crystal coupled to a PSPMT array. Several crystal properties were taken into account as well as the intrinsic response of PSPMTs. Images obtained by simulations are compared with experimental results. Agreement between simulation and experimental results validate our simulation model.
The Tunneling Hybrid Monte-Carlo algorithm
Maarten Golterman; Yigal Shamir
2007-10-09
The hermitian Wilson kernel used in the construction of the domain-wall and overlap Dirac operators has exceptionally small eigenvalues that make it expensive to reach high-quality chiral symmetry for domain-wall fermions, or high precision in the case of the overlap operator. An efficient way of suppressing such eigenmodes consists of including a positive power of the determinant of the Wilson kernel in the Boltzmann weight, but doing this also suppresses tunneling between topological sectors. Here we propose a modification of the Hybrid Monte-Carlo algorithm which aims to restore tunneling between topological sectors by excluding the lowest eigenmodes of the Wilson kernel from the molecular-dynamics evolution, and correcting for this at the accept/reject step. We discuss the implications of this modification for the acceptance rate.
Vectorization of Monte Carlo particle transport
Burns, P.J.; Christon, M.; Schweitzer, R.; Lubeck, O.M.; Wasserman, H.J.; Simmons, M.L.; Pryor, D.V. (Colorado State Univ., Fort Collins, CO (USA). Computer Center; Los Alamos National Lab., NM (USA); Supercomputing Research Center, Bowie, MD (USA))
1989-01-01
Fully vectorized versions of the Los Alamos National Laboratory benchmark code Gamteb, a Monte Carlo photon transport algorithm, were developed for the Cyber 205/ETA-10 and Cray X-MP/Y-MP architectures. Single-processor performance measurements of the vector and scalar implementations were modeled in a modified Amdahl's Law that accounts for additional data motion in the vector code. The performance and implementation strategy of the vector codes are related to architectural features of each machine. Speedups between fifteen and eighteen for Cyber 205/ETA-10 architectures, and about nine for CRAY X-MP/Y-MP architectures are observed. The best single processor execution time for the problem was 0.33 seconds on the ETA-10G, and 0.42 seconds on the CRAY Y-MP. 32 refs., 12 figs., 1 tab.
MORSE Monte Carlo radiation transport code system
Emmett, M.B.
1983-02-01
This report is an addendum to the MORSE report, ORNL-4972, originally published in 1975. This addendum contains descriptions of several modifications to the MORSE Monte Carlo Code, replacement pages containing corrections, Part II of the report which was previously unpublished, and a new Table of Contents. The modifications include a Klein Nishina estimator for gamma rays. Use of such an estimator required changing the cross section routines to process pair production and Compton scattering cross sections directly from ENDF tapes and writing a new version of subroutine RELCOL. Another modification is the use of free form input for the SAMBO analysis data. This required changing subroutines SCORIN and adding new subroutine RFRE. References are updated, and errors in the original report have been corrected. (WHK)
Monte Carlo Sampling in Fractal Landscapes
Jorge C. Leitão; João M. Viana Parente Lopes; Eduardo G. Altmann
2013-05-30
We propose a flat-histogram Monte Carlo method to efficiently sample fractal landscapes such as escape time functions of open chaotic systems. This is achieved by using a random-walk step which depends on the height of the landscape via the largest Lyapunov exponent of the associated chaotic system. By generalizing the Wang-Landau algorithm, we obtain a method which simultaneously constructs the density of states (escape time distribution) and the correct step-length distribution. As a result, averages are obtained in polynomial computational time, a dramatic improvement over the exponential scaling of traditional uniform sampling. Our results are not limited by the dimensionality of the phase space and are confirmed numerically for dimensions as large as 30.
Monte Carlo Sampling in Fractal Landscapes
NASA Astrophysics Data System (ADS)
Leitão, Jorge C.; Lopes, J. M. Viana Parente; Altmann, Eduardo G.
2013-05-01
We design a random walk to explore fractal landscapes such as those describing chaotic transients in dynamical systems. We show that the random walk moves efficiently only when its step length depends on the height of the landscape via the largest Lyapunov exponent of the chaotic system. We propose a generalization of the Wang-Landau algorithm which constructs not only the density of states (transient time distribution) but also the correct step length. As a result, we obtain a flat-histogram Monte Carlo method which samples fractal landscapes in polynomial time, a dramatic improvement over the exponential scaling of traditional uniform-sampling methods. Our results are not limited by the dimensionality of the landscape and are confirmed numerically in chaotic systems with up to 30 dimensions.
Monte Carlo scatter correction for SPECT
NASA Astrophysics Data System (ADS)
Liu, Zemei
The goal of this dissertation is to present a quantitatively accurate and computationally fast scatter correction method that is robust and easily accessible for routine applications in SPECT imaging. A Monte Carlo based scatter estimation method is investigated and developed further. The Monte Carlo simulation program SIMIND (Simulating Medical Imaging Nuclear Detectors), was specifically developed to simulate clinical SPECT systems. The SIMIND scatter estimation (SSE) method was developed further using a multithreading technique to distribute the scatter estimation task across multiple threads running concurrently on multi-core CPU's to accelerate the scatter estimation process. An analytical collimator that ensures less noise was used during SSE. The research includes the addition to SIMIND of charge transport modeling in cadmium zinc telluride (CZT) detectors. Phenomena associated with radiation-induced charge transport including charge trapping, charge diffusion, charge sharing between neighboring detector pixels, as well as uncertainties in the detection process are addressed. Experimental measurements and simulation studies were designed for scintillation crystal based SPECT and CZT based SPECT systems to verify and evaluate the expanded SSE method. Jaszczak Deluxe and Anthropomorphic Torso Phantoms (Data Spectrum Corporation, Hillsborough, NC, USA) were used for experimental measurements and digital versions of the same phantoms employed during simulations to mimic experimental acquisitions. This study design enabled easy comparison of experimental and simulated data. The results have consistently shown that the SSE method performed similarly or better than the triple energy window (TEW) and effective scatter source estimation (ESSE) methods for experiments on all the clinical SPECT systems. The SSE method is proven to be a viable method for scatter estimation for routine clinical use.
A hybrid Monte Carlo and response matrix Monte Carlo method in criticality calculation
Li, Z.; Wang, K. [Dept. of Engineering Physics, Tsinghua Univ., Beijing, 100084 (China)
2012-07-01
Full core calculations are very useful and important in reactor physics analysis, especially in computing the full core power distributions, optimizing the refueling strategies and analyzing the depletion of fuels. To reduce the computing time and accelerate the convergence, a method named Response Matrix Monte Carlo (RMMC) method based on analog Monte Carlo simulation was used to calculate the fixed source neutron transport problems in repeated structures. To make more accurate calculations, we put forward the RMMC method based on non-analog Monte Carlo simulation and investigate the way to use RMMC method in criticality calculations. Then a new hybrid RMMC and MC (RMMC+MC) method is put forward to solve the criticality problems with combined repeated and flexible geometries. This new RMMC+MC method, having the advantages of both MC method and RMMC method, can not only increase the efficiency of calculations, also simulate more complex geometries rather than repeated structures. Several 1-D numerical problems are constructed to test the new RMMC and RMMC+MC method. The results show that RMMC method and RMMC+MC method can efficiently reduce the computing time and variations in the calculations. Finally, the future research directions are mentioned and discussed at the end of this paper to make RMMC method and RMMC+MC method more powerful. (authors)
Recent advances and future prospects for Monte Carlo
Brown, Forrest B [Los Alamos National Laboratory
2010-01-01
The history of Monte Carlo methods is closely linked to that of computers: The first known Monte Carlo program was written in 1947 for the ENIAC; a pre-release of the first Fortran compiler was used for Monte Carlo In 1957; Monte Carlo codes were adapted to vector computers in the 1980s, clusters and parallel computers in the 1990s, and teraflop systems in the 2000s. Recent advances include hierarchical parallelism, combining threaded calculations on multicore processors with message-passing among different nodes. With the advances In computmg, Monte Carlo codes have evolved with new capabilities and new ways of use. Production codes such as MCNP, MVP, MONK, TRIPOLI and SCALE are now 20-30 years old (or more) and are very rich in advanced featUres. The former 'method of last resort' has now become the first choice for many applications. Calculations are now routinely performed on office computers, not just on supercomputers. Current research and development efforts are investigating the use of Monte Carlo methods on FPGAs. GPUs, and many-core processors. Other far-reaching research is exploring ways to adapt Monte Carlo methods to future exaflop systems that may have 1M or more concurrent computational processes.
Ballarini, F; Biaggi, M; Merzagora, M; Ottolenghi, A; Dingfelder, M; Friedland, W; Jacob, P; Paretzke, H G
2000-09-01
A new physical module for the biophysical simulation code PARTRAC has recently been developed, based on newly derived electron inelastic-scattering cross-sections in liquid water. In the present work, two modules of PARTRAC describing the production, diffusion and interaction of chemical species were developed with the specific purpose of quantifying the role of the uncertainties in the parameters controlling the early stages of liquid water radiolysis. A set of values for such parameters was identified, and time-dependent yields and frequency distributions of chemical species produced by electrons of different energies were calculated. The calculated yields were in good agreement with available data and simulations, thus confirming the reliability of the code. As the primary-electron energy decreases down to 1 keV, the *OH decay kinetics were found to get faster, reflecting variations in the spatial distribution of the initial energy depositions. In agreement with analogous works, an opposite trend was found for energies of a few hundred eV, due to the very small number of species involved. The spreading effects shown at long times by *OH frequency distributions following 1 keV irradiation were found to be essentially due to stochastic aspects of the chemical stage, whereas for 1 MeV tracks the physical and pre-chemical stages also were found to play a significant role. Relevant differences in the calculated e(aq) -yields were found by coupling the physics of PARTRAC with descriptions of the pre-chemical and chemical stages adopted in different models. This indicates a strict interrelation of the various stages, and thus a strong dependence of the parameter values on the assumptions made for the preceding and subsequent stages of the process. Although equally acceptable results can be obtained starting from different assumptions, it is necessary to keep control of such uncertainties, since they can significantly influence the modeling of radical attack on DNA and, more generally, radiobiological damage estimation. This study confirms the need for new, independently derived data on specific steps of water radiolysis, to be included in comprehensive biophysical simulation codes. PMID:11095148
Continuous-time quantum Monte Carlo impurity solvers
NASA Astrophysics Data System (ADS)
Gull, Emanuel; Werner, Philipp; Fuchs, Sebastian; Surer, Brigitte; Pruschke, Thomas; Troyer, Matthias
2011-04-01
Continuous-time quantum Monte Carlo impurity solvers are algorithms that sample the partition function of an impurity model using diagrammatic Monte Carlo techniques. The present paper describes codes that implement the interaction expansion algorithm originally developed by Rubtsov, Savkin, and Lichtenstein, as well as the hybridization expansion method developed by Werner, Millis, Troyer, et al. These impurity solvers are part of the ALPS-DMFT application package and are accompanied by an implementation of dynamical mean-field self-consistency equations for (single orbital single site) dynamical mean-field problems with arbitrary densities of states. Program summaryProgram title: dmft Catalogue identifier: AEIL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: ALPS LIBRARY LICENSE version 1.1 No. of lines in distributed program, including test data, etc.: 899 806 No. of bytes in distributed program, including test data, etc.: 32 153 916 Distribution format: tar.gz Programming language: C++ Operating system: The ALPS libraries have been tested on the following platforms and compilers: Linux with GNU Compiler Collection (g++ version 3.1 and higher), and Intel C++ Compiler (icc version 7.0 and higher) MacOS X with GNU Compiler (g++ Apple-version 3.1, 3.3 and 4.0) IBM AIX with Visual Age C++ (xlC version 6.0) and GNU (g++ version 3.1 and higher) compilers Compaq Tru64 UNIX with Compq C++ Compiler (cxx) SGI IRIX with MIPSpro C++ Compiler (CC) HP-UX with HP C++ Compiler (aCC) Windows with Cygwin or coLinux platforms and GNU Compiler Collection (g++ version 3.1 and higher) RAM: 10 MB-1 GB Classification: 7.3 External routines: ALPS [1], BLAS/LAPACK, HDF5 Nature of problem: (See [2].) Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of "correlated electron" materials as auxiliary problems whose solution gives the "dynamical mean field" approximation to the self-energy and local correlation functions. Solution method: Quantum impurity models require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms for which we present implementations here meet this challenge. Continuous-time quantum impurity methods are based on partition function expansions of quantum impurity models that are stochastically sampled to all orders using diagrammatic quantum Monte Carlo techniques. For a review of quantum impurity models and their applications and of continuous-time quantum Monte Carlo methods for impurity models we refer the reader to [2]. Additional comments: Use of dmft requires citation of this paper. Use of any ALPS program requires citation of the ALPS [1] paper. Running time: 60 s-8 h per iteration.
Accurate rotational barrier calculations with diffusion quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Klahm, Sebastian; Lüchow, Arne
2014-04-01
Accurate quantum Monte Carlo, MP2, coupled cluster, and DFT calculations of rotational barriers of several small molecules are presented. With the diffusion quantum Monte Carlo method (DMC) excellent agreement with experimental barriers is obtained except for the gauche-gauche barriers of n-butane and ethylmethylether. It is argued that these two experimental values might be erroneous. Additionally, barriers calculated with the more efficient variational quantum Monte Carlo method (VMC) are presented. The VMC barriers are less accurate than the DMC results, but it is demonstrated that accurate barriers can be obtained with sophisticated Jastrow correlation functions.
Variance reduction in Monte Carlo analysis of rarefied gas diffusion.
NASA Technical Reports Server (NTRS)
Perlmutter, M.
1972-01-01
The problem of rarefied diffusion between parallel walls is solved using the Monte Carlo method. The diffusing molecules are evaporated or emitted from one of the two parallel walls and diffuse through another molecular species. The Monte Carlo analysis treats the diffusing molecule as undergoing a Markov random walk, and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs, the expected Markov walk payoff is retained but its variance is reduced so that the Monte Carlo result has a much smaller error.
A radiating shock evaluated using Implicit Monte Carlo Diffusion
Cleveland, M.; Gentile, N. [Lawrence Livermore National Laboratory, P. O. Box 808, Livermore CA 94550 (United States)
2013-07-01
Implicit Monte Carlo [1] (IMC) has been shown to be very expensive when used to evaluate a radiation field in opaque media. Implicit Monte Carlo Diffusion (IMD) [2], which evaluates a spatial discretized diffusion equation using a Monte Carlo algorithm, can be used to reduce the cost of evaluating the radiation field in opaque media [2]. This work couples IMD to the hydrodynamics equations to evaluate opaque diffusive radiating shocks. The Lowrie semi-analytic diffusive radiating shock benchmark[a] is used to verify our implementation of the coupled system of equations. (authors)
Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth
NASA Astrophysics Data System (ADS)
Schulze, Tim P.; Smereka, Peter; E, Weinan
2003-07-01
We present a hybrid method for simulating epitaxial growth that combines kinetic Monte-Carlo (KMC) simulations with the Burton-Cabrera-Frank model for crystal growth. This involves partitioning the computational domain into KMC regions and regions where we time-step a discretized diffusion equation. Computational speed and accuracy are discussed. We find that the method is significantly faster than KMC while accounting for stochastic fluctuations in a comparable way.
Atomistic Monte Carlo Simulation of Lipid Membranes
Wüstner, Daniel; Sklenar, Heinz
2014-01-01
Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol. PMID:24469314
Error modes in implicit Monte Carlo
Martin, William Russell,; Brown, F. B. (Forrest B.)
2001-01-01
The Implicit Monte Carlo (IMC) method of Fleck and Cummings [1] has been used for years to analyze radiative transfer problems, such as those encountered in stellar atmospheres or inertial confinement fusion. Larsen and Mercier [2] have shown that the IMC method violates a maximum principle that is satisfied by the exact solution to the radiative transfer equation. Except for [2] and related papers regarding the maximum principle, there have been no other published results regarding the analysis of errors or convergence properties for the IMC method. This work presents an exact error analysis for the IMC method by using the analytical solutions for infinite medium geometry (0-D) to determine closed form expressions for the errors. The goal is to gain insight regarding the errors inherent in the IMC method by relating the exact 0-D errors to multi-dimensional geometry. Additional work (not described herein) has shown that adding a leakage term (i.e., a 'buckling' term) to the 0-D equations has relatively little effect on the IMC errors analyzed in this paper, so that the 0-D errors should provide useful guidance for the errors observed in multi-dimensional simulations.
Monte Carlo simulation of stoquastic Hamiltonians
Sergey Bravyi
2015-01-08
Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field Ising Model (TIM), the Heisenberg model on bipartite graphs, and the bosonic Hubbard model. Here we consider the problem of estimating the ground state energy of a local stoquastic Hamiltonian $H$ with a promise that the ground state of $H$ has a non-negligible correlation with some `guiding' state that admits a concise classical description. A formalized version of this problem called Guided Stoquastic Hamiltonian is shown to be complete for the complexity class MA (a probabilistic analogue of NP). To prove this result we employ the Projection Monte Carlo algorithm with a variable number of walkers. Secondly, we show that the ground state and thermal equilibrium properties of the ferromagnetic TIM can be simulated in polynomial time on a classical probabilistic computer. This result is based on the approximation algorithm for the classical ferromagnetic Ising model due to Jerrrum and Sinclair (1993).
Monte Carlo simulations of the NIMROD diffractometer
NASA Astrophysics Data System (ADS)
Botti, A.; Ricci, M. A.; Bowron, D. T.; Soper, A. K.
2006-11-01
The near and intermediate range order diffractometer (NIMROD) has been selected as a day one instrument on the second target station at ISIS. Uniquely, NIMROD will provide continuous access to particle separations ranging from the interatomic (<1 Å) to the mesoscopic (<300 Å). This instrument is mainly designed for structural investigations, although the possibility of putting a Fermi chopper (and corresponding NIMONIC chopper) in the incident beam line, will potentially allow the performance of low resolution inelastic scattering measurements. The performance characteristics of the TOF diffractometer have been simulated by means of a series of Monte Carlo calculations. In particular, the flux as a function of the transferred momentum Q as well as the resolution in Q and transferred energy have been estimated. Moreover, the possibility of including a honeycomb collimator in order to achieve better resolution has been tested. Here, we want to present the design of this diffractometer that will bridge the gap between wide- and small-angle neutron scattering experiments.
DETERMINING UNCERTAINTY IN PHYSICAL PARAMETER MEASUREMENTS BY MONTE CARLO SIMULATION
A statistical approach, often called Monte Carlo Simulation, has been used to examine propagation of error with measurement of several parameters important in predicting environmental transport of chemicals. These parameters are vapor pressure, water solubility, octanol-water par...
Variance Reduction Techniques for Implicit Monte Carlo Simulations
Landman, Jacob Taylor
2013-09-19
The Implicit Monte Carlo (IMC) method is widely used for simulating thermal radiative transfer and solving the radiation transport equation. During an IMC run a grid network is constructed and particles are sourced into the problem to simulate...
Implementing Markov chain Monte Carlo: Estimating with confidence
Jones, Galin
, calculating and reporting the Monte Carlo standard error (MCSE), ^n/ n, allows everyone to judge in the reported estimate, and moreover, including an MCSE with the point estimate allows others to assess its
Calculating Air Resistance using the Monte Carlo Method
NSDL National Science Digital Library
Students will discover the terminal velocity to mass relationship and use this information to calculate the air resistance constant. They will evaluate the accuracy of their lab using the Monte Carlo method.
Markovian Monte Carlo solutions of the NLO QCD evolution equations
K. Golec-Biernat; S. Jadach; W. Placzek; M. Skrzypek
2006-03-03
We present precision Monte Carlo calculations solving the QCD evolution equations up to the next-to-leading-order (NLO) level. They employ forward Markovian Monte Carlo (FMC) algorithms, which provide the rigorous solutions of the QCD evolution equations. Appropriate Monte Carlo algorithms are described in detail. They are implemented in the form of the Monte Carlo program EvolFMC, which features the NLO kernels for the QCD evolution. The presented numerical results agree with those from independent, non-MC, programs (QCDNum16, APCheb33) at the level of 0.1%. In this way we have demonstrated the feasibility of the precision MC calculations for the QCD evolution and provided very useful numerical tests (benchmarks) for other, non-Markovian, MC algorithms developed recently.
Monte Carlo Simulations of Thermal Conductivity in Nanoporous Si Membranes
; Boltzmann-Transport-Equation; Monte-Carlo; nanoporous silicon; nanomesh; thermoelectrics Introduction candidates for thermoelectric materials as they can provide extremely low thermal conductivity , relatively high thermoelectric power factors, and the structure stability that other low-dimensional systems
Monte Carlo Sensor Networks Thomas C. Henderson, Brandt Erickson,
Henderson, Thomas C.
Monte Carlo Sensor Networks Thomas C. Henderson, Brandt Erickson, Travis Longoria, Eddie Grant*, Kyle Luthy*, Leonardo Mattos*, and Matt Craver* UUCS-05-001 School of Computing University of Utah Salt
Variance Reduction Techniques for Implicit Monte Carlo Simulations
Landman, Jacob Taylor
2013-09-19
The Implicit Monte Carlo (IMC) method is widely used for simulating thermal radiative transfer and solving the radiation transport equation. During an IMC run a grid network is constructed and particles are sourced into the problem to simulate...
Low variance methods for Monte Carlo simulation of phonon transport
Péraud, Jean-Philippe M. (Jean-Philippe Michel)
2011-01-01
Computational studies in kinetic transport are of great use in micro and nanotechnologies. In this work, we focus on Monte Carlo methods for phonon transport, intended for studies in microscale heat transfer. After reviewing ...
Monte Carlo methods for parallel processing of diffusion equations
Vafadari, Cyrus
2013-01-01
A Monte Carlo algorithm for solving simple linear systems using a random walk is demonstrated and analyzed. The described algorithm solves for each element in the solution vector independently. Furthermore, it is demonstrated ...
Enhancements in Continuous-Energy Monte Carlo Capabilities in SCALE
Bekar, Kursat B [ORNL] [ORNL; Celik, Cihangir [ORNL] [ORNL; Wiarda, Dorothea [ORNL] [ORNL; Peplow, Douglas E. [ORNL] [ORNL; Rearden, Bradley T [ORNL] [ORNL; Dunn, Michael E [ORNL] [ORNL
2013-01-01
Monte Carlo tools in SCALE are commonly used in criticality safety calculations as well as sensitivity and uncertainty analysis, depletion, and criticality alarm system analyses. Recent improvements in the continuous-energy data generated by the AMPX code system and significant advancements in the continuous-energy treatment in the KENO Monte Carlo eigenvalue codes facilitate the use of SCALE Monte Carlo codes to model geometrically complex systems with enhanced solution fidelity. The addition of continuous-energy treatment to the SCALE Monaco code, which can be used with automatic variance reduction in the hybrid MAVRIC sequence, provides significant enhancements, especially for criticality alarm system modeling. This paper describes some of the advancements in continuous-energy Monte Carlo codes within the SCALE code system.
OBJECT KINETIC MONTE CARLO SIMULATIONS OF CASCADE ANNEALING IN TUNGSTEN
Nandipati, Giridhar; Setyawan, Wahyu; Heinisch, Howard L.; Roche, Kenneth J.; Kurtz, Richard J.; Wirth, Brian D.
2014-03-31
The objective of this work is to study the annealing of primary cascade damage created by primary knock-on atoms (PKAs) of various energies, at various temperatures in bulk tungsten using the object kinetic Monte Carlo (OKMC) method.
Combinatorial geometry domain decomposition strategies for Monte Carlo simulations
Li, G.; Zhang, B.; Deng, L.; Mo, Z.; Liu, Z.; Shangguan, D.; Ma, Y.; Li, S.; Hu, Z. [Institute of Applied Physics and Computational Mathematics, Beijing, 100094 (China)
2013-07-01
Analysis and modeling of nuclear reactors can lead to memory overload for a single core processor when it comes to refined modeling. A method to solve this problem is called 'domain decomposition'. In the current work, domain decomposition algorithms for a combinatorial geometry Monte Carlo transport code are developed on the JCOGIN (J Combinatorial Geometry Monte Carlo transport INfrastructure). Tree-based decomposition and asynchronous communication of particle information between domains are described in the paper. Combination of domain decomposition and domain replication (particle parallelism) is demonstrated and compared with that of MERCURY code. A full-core reactor model is simulated to verify the domain decomposition algorithms using the Monte Carlo particle transport code JMCT (J Monte Carlo Transport Code), which has being developed on the JCOGIN infrastructure. Besides, influences of the domain decomposition algorithms to tally variances are discussed. (authors)
Monte Carlo Methods for Uncertainty Quantification Mathematical Institute, University of Oxford
Giles, Mike
Monte Carlo Methods for Uncertainty Quantification Mike Giles Mathematical Institute, University October 25, 2013 Mike Giles (Oxford) Monte Carlo methods October 25, 2013 1 / 28 Lecture outline Lecture 2 Hypercube randomised quasi-Monte Carlo Mike Giles (Oxford) Monte Carlo methods October 25, 2013 2 / 28
Monte Carlo Methods for Uncertainty Quantification Mathematical Institute, University of Oxford
Giles, Mike
Monte Carlo Methods for Uncertainty Quantification Mike Giles Mathematical Institute, University October 25, 2013 Mike Giles (Oxford) Monte Carlo methods October 25, 2013 1 / 28 #12;Lecture outline-Monte Carlo Mike Giles (Oxford) Monte Carlo methods October 25, 2013 2 / 28 #12;Lecture outline Lecture 3
Monte Carlo Methods for Uncertainty Quantification Mathematical Institute, University of Oxford
Giles, Mike
Monte Carlo Methods for Uncertainty Quantification Mike Giles Mathematical Institute, University October 25, 2013 Mike Giles (Oxford) Monte Carlo methods October 25, 2013 1 / 28 #12;Lecture outline sampling Latin Hypercube randomised quasi-Monte Carlo Mike Giles (Oxford) Monte Carlo methods October 25
A Monte Carlo method to compute the exchange coefficient in the double porosity model
Paris-Sud XI, UniversitÃ© de
A Monte Carlo method to compute the exchange coefficient in the double porosity model Fabien: Monte Carlo methods, double porosity model, ran- dom walk on squares, fissured media AMS Classification: 76S05 (65C05 76M35) Published in Monte Carlo Methods Appl.. Proc. of Monte Carlo and probabilistic
Monte Carlo study of the Baxter-Wu model Nir Schreiber and Dr. Joan Adler
Adler, Joan
Monte Carlo study of the Baxter-Wu model Nir Schreiber and Dr. Joan Adler Monte Carlo study of the Baxter-Wu model Â p.1/40 #12;Outline Theory of phase transitions, Monte Carlo simulations and finite size scaling Landau-Wang algorithm Results Summary Monte Carlo study of the Baxter-Wu model Â p.2/40 #12;Phase
Monte Carlo Simulation of Electrodeposition of Copper: A Multistep Free Energy Calculation
Subramanian, Venkat
Monte Carlo Simulation of Electrodeposition of Copper: A Multistep Free Energy Calculation S such as continuum Monte Carlo, kinetic Monte Carlo (KMC), and molecular dynamics have been used for simulating is very time-consuming. Thus a less time-consuming and novel multistep continuum Monte Carlo simulation
Monte Carlo EM for Generalized Linear Mixed Models using Randomized Spherical Radial
Booth, James
Monte Carlo EM for Generalized Linear Mixed Models using Randomized Spherical Radial Integration by Monte Carlo methods. However, in practice, the Monte Carlo sample sizes required for convergence for such methods. One solution is to use Monte Carlo approximation, as proposed by Wei and Tanner (1990
Development of Monte Carlo Capability for Orion Parachute Simulations
NASA Technical Reports Server (NTRS)
Moore, James W.
2011-01-01
Parachute test programs employ Monte Carlo simulation techniques to plan testing and make critical decisions related to parachute loads, rate-of-descent, or other parameters. This paper describes the development and use of a MATLAB-based Monte Carlo tool for three parachute drop test simulations currently used by NASA. The Decelerator System Simulation (DSS) is a legacy 6 Degree-of-Freedom (DOF) simulation used to predict parachute loads and descent trajectories. The Decelerator System Simulation Application (DSSA) is a 6-DOF simulation that is well suited for modeling aircraft extraction and descent of pallet-like test vehicles. The Drop Test Vehicle Simulation (DTVSim) is a 2-DOF trajectory simulation that is convenient for quick turn-around analysis tasks. These three tools have significantly different software architectures and do not share common input files or output data structures. Separate Monte Carlo tools were initially developed for each simulation. A recently-developed simulation output structure enables the use of the more sophisticated DSSA Monte Carlo tool with any of the core-simulations. The task of configuring the inputs for the nominal simulation is left to the existing tools. Once the nominal simulation is configured, the Monte Carlo tool perturbs the input set according to dispersion rules created by the analyst. These rules define the statistical distribution and parameters to be applied to each simulation input. Individual dispersed parameters are combined to create a dispersed set of simulation inputs. The Monte Carlo tool repeatedly executes the core-simulation with the dispersed inputs and stores the results for analysis. The analyst may define conditions on one or more output parameters at which to collect data slices. The tool provides a versatile interface for reviewing output of large Monte Carlo data sets while preserving the capability for detailed examination of individual dispersed trajectories. The Monte Carlo tool described in this paper has proven useful in planning several Crew Exploration Vehicle parachute tests.
Public Infrastructure for Monte Carlo Simulation : publicMCatBATAN
NASA Astrophysics Data System (ADS)
Waskita, A. A.; Prasetyo, N. A.; Akbar, Z.; Handoko, L. T.
2010-06-01
The first cluster-based public computing for Monte Carlo simulation in Indonesia is introduced. The system has been developed to enable public to perform Monte Carlo simulation on a parallel computer through an integrated and user friendly dynamic web interface. The beta version, so called publicMC@BATAN, has been released and implemented for internal users at the National Nuclear Energy Agency (BATAN). In this paper the concept and architecture of publicMC@BATAN are presented.
Molecular physics and chemistry applications of quantum Monte Carlo
P. J. Reynolds; R. N. Barnett; B. L. Hammond; W. A. Lester
1986-01-01
We discuss recent work with the diffusion quantum Monte Carlo (QMC) method in its application to molecular systems. The formal\\u000a correspondence of the imaginary-time Schrödinger equation to a diffusion equation allows one to calculate quantum mechanical\\u000a expectation values as Monte Carlo averages over an ensemble of random walks. We report work on atomic and molecular total\\u000a energies, as well as
MOS2: an efficient MOnte Carlo Simulator for MOS devices
Enrico Sangiorgi; Bruno Riccò; Franco Venturi
1988-01-01
An efficient Monte Carlo device simulator has been developed as a postprocessor of a two-dimensional numerical analyzer based on the drift-diffusion model. The Monte Carlo package analyzes real VLSI MOSFETs in a minicomputer environment, overcoming some existing theoretical and practical problems. In particular, the particle free-flight time distribution is obtained by a new algorithm, leading to a CPU time saving
Shell model Monte Carlo calculations for Dy-170
D. J. Dean; S. E. Koonin; G. H. Lang; P. B. Radha; W. E. Ormand
1993-09-28
We present the first auxiliary field Monte Carlo calculations for a rare earth nucleus, Dy-170. A pairing plus quadrupole Hamiltonian is used to demonstrate the physical properties that can be studied in this region. We calculate various static observables for both uncranked and cranked systems and show how the shape distribution evolves with temperature. We also introduce a discretization of the path integral that allows a more efficient Monte Carlo sampling.
Path Integral Quantum Monte Carlo Benchmarks for Molecules and Plasmas
NASA Astrophysics Data System (ADS)
Shumway, John
2013-03-01
Path integral quantum Monte Carlo is used to simulate hot dense plasmas and other systems where quantum and thermal fluctuations are important. The fixed node approximation--ubiquitous in ab initio ground state Quantum Monte Carlo--is more complicated at finite temperatures, with many unanswered questions. In this talk I discuss the current state of fermionic path integral quantum Monte Carlo, with an emphasis on molecular systems where good benchmark data exists. We look at two ways of formulating the fixed node constraint and strategies for constructing finite-temperature nodal surfaces. We compare different the free energies of different nodal choices by sampling an ensemble of nodal models within a Monte Carlo simulation. We also present data on imaginary-time correlation fluctuations, which can be surprisingly accurate for molecular vibrations and polarizabilty. Path integral quantum Monte Carlo is used to simulate hot dense plasmas and other systems where quantum and thermal fluctuations are important. The fixed node approximation--ubiquitous in ab initio ground state Quantum Monte Carlo--is more complicated at finite temperatures, with many unanswered questions. In this talk I discuss the current state of fermionic path integral quantum Monte Carlo, with an emphasis on molecular systems where good benchmark data exists. We look at two ways of formulating the fixed node constraint and strategies for constructing finite-temperature nodal surfaces. We compare different the free energies of different nodal choices by sampling an ensemble of nodal models within a Monte Carlo simulation. We also present data on imaginary-time correlation fluctuations, which can be surprisingly accurate for molecular vibrations and polarizabilty. Work supported by NSF OCI 1148502.
Methods for calculating forces within quantum Monte Carlo simulations.
Badinski, A; Haynes, P D; Trail, J R; Needs, R J
2010-02-24
Atomic force calculations within the variational and diffusion quantum Monte Carlo methods are described. The advantages of calculating diffusion quantum Monte Carlo forces with the 'pure' rather than the 'mixed' probability distribution are discussed. An accurate and practical method for calculating forces using the pure distribution is presented and tested for the SiH molecule. The statistics of force estimators are explored and violations of the central limit theorem are found in some cases. PMID:21386380
Green's function Monte Carlo calculations of /sup 4/He
Carlson, J.A.
1988-01-01
Green's Function Monte Carlo methods have been developed to study the ground state properties of light nuclei. These methods are shown to reproduce results of Faddeev calculations for A = 3, and are then used to calculate ground state energies, one- and two-body distribution functions, and the D-state probability for the alpha particle. Results are compared to variational Monte Carlo calculations for several nuclear interaction models. 31 refs.
Shift: A Massively Parallel Monte Carlo Radiation Transport Package
Pandya, Tara M [ORNL; Johnson, Seth R [ORNL; Davidson, Gregory G [ORNL; Evans, Thomas M [ORNL; Hamilton, Steven P [ORNL
2015-01-01
This paper discusses the massively-parallel Monte Carlo radiation transport package, Shift, de- veloped at Oak Ridge National Laboratory. It reviews the capabilities, implementation, and parallel performance of this code package. Scaling results demonstrate very good strong and weak scaling behavior of the implemented algorithms. Benchmark results from various reactor problems show that Shift results compare well to other contemporary Monte Carlo codes and experimental results.
Monte Carlo for top background at the Tevatron
Amnon Harel
2008-07-25
We review the use of Monte Carlo simulation to model backgrounds to top signal at the Tevatron experiments, CDF and D0, as well as the relevant measurements done by the experiments. We'll concentrate on the modeling of W and Z boson production in association with jets, in particular heavy flavor jets, and also comment on the Tevatron experience using matched Monte Carlo.
Monte Carlo simulations of the Galileo energetic particle detector
I Jun; J. M Ratliff; H. B Garrett; R. W McEntire
2002-01-01
Monte Carlo radiation transport studies have been performed for the Galileo spacecraft energetic particle detector (EPD) in order to study its response to energetic electrons and protons. Three-dimensional Monte Carlo radiation transport codes, MCNP version 4B (for electrons) and MCNPX version 2.2.3 (for protons), were used throughout the study. The results are presented in the form of “geometric factors” for
Study of the Transition Flow Regime using Monte Carlo Methods
NASA Technical Reports Server (NTRS)
Hassan, H. A.
1999-01-01
This NASA Cooperative Agreement presents a study of the Transition Flow Regime Using Monte Carlo Methods. The topics included in this final report are: 1) New Direct Simulation Monte Carlo (DSMC) procedures; 2) The DS3W and DS2A Programs; 3) Papers presented; 4) Miscellaneous Applications and Program Modifications; 5) Solution of Transitional Wake Flows at Mach 10; and 6) Turbulence Modeling of Shock-Dominated Fows with a k-Enstrophy Formulation.
Markov Chain Monte Carlo Methods in Biostatistics Andrew Gelman
Gelman, Andrew
Markov Chain Monte Carlo Methods in Biostatistics Andrew Gelman Department of Statistics Columbia May 21, 1996 1 Introduction Appropriate models in biostatistics are often quite complicated, re ecting in biostatistics. These readers can use this article as an introduction to the ways in which Markov chain Monte
4 Monte Carlo Methods in Classical Statistical Physics
Janke, Wolfhard
4 Monte Carlo Methods in Classical Statistical Physics Wolfhard Janke Institut f¨ur Theoretische update algorithms (Metropolis, heat-bath, Glauber). Then methods for the statistical analysis of the thus Carlo Methods in Classical Statistical Physics, Lect. Notes Phys. 739, 79140 (2008) DOI 10
Monte Carlo simulations of supported bimetallic catalysts
Strohl, J.K.; King, T.S. (Iowa State Univ., Ames (USA))
1989-04-01
Supported bimetallic catalysts are modeled with a Monte Carlo simulation technique that uses a coordination-dependent potential model. Cubo-octahedral particles with dispersions ranging from 30 to 60% are studied as well as particles that have irregular shapes. Systems modeled include the Pt-Ib (Ib = Cu, Ag, Au), Ag-Ru, and Pt-Rh bimetallics. In the Pt-Ib systems, the Ib element segregates to the surface of the catalyst and tends to occupy the lowest coordinated sites first. Differences in the degree of surface segregation among the Ib elements are easily seen at higher Ib concentrations where Au is shown to segregate to the surface more strongly than Ag or Cu. The degree of clustering of Pt atoms on the surface of the catalyst particles depends on which Ib element is present. For a given amount of Ib atoms present on the surface the Au-Pt system is observed to produce large ensembles of surface Pt atoms than the Ag-Pt or Cu-Pt systems. Predicted relative platinum dispersions for the Ag-Pt system were compared to hydrogen chemisorption measurements and found to be in good agreement except for one sample (30 wt% Ag) in which the measured value was found to be higher than the predicted value. This difference could be explained by a nonuniform distribution of silver in the catalyst sample or by the effect of chemisorption. In the Ag-Ru system, silver atoms are found to segregate to the surface and cluster together. Predicted relative ruthenium dispersion is compared to hydrogen chemisorption measurements and found to be in agreement. The Pt-Rh system showed that platinum atoms undergo net surface segregation, although rhodium atoms tended to dominate the corner and edge sites of the crystallites.
Lattice Monte Carlo Simulations of Polymer Melts
Hsiao-Ping Hsu
2015-03-03
We use Monte Carlo simulations to study polymer melts consisting of fully flexible and moderately stiff chains in the bond fluctuation model at a volume fraction $0.5$. In order to reduce the local density fluctuations, we test a pre-packing process for the preparation of the initial configurations of the polymer melts, before the excluded volume interaction is switched on completely. This process leads to a significantly faster decrease of the number of overlapping monomers on the lattice. This is useful for simulating very large systems, where the statistical properties of the model with a marginally incomplete elimination of excluded volume violations are the same as those of the model with strictly excluded volume. We find that the internal mean square end-to-end distance for moderately stiff chains in a melt can be very well described by a freely rotating chain model with a precise estimate of the bond-bond orientational correlation between two successive bond vectors in equilibrium. The plot of the probability distributions of the reduced end-to-end distance of chains of different stiffness also shows that the data collapse is excellent and described very well by the Gaussian distribution for ideal chains. However, while our results confirm the systematic deviations between Gaussian statistics for the chain structure factor $S_c(q)$ [minimum in the Kratky-plot] found by Wittmer et al.~\\{EPL {\\bf 77} 56003 (2007).\\} for fully flexible chains in a melt, we show that for the available chain length these deviations are no longer visible, when the chain stiffness is included. The mean square bond length and the compressibility estimated from collective structure factors depend slightly on the stiffness of the chains.
Extending Diffusion Monte Carlo to Internal Coordinates
NASA Astrophysics Data System (ADS)
Petit, Andrew S.; McCoy, Anne B.
2013-06-01
Diffusion Monte Carlo (DMC) is a powerful technique for studying the properties of molecules and clusters that undergo large-amplitude, zero-point vibrational motions. However, the overall applicability of the method is limited by the need to work in Cartesian coordinates and therefore have available a full-dimensional potential energy surface (PES). As a result, the development of a reduced-dimensional DMC methodology has the potential to significantly extend the range of problems that DMC can address by allowing the calculations to be performed in the subset of coordinates that is physically relevant to the questions being asked, thereby eliminating the need for a full-dimensional PES. As a first step towards this goal, we describe here an internal coordinate extension of DMC that places no constraints on the choice of internal coordinates other than requiring them all to be independent. Using H_3^+ and its isotopologues as model systems, we demonstrate that the methodology is capable of successfully describing the ground state properties of highly fluxional molecules as well as, in conjunction with the fixed-node approximation, the ?=1 vibrationally excited states. The calculations of the fundamentals of H_3^+ and its isotopologues provided general insights into the properties of the nodal surfaces of vibrationally excited states. Specifically, we will demonstrate that analysis of ground state probability distributions can point to the set of coordinates that are less strongly coupled and therefore more suitable for use as nodal coordinates in the fixed-node approximation. In particular, we show that nodal surfaces defined in terms of the curvilinear normal mode coordinates are reasonable for the fundamentals of H_2D^+ and D_2H^+ despite both molecules being highly fluxional.
Monte carlo sampling of fission multiplicity.
Hendricks, J. S. (John S.)
2004-01-01
Two new methods have been developed for fission multiplicity modeling in Monte Carlo calculations. The traditional method of sampling neutron multiplicity from fission is to sample the number of neutrons above or below the average. For example, if there are 2.7 neutrons per fission, three would be chosen 70% of the time and two would be chosen 30% of the time. For many applications, particularly {sup 3}He coincidence counting, a better estimate of the true number of neutrons per fission is required. Generally, this number is estimated by sampling a Gaussian distribution about the average. However, because the tail of the Gaussian distribution is negative and negative neutrons cannot be produced, a slight positive bias can be found in the average value. For criticality calculations, the result of rejecting the negative neutrons is an increase in k{sub eff} of 0.1% in some cases. For spontaneous fission, where the average number of neutrons emitted from fission is low, the error also can be unacceptably large. If the Gaussian width approaches the average number of fissions, 10% too many fission neutrons are produced by not treating the negative Gaussian tail adequately. The first method to treat the Gaussian tail is to determine a correction offset, which then is subtracted from all sampled values of the number of neutrons produced. This offset depends on the average value for any given fission at any energy and must be computed efficiently at each fission from the non-integrable error function. The second method is to determine a corrected zero point so that all neutrons sampled between zero and the corrected zero point are killed to compensate for the negative Gaussian tail bias. Again, the zero point must be computed efficiently at each fission. Both methods give excellent results with a negligible computing time penalty. It is now possible to include the full effects of fission multiplicity without the negative Gaussian tail bias.
Marc Soutter; André Musy
1998-01-01
A method to predict groundwater vulnerability to pesticide contamination on a regional scale has been developed and applied to a part of the upper Rhone river valley in Western Switzerland. Stochastic application of deterministic pesticide leaching models (Monte-Carlo), along with geostatistical interpolation techniques, were used to map both vulnerability levels and uncertainties. The various tested leaching models (numerical and analytical
1/ 17 Monte Carlo Simulation of the Law of the Maximum of a L´evy Process Monte Carlo Simulation of Mathematical Sciences, University of Bath #12;2/ 17 Monte Carlo Simulation of the Law of the Maximum of a L´evy Process Motivation #12;2/ 17 Monte Carlo Simulation of the Law of the Maximum of a L´evy Process
Lattice Monte Carlo simulation of Galilei variant anomalous diffusion
NASA Astrophysics Data System (ADS)
Guo, Gang; Bittig, Arne; Uhrmacher, Adelinde
2015-05-01
The observation of an increasing number of anomalous diffusion phenomena motivates the study to reveal the actual reason for such stochastic processes. When it is difficult to get analytical solutions or necessary to track the trajectory of particles, lattice Monte Carlo (LMC) simulation has been shown to be particularly useful. To develop such an LMC simulation algorithm for the Galilei variant anomalous diffusion, we derive explicit solutions for the conditional and unconditional first passage time (FPT) distributions with double absorbing barriers. According to the theory of random walks on lattices and the FPT distributions, we propose an LMC simulation algorithm and prove that such LMC simulation can reproduce both the mean and the mean square displacement exactly in the long-time limit. However, the error introduced in the second moment of the displacement diverges according to a power law as the simulation time progresses. We give an explicit criterion for choosing a small enough lattice step to limit the error within the specified tolerance. We further validate the LMC simulation algorithm and confirm the theoretical error analysis through numerical simulations. The numerical results agree with our theoretical predictions very well.
Monte Carlo role in radiobiological modelling of radiotherapy outcomes
NASA Astrophysics Data System (ADS)
El Naqa, Issam; Pater, Piotr; Seuntjens, Jan
2012-06-01
Radiobiological models are essential components of modern radiotherapy. They are increasingly applied to optimize and evaluate the quality of different treatment planning modalities. They are frequently used in designing new radiotherapy clinical trials by estimating the expected therapeutic ratio of new protocols. In radiobiology, the therapeutic ratio is estimated from the expected gain in tumour control probability (TCP) to the risk of normal tissue complication probability (NTCP). However, estimates of TCP/NTCP are currently based on the deterministic and simplistic linear-quadratic formalism with limited prediction power when applied prospectively. Given the complex and stochastic nature of the physical, chemical and biological interactions associated with spatial and temporal radiation induced effects in living tissues, it is conjectured that methods based on Monte Carlo (MC) analysis may provide better estimates of TCP/NTCP for radiotherapy treatment planning and trial design. Indeed, over the past few decades, methods based on MC have demonstrated superior performance for accurate simulation of radiation transport, tumour growth and particle track structures; however, successful application of modelling radiobiological response and outcomes in radiotherapy is still hampered with several challenges. In this review, we provide an overview of some of the main techniques used in radiobiological modelling for radiotherapy, with focus on the MC role as a promising computational vehicle. We highlight the current challenges, issues and future potentials of the MC approach towards a comprehensive systems-based framework in radiobiological modelling for radiotherapy.
Uncertainty Analyses for Localized Tallies in Monte Carlo Eigenvalue Calculations
Mervin, Brenden T. [Oak Ridge Associated Universities (ORAU); Maldonado, G Ivan [ORNL; Mosher, Scott W [ORNL; Wagner, John C [ORNL
2011-01-01
It is well known that statistical estimates obtained from Monte Carlo criticality simulations can be adversely affected by cycle-to-cycle correlations in the fission source. In addition there are several other more fundamental issues that may lead to errors in Monte Carlo results. These factors can have a significant impact on the calculated eigenvalue, localized tally means and their associated standard deviations. In fact, modern Monte Carlo computational tools may generate standard deviation estimates that are a factor of five or more lower than the true standard deviation for a particular tally due to the inter-cycle correlations in the fission source. The magnitude of this under-prediction can climb as high as one hundred when combined with an ill-converged fission source or poor sampling techniques. Since Monte Carlo methods are widely used in reactor analysis (as a benchmarking tool) and criticality safety applications, an in-depth understanding of the effects of these issues must be developed in order to support the practical use of Monte Carlo software packages. A rigorous statistical analysis of localized tally results in eigenvalue calculations is presented using the SCALE/KENO-VI and MCNP Monte Carlo codes. The purpose of this analysis is to investigate the under-prediction in the uncertainty and its sensitivity to problem characteristics and calculational parameters, and to provide a comparative study between the two codes with respect to this under-prediction. It is shown herein that adequate source convergence along with proper specification of Monte Carlo parameters can reduce the magnitude of under-prediction in the uncertainty to reasonable levels; below a factor of 2 when inter-cycle correlations in the fission source are not a significant factor. In addition, through the use of a modified sampling procedure, the effects of inter-cycle correlations on both the mean value and standard deviation estimates can be isolated.
Mascagni, Michael
Analysis of Large-scale Grid-based Monte Carlo Applications Analysis of Large-scale Grid-based Monte Carlo Applications Yaohang Li and Michael Mascagni Department of Computer Science and School-based Monte Carlo Applications Yaohang Li* Department of Computer Science and School of Computational Science
A rare event sampling method for diffusion Monte Carlo using smart darting
NASA Astrophysics Data System (ADS)
Roberts, K.; Sebsebie, R.; Curotto, E.
2012-02-01
We identify a set of multidimensional potential energy surfaces sufficiently complex to cause both the classical parallel tempering and the guided or unguided diffusion Monte Carlo methods to converge too inefficiently for practical applications. The mathematical model is constructed as a linear combination of decoupled Double Wells [(DDW)n]. We show that the set (DDW)n provides a serious test for new methods aimed at addressing rare event sampling in stochastic simulations. Unlike the typical numerical tests used in these cases, the thermodynamics and the quantum dynamics for (DDW)n can be solved deterministically. We use the potential energy set (DDW)n to explore and identify methods that can enhance the diffusion Monte Carlo algorithm. We demonstrate that the smart darting method succeeds at reducing quasiergodicity for n ? 100 using just 1 × 106 moves in classical simulations (DDW)n. Finally, we prove that smart darting, when incorporated into the regular or the guided diffusion Monte Carlo algorithm, drastically improves its convergence. The new method promises to significantly extend the range of systems computationally tractable by the diffusion Monte Carlo algorithm.
Smith, Leon E.; Gesh, Christopher J.; Pagh, Richard T.; Miller, Erin A.; Shaver, Mark W.; Ashbaker, Eric D.; Batdorf, Michael T.; Ellis, J. E.; Kaye, William R.; McConn, Ronald J.; Meriwether, George H.; Ressler, Jennifer J.; Valsan, Andrei B.; Wareing, Todd A.
2008-10-31
Radiation transport modeling methods used in the radiation detection community fall into one of two broad categories: stochastic (Monte Carlo) and deterministic. Monte Carlo methods are typically the tool of choice for simulating gamma-ray spectrometers operating in homeland and national security settings (e.g. portal monitoring of vehicles or isotope identification using handheld devices), but deterministic codes that discretize the linear Boltzmann transport equation in space, angle, and energy offer potential advantages in computational efficiency for many complex radiation detection problems. This paper describes the development of a scenario simulation framework based on deterministic algorithms. Key challenges include: formulating methods to automatically define an energy group structure that can support modeling of gamma-ray spectrometers ranging from low to high resolution; combining deterministic transport algorithms (e.g. ray-tracing and discrete ordinates) to mitigate ray effects for a wide range of problem types; and developing efficient and accurate methods to calculate gamma-ray spectrometer response functions from the deterministic angular flux solutions. The software framework aimed at addressing these challenges is described and results from test problems that compare coupled deterministic-Monte Carlo methods and purely Monte Carlo approaches are provided.
Lee, Anthony; Yau, Christopher; Giles, Michael B; Doucet, Arnaud; Holmes, Christopher C
2010-12-01
We present a case-study on the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods. Graphics cards, containing multiple Graphics Processing Units (GPUs), are self-contained parallel computational devices that can be housed in conventional desktop and laptop computers and can be thought of as prototypes of the next generation of many-core processors. For certain classes of population-based Monte Carlo algorithms they offer massively parallel simulation, with the added advantage over conventional distributed multi-core processors that they are cheap, easily accessible, easy to maintain, easy to code, dedicated local devices with low power consumption. On a canonical set of stochastic simulation examples including population-based Markov chain Monte Carlo methods and Sequential Monte Carlo methods, we nd speedups from 35 to 500 fold over conventional single-threaded computer code. Our findings suggest that GPUs have the potential to facilitate the growth of statistical modelling into complex data rich domains through the availability of cheap and accessible many-core computation. We believe the speedup we observe should motivate wider use of parallelizable simulation methods and greater methodological attention to their design. PMID:22003276
Probability Forecasting Using Monte Carlo Simulation
NASA Astrophysics Data System (ADS)
Duncan, M.; Frisbee, J.; Wysack, J.
2014-09-01
Space Situational Awareness (SSA) is defined as the knowledge and characterization of all aspects of space. SSA is now a fundamental and critical component of space operations. Increased dependence on our space assets has in turn lead to a greater need for accurate, near real-time knowledge of all space activities. With the growth of the orbital debris population, satellite operators are performing collision avoidance maneuvers more frequently. Frequent maneuver execution expends fuel and reduces the operational lifetime of the spacecraft. Thus the need for new, more sophisticated collision threat characterization methods must be implemented. The collision probability metric is used operationally to quantify the collision risk. The collision probability is typically calculated days into the future, so that high risk and potential high risk conjunction events are identified early enough to develop an appropriate course of action. As the time horizon to the conjunction event is reduced, the collision probability changes. A significant change in the collision probability will change the satellite mission stakeholder's course of action. So constructing a method for estimating how the collision probability will evolve improves operations by providing satellite operators with a new piece of information, namely an estimate or 'forecast' of how the risk will change as time to the event is reduced. Collision probability forecasting is a predictive process where the future risk of a conjunction event is estimated. The method utilizes a Monte Carlo simulation that produces a likelihood distribution for a given collision threshold. Using known state and state uncertainty information, the simulation generates a set possible trajectories for a given space object pair. Each new trajectory produces a unique event geometry at the time of close approach. Given state uncertainty information for both objects, a collision probability value can be computed for every trail. This yields a collision probability distribution given known, predicted uncertainty. This paper presents the details of the collision probability forecasting method. We examine various conjunction event scenarios and numerically demonstrate the utility of this approach in typical event scenarios. We explore the utility of a probability-based track scenario simulation that models expected tracking data frequency as the tasking levels are increased. The resulting orbital uncertainty is subsequently used in the forecasting algorithm.
Monte Carlo evaluation of kerma in an HDR brachytherapy bunker.
Pérez-Calatayud, J; Granero, D; Ballester, F; Casal, E; Crispin, V; Puchades, V; León, A; Verdú, G
2004-12-21
In recent years, the use of high dose rate (HDR) after-loader machines has greatly increased due to the shift from traditional Cs-137/Ir-192 low dose rate (LDR) to HDR brachytherapy. The method used to calculate the required concrete and, where appropriate, lead shielding in the door is based on analytical methods provided by documents published by the ICRP, the IAEA and the NCRP. The purpose of this study is to perform a more realistic kerma evaluation at the entrance maze door of an HDR bunker using the Monte Carlo code GEANT4. The Monte Carlo results were validated experimentally. The spectrum at the maze entrance door, obtained with Monte Carlo, has an average energy of about 110 keV, maintaining a similar value along the length of the maze. The comparison of results from the aforementioned values with the Monte Carlo ones shows that results obtained using the albedo coefficient from the ICRP document more closely match those given by the Monte Carlo method, although the maximum value given by MC calculations is 30% greater. PMID:15724543
A new method to assess Monte Carlo convergence
Forster, R.A.; Booth, T.E.; Pederson, S.P.
1993-05-01
The central limit theorem can be applied to a Monte Carlo solution if the following two requirements are satisfied: (1) the random variable has a finite mean and a finite variance; and (2) the number N of independent observations grows large. When these are satisfied, a confidence interval based on the normal distribution with a specified coverage probability can be formed. The first requirement is generally satisfied by the knowledge of the type of Monte Carlo tally being used. The Monte Carlo practitioner has only a limited number of marginally quantifiable methods that use sampled values to assess the fulfillment of the second requirement; e.g., statistical error reduction proportional to 1{radical}N with error magnitude guidelines. No consideration is given to what has not yet been sampled. A new method is presented here to assess the convergence of Monte Carlo solutions by analyzing the shape of the empirical probability density function (PDF) of history scores, f(x), where the random variable x is the score from one particle history and {integral}{sub {minus}{infinity}}{sup {infinity}} f(x) dx = 1. Since f(x) is seldom known explicitly, Monte Carlo particle random walks sample f(x) implicitly. Unless there is a largest possible history score, the empirical f(x) must eventually decrease more steeply than l/x{sup 3} for the second moment ({integral}{sub {minus}{infinity}}{sup {infinity}} x{sup 2}f(x) dx) to exist.
An Unbiased Hessian Representation for Monte Carlo PDFs
Carrazza, Stefano; Kassabov, Zahari; Latorre, Jose Ignacio; Rojo, Juan
2015-01-01
We develop a methodology for the construction of a Hessian representation of Monte Carlo sets of parton distributions, based on the use of a subset of the Monte Carlo PDF replicas as an unbiased linear basis, and of a genetic algorithm for the determination of the optimal basis. We validate the methodology by first showing that it faithfully reproduces a native Monte Carlo PDF set (NNPDF3.0), and then, that if applied to Hessian PDF set (MMHT14) which was transformed into a Monte Carlo set, it gives back the starting PDFs with minimal information loss. We then show that, when applied to a large Monte Carlo PDF set obtained as combination of several underlying sets, the methodology leads to a Hessian representation in terms of a rather smaller set of parameters (CMC-H PDFs), thereby providing an alternative implementation of the recently suggested Meta-PDF idea and a Hessian version of the recently suggested PDF compression algorithm (CMC-PDFs). The mc2hessian conversion code is made publicly available togethe...
An Unbiased Hessian Representation for Monte Carlo PDFs
Stefano Carrazza; Stefano Forte; Zahari Kassabov; Jose Ignacio Latorre; Juan Rojo
2015-05-29
We develop a methodology for the construction of a Hessian representation of Monte Carlo sets of parton distributions, based on the use of a subset of the Monte Carlo PDF replicas as an unbiased linear basis, and of a genetic algorithm for the determination of the optimal basis. We validate the methodology by first showing that it faithfully reproduces a native Monte Carlo PDF set (NNPDF3.0), and then, that if applied to Hessian PDF set (MMHT14) which was transformed into a Monte Carlo set, it gives back the starting PDFs with minimal information loss. We then show that, when applied to a large Monte Carlo PDF set obtained as combination of several underlying sets, the methodology leads to a Hessian representation in terms of a rather smaller set of parameters (CMC-H PDFs), thereby providing an alternative implementation of the recently suggested Meta-PDF idea and a Hessian version of the recently suggested PDF compression algorithm (CMC-PDFs). The mc2hessian conversion code is made publicly available together with (through LHAPDF6) a Hessian representations of the NNPDF3.0 set, and the CMC-H PDF set.
Quantum Monte-Carlo method applied to Non-Markovian barrier transmission
G. Hupin; D. Lacroix
2010-01-05
In nuclear fusion and fission, fluctuation and dissipation arise due to the coupling of collective degrees of freedom with internal excitations. Close to the barrier, both quantum, statistical and non-Markovian effects are expected to be important. In this work, a new approach based on quantum Monte-Carlo addressing this problem is presented. The exact dynamics of a system coupled to an environment is replaced by a set of stochastic evolutions of the system density. The quantum Monte-Carlo method is applied to systems with quadratic potentials. In all range of temperature and coupling, the stochastic method matches the exact evolution showing that non-Markovian effects can be simulated accurately. A comparison with other theories like Nakajima-Zwanzig or Time-ConvolutionLess ones shows that only the latter can be competitive if the expansion in terms of coupling constant is made at least to fourth order. A systematic study of the inverted parabola case is made at different temperatures and coupling constants. The asymptotic passing probability is estimated in different approaches including the Markovian limit. Large differences with the exact result are seen in the latter case or when only second order in the coupling strength is considered as it is generally assumed in nuclear transport models. On opposite, if fourth order in the coupling or quantum Monte-Carlo method is used, a perfect agreement is obtained.
Monte Carlo Methods for Uncertainty Quantification Mathematical Institute, University of Oxford
Giles, Mike
Monte Carlo Methods for Uncertainty Quantification Mike Giles Mathematical Institute, University of Oxford KU Leuven Summer School on Uncertainty Quantification May 3031, 2013 Mike Giles (Oxford) Monte sampling Latin Hypercube randomised quasi-Monte Carlo Mike Giles (Oxford) Monte Carlo methods May 30
Communication: Monte Carlo calculation of the exchange energy Roi Baer and Daniel Neuhauser
Baer, Roi
Communication: Monte Carlo calculation of the exchange energy Roi Baer and Daniel Neuhauser OF CHEMICAL PHYSICS 137, 051103 (2012) Communication: Monte Carlo calculation of the exchange energy Roi Baer1 Monte Carlo (MC) methods for calculating the exchange energy. The Monte a)E-mail: roi.baer@huji.ac.il. b
Applications of the Fixed-Node Quantum Monte Carlo Method
NASA Astrophysics Data System (ADS)
Kulahlioglu, Adem Halil
Quantum Monte Carlo (QMC) is a highly sophisticated quantum many-body method. Diffusion Monte Carlo (DMC), a projected QMC method, is a stochastic solution of the stationary Schrodinger's equation. It is, in principle, an exact method. However, in dealing with fermions, since trial wave functions meet the antisymmetric condition of the many-body fermionic systems, it inevitably encounters the fermion sign problem. One of the ways to circumvent the sign problem is by imposing the so-called fixed-node approximation. The fixed-node DMC (FN-DMC), a highly promising method, is emerging as the method of choice for correlated treatment of many-body electronic structure problems since it is much more accurate than Khon-Sham DFT and has a competitive accuracy with CCSD(T) but scales better with system size than CCSD(T). An important drawback in FN-DMC is the fixed-node bias introduced by the approximate nature of the trial wave function nodes. In this dissertation, we examine the fixed-node bias and its restrictive impact on the accuracy of FN-DMC. Also, electron density dependence of the fixed-node bias is discussed by taking a relatively small atomic system. In our dissertation, we also applied FN-DMC in a relatively large molecular system with a transition metal, Zinc-porphyrin, to calculate the excitation energy in an adiabatic limit (vertical excitation). We found that FN-DMC results agree well with experimental values as well as with results obtained by some other correlated ab initio methods such as CCSD. In addition, we used FN-DMC to study a transition metal dimer, Mo 2, which is a challenging system for theoretical studies since there is large amount of many-body correlation effects. We constructed the antisymmetric part (Slater part) of the trial wave function by means of the Selected-CI method. Moreover, we carried out CCSD(T) calculations in order to be able to compare FN-DMC energies with another correlated method energies. FN-DMC and CCSD(T) calculations in Mo2, which is dominant with d-d bondings, enabled us to make comparisons between these two competitive methods and investigate the limitations impairing FN-DMC accuracy.
Tool for Rapid Analysis of Monte Carlo Simulations
NASA Technical Reports Server (NTRS)
Restrepo, Carolina; McCall, Kurt E.; Hurtado, John E.
2011-01-01
Designing a spacecraft, or any other complex engineering system, requires extensive simulation and analysis work. Oftentimes, the large amounts of simulation data generated are very di cult and time consuming to analyze, with the added risk of overlooking potentially critical problems in the design. The authors have developed a generic data analysis tool that can quickly sort through large data sets and point an analyst to the areas in the data set that cause specific types of failures. The Tool for Rapid Analysis of Monte Carlo simulations (TRAM) has been used in recent design and analysis work for the Orion vehicle, greatly decreasing the time it takes to evaluate performance requirements. A previous version of this tool was developed to automatically identify driving design variables in Monte Carlo data sets. This paper describes a new, parallel version, of TRAM implemented on a graphical processing unit, and presents analysis results for NASA's Orion Monte Carlo data to demonstrate its capabilities.
Skin image reconstruction using Monte Carlo based color generation
NASA Astrophysics Data System (ADS)
Aizu, Yoshihisa; Maeda, Takaaki; Kuwahara, Tomohiro; Hirao, Tetsuji
2010-11-01
We propose a novel method of skin image reconstruction based on color generation using Monte Carlo simulation of spectral reflectance in the nine-layered skin tissue model. The RGB image and spectral reflectance of human skin are obtained by RGB camera and spectrophotometer, respectively. The skin image is separated into the color component and texture component. The measured spectral reflectance is used to evaluate scattering and absorption coefficients in each of the nine layers which are necessary for Monte Carlo simulation. Various skin colors are generated by Monte Carlo simulation of spectral reflectance in given conditions for the nine-layered skin tissue model. The new color component is synthesized to the original texture component to reconstruct the skin image. The method is promising for applications in the fields of dermatology and cosmetics.
SPQR: a Monte Carlo reactor kinetics code. [LMFBR
Cramer, S.N.; Dodds, H.L.
1980-02-01
The SPQR Monte Carlo code has been developed to analyze fast reactor core accident problems where conventional methods are considered inadequate. The code is based on the adiabatic approximation of the quasi-static method. This initial version contains no automatic material motion or feedback. An existing Monte Carlo code is used to calculate the shape functions and the integral quantities needed in the kinetics module. Several sample problems have been devised and analyzed. Due to the large statistical uncertainty associated with the calculation of reactivity in accident simulations, the results, especially at later times, differ greatly from deterministic methods. It was also found that in large uncoupled systems, the Monte Carlo method has difficulty in handling asymmetric perturbations.
Photon beam description in PEREGRINE for Monte Carlo dose calculations
Cox, L. J., LLNL
1997-03-04
Goal of PEREGRINE is to provide capability for accurate, fast Monte Carlo calculation of radiation therapy dose distributions for routine clinical use and for research into efficacy of improved dose calculation. An accurate, efficient method of describing and sampling radiation sources is needed, and a simple, flexible solution is provided. The teletherapy source package for PEREGRINE, coupled with state-of-the-art Monte Carlo simulations of treatment heads, makes it possible to describe any teletherapy photon beam to the precision needed for highly accurate Monte Carlo dose calculations in complex clinical configurations that use standard patient modifiers such as collimator jaws, wedges, blocks, and/or multi-leaf collimators. Generic beam descriptions for a class of treatment machines can readily be adjusted to yield dose calculation to match specific clinical sites.
TAKING THE NEXT STEP WITH INTELLIGENT MONTE CARLO
Booth, T.E.; Carlson, J.A. [and others
2000-10-01
For many scientific calculations, Monte Carlo is the only practical method available. Unfortunately, standard Monte Carlo methods converge slowly as the square root of the computer time. We have shown, both numerically and theoretically, that the convergence rate can be increased dramatically if the Monte Carlo algorithm is allowed to adapt based on what it has learned from previous samples. As the learning continues, computational efficiency increases, often geometrically fast. The particle transport work achieved geometric convergence for a two-region problem as well as for problems with rapidly changing nuclear data. The statistics work provided theoretical proof of geometic convergence for continuous transport problems and promising initial results for airborne migration of particles. The statistical physics work applied adaptive methods to a variety of physical problems including the three-dimensional Ising glass, quantum scattering, and eigenvalue problems.
The Monte Carlo method in quantum field theory
Colin Morningstar
2007-02-20
This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo method with Markov-chain based importance sampling is presented. Properties of Markov chains are discussed in detail and several proofs are presented, culminating in the fundamental limit theorem for irreducible Markov chains. The example of a real scalar field theory is used to illustrate the Metropolis-Hastings method and to demonstrate the effectiveness of an action-preserving (microcanonical) local updating algorithm in reducing autocorrelations. The goal of these lectures is to provide the beginner with the basic skills needed to start carrying out Monte Carlo studies in quantum field theories, as well as to present the underlying theoretical foundations of the method.
Efficiency of Monte Carlo Sampling in Chaotic Systems
Jorge C. Leitão; Eduardo G. Altmann; J. M. Viana Parente Lopes
2014-07-20
In this paper we investigate how the complexity of chaotic phase spaces affect the efficiency of importance sampling Monte Carlo simulations. We focus on a flat-histogram simulation of the distribution of finite-time Lyapunov exponent in a simple chaotic system and obtain analytically that the computational effort of the simulation: (i) scales polynomially with the finite-time, a tremendous improvement over the exponential scaling obtained in usual uniform sampling simulations; and (ii) the polynomial scaling is sub-optimal, a phenomenon known as critical slowing down. We show that critical slowing down appears because of the limited possibilities to issue a local proposal on the Monte Carlo procedure in chaotic systems. These results remain valid in other methods and show how generic properties of chaotic systems limit the efficiency of Monte Carlo simulations.
Efficiency of Monte Carlo sampling in chaotic systems
NASA Astrophysics Data System (ADS)
Leitão, Jorge C.; Lopes, J. M. Viana Parente; Altmann, Eduardo G.
2014-11-01
In this paper we investigate how the complexity of chaotic phase spaces affect the efficiency of importance sampling Monte Carlo simulations. We focus on flat-histogram simulations of the distribution of finite-time Lyapunov exponent in a simple chaotic system and obtain analytically that the computational effort: (i) scales polynomially with the finite time, a tremendous improvement over the exponential scaling obtained in uniform sampling simulations; and (ii) the polynomial scaling is suboptimal, a phenomenon known as critical slowing down. We show that critical slowing down appears because of the limited possibilities to issue a local proposal in the Monte Carlo procedure when it is applied to chaotic systems. These results show how generic properties of chaotic systems limit the efficiency of Monte Carlo simulations.
Efficiency of Monte Carlo sampling in chaotic systems.
Leitão, Jorge C; Lopes, J M Viana Parente; Altmann, Eduardo G
2014-11-01
In this paper we investigate how the complexity of chaotic phase spaces affect the efficiency of importance sampling Monte Carlo simulations. We focus on flat-histogram simulations of the distribution of finite-time Lyapunov exponent in a simple chaotic system and obtain analytically that the computational effort: (i) scales polynomially with the finite time, a tremendous improvement over the exponential scaling obtained in uniform sampling simulations; and (ii) the polynomial scaling is suboptimal, a phenomenon known as critical slowing down. We show that critical slowing down appears because of the limited possibilities to issue a local proposal in the Monte Carlo procedure when it is applied to chaotic systems. These results show how generic properties of chaotic systems limit the efficiency of Monte Carlo simulations. PMID:25493867
Study of nuclear pairing with Configuration-Space Monte-Carlo approach
Mark Lingle; Alexander Volya
2015-03-20
Pairing correlations in nuclei play a decisive role in determining nuclear drip-lines, binding energies, and many collective properties. In this work a new Configuration-Space Monte-Carlo (CSMC) method for treating nuclear pairing correlations is developed, implemented, and demonstrated. In CSMC the Hamiltonian matrix is stochastically generated in Krylov subspace, resulting in the Monte-Carlo version of Lanczos-like diagonalization. The advantages of this approach over other techniques are discussed; the absence of the fermionic sign problem, probabilistic interpretation of quantum-mechanical amplitudes, and ability to handle truly large-scale problems with defined precision and error control, are noteworthy merits of CSMC. The features of our CSMC approach are shown using models and realistic examples. Special attention is given to difficult limits: situations with non-constant pairing strengths, cases with nearly degenerate excited states, limits when pairing correlations in finite systems are weak, and problems when the relevant configuration space is large.
Monte Carlo studies of model Langmuir monolayers
NASA Astrophysics Data System (ADS)
Opps, S. B.; Yang, B.; Gray, C. G.; Sullivan, D. E.
2001-04-01
This paper examines some of the basic properties of a model Langmuir monolayer, consisting of surfactant molecules deposited onto a water subphase. The surfactants are modeled as rigid rods composed of a head and tail segment of diameters ?hh and ?tt, respectively. The tails consist of nt~4-7 effective monomers representing methylene groups. These rigid rods interact via site-site Lennard-Jones potentials with different interaction parameters for the tail-tail, head-tail, and head-head interactions. In a previous paper, we studied the ground-state properties of this system using a Landau approach. In the present paper, Monte Carlo simulations were performed in the canonical ensemble to elucidate the finite-temperature behavior of this system. Simulation techniques, incorporating a system of dynamic filters, allow us to decrease CPU time with negligible statistical error. This paper focuses on several of the key parameters, such as density, head-tail diameter mismatch, and chain length, responsible for driving transitions from uniformly tilted to untilted phases and between different tilt-ordered phases. Upon varying the density of the system, with ?hh=?tt, we observe a transition from a tilted (NNN)-condensed phase to an untilted-liquid phase and, upon comparison with recent experiments with fatty acid-alcohol and fatty acid-ester mixtures [M. C. Shih, M. K. Durbin, A. Malik, P. Zschack, and P. Dutta, J. Chem. Phys. 101, 9132 (1994); E. Teer, C. M. Knobler, C. Lautz, S. Wurlitzer, J. Kildae, and T. M. Fischer, J. Chem. Phys. 106, 1913 (1997)], we identify this as the L'2/Ov-L1 phase boundary. By varying the head-tail diameter ratio, we observe a decrease in Tc with increasing mismatch. However, as the chain length was increased we observed that the transition temperatures increased and differences in Tc due to head-tail diameter mismatch were diminished. In most of the present research, the water was treated as a hard surface, whereby the surfactants are only allowed to move within the plane of this surface. However, we have also utilized a more realistic model for the surfactant-water interactions, developed by Karaborni and Toxvaerd, in order to examine the role which the coupled effects of head group size and head group-subphase interactions plays in determining tilt ordering and on the stability of the monolayer. It is found that increasing the head diameter results in a widening of the air-water interface and an associated destruction of orientational order. Furthermore, the onset of capillary waves at lower temperatures for larger head diameters implies that the L2-L1 phase boundary for acids and acetates should move to lower temperatures relative to the L'2/Ov-L1 phase boundary for alcohols and esters. This feature has yet to be seen in experimental studies.
Superposition dose calculation incorporating Monte Carlo generated electron track kernels.
Keall, P J; Hoban, P W
1996-04-01
The superposition/convolution method and the transport of pregenerated Monte Carlo electron track data have been combined into the Super-Monte Carlo (SMC) method, an accurate 3-D x-ray dose calculation algorithm. The primary dose (dose due to electrons ejected by primary photons) is calculated by transporting pregenerated (in water) Monte Carlo electron tracks from each primary photon interaction site, weighted by the terma for that site. The length of each electron step is scaled by the inverse of the density of the medium at the beginning of the step. Because the density scaling of the electron tracks is performed for each individual transport step, the limitations of the macroscopic scaling of kernels (in the superposition algorithm) are overcome. This time-consuming step-by-step transport is only performed for the primary dose calculation, where current superposition methods are most lacking. The scattered dose (dose due to electrons set in motion by scattered photons) is calculated by superposition. In both a water-lung-water phantom and a two lung-block phantom, SMC dose distributions are more consistent with Monte Carlo generated dose distributions than are superposition dose distributions, especially for small fields and high energies-for an 18-MV, 5 X 5-cm(2) beam, the central axis dose discrepancy from Monte Carlo is reduced from 4.5% using superposition to 1.5% using SMC. The computation time for this technique is approximately 2 h (depending on the simulation history), 20 times slower than superposition, but 15 times faster than a full Monte Carlo simulation (on our platform). PMID:9157258
Monte Carlo simulations of phosphate polyhedron connectivity in glasses
ALAM,TODD M.
2000-01-01
Monte Carlo simulations of phosphate tetrahedron connectivity distributions in alkali and alkaline earth phosphate glasses are reported. By utilizing a discrete bond model, the distribution of next-nearest neighbor connectivities between phosphate polyhedron for random, alternating and clustering bonding scenarios was evaluated as a function of the relative bond energy difference. The simulated distributions are compared to experimentally observed connectivities reported for solid-state two-dimensional exchange and double-quantum NMR experiments of phosphate glasses. These Monte Carlo simulations demonstrate that the polyhedron connectivity is best described by a random distribution in lithium phosphate and calcium phosphate glasses.
Monte Carlo Simulations of Phosphate Polyhedron Connectivity in Glasses
ALAM,TODD M.
1999-12-21
Monte Carlo simulations of phosphate tetrahedron connectivity distributions in alkali and alkaline earth phosphate glasses are reported. By utilizing a discrete bond model, the distribution of next-nearest neighbor connectivities between phosphate polyhedron for random, alternating and clustering bonding scenarios was evaluated as a function of the relative bond energy difference. The simulated distributions are compared to experimentally observed connectivities reported for solid-state two-dimensional exchange and double-quantum NMR experiments of phosphate glasses. These Monte Carlo simulations demonstrate that the polyhedron connectivity is best described by a random distribution in lithium phosphate and calcium phosphate glasses.
Monte Carlo calculation of monitor unit for electron arc therapy
Chow, James C. L.; Jiang Runqing [Radiation Medicine Program, Princess Margaret Hospital, University Health Network, Toronto, Ontario M5G 2M9 (Canada); Department of Radiation Oncology, University of Toronto, Toronto, Ontario M5G 2M9 (Canada) and Department of Physics, Ryerson University, Toronto, Ontario M5B 2K3 (Canada); Department of Medical Physics, Grand River Regional Cancer Center, Kitchener, Ontario N2G 1G3 (Canada)
2010-04-15
Purpose: Monitor unit (MU) calculations for electron arc therapy were carried out using Monte Carlo simulations and verified by measurements. Variations in the dwell factor (DF), source-to-surface distance (SSD), and treatment arc angle ({alpha}) were studied. Moreover, the possibility of measuring the DF, which requires gantry rotation, using a solid water rectangular, instead of cylindrical, phantom was investigated. Methods: A phase space file based on the 9 MeV electron beam with rectangular cutout (physical size=2.6x21 cm{sup 2}) attached to the block tray holder of a Varian 21 EX linear accelerator (linac) was generated using the EGSnrc-based Monte Carlo code and verified by measurement. The relative output factor (ROF), SSD offset, and DF, needed in the MU calculation, were determined using measurements and Monte Carlo simulations. An ionization chamber, a radiographic film, a solid water rectangular phantom, and a cylindrical phantom made of polystyrene were used in dosimetry measurements. Results: Percentage deviations of ROF, SSD offset, and DF between measured and Monte Carlo results were 1.2%, 0.18%, and 1.5%, respectively. It was found that the DF decreased with an increase in {alpha}, and such a decrease in DF was more significant in the {alpha} range of 0 deg. - 60 deg. than 60 deg. - 120 deg. Moreover, for a fixed {alpha}, the DF increased with an increase in SSD. Comparing the DF determined using the rectangular and cylindrical phantom through measurements and Monte Carlo simulations, it was found that the DF determined by the rectangular phantom agreed well with that by the cylindrical one within {+-}1.2%. It shows that a simple setup of a solid water rectangular phantom was sufficient to replace the cylindrical phantom using our specific cutout to determine the DF associated with the electron arc. Conclusions: By verifying using dosimetry measurements, Monte Carlo simulations proved to be an alternative way to perform MU calculations effectively for electron arc therapy. Since Monte Carlo simulations can generate a precalculated database of ROF, SSD offset, and DF for the MU calculation, with a reduction in human effort and linac beam-on time, it is recommended that Monte Carlo simulations be partially or completely integrated into the commissioning of electron arc therapy.
General Construction of Irreversible Kernel in Markov Chain Monte Carlo
Hidemaro Suwa; Synge Todo
2012-07-02
The Markov chain Monte Carlo update method to construct an irreversible kernel has been reviewed and extended to general state spaces. The several convergence conditions of the Markov chain were discussed. The alternative methods to the Gibbs sampler and the Metropolis-Hastings algorithm were proposed and assessed in some models. The distribution convergence and the sampling efficiency are significantly improved in the Potts model, the bivariate Gaussian model, and so on. This approach using the irreversible kernel can be applied to any Markov chain Monte Carlo sampling and it is expected to improve the efficiency in general.
Modelling cerebral blood oxygenation using Monte Carlo XYZ-PA
NASA Astrophysics Data System (ADS)
Zam, Azhar; Jacques, Steven L.; Alexandrov, Sergey; Li, Youzhi; Leahy, Martin J.
2013-02-01
Continuous monitoring of cerebral blood oxygenation is critically important for the management of many lifethreatening conditions. Non-invasive monitoring of cerebral blood oxygenation with a photoacoustic technique offers advantages over current invasive and non-invasive methods. We introduce a Monte Carlo XYZ-PA to model the energy deposition in 3D and the time-resolved pressures and velocity potential based on the energy absorbed by the biological tissue. This paper outlines the benefits of using Monte Carlo XYZ-PA for optimization of photoacoustic measurement and imaging. To the best of our knowledge this is the first fully integrated tool for photoacoustic modelling.
Uncertainties in ozone concentrations predicted with a Lagrangian photochemical air quality model have been estimated using Bayesian Monte Carlo (BMC) analysis. Bayesian Monte Carlo analysis provides a means of combining subjective "prior" uncertainty estimates developed ...
Physics-based Predictive Time Propagation Method for Monte Carlo Coupled Depletion Simulations
Johns, Jesse Merlin
2014-12-18
The Monte Carlo method for solving reactor physics problems is one of the most robust numerical techniques for analyzing a wide variety of systems in the realm of reactor engineering. Monte Carlo simulations sample on fundamental physical processes...
Monte Carlo f calculation of the neoclassical ion current in a rotating island
Monte Carlo f calculation of the neoclassical ion current in a rotating island A. Bergmann, E. Poli is considered. We use a guiding centre f code augmented by a Monte Carlo model of pitch angle collisions
ITER Neutronics Modeling Using Hybrid Monte Carlo/Deterministic and CAD-Based Monte Carlo Methods
Ibrahim, A. [University of Wisconsin; Mosher, Scott W [ORNL; Evans, Thomas M [ORNL; Peplow, Douglas E. [ORNL; Sawan, M. [University of Wisconsin; Wilson, P. [University of Wisconsin; Wagner, John C [ORNL; Heltemes, Thad [University of Wisconsin, Madison
2011-01-01
The immense size and complex geometry of the ITER experimental fusion reactor require the development of special techniques that can accurately and efficiently perform neutronics simulations with minimal human effort. This paper shows the effect of the hybrid Monte Carlo (MC)/deterministic techniques - Consistent Adjoint Driven Importance Sampling (CADIS) and Forward-Weighted CADIS (FW-CADIS) - in enhancing the efficiency of the neutronics modeling of ITER and demonstrates the applicability of coupling these methods with computer-aided-design-based MC. Three quantities were calculated in this analysis: the total nuclear heating in the inboard leg of the toroidal field coils (TFCs), the prompt dose outside the biological shield, and the total neutron and gamma fluxes over a mesh tally covering the entire reactor. The use of FW-CADIS in estimating the nuclear heating in the inboard TFCs resulted in a factor of ~ 275 increase in the MC figure of merit (FOM) compared with analog MC and a factor of ~ 9 compared with the traditional methods of variance reduction. By providing a factor of ~ 21 000 increase in the MC FOM, the radiation dose calculation showed how the CADIS method can be effectively used in the simulation of problems that are practically impossible using analog MC. The total flux calculation demonstrated the ability of FW-CADIS to simultaneously enhance the MC statistical precision throughout the entire ITER geometry. Collectively, these calculations demonstrate the ability of the hybrid techniques to accurately model very challenging shielding problems in reasonable execution times.
Monte Carlo very next free flight are accumulated after
Monte Carlo very next free flight are accumulated after each collision. Random-Number Generators the "worthiness" of the random numbers generated, a variety of generators have been developed, each with its own of numbers generated by a truly random process is most desirable. This type of sequence is called a random-number
Probabilistic Assessments of the Plate Using Monte Carlo Simulation
A. E. Ismail; A. K. Ariffin; S. Abdullah; M. J. Ghazali
2011-01-01
This paper presents the probabilistic analysis of the plate with a hole using several multiaxial high cycle fatigue criteria (MHFC). Dang Van, Sines, Crossland criteria were used and von Mises criterion was also considered for comparison purpose. Parametric finite element model of the plate was developed and several important random variable parameters were selected and Latin Hypercube Sampling Monte-Carlo Simulation
Numerical Integration of the Langevin Equation: Monte Carlo Simulation
Donald L. Ermak; Helen Buckholz
1980-01-01
Monte Carlo simulation techniques are derived for solving the ordinary Langevin equation of motion for a Brownian particle in the presence of an external force. These methods allow considerable freedom in selecting the size of the time step, which is restricted only by the rate of change in the external force. This approach is extended to the generalized Langevin equation
APS undulator and wiggler sources: Monte-Carlo simulation
Xu, S.L.; Lai, B.; Viccaro, P.J.
1992-02-01
Standard insertion devices will be provided to each sector by the Advanced Photon Source. It is important to define the radiation characteristics of these general purpose devices. In this document,results of Monte-Carlo simulation are presented. These results, based on the SHADOW program, include the APS Undulator A (UA), Wiggler A (WA), and Wiggler B (WB).
Microbial contamination in poultry chillers estimated by Monte Carlo simulations
Technology Transfer Automated Retrieval System (TEKTRAN)
The risk of microbial contamination during poultry processing may be reduced by the operating characteristics of the chiller. The performance of air chillers and immersion chillers were compared in terms of pre-chill and post-chill contamination using Monte Carlo simulations. Three parameters were u...
Monte Carlo simulation of ?-scattering for density variation measurement
NASA Astrophysics Data System (ADS)
Khiem, L. H.; Trong, T. D.
2015-05-01
This report studies the possibility of using backscattered ?-radiation for checking the density fluctuations of concrete thickness of newly constructed highways by means of Monte Carlo simulation. A computer program named NUCLGAUGE has been written in Visual Basics language. It should be useful for designing a device for density variation measurement of concrete layer of newly constructed highways using backscattered ?-radiation.
Monte Carlo Simulations of Light Propagation in Apples
Technology Transfer Automated Retrieval System (TEKTRAN)
This paper reports on the investigation of light propagation in fresh apples in the visible and short-wave near-infrared region using Monte Carlo simulations. Optical properties of ‘Golden Delicious’ apples were determined over the spectral range of 500-1100 nm using a hyperspectral imaging method, ...
A Variational Monte Carlo Approach to Atomic Structure
ERIC Educational Resources Information Center
Davis, Stephen L.
2007-01-01
The practicality and usefulness of variational Monte Carlo calculations to atomic structure are demonstrated. It is found to succeed in quantitatively illustrating electron shielding, effective nuclear charge, l-dependence of the orbital energies, and singlet-tripetenergy splitting and ionization energy trends in atomic structure theory.
On Monte Carlo simulations of the LAser RElativity Satellite experiment
NASA Astrophysics Data System (ADS)
Renzetti, G.
2015-05-01
I offer some critical reflections on recent Monte Carlo simulations of the Lageos-LARES experiment which aims to measure Earth×³s frame-dragging to percent level. I demonstrate that, in fact, they did not add anything new in support of this goal, being essentially affected by some of the issues already found in past analyses. I suggest some possible ameliorations.
Monte Carlo Evaluation and Development of Weibull Analysis Techniques
Lloyd Schlitzer
1966-01-01
Monte Carlo simulation studies have been conducted to provide improved techniques for fatigue data analysis with the Weibull equation. Three methods of estimating the Weibull parameters were evaluated by empirically measuring the bias associated with each method when used on data from small samples. Various methods of treating suspended data were similarly compared. Confidence bands were then developed on the
Catalytic reactions over modified surfaces: a Monte Carlo study
A. Patrykiejew; P Szabelski
2000-01-01
This paper deals with a simple model of bidirectional dimer–monomer reaction over a modified catalyst surface, studied by means of the Monte Carlo simulation method. It is assumed that certain active sites of a catalyst surface are blocked by modifier (or poison) atoms and thus unable to catalyze the reactions. The influence of the modifier species concentration and the topography
Monte Carlo study of the Abelian Higgs model
Toussaint, W.D.; Sugar, R.L.
1985-10-15
A Monte Carlo study of the Abelian Higgs model demonstrates a first-order phase transition between the Higgs phase and the Coulomb phase for a wide range of gauge and Higgs coupling constants. For small gauge coupling the discontinuity becomes very small, making it difficult to determine the order of the transition.
Evolutionary Monte Carlo for protein folding simulations Faming Lianga)
Liang, Faming
Evolutionary Monte Carlo for protein folding simulations Faming Lianga) Department of Statistics to simulations of protein folding on simple lattice models, and to finding the ground state of a protein. In all structures in protein folding. The numerical results show that it is drastically superior to other methods
CMS Monte Carlo production operations in a distributed computing environment
Mohapatra, A.; Lazaridis, C.; /Wisconsin U., Madison; Hernandez, J.M.; Caballero, J.; /Madrid, CIEMAT; Hof, C.; Kalinin, S.; /Aachen, Tech. Hochsch.; Flossdorf, A.; /DESY; Abbrescia, M.; De Filippis, N.; Donvito, G.; Maggi, G.; /Bari U. /INFN, Bari /INFN, Pisa /Vrije U., Brussels /Brussels U. /Imperial Coll., London /CERN /Princeton U. /Fermilab
2008-01-01
Monte Carlo production for the CMS experiment is carried out in a distributed computing environment; the goal of producing 30M simulated events per month in the first half of 2007 has been reached. A brief overview of the production operations and statistics is presented.
A multilayer Monte Carlo method with free phase function choice
NASA Astrophysics Data System (ADS)
Watté, R.; Aernouts, B.; Saeys, W.
2012-06-01
This paper presents an adaptation of the widely accepted Monte Carlo method for Multi-layered media (MCML). Its original Henyey-Greenstein phase function is an interesting approach for describing how light scattering inside biological tissues occurs. It has the important advantage of generating deflection angles in an efficient - and therefore computationally fast- manner. However, in order to allow the fast generation of the phase function, the MCML code generates a distribution for the cosine of the deflection angle instead of generating a distribution for the deflection angle, causing a bias in the phase function. Moreover, other, more elaborate phase functions are not available in the MCML code. To overcome these limitations of MCML, it was adapted to allow the use of any discretized phase function. An additional tool allows generating a numerical approximation for the phase function for every layer. This could either be a discretized version of (1) the Henyey-Greenstein phase function, (2) a modified Henyey-Greenstein phase function or (3) a phase function generated from the Mie theory. These discretized phase functions are then stored in a look-up table, which can be used by the adapted Monte Carlo code. The Monte Carlo code with flexible phase function choice (fpf-MC) was compared and validated with the original MCML code. The novelty of the developed program is the generation of a user-friendly algorithm, which allows several types of phase functions to be generated and applied into a Monte Carlo method, without compromising the computational performance.
Compartment fire risk analysis by advanced Monte Carlo simulation
Siu Kui Au; Zhi-Hua Wang; Siu-Ming Lo
2007-01-01
Quantitative fire risk analysis aims at providing an assessment of fire safety on a scientific basis and taking relevant uncertainties into account in a rational quantitative manner. Under a probabilistic approach, performance measures are formulated as multi-dimensional probability integrals, whose efficient computation is pivotal for practical implementation. Direct Monte Carlo method is a well-known technique, but it is not efficient
Monte Carlo simulation of entry in the Martian atmosphere
NASA Technical Reports Server (NTRS)
Hash, David B.; Hassan, H. A.
1992-01-01
The Direct Simulation Monte Carlo method of Bird is used to investigate the characteristics of low density hypersonic flowfields for typical aerobrakes during Martian atmospheric entry. The method allows for both thermal and chemical nonequilibrium. Results are presented for a sixty-degree spherically blunt cone for various nose radii and altitudes.
Monte Carlo Radiation Analysis of a Spacecraft Radioisotope Power System
NASA Technical Reports Server (NTRS)
Wallace, M.
1994-01-01
A Monte Carlo statistical computer analysis was used to create neutron and photon radiation predictions for the General Purpose Heat Source Radioisotope Thermoelectric Generator (GPHS RTG). The GPHS RTG is being used on several NASA planetary missions. Analytical results were validated using measured health physics data.
MONTE CARLO EXPLORATIONS OF POLYGONAL KNOT SPACES KENNETH C. MILLETT
Bigelow, Stephen
1 MONTE CARLO EXPLORATIONS OF POLYGONAL KNOT SPACES KENNETH C. MILLETT Department of Mathematics Polygonal knots are embeddings of polygons in three space. For each n, the collection of embedded nÂgons determines a subset of Euclidean space whose structure is the subject of this paper. Which knots can
Efficient Monte Carlo Methods for Conditional Logistic Regression
Lee, Stephen
Efficient Monte Carlo Methods for Conditional Logistic Regression Cyrus R. MEHTA, Nitin R. PATEL, and Pralay SENCHAUDHURI Exact inference for the logistic regression model is based on generating the permutation distribution of the sufficient statistics for the regression parameters of interest conditional
Monte Carlo calculations of the vacuum Compton detector sensitivities
Hsu, H.H.; Lee, H. (Univ. of California, Los Alamos National Lab, Los Alamos, NM (US))
1989-12-01
Monte Carlo simulations have been carried out to compute the static sensitivity of the vacuum Compton detector for monoenergetic gamma rays and electrons. A similar calculation using {sup 60}Co spectrum as input is found in good agreement with measurements. The authors also calculate the detector sensitivities for bremsstrahlung spectra produced by monoenergetic e-beams and compare with experimental data.
Direct calculation of bubble points by Monte Carlo simulation
Philippe Ungerer; Anne Boutin; Alain H. Fuchs
1999-01-01
The calculation of bubble points, i.e. the conditions in which a liquid starts to form a vapour phase, is a problem of industrial interest in petroleum and chemical engineering. Phase equilibrium at specified global composition, temperature and volume or pressure can be computed by the Gibbs Ensemble Monte Carlo method (GEMC). However it is not directly applicable to bubble points,
A separable shadow Hamiltonian hybrid Monte Carlo method.
Sweet, Christopher R; Hampton, Scott S; Skeel, Robert D; Izaguirre, Jesús A
2009-11-01
Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The shadow hybrid Monte Carlo (SHMC) was previously introduced to reduce this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. SHMC's performance is limited by the need to generate momenta for the MD step from a nonseparable shadow Hamiltonian. We introduce the separable shadow Hamiltonian hybrid Monte Carlo (S2HMC) method based on a formulation of the leapfrog/Verlet integrator that corresponds to a separable shadow Hamiltonian, which allows efficient generation of momenta. S2HMC gives the acceptance rate of a fourth order integrator at the cost of a second-order integrator. Through numerical experiments we show that S2HMC consistently gives a speedup greater than two over HMC for systems with more than 4000 atoms for the same variance. By comparison, SHMC gave a maximum speedup of only 1.6 over HMC. S2HMC has the additional advantage of not requiring any user parameters beyond those of HMC. S2HMC is available in the program PROTOMOL 2.1. A Python version, adequate for didactic purposes, is also in MDL (http://mdlab.sourceforge.net/s2hmc). PMID:19894997
Yield to maturity modelling and a Monte Carlo Technique for
Paris-Sud XI, Université de
Yield to maturity modelling and a Monte Carlo Technique for pricing Derivatives on Constant Maturity Treasury (CMT) and Derivatives on forward Bonds By Didier KOUOKAP YOUMBI1 First version: 29 rate function, yield to maturity, CMS, CMT, volatility, convexity adjustment, martingale Abstract
Monte Carlo calculations of the vacuum Compton detector sensitivities
Hsu- Hsiao-Hua; Lee, Huan
1989-01-01
Monte Carlo simulations have been carried out to compute the static sensitivity of the vacuum Compton detector for monoenergetic gamma rays and electrons. A similar calculation using /sup 60/Co spectrum as input is found in good agreement with measurements. We also calculate the detector sensitivities for bremsstrahlung spectra produced by monoenergetic e-beam and compare with experimental data. 8 refs., 6 figs.
Respondent-driven sampling as Markov chain Monte Carlo
Sharad Goel; Matthew J. Salganik
2009-01-01
SUMMARY Respondent-driven sampling (RDS) is a recently introduced, and now widely used, technique for estimating disease prevalence in hidden populations. RDS data are collected through a snowball mechanism, in which current sample members recruit future sample members. In this paper we present RDS as Markov chain Monte Carlo importance sampling, and we examine the effects of community structure and the
Monte Carlo Optimization for Conflict Resolution in Air Traffic Control
Cambridge, University of
Monte Carlo Optimization for Conflict Resolution in Air Traffic Control A. Lecchini , W. Glover assurance, is one of the main tasks of Air Traffic Control. Conflict resolution refers to the process used by air traffic controllers to prevent loss of separation. Conflict resolution involves issuing
Adaptive Mesh and Algorithm Refinement using Direct Simulation Monte Carlo
Bell, John B.
Adaptive Mesh and Algorithm Refinement using Direct Simulation Monte Carlo Alejandro L. Garcia@llnl.gov Submitted to Journal of Computational Physics Abstract Adaptive Mesh and Algorithm Refinement (AMAR) embeds a particle method within a continuum method at the finest level of an adaptive mesh
Thermal Properties of Supercritical Carbon Dioxide by Monte Carlo Simulations
Lisal, Martin
Thermal Properties of Supercritical Carbon Dioxide by Monte Carlo Simulations C.M. COLINAa,b, *, C and speed of sound for carbon dioxide (CO2) in the supercritical region, using the fluctuation method based: Fluctuations; Carbon dioxide; 2CLJQ; JouleThomson coefficient; Speed of sound INTRODUCTION Simulation methods
Multiple scattering in reflection nebulae. I. A Monte Carlo approach
A. N. Witt
1977-01-01
A method is described which permits the calculation of the surface brightness distribution on a plane-parallel reflection nebula of uniform density, illuminated by a single star located in front of, behind, or arbitrarily inside the nebula. The multiple scattering problem is solved by the Monte Carlo technique in a three-dimensional simulation. The models are completely parametrized by describing particle properties
Monte Carlo: in the beginning and some great expectations
Metropolis, N.
1985-01-01
The central theme will be on the historical setting and origins of the Monte Carlo Method. The scene was post-war Los Alamos Scientific Laboratory. There was an inevitability about the Monte Carlo Event: the ENIAC had recently enjoyed its meteoric rise (on a classified Los Alamos problem); Stan Ulam had returned to Los Alamos; John von Neumann was a frequent visitor. Techniques, algorithms, and applications developed rapidly at Los Alamos. Soon, the fascination of the Method reached wider horizons. The first paper was submitted for publication in the spring of 1949. In the summer of 1949, the first open conference was held at the University of California at Los Angeles. Of some interst perhaps is an account of Fermi's earlier, independent application in neutron moderation studies while at the University of Rome. The quantum leap expected with the advent of massively parallel processors will provide stimuli for very ambitious applications of the Monte Carlo Method in disciplines ranging from field theories to cosmology, including more realistic models in the neurosciences. A structure of multi-instruction sets for parallel processing is ideally suited for the Monte Carlo approach. One may even hope for a modest hardening of the soft sciences.
Monte Carlo studies of sampling strategies for estimating tributary loads
R. Peter Richards; Jim Holloway
1987-01-01
Monte Carlo techniques were used to evaluate the accuracy and precision of tributary load estimates, as these are affected by sampling frequency and pattern, calculation method, watershed size, and parameter behavior during storm runoff events. Simulated years consisting of 1460 observations were chosen at random with replacement from data sets of more than 4000 samples. Patterned subsampling of these simulated
Monte Carlo Studies of Sampling Strategies for Estimating Tributary Loads
R. Peter Richards; Jim Holloway
1987-01-01
Monte Carlo techniques were used to evaluate the accuracy and precision of tributary load estimates, as these are affected by sampling frequency and pattern, calculation method, watershed size, and parameter behavior during storm runoff events. Simulated years consisting of 1460 observations were chosen at random with replacement from data sets of more than 4000 samples. Patterned subsampling of these simulated
Pluto: A Monte Carlo Simulation Tool for Hadronic Physics
I. Froehlich; L. Cazon Boado; T. Galatyuk; V. Hejny; R. Holzmann; M. Kagarlis; W. Kuehn; J. G. Messchendorp; V. Metag; M. -A. Pleier; W. Przygoda; B. Ramstein; J. Ritman; P. Salabura; J. Stroth; M. Sudol
2007-11-06
Pluto is a Monte-Carlo event generator designed for hadronic interactions from Pion production threshold to intermediate energies of a few GeV per nucleon, as well as for studies of heavy ion reactions. This report gives an overview of the design of the package, the included models and the user interface.
Markov Chain Monte Carlo and Numerical Differential Equations
Sanz-Serna , J M
Markov Chain Monte Carlo and Numerical Differential Equations J.M. Sanz-Serna 1 Introduction here. J.M. Sanz-Serna Depto. de MatemÂ´atica Aplicada, Facultad de Ciencias, Universidad de Valladolid variables, expectation, variance, conditional probability and independence. 1 #12;2 J.M. Sanz-Serna 2
MAGNETIC PROPERTIES OF MAGHEMITE: A HEISENBERG-MONTE CARLO APPROACH
J. Restrepo
Magnetic properties of bulk maghemite are addressed by means of the Monte Carlo method in the framework of a three dimensional classical Heisenberg model with cubic crystalline anisotropy. The crystalline structure has been simulated in the most realistic way and different sets of exchan- ge integrals have been taken from literature in order to check their influence upon the magnetic
Antithetic multilevel Monte Carlo estimation for multidimensional SDES
Giles, Mike
Antithetic multilevel Monte Carlo estimation for multidimensional SDES Michael B. Giles and Lukasz for multidimensional SDEs driven by Brownian motion. Giles has previously shown that if we combine a numerical/2) requires simulation, or approximation, of LÂ´evy areas. Recently, Giles and Szpruch [5] constructed
Monte Carlo sampling from the quantum state space. II
NASA Astrophysics Data System (ADS)
Seah, Yi-Lin; Shang, Jiangwei; Khoon Ng, Hui; Nott, David John; Englert, Berthold-Georg
2015-04-01
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local maxima or evaluating an integral over a region in the quantum state space are but two exemplary applications of many. These tasks can only be performed reliably and efficiently with Monte Carlo methods, which involve good samplings of the parameter space in accordance with the relevant target distribution. We show how the Markov-chain Monte Carlo method known as Hamiltonian Monte Carlo, or hybrid Monte Carlo, can be adapted to this context. It is applicable when an efficient parameterization of the state space is available. The resulting random walk is entirely inside the physical parameter space, and the Hamiltonian dynamics enable us to take big steps, thereby avoiding strong correlations between successive sample points while enjoying a high acceptance rate. We use examples of single and double qubit measurements for illustration.
Monte-Carlo investigation of an anisotropic Ising model
A. K. Murtazaev; Zh. G. Ibaev
2009-01-01
The Monte Carlo method is used to study long-period modulated structures in an anisotropic Ising model with competing interactions (ANNNI model). The character, particularities, and dependence of the modulated structures on the temperature and ratio of the exchange interaction constants between the nearest and next-to-nearest neighbors are determined. The phase diagram is constructed.
Monte Carlo results for the hydrogen Hugoniot V. Bezkrovniy,1
Bonitz, Michael
Monte Carlo results for the hydrogen Hugoniot V. Bezkrovniy,1 V. S. Filinov,2 D. Kremp,3 M. Bonitz propose a theoretical Hugoniot relation obtained by combining results for the equation of state from by applying effective potentials. The resulting Hugoniot is located between the experimental values of Knudson
Monte Carlo simulation using polarized light in biological tissue
Sergei V. Gangnus; Stephen J. Matcher; Igor V. Meglinski
2002-01-01
Polarization-sensitive optical coherence tomography is a new important technique in biomedical imaging. To describe PS- OCT we have developed a Monte Carlo model for polarized light propagation in a multiple layered birefringent scattering medium based on the Jones formalism. Our algorithm makes it possible to derive the depth-resolved Stokes vector and Mueller matrix, which provides a compete characterization of the
Skin fluorescence model based on the Monte Carlo technique
Dmitry Y. Churmakov; Igor V. Meglinski; Sergey A. Piletsky; Douglas A. Greenhalgh
2003-01-01
The novel Monte Carlo technique of simulation of spatial fluorescence distribution within the human skin is presented. The computational model of skin takes into account spatial distribution of fluorophores following the collagen fibers packing, whereas in epidermis and stratum corneum the distribution of fluorophores assumed to be homogeneous. The results of simulation suggest that distribution of auto-fluorescence is significantly suppressed
ENVIRONMENTAL MODELING: 1 APPLICATIONS: MONTE CARLO SENSITIVITY SIMULATIONS
Dimov, Ivan
the large emission sources can also be highly polluted (under certain meteorological conditions, at least SIMULATIONS TO THE PROBLEM OF AIR POLLUTION TRANSPORT 3 1.1 The Danish Eulerian Model #12;Chapter 1 APPLICATIONS: MONTE CARLO SENSITIVITY SIMULATIONS TO THE PROBLEM OF AIR POLLUTION
The Number of Iterations in Monte Carlo Studies of Robustness.
ERIC Educational Resources Information Center
Robey, Randall R.; Barcikowski, Robert S.
A recent survey of simulation studies concluded that an overwhelming majority of papers do not report a rationale for the number of iterations carried out in Monte Carlo robustness (MCR) experiments. The survey suggested that researchers might benefit from adopting a hypothesis testing strategy in the planning and reporting of simulation studies.…
The All Particle Monte Carlo Method: 1990 Status Report
J. A. Rathkopf; C. T. Ballinger; D. E. Cullen; S. T. Perkins; E. F. Plechaty
1990-01-01
Development of the All Particle Method, a project to simulate the transport of particles via the Monte Carlo method, has proceeded on two fronts: data collection and algorithm development. In this paper we report on the status of both these aspects. The data collection is nearly complete with the addition of electron and atomic data libraries and a newly revised
Monte Carlo Simulation of Sintering on Multiprocessor Systems
Maguire Jr., Gerald Q.
Monte Carlo Simulation of Sintering on Multiprocessor Systems Jens R. Lind Master of Science Thesis of Sintering on Multiprocessor Systems Author: Jens R. Lind Examiner: Vladimir Vlassov Master of Science Thesis great time and memory constraints. A metallurgy process called sintering, by which powders are formed
A new method to assess Monte Carlo convergence
Forster, R.A.; Booth, T.E.; Pederson, S.P.
1993-01-01
The central limit theorem can be applied to a Monte Carlo solution if the following two requirements are satisfied: (1) the random variable has a finite mean and a finite variance; and (2) the number N of independent observations grows large. When these are satisfied, a confidence interval based on the normal distribution with a specified coverage probability can be formed. The first requirement is generally satisfied by the knowledge of the type of Monte Carlo tally being used. The Monte Carlo practitioner has only a limited number of marginally quantifiable methods that use sampled values to assess the fulfillment of the second requirement; e.g., statistical error reduction proportional to 1[radical]N with error magnitude guidelines. No consideration is given to what has not yet been sampled. A new method is presented here to assess the convergence of Monte Carlo solutions by analyzing the shape of the empirical probability density function (PDF) of history scores, f(x), where the random variable x is the score from one particle history and [integral][sub [minus][infinity
Quantum Monte Carlo calculations of symmetric nuclear matter
Stefano Gandolfi; Francesco Pederiva; Stefano Fantoni; Kevin E. Schmidt
2007-04-13
We present an accurate numerical study of the equation of state of nuclear matter based on realistic nucleon--nucleon interactions by means of Auxiliary Field Diffusion Monte Carlo (AFDMC) calculations. The AFDMC method samples the spin and isospin degrees of freedom allowing for quantum simulations of large nucleonic systems and can provide quantitative understanding of problems in nuclear structure and astrophysics.
Recent improvements on Monte Carlo modelling at ATLAS
Soualah, Rachik; The ATLAS collaboration
2015-01-01
The most recent findings on the Monte Carlo simulation of proton-proton collisions at ATLAS are presented. In this, the most recent combined MPI and shower tunes performed using 7 TeV ATLAS data are reported, as well as improved modeling of electroweak processes, and processes containing top using recent MC generators and PDF sets.
A Monte Carlo approach to rolling leukocyte tracking in vivo.
Cui, Jing; Acton, Scott T; Lin, Zongli
2006-08-01
Tracking the movement of rolling leukocytes in vivo contributes to the understanding of the mechanism of the inflammatory process and to the development of anti-inflammatory drugs. Several roadblocks exist that hinder successful automated tracking including the moving background, the severe image noise and clutter, the occlusion of the target leukocyte by other leukocytes and structures, the jitter caused by the breathing movement of the living animal, and the weak image contrast. In this paper, a Monte Carlo tracker is developed for automatically tracking a single rolling leukocyte in vivo. Based on the leukocyte movement information and the image intensity features, a specialized sample-weighting criterion is tailored to the application. In comparison with a snake-based tracker, our experiments show that, as the noise intensity level increases, the performance of the snake tracker degrades more than that of the Monte Carlo tracker. In cases, where the leukocyte is observed in contact with the vessel wall, the Monte Carlo tracker is less affected by the image clutter. From tracking within 99 intravital microscopic video sequences, the Monte Carlo tracker exhibits superior performance in the reduced localization error and the increased number of frames tracked when compared with the centroid tracker, the correlation tracker and the GVF snake tracker. PMID:16876461
A Monte Carlo Approach for Adaptive Testing with Content Constraints
ERIC Educational Resources Information Center
Belov, Dmitry I.; Armstrong, Ronald D.; Weissman, Alexander
2008-01-01
This article presents a new algorithm for computerized adaptive testing (CAT) when content constraints are present. The algorithm is based on shadow CAT methodology to meet content constraints but applies Monte Carlo methods and provides the following advantages over shadow CAT: (a) lower maximum item exposure rates, (b) higher utilization of the…
Monte Carlo Capabilities of the SCALE Code System
NASA Astrophysics Data System (ADS)
Rearden, B. T.; Petrie, L. M.; Peplow, D. E.; Bekar, K. B.; Wiarda, D.; Celik, C.; Perfetti, C. M.; Ibrahim, A. M.; Hart, S. W. D.; Dunn, M. E.
2014-06-01
SCALE is a widely used suite of tools for nuclear systems modeling and simulation that provides comprehensive, verified and validated, user-friendly capabilities for criticality safety, reactor physics, radiation shielding, and sensitivity and uncertainty analysis. For more than 30 years, regulators, licensees, and research institutions around the world have used SCALE for nuclear safety analysis and design. SCALE provides a "plug-and-play" framework that includes three deterministic and three Monte Carlo radiation transport solvers that can be selected based on the desired solution, including hybrid deterministic/Monte Carlo simulations. SCALE includes the latest nuclear data libraries for continuous-energy and multigroup radiation transport as well as activation, depletion, and decay calculations. SCALE's graphical user interfaces assist with accurate system modeling, visualization, and convenient access to desired results. SCALE 6.2, to be released in 2014, will provide several new capabilities and significant improvements in many existing features, especially with expanded continuous-energy Monte Carlo capabilities for criticality safety, shielding, depletion, and sensitivity and uncertainty analysis. An overview of the Monte Carlo capabilities of SCALE is provided here, with emphasis on new features for SCALE 6.2.
A framework for adaptive Monte-Carlo procedures Bernard Lapeyre
Paris-Sud XI, Université de
Abstract Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose an automatic variance reduc- tion method, see [8] for a recent survey on adaptive variance reduction of using it to devise a variance reduction method. The non-adaptive algorithm Algorithm 1.1 (Non adaptive
Variance Reduction in Monte-Carlo Tree Search Joel Veness
Bowling, Michael
Variance Reduction in Monte-Carlo Tree Search Joel Veness University of Alberta veness the application of some standard techniques for variance reduction in MCTS, including common random numbers, the application of classical variance reduction techniques to MCTS has remained unexplored. In this paper we
Variance Reduction The statistical efficiency of Monte Carlo simulation can
Lyuu, Yuh-Dauh
Variance Reduction · The statistical efficiency of Monte Carlo simulation can be measured replications are needed. · Methods that improve efficiency in this manner are called variance-reduction Taiwan University Page 634 Variance Reduction: Antithetic Variates · We are interested in estimating E[ g
Yet another variance reduction method for direct monte carlo
Gabrieli, John
Yet another variance reduction method for direct monte carlo simulations of low-signal flows H. AHSignalL " Signal Presentation.nb 3 #12;1.1 Previous Work ü Baker & Hadjiconstantinou: Variance Reduction.nb #12;1.2 Objective ü Can we develop a variance-reduction technique that: ü Uses DSMC as its main
Variance Reduction Techniques for Monte Carlo Sampling from Student Distributions
Daniel A. Relles
1970-01-01
A Monte Carlo design is presented for estimating the variance and cumulative distribution function of translation and scale invariant statistics based on independent Student random variables. One obvious application is studying estimates of the location parameter from a symmetric, possibly long-tailed distribution. The method itself amounts to suppressing some of the variability in the sampled objects by integrating these objects
Monte Carlo variance reduction using finite element adjoint weight windows
Shahdatullah, M. S. [Applied Modelling and Computation Group AMCG, Imperial College of Science, Technology and Medicine, Dept. of Earth Science and Engineering, London, SW7 2AZ (United Kingdom); Ziver, K. [Applied Modelling and Computation Group AMCG, Imperial College of Science, Technology and Medicine, Dept. of Earth Science and Engineering, London, SW7 2AZ (United Kingdom); AMCG Group (United Kingdom); RM Consultants Ltd. Abingdon, Oxfordshire (United Kingdom); Eaton, M. D.; Pain, C. C.; Goddard, A. J. H. [Applied Modelling and Computation Group AMCG, Imperial College of Science, Technology and Medicine, Dept. of Earth Science and Engineering, London, SW7 2AZ (United Kingdom)
2006-07-01
The use of Monte Carlo variance reduction techniques is unavoidable on present day computers in obtaining numerical solutions in complex shielding, deep penetration or other radiation transport problems such as nuclear well logging and ex-core reactor core modeling etc. A deterministic variance reduction technique based on the finite element adjoint weight window (FEAWW) scheme is developed and applied in the well-known and widely used Monte Carlo radiation transport code MCNP. The scheme involves generating importance maps from the adjoint deterministic EVENT transport calculations which are then extracted and used as 'weight window lower bounds' suitable for acceleration of the forward Monte Carlo radiation transport calculations. The 'holy grail' of an automatic variance reduction technique is to provide a single method which provides systematic or nearly systematic ways to eliminate much of the user's intervention. The proposed method employs the adjoint solutions to the problem of interest which has been folded into the MCNP weight window scheme. The FEAWW method is tested on a number of complex deep penetration and neutron streaming problems and compared against the standard Monte Carlo generated variance reduction techniques with encouraging results. (authors)
Smart Monte Carlo for Yield Estimation Serdar Tasiran Alper Demir
Tasiran, Serdar
techniques are based on well-known variance reduction approaches from Monte Carlo simulation literature be obtained with much fewer circuit-level simulations. The variance reduction techniques we use require but is generally considered to be too expensive computationally. The use of variance reduction techniques has
Precision Localization in Monte Carlo Sensor Thomas C. Henderson
Henderson, Thomas C.
Precision Localization in Monte Carlo Sensor Networks Thomas C. Henderson School of Computing University of Utah Salt Lake City, UT, USA Email: tch@cs.utah.edu Edward Grant, Kyle Luthy, Leonardo Mattos that it is within the convex hull of the enemy locations). See Biswas et al.[1] and Henderson et al.[2] for details
A Monte Carlo Investigation of Mode Estimators in small Samples
Masci, Frank
. An alternative approach is to reformulate the problem as a search for the mode off. In applications, the mean. 53) for the similarly shaped log-normal distribution. It seems that the mode was "the neglectedA Monte Carlo Investigation of Mode Estimators in small Samples University of Lund, Sweden SUMMARY
Difficulties in vector-parallel processing of Monte Carlo codes
Higuchi, Kenji; Asai, Kiyoshi [Japan Atomic Energy Research Inst., Tokyo (Japan). Center for Promotion of Computational Science and Engineering; Hasegawa, Yukihiro [Research Organization for Information Science and Technology, Tokai, Ibaraki (Japan)
1997-09-01
Experiences with vectorization of production-level Monte Carlo codes such as KENO-IV, MCNP, VIM, and MORSE have shown that it is difficult to attain high speedup ratios on vector processors because of indirect addressing, nests of conditional branches, short vector length, cache misses, and operations for realization of robustness and generality. A previous work has already shown that the first, second, and third difficulties can be resolved by using special computer hardware for vector processing of Monte Carlo codes. Here, the fourth and fifth difficulties are discussed in detail using the results for a vectorized version of the MORSE code. As for the fourth difficulty, it is shown that the cache miss-hit ratio affects execution times of the vectorized Monte Carlo codes and the ratio strongly depends on the number of the particles simultaneously tracked. As for the fifth difficulty, it is shown that remarkable speedup ratios are obtained by removing operations that are not essential to the specific problem being solved. These experiences have shown that if a production-level Monte Carlo code system had a capability to selectively construct source coding that complements the input data, then the resulting code could achieve much higher performance.
Monte Carlo Study of Supernova Neutrino Spectra Formation
Mathias Th. Keil; Georg G. Raffelt; Hans-Thomas Janka
2003-01-01
The neutrino flux and spectra formation in a supernova core is studied by using a Monte Carlo code. The dominant opacity contribution for numu is elastic scattering on nucleons numuN-->Nnumu, where numu always stands for either numu or nutau. In addition, we switch on or off a variety of processes that allow for the exchange of energy or the creation
Number of Magic Squares from Parallel Tempering Monte Carlo
K. Pinn; C. Wieczerkowski
1998-01-01
There are 880 magic squares of size 4 by 4, and 275 305 224 of size 5 by 5. It seems very difficult if not impossible to count exactly the number of higher order magic squares. We propose a method to estimate these numbers by Monte Carlo simulating magic squares at finite temperature. One is led to perform low temperature
Monte Carlo simulation by computer for life-cycle costing
NASA Technical Reports Server (NTRS)
Gralow, F. H.; Larson, W. J.
1969-01-01
Prediction of behavior and support requirements during the entire life cycle of a system enables accurate cost estimates by using the Monte Carlo simulation by computer. The system reduces the ultimate cost to the procuring agency because it takes into consideration the costs of initial procurement, operation, and maintenance.
Monte Carlo simulation of absolute secondary electron yield of Cu
Z. J. Ding; H. M. Li; X. D. Tang; R. Shimizu
2004-01-01
A Monte Carlo simulation model of electron interaction with solids that includes cascade secondary electron production has been used to study secondary electron emission from Cu. An optical dielectric function was used to describe electron energy loss and the associated secondary electron excitation. From the simulation, the absolute primary energy dependence of the secondary yield and the energy distribution of
Calculating Potential Energy Curves with Quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Powell, Andrew D.; Dawes, Richard
2014-06-01
Quantum Monte Carlo (QMC) is a computational technique that can be applied to the electronic Schrödinger equation for molecules. QMC methods such as Variational Monte Carlo (VMC) and Diffusion Monte Carlo (DMC) have demonstrated the capability of capturing large fractions of the correlation energy, thus suggesting their possible use for high-accuracy quantum chemistry calculations. QMC methods scale particularly well with respect to parallelization making them an attractive consideration in anticipation of next-generation computing architectures which will involve massive parallelization with millions of cores. Due to the statistical nature of the approach, in contrast to standard quantum chemistry methods, uncertainties (error-bars) are associated with each calculated energy. This study focuses on the cost, feasibility and practical application of calculating potential energy curves for small molecules with QMC methods. Trial wave functions were constructed with the multi-configurational self-consistent field (MCSCF) method from GAMESS-US.[1] The CASINO Monte Carlo quantum chemistry package [2] was used for all of the DMC calculations. An overview of our progress in this direction will be given. References: M. W. Schmidt et al. J. Comput. Chem. 14, 1347 (1993). R. J. Needs et al. J. Phys.: Condensed Matter 22, 023201 (2010).
Exploring Mass Perception with Markov Chain Monte Carlo
ERIC Educational Resources Information Center
Cohen, Andrew L.; Ross, Michael G.
2009-01-01
Several previous studies have examined the ability to judge the relative mass of objects in idealized collisions. With a newly developed technique of psychological Markov chain Monte Carlo sampling (A. N. Sanborn & T. L. Griffiths, 2008), this work explores participants; perceptions of different collision mass ratios. The results reveal…
Image Segmentation by Data-Driven Markov Chain Monte Carlo
Zhuowen Tu; Song-Chun Zhu
2002-01-01
Abstract: This paper presents a computational paradigm called Data-Driven Markov Chain MonteCarlo (DDMCMC) for image segmentation in the Bayesian statistical framework. The papercontributes to image segmentation in four aspects. Firstly, it designs ecient andwell balanced Markov Chain dynamics to explore the complex solution space, and thusachieves a nearly global optimal solution independent of initial segmentations. Secondly, itpresents a mathematical principle
Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review
Mary Kathryn Cowles; Bradley P. Carlin
1996-01-01
A critical issue for users of Markov chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use
Monte Carlo sampling from the quantum state space. II
Yi-Lin Seah; Jiangwei Shang; Hui Khoon Ng; David John Nott; Berthold-Georg Englert
2015-04-27
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local maxima or evaluating an integral over a region in the quantum state space are but two exemplary applications of many. These tasks can only be performed reliably and efficiently with Monte Carlo methods, which involve good samplings of the parameter space in accordance with the relevant target distribution. We show how the Markov-chain Monte Carlo method known as Hamiltonian Monte Carlo, or hybrid Monte Carlo, can be adapted to this context. It is applicable when an efficient parameterization of the state space is available. The resulting random walk is entirely inside the physical parameter space, and the Hamiltonian dynamics enable us to take big steps, thereby avoiding strong correlations between successive sample points while enjoying a high acceptance rate. We use examples of single and double qubit measurements for illustration.
Dynamic Conditional Independence Models And Markov Chain Monte Carlo Methods
Carlo Berzuini; Nicola G. Best; Walter R. Gilks; Cristiana Larizza
1997-01-01
In dynamic statistical modeling situations, observations arise sequentially, causingthe model to expand by progressive incorporation of new data items and new unknownparameters. For example, in clinical monitoring, new patient-specific parameters areintroduced with each new patient. Markov chain Monte Carlo (MCMC) might be usedfor posterior inference, but would need to be redone at each expansion stage. Thus suchmethods are often too
Analysis of random magnetization switching using Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Lee, A.; Liu, Z.; Bertotti, G.; Serpico, C.; Mayergoyz, I.
2014-02-01
Numerical modeling of random magnetization switching in uniaxial particles is studied by using Monte Carlo simulations of magnetization dynamics driven by a jump-noise process. Numerical results on cumulative distribution functions for random switching (exit) times are reported along with the numerical testing of the Kramers-Brown approximation.
Adaptive Monte Carlo methods for rare event simulations
Ming-hua Hsieh
2002-01-01
We review two types of adaptive Monte Carlo methods for rare event simulations. These methods are based on importance sampling. The first approach selects importance sampling distributions by minimizing the variance of importance sampling estimator. The second approach selects importance sampling distributions by minimizing the cross entropy to the optimal importance sampling distribution. We also review the basic concepts of
When Are Quasi-Monte Carlo Algorithms Efficient for High Dimensional Integrals?
Ian H. Sloan; Henryk Wozniakowski
1998-01-01
Recently, quasi-Monte Carlo algorithms have been successfully used for multivariate integration of high dimensiond, and were significantly more efficient than Monte Carlo algorithms. The existing theory of the worst case error bounds of quasi-Monte Carlo algorithms does not explain this phenomenon. This paper presents a partial answer to why quasi-Monte Carlo algorithms can work well for arbitrarily larged. It is
Unloading the dice: Minimising biases in Full Configuration Interaction Quantum Monte Carlo
Vigor, W A; Bearpark, M J; Thom, A J W
2014-01-01
We show that Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a Markov Chain in its present form. We construct the Markov Matrix of FCIQMC for a two determinant system and hence compute the stationary distribution. These solutions are used to quantify the dependence of the population dynamics on the parameters defining Markov Chain. Despite the simplicity of the system, it still reveals a finite population bias inherent to the FCIQMC algorithm. We investigate the finite population bias for the neon atom and suggest simulation setups to in general minimise the bias compared to the stochastic noise.
Phase diagram of the 3D quantum anisotropic XY model—A quantum Monte Carlo calculation
NASA Astrophysics Data System (ADS)
Guimarães, M.; Costa, B. V.; Pires, A. S. T.; Souza, A.
2013-04-01
In this work we apply the stochastic series expansion quantum Monte Carlo method to study the quantum phase transition of the spin 1 three-dimensional XY model with easy-plane anisotropy D. We simulate this model in cubic lattices (L×L×L) with L?(4,24) and periodic boundary condition. Using finite size scaling we obtained the phase diagram for the model, the critical exponent z?=0.501(5) and the quantum critical point Dc=9.7950(3)J. Using a low temperature expansion for the magnetic susceptibility we obtained z?=0.59(1).
SCOUT: A Fast Monte-Carlo Modeling Tool of Scintillation Camera Output
Hunter, William C. J.; Barrett, Harrison H.; Lewellen, Thomas K.; Miyaoka, Robert S.; Muzi, John P.; Li, Xiaoli; McDougald, Wendy; MacDonald, Lawrence R.
2011-01-01
We have developed a Monte-Carlo photon-tracking and readout simulator called SCOUT to study the stochastic behavior of signals output from a simplified rectangular scintillation-camera design. SCOUT models the salient processes affecting signal generation, transport, and readout. Presently, we compare output signal statistics from SCOUT to experimental results for both a discrete and a monolithic camera. We also benchmark the speed of this simulation tool and compare it to existing simulation tools. We find this modeling tool to be relatively fast and predictive of experimental results. Depending on the modeled camera geometry, we found SCOUT to be 4 to 140 times faster than other modeling tools. PMID:22072297
Quantum Monte Carlo Simulation of Nanoscale MgH2 Cluster Thermodynamics
Wu, Zhigang
Quantum Monte Carlo Simulation of Nanoscale MgH2 Cluster Thermodynamics Zhigang Wu,,§ Mark D-7 el; Nel ) number of electrons) severely limits application to larger systems. The quantum Monte Carlo simulations are performed using the fixed-node diffusion Monte Carlo7 (DMC) method with the QWalk code.8