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
Stabilized multilevel Monte Carlo method for stiff stochastic differential equations
Abdulle, Assyr, E-mail: assyr.abdulle@epfl.ch; Blumenthal, Adrian, E-mail: adrian.blumenthal@epfl.ch
2013-10-15
A multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales is proposed. For such problems, that we call stiff, the performance of MLMC methods based on classical explicit methods deteriorates because of the time step restriction to resolve the fastest scales that prevents to exploit all the levels of the MLMC approach. We show that by switching to explicit stabilized stochastic methods and balancing the stabilization procedure simultaneously with the hierarchical sampling strategy of MLMC methods, the computational cost for stiff systems is significantly reduced, while keeping the computational algorithm fully explicit and easy to implement. Numerical experiments on linear and nonlinear stochastic differential equations and on a stochastic partial differential equation illustrate the performance of the stabilized MLMC method and corroborate our theoretical findings.
Semi-stochastic full configuration interaction quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Holmes, Adam; Petruzielo, Frank; Khadilkar, Mihir; Changlani, Hitesh; Nightingale, M. P.; Umrigar, C. J.
2012-02-01
In the recently proposed full configuration interaction quantum Monte Carlo (FCIQMC) [1,2], the ground state is projected out stochastically, using a population of walkers each of which represents a basis state in the Hilbert space spanned by Slater determinants. The infamous fermion sign problem manifests itself in the fact that walkers of either sign can be spawned on a given determinant. We propose an improvement on this method in the form of a hybrid stochastic/deterministic technique, which we expect will improve the efficiency of the algorithm by ameliorating the sign problem. We test the method on atoms and molecules, e.g., carbon, carbon dimer, N2 molecule, and stretched N2. [4pt] [1] Fermion Monte Carlo without fixed nodes: a Game of Life, death and annihilation in Slater Determinant space. George Booth, Alex Thom, Ali Alavi. J Chem Phys 131, 050106, (2009).[0pt] [2] Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo. Deidre Cleland, George Booth, and Ali Alavi. J Chem Phys 132, 041103 (2010).
Reich, Sebastian
A guided sequential Monte Carlo method for the assimilation of data into stochastic dynamical functions. While sequential Monte Carlo methods have emerged as a methodology for tackling as- similation alternatives to sequential Monte Carlo methods since they also work for high dimensional problems. Typical
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)
Philip D. O’Neill
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.
Monte Carlo simulations of two-component drop growth by stochastic coalescence
L. Alfonso; G. B. Raga; D. Baumgardner
2009-01-01
The evolution of two-dimensional drop distributions is simulated in this study using a Monte Carlo method. The stochastic algorithm of Gillespie (1976) for chemical reactions in the formulation proposed by Laurenzi et al. (2002) was used to simulate the kinetic behavior of the drop population. Within this framework, species are defined as droplets of specific size and aerosol composition. The
GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study
Torben G. Andersen; Bent E. Sørensen; Bent E. Sorensen
1996-01-01
We examine alternative generalized method of moments procedures for estimation of a stochastic autoregressive volatility model by Monte Carlo methods. We document the existence of a tradeoff between the number of moments, or information, included in estimation and the quality, or precision, of the objective function used for estimation. Furthermore, an approximation to the optimal weighting matrix is used to
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.
Monte Carlo Sampling-Based Methods for Stochastic Optimization
2014-01-22
as a classical expectation but in a different form, such as a value-at-risk or ... care, finance, transportation, revenue management, and many others. ...... sampling methods is closely related to the issues of assessment of solution ...... criteria for stochastic dual dynamic programming: a case study in long-term hydrothermal.
Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems
NASA Astrophysics Data System (ADS)
Katsoulakis, Markos A.; Majda, Andrew J.; Vlachos, Dionisios G.
2003-03-01
In this paper we present a new class of coarse-grained stochastic processes and Monte Carlo simulations, derived directly from microscopic lattice systems and describing mesoscopic length scales. As our primary example, we mainly focus on a microscopic spin-flip model for the adsorption and desorption of molecules between a surface adjacent to a gas phase, although a similar analysis carries over to other processes. The new model can capture large scale structures, while retaining microscopic information on intermolecular forces and particle fluctuations. The requirement of detailed balance is utilized as a systematic design principle to guarantee correct noise fluctuations for the coarse-grained model. We carry out a rigorous asymptotic analysis of the new system using techniques from large deviations and present detailed numerical comparisons of coarse-grained and microscopic Monte Carlo simulations. The coarse-grained stochastic algorithms provide large computational savings without increasing programming complexity or the CPU time per executed event compared to microscopic Monte Carlo simulations.
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
Monte Carlo simulations of two-component drop growth by stochastic coalescence
NASA Astrophysics Data System (ADS)
Alfonso, L.; Raga, G. B.; Baumgardner, D.
2009-02-01
The evolution of two-dimensional drop distributions is simulated in this study using a Monte Carlo method. The stochastic algorithm of Gillespie (1976) for chemical reactions in the formulation proposed by Laurenzi et al. (2002) was used to simulate the kinetic behavior of the drop population. Within this framework, species are defined as droplets of specific size and aerosol composition. The performance of the algorithm was checked by a comparison with the analytical solutions found by Lushnikov (1975) and Golovin (1963) and with finite difference solutions of the two-component kinetic collection equation obtained for the Golovin (sum) and hydrodynamic kernels. Very good agreement was observed between the Monte Carlo simulations and the analytical and numerical solutions. A simulation for realistic initial conditions is presented for the hydrodynamic kernel. As expected, the aerosol mass is shifted from small to large particles due to collection process. This algorithm could be extended to incorporate various properties of clouds such several crystals habits, different types of soluble CCN, particle charging and drop breakup.
Efficient Monte Carlo and greedy heuristic for the inference of stochastic block models.
Peixoto, Tiago P
2014-01-01
We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo (MCMC) method, with a fast mixing time and a much reduced susceptibility to getting trapped in metastable states, or as a greedy agglomerative heuristic, with an almost linear O(Nln2N) complexity, where N is the number of nodes in the network, independent of the number of blocks being inferred. We show that the heuristic is capable of delivering results which are indistinguishable from the more exact and numerically expensive MCMC method in many artificial and empirical networks, despite being much faster. The method is entirely unbiased towards any specific mixing pattern, and in particular it does not favor assortative community structures. PMID:24580278
Efficient Monte Carlo and greedy heuristic for the inference of stochastic block models
NASA Astrophysics Data System (ADS)
Peixoto, Tiago P.
2014-01-01
We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo (MCMC) method, with a fast mixing time and a much reduced susceptibility to getting trapped in metastable states, or as a greedy agglomerative heuristic, with an almost linear O (Nln2N) complexity, where N is the number of nodes in the network, independent of the number of blocks being inferred. We show that the heuristic is capable of delivering results which are indistinguishable from the more exact and numerically expensive MCMC method in many artificial and empirical networks, despite being much faster. The method is entirely unbiased towards any specific mixing pattern, and in particular it does not favor assortative community structures.
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
Deterministic flows of order-parameters in stochastic processes of quantum Monte Carlo method
NASA Astrophysics Data System (ADS)
Inoue, Jun-ichi
2010-06-01
In terms of the stochastic process of quantum-mechanical version of Markov chain Monte Carlo method (the MCMC), we analytically derive macroscopically deterministic flow equations of order parameters such as spontaneous magnetization in infinite-range (d(= ?)-dimensional) quantum spin systems. By means of the Trotter decomposition, we consider the transition probability of Glauber-type dynamics of microscopic states for the corresponding (d + 1)-dimensional classical system. Under the static approximation, differential equations with respect to macroscopic order parameters are explicitly obtained from the master equation that describes the microscopic-law. In the steady state, we show that the equations are identical to the saddle point equations for the equilibrium state of the same system. The equation for the dynamical Ising model is recovered in the classical limit. We also check the validity of the static approximation by making use of computer simulations for finite size systems and discuss several possible extensions of our approach to disordered spin systems for statistical-mechanical informatics. Especially, we shall use our procedure to evaluate the decoding process of Bayesian image restoration. With the assistance of the concept of dynamical replica theory (the DRT), we derive the zero-temperature flow equation of image restoration measure showing some 'non-monotonic' behaviour in its time evolution.
NASA Astrophysics Data System (ADS)
Franke, Brian C.; Kensek, Ronald P.; Prinja, Anil K.
2014-06-01
Stochastic-media simulations require numerous boundary crossings. We consider two Monte Carlo electron transport approaches and evaluate accuracy with numerous material boundaries. In the condensed-history method, approximations are made based on infinite-medium solutions for multiple scattering over some track length. Typically, further approximations are employed for material-boundary crossings where infinite-medium solutions become invalid. We have previously explored an alternative "condensed transport" formulation, a Generalized Boltzmann-Fokker-Planck GBFP method, which requires no special boundary treatment but instead uses approximations to the electron-scattering cross sections. Some limited capabilities for analog transport and a GBFP method have been implemented in the Integrated Tiger Series (ITS) codes. Improvements have been made to the condensed history algorithm. The performance of the ITS condensed-history and condensed-transport algorithms are assessed for material-boundary crossings. These assessments are made both by introducing artificial material boundaries and by comparison to analog Monte Carlo simulations.
Noritaka Shimizu; Takahiro Mizusaki; Kazunari Kaneko
2013-05-09
We propose a new variational Monte Carlo (VMC) approach based on the Krylov subspace for large-scale shell-model calculations. A random walker in the VMC is formulated with the $M$-scheme representation, and samples a small number of configurations from a whole Hilbert space stochastically. This VMC framework is demonstrated in the shell-model calculations of $^{48}$Cr and $^{60}$Zn, and we discuss its relation to a small number of Lanczos iterations. By utilizing the wave function obtained by the conventional particle-hole-excitation truncation as an initial state, this VMC approach provides us with a sequence of systematically improved results.
Solution of deterministic–stochastic epidemic models by dynamical Monte Carlo method
O. E Aièllo; V. J Haas; M. A. A daSilva; A Caliri
2000-01-01
This work is concerned with dynamical Monte Carlo (MC) method and its application to models originally formulated in a continuous-deterministic approach. Specifically, a susceptible–infected–removed–susceptible (SIRS) model is used in order to analyze aspects of the dynamical MC algorithm and achieve its applications in epidemic contexts. We first examine two known approaches to the dynamical interpretation of the MC method and
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.
Multigrid Monte Carlo method. Conceptual foundations
Jonathan Goodman; Alan D. Sokal
1989-01-01
We present details of a stochastic generalization of the multigrid method, called multigrid Monte Carlo (MGMC), that reduces critical slowing down in Monte Carlo computations of lattice field theories. For Gaussian (free) fields, critical slowing down is completely eliminated. For a phi4 model, numerical experiments show a factor of ~=10 reduction, over a standard heat-bath algorithm, in the CPU time
Heinz-Peter Breuer
2003-09-15
It is shown that the exact dynamics of a composite quantum system can be represented through a pair of product states which evolve according to a Markovian random jump process. This representation is used to design a general Monte Carlo wave function method that enables the stochastic treatment of the full non-Markovian behavior of open quantum systems. Numerical simulations are carried out which demonstrate that the method is applicable to open systems strongly coupled to a bosonic reservoir, as well as to the interaction with a spin bath. Full details of the simulation algorithms are given, together with an investigation of the dynamics of fluctuations. Several potential generalizations of the method are outlined.
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
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.
Brown, F.B.
1981-01-01
Examination of the global algorithms and local kernels of conventional general-purpose Monte Carlo codes shows that multigroup Monte Carlo methods have sufficient structure to permit efficient vectorization. A structured multigroup Monte Carlo algorithm for vector computers is developed in which many particle events are treated at once on a cell-by-cell basis. Vectorization of kernels for tracking and variance reduction is described, and a new method for discrete sampling is developed to facilitate the vectorization of collision analysis. To demonstrate the potential of the new method, a vectorized Monte Carlo code for multigroup radiation transport analysis was developed. This code incorporates many features of conventional general-purpose production codes, including general geometry, splitting and Russian roulette, survival biasing, variance estimation via batching, a number of cutoffs, and generalized tallies of collision, tracklength, and surface crossing estimators with response functions. Predictions of vectorized performance characteristics for the CYBER-205 were made using emulated coding and a dynamic model of vector instruction timing. Computation rates were examined for a variety of test problems to determine sensitivities to batch size and vector lengths. Significant speedups are predicted for even a few hundred particles per batch, and asymptotic speedups by about 40 over equivalent Amdahl 470V/8 scalar codes arepredicted for a few thousand particles per batch. The principal conclusion is that vectorization of a general-purpose multigroup Monte Carlo code is well worth the significant effort required for stylized coding and major algorithmic changes.
An efficient Markov chain Monte Carlo simulation of a stochastic inverse radiation problem
Zabaras, Nicholas J.
is to reveal the potential of using statistical approaches, mainly Bayesian com- putational statistics as a stochastic process, of which the joint posterior probability density function (PPDF) is com- puted using stochastic optimization and uncertainty quantifica- tion methodologies and algorithms is critical [1
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.
Error in Monte Carlo, quasi-error in Quasi-Monte Carlo
R. H. Kleiss; A. Lazopoulos
2005-04-12
While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error. The standard Monte Carlo error estimator relies on the assumption that the points are generated independently of each other and, therefore, fails to account for the error improvement advertised by the Quasi-Monte Carlo method. We advocate the construction of an estimator of stochastic nature, based on the ensemble of pointsets with a particular discrepancy value. We investigate the consequences of this choice and give some first empirical results on the suggested estimators.
T.J. Donovan; Y. Danon
2002-03-15
Monte Carlo algorithms are developed to calculate the ensemble-average particle leakage through the boundaries of a 2-D binary stochastic material. The mixture is specified within a rectangular area and consists of a fixed number of disks of constant radius randomly embedded in a matrix material. The algorithms are extensions of the proposal of Zimmerman et al., using chord-length sampling to eliminate the need to explicitly model the geometry of the mixture. Two variations are considered. The first algorithm uses Chord-Length Sampling (CLS) for both material regions. The second algorithm employs Limited Chord Length Sampling (LCLS), only using chord-length sampling in the matrix material. Ensemble-average leakage results are computed for a range of material interaction coefficients and compared against benchmark results for both accuracy and efficiency. both algorithms are exact for purely absorbing materials and provide decreasing accuracy as scattering is increased in the matrix material. The LCLS algorithm shows a better accuracy than the CLS algorithm for all cases while maintaining an equivalent or better efficiency. Accuracy and efficiency problems with the CLS algorithm are due principally to assumptions made in determining the chord-length distribution within the disks.
G. Groeneweg
This paper explores the card game Machi- avelli. 1 In this game, many turns have to be played and many actions can be carried out per turn, which results in a large game tree. Because traditional search methods will take too much time to play the game in a reasonable amount of time, this paper deals with applying Monte Carlo
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.
Experiments with Monte Carlo Othello
Philip Hingston; Martin Masek
2007-01-01
In this paper, we report on our experiments with using Monte Carlo simulation (specifically the UCT algorithm) as the basis for an Othello playing program. Monte Carlo methods have been used for other games in the past, most recently and notably in successful Go playing programs. We show that Monte Carlo-based players have potential for Othello, and that evolutionary algorithms
Monte Carlo photon benchmark problems
Whalen, D.J.; Hollowell, D.E.; Hendricks, J.S.
1991-01-01
Photon benchmark calculations have been performed to validate the MCNP Monte Carlo computer code. These are compared to both the COG Monte Carlo computer code and either experimental or analytic results. The calculated solutions indicate that the Monte Carlo method, and MCNP and COG in particular, can accurately model a wide range of physical problems.
Monte-Carlo Tests Diplomarbeit
Monte-Carlo Tests Diplomarbeit Wiebke Werft Mathematisches Institut der Heinrich.2 Suffizienz und VollstÃ¤ndigkeit . . . . . . . . . . . . . . . . . . . . 5 2 Monte-Carlo Tests 8 2.1 Formulierung des Testproblems . . . . . . . . . . . . . . . . . . . 8 2.2 Definition des Monte-Carlo Tests
Quantum Monte Carlo Helsinki 2011
Boyer, Edmond
Quantum Monte Carlo Helsinki 2011 Marius Lewerenz MSME/CT, UMR 8208 CNRS, UniversitÂ´e Paris Est? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 What is a Monte Carlo method? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 What are Monte Carlo methods good for? . . . . . . . . . . . . . . . . . . . . . . . 5 1
Stochastic Inversion of Electrical Resistivity Changes Using a Markov Chain, Monte Carlo Approach
Ramirez, A; Nitao, J; Hanley, W; Aines, R; Glaser, R; Sengupta, S; Dyer, K; Hickling, T; Daily, W
2004-09-21
We describe a stochastic inversion method for mapping subsurface regions where the electrical resistivity is changing. The technique combines prior information, electrical resistance data and forward models to produce subsurface resistivity models that are most consistent with all available data. Bayesian inference and a Metropolis simulation algorithm form the basis for this approach. Attractive features include its ability to: (1) provide quantitative measures of the uncertainty of a generated estimate and, (2) allow alternative model estimates to be identified, compared and ranked. Methods that monitor convergence and summarize important trends of the posterior distribution are introduced. Results from a physical model test and a field experiment were used to assess performance. The stochastic inversions presented provide useful estimates of the most probable location, shape, and volume of the changing region, and the most likely resistivity change. The proposed method is computationally expensive, requiring the use of extensive computational resources to make its application practical.
Dytman, Steven [Department.of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 (United States)
2011-10-06
Every neutrino experiment requires a Monte Carlo event generator for various purposes. Historically, each series of experiments developed their own code which tuned to their needs. Modern experiments would benefit from a universal code (e.g. PYTHIA) which would allow more direct comparison between experiments. GENIE attempts to be that code. This paper compares most commonly used codes and provides some details of GENIE.
NASA Astrophysics Data System (ADS)
Dytman, Steven
2011-10-01
Every neutrino experiment requires a Monte Carlo event generator for various purposes. Historically, each series of experiments developed their own code which tuned to their needs. Modern experiments would benefit from a universal code (e.g. PYTHIA) which would allow more direct comparison between experiments. GENIE attempts to be that code. This paper compares most commonly used codes and provides some details of GENIE.
2010-01-01
Background Although many infections that are transmissible from person to person are acquired through direct contact between individuals, a minority, notably pulmonary tuberculosis (TB), measles and influenza are known to be spread by the airborne route. Airborne infections pose a particular threat to susceptible individuals whenever they are placed together with the index case in confined spaces. With this in mind, waiting areas of healthcare facilities present a particular challenge, since large numbers of people, some of whom may have underlying conditions which predispose them to infection, congregate in such spaces and can be exposed to an individual who may be shedding potentially pathogenic microorganisms. It is therefore important to understand the risks posed by infectious individuals in waiting areas, so that interventions can be developed to minimise the spread of airborne infections. Method A stochastic Monte Carlo model was constructed to analyse the transmission of airborne infection in a hypothetical 132 m3 hospital waiting area in which occupancy levels, waiting times and ventilation rate can all be varied. In the model the Gammaitoni-Nucci equation was utilized to predict probability of susceptible individuals becoming infected. The model was used to assess the risk of transmission of three infectious diseases, TB, influenza and measles. In order to allow for stochasticity a random number generator was applied to the variables in the model and a total of 10000 individual simulations were undertaken. The mean quanta production rates used in the study were 12.7, 100 and 570 per hour for TB, influenza and measles, respectively. Results The results of the study revealed the mean probability of acquiring a TB infection during a 30-minute stay in the waiting area to be negligible (i.e. 0.0034), while that for influenza was an order of magnitude higher at 0.0262. By comparison the mean probability of acquiring a measles infection during the same period was 0.1349. If the duration of the stay was increased to 60 minutes then these values increased to 0.0087, 0.0662 and 0.3094, respectively. Conclusion Under normal circumstances the risk of acquiring a TB infection during a visit to a hospital waiting area is minimal. Likewise the risks associated with the transmission of influenza, although an order of magnitude greater than those for TB, are relatively small. By comparison, the risks associated with measles are high. While the installation of air disinfection may be beneficial, when seeking to prevent the transmission of airborne viral infection it is important to first minimize waiting times and the number of susceptible individuals present before turning to expensive technological solutions. PMID:20727178
Monte Carlo method in optical radiometry
A. V. Prokhorov
1998-01-01
State-of-the-art in the application of the Monte Carlo method (MCM) to the computational problems of optical radiometry is discussed. The MCM offers a universal technique for radiation transfer modelling based on the stochastic approach. Developments of the original MCM algorithms and software for calculation of effective emissivities of black bodies, absorption characteristics of cavity radiometers and photometric properties of integrating
Quantum Gibbs ensemble Monte Carlo
Riccardo Fantoni; Saverio Moroni
2014-08-24
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 $^4$He in two dimensions.
The fermion Monte Carlo revisited
NASA Astrophysics Data System (ADS)
Assaraf, Roland; Caffarel, Michel; Khelif, Anatole
2007-02-01
In this work we present a detailed study of the fermion Monte Carlo algorithm (FMC), a recently proposed stochastic method for calculating fermionic ground-state energies. A proof that the FMC method is an exact method is given. In this work the stability of the method is related to the difference between the lowest (bosonic-type) eigenvalue of the FMC diffusion operator and the exact Fermi energy. It is shown that within a FMC framework the lowest eigenvalue of the new diffusion operator is no longer the bosonic ground-state eigenvalue as in standard exact diffusion Monte Carlo (DMC) schemes but a modified value which is strictly greater. Accordingly, FMC can be viewed as an exact DMC method built from a correlated diffusion process having a reduced Bose-Fermi gap. As a consequence, the FMC method is more stable than any transient method (or nodal release-type approaches). It is shown that the most recent ingredient of the FMC approach (Kalos M H and Pederiva F 2000 Phys. Rev. Lett. 85 3547), namely the introduction of non-symmetric guiding functions, does not necessarily improve the stability of the algorithm. We argue that the stability observed with such guiding functions is in general a finite-size population effect disappearing for a very large population of walkers. The counterpart of this stability is a control population error which is different in nature from the standard diffusion Monte Carlo algorithm and which is at the origin of an uncontrolled approximation in FMC. We illustrate the various ideas presented in this work with calculations performed on a very simple model having only nine states but a full 'sign problem'. Already for this toy model it is clearly seen that FMC calculations are inherently uncontrolled.
MONTE CARLO EXTENSION OF QUASIMONTE CARLO Art B. Owen
Owen, Art
MONTE CARLO EXTENSION OF QUASIÂMONTE 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 quasiÂMonte Carlo techÂ niques. Randomized quasiÂMonte Carlo methods proÂ vide a basis for error
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
Design of Monte Carlo Studies.
ERIC Educational Resources Information Center
Halperin, Silas
There are good reasons for the growing popularity of Monte Carlo procedures; but with increasing use comes increasing misuse. A variety of exact and approximate alternatives should be considered before one chooses to approach a problem with Monte Carlo methods. Once it has been decided that simulation is desirable, consideration should be given to…
Marcus, Ryan C. [Los Alamos National Laboratory
2012-07-25
MCMini is a proof of concept that demonstrates the possibility for Monte Carlo neutron transport using OpenCL with a focus on performance. This implementation, written in C, shows that tracing particles and calculating reactions on a 3D mesh can be done in a highly scalable fashion. These results demonstrate a potential path forward for MCNP or other Monte Carlo codes.
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.
Secondproofs Monte Carlo and Quasi-Monte Carlo Methods 2008
L'Ecuyer, Pierre
Pierre L'Ecuyer r Art B. Owen Editors Monte Carlo and Quasi-Monte Carlo Methods 2008 #12;Secondproofs Classification (2000): Primary 11K45, 65-06, 65C05, 65C10; Secondary 11K38, 65D18, 65D30, 65D32, 65R20, 91B28 Universiteit Leuven Luc Devroye, McGill University Henri Faure, CNRS Marseille Paul Glasserman, Columbia
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.
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 Â·Monte Carlo basics Â·Rejection and Importance sampling Â·Markov chain Monte Carlo Â·Metropolis-Hastings and Gibbs sampling Â·Slice sampling Â·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
Limit theorems for weighted samples with applications to sequential Monte Carlo methods
Randal Douc; Eric Moulines
2008-01-01
In the last decade, sequential Monte Carlo methods (SMC) emerged as a key tool in computational statistics [see, e.g., Sequential Monte Carlo Methods in Practice (2001) Springer, New York, Monte Carlo Strategies in Scientific Computing (2001) Springer, New York, Complex Stochastic Systems (2001) 109–173]. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to
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
Semistochastic Projector Monte Carlo Method F. R. Petruzielo,1,* A. A. Holmes,1,
Nightingale, Peter
Semistochastic Projector Monte Carlo Method F. R. Petruzielo,1,* A. A. Holmes,1, Hitesh J. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem, for sufficiently large N, this is no longer feasible, Monte Carlo methods can be used to represent stochastically
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
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
Plante, Ianik; Ponomarev, Artem; Cucinotta, Francis A
2011-02-01
The description of energy deposition by high charge and energy (HZE) nuclei is of importance for space radiation risk assessment and due to their use in hadrontherapy. Such ions deposit a large fraction of their energy within the so-called core of the track and a smaller proportion in the penumbra (or track periphery). We study the stochastic patterns of the radial dependence of energy deposition using Monte Carlo track structure codes RITRACKS and RETRACKS, that were used to simulate HZE tracks and calculate energy deposition in voxels of 40 nm. The simulation of a (56)Fe(26+) ion of 1 GeV u(-1) revealed zones of high-energy deposition which maybe found as far as a few millimetres away from the track core in some simulations. The calculation also showed that ?43 % of the energy was deposited in the penumbra. These 3D stochastic simulations combined with a visualisation interface are a powerful tool for biophysicists which may be used to study radiation-induced biological effects such as double strand breaks and oxidative damage and the subsequent cellular and tissue damage processing and signalling. PMID:21199826
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.
A Classroom Note on Monte Carlo Integration.
ERIC Educational Resources Information Center
Kolpas, Sid
1998-01-01
The Monte Carlo method provides approximate solutions to a variety of mathematical problems by performing random sampling simulations with a computer. Presents a program written in Quick BASIC simulating the steps of the Monte Carlo method. (ASK)
Applications of Monte Carlo Methods in Calculus.
ERIC Educational Resources Information Center
Gordon, Sheldon P.; Gordon, Florence S.
1990-01-01
Discusses the application of probabilistic ideas, especially Monte Carlo simulation, to calculus. Describes some applications using the Monte Carlo method: Riemann sums; maximizing and minimizing a function; mean value theorems; and testing conjectures. (YP)
Suitable Candidates for Monte Carlo Solutions.
ERIC Educational Resources Information Center
Lewis, Jerome L.
1998-01-01
Discusses Monte Carlo methods, powerful and useful techniques that rely on random numbers to solve deterministic problems whose solutions may be too difficult to obtain using conventional mathematics. Reviews two excellent candidates for the application of Monte Carlo methods. (ASK)
Monte Carlo integration with subtraction
NASA Astrophysics Data System (ADS)
Arthur, Rudy; Kennedy, A. D.
2013-12-01
This paper investigates a class of algorithms for numerical integration of a function in d dimensions over a compact domain by Monte Carlo methods. We construct a histogram approximation to the function using a partition of the integration domain into a set of bins specified by some parameters. We then consider two adaptations: the first is to subtract the histogram approximation, whose integral we may easily evaluate explicitly, from the function and integrate the difference using Monte Carlo; the second is to modify the bin parameters in order to make the variance of the Monte Carlo estimate of the integral the same for all bins. This allows us to use Student’s t-test as a trigger for rebinning, which we claim is more stable than the ?2 test that is commonly used for this purpose. We provide a program that we have used to study the algorithm for the case where the histogram is represented as a product of one-dimensional histograms. We discuss the assumptions and approximations made, as well as giving a pedagogical discussion of the myriad ways in which the results of any such Monte Carlo integration program can be misleading.
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.
NSDL National Science Digital Library
2008-12-30
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.
Synchronous Parallel Kinetic Monte Carlo
Mart?nez, E; Marian, J; Kalos, M H
2006-12-14
A novel parallel kinetic Monte Carlo (kMC) algorithm formulated on the basis of perfect time synchronicity is presented. The algorithm provides an exact generalization of any standard serial kMC model and is trivially implemented in parallel architectures. We demonstrate the mathematical validity and parallel performance of the method by solving several well-understood problems in diffusion.
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
On Monte Carlo methods for Bayesian inference
Song S. Qian; Craig A. Stow; Mark E. Borsuky
2003-01-01
Bayesian methods are experiencing increased use for probabilistic ecological modelling. Most Bayesian inference requires the numerical approximation of analytically intractable integrals. Two methods based on Monte Carlo simulation have appeared in the ecological\\/environmental modelling literature. Though they sound similar, the Bayesian Monte Carlo (BMC) and Markov Chain Monte Carlo (MCMC) methods are very different in their efficiency and effectiveness in
Monte Carlo Methods in Statistics Christian Robert
Boyer, Edmond
Monte Carlo Methods in Statistics Christian Robert UniversitÂ´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
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 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
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
A Monte Carlo Study of Titrating Polyelectrolytes
Peterson, Carsten
A Monte Carlo Study of Titrating Polyelectrolytes Magnus Ullner y and Bo JÂ¨onsson z Physical, Sweden Journal of Chemical Physics 104, 3048Â3057 (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
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 Simulation for Perusal and Practice.
ERIC Educational Resources Information Center
Brooks, Gordon P.; Barcikowski, Robert S.; Robey, Randall R.
The meaningful investigation of many problems in statistics can be solved through Monte Carlo methods. Monte Carlo studies can help solve problems that are mathematically intractable through the analysis of random samples from populations whose characteristics are known to the researcher. Using Monte Carlo simulation, the values of a statistic are…
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.
Khromov, K. Yu.; Vaks, V. G., E-mail: vaks@mbslab.kiae.ru; Zhuravlev, I. A. [National Research Center 'Kurchatov Institute' (Russian Federation)] [National Research Center 'Kurchatov Institute' (Russian Federation)
2013-02-15
The previously developed ab initio model and the kinetic Monte Carlo method (KMCM) are used to simulate precipitation in a number of iron-copper alloys with different copper concentrations x and temperatures T. The same simulations are also made using an improved version of the previously suggested stochastic statistical method (SSM). The results obtained enable us to make a number of general conclusions about the dependences of the decomposition kinetics in Fe-Cu alloys on x and T. We also show that the SSM usually describes the precipitation kinetics in good agreement with the KMCM, and using the SSM in conjunction with the KMCM allows extending the KMC simulations to the longer evolution times. The results of simulations seem to agree with available experimental data for Fe-Cu alloys within statistical errors of simulations and the scatter of experimental results. Comparison of simulation results with experiments for some multicomponent Fe-Cu-based alloys allows making certain conclusions about the influence of alloying elements in these alloys on the precipitation kinetics at different stages of evolution.
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.
Sencer Taneri
2008-01-01
We investigate the folding dynamics of the plant-seed protein Crambin in a liquid environment, that usually happens to be water with some certain viscosity. To take into account the viscosity, necessitates a stochastic approach. This can be summarized by a 2D-Langevin equation, even though the simulation is still carried out in 3D. Solution of the Langevin equation will be the
Sequential Monte Carlo for Model Predictive , J.M. Maciejowski
Kantas, Nikolas
) as the computational engine for general (non-convex) stochastic Model Predictive Control (MPC) problems. It shows howSequential Monte Carlo for Model Predictive Control N. Kantas , J.M. Maciejowski and A. Lecchini agents. 1 Introduction Nonlinear Model Predictive Control (MPC) usually involves non-convex optimisation
Some Continuous Monte Carlo Methods for the Dirichlet Problem
Mervin E. Muller
1956-01-01
Monte Carlo techniques are introduced, using stochastic models which are Markov processes. This material includes the $N$-dimensional Spherical, General Spherical, and General Dirichlet Domain processes. These processes are proved to converge with probability 1, and thus to yield direct statistical estimates of the solution to the $N$-dimensional Dirichlet problem. The results are obtained without requiring any further restrictions on the
Monte Python: Monte Carlo code for CLASS in Python
NASA Astrophysics Data System (ADS)
Audren, Benjamin; Lesgourgues, Julien; Benabed, Karim; Prunet, Simon
2013-07-01
Monte Python is a parameter inference code which combines the flexibility of the python language and the robustness of the cosmological code CLASS into a simple and easy to manipulate Monte Carlo Markov Chain code.
Glaser, R E; Johannesson, G; Sengupta, S; Kosovic, B; Carle, S; Franz, G A; Aines, R D; Nitao, J J; Hanley, W G; Ramirez, A L; Newmark, R L; Johnson, V M; Dyer, K M; Henderson, K A; Sugiyama, G A; Hickling, T L; Pasyanos, M E; Jones, D A; Grimm, R J; Levine, R A
2004-03-11
Accurate prediction of complex phenomena can be greatly enhanced through the use of data and observations to update simulations. The ability to create these data-driven simulations is limited by error and uncertainty in both the data and the simulation. The stochastic engine project addressed this problem through the development and application of a family of Markov Chain Monte Carlo methods utilizing importance sampling driven by forward simulators to minimize time spent search very large state spaces. The stochastic engine rapidly chooses among a very large number of hypothesized states and selects those that are consistent (within error) with all the information at hand. Predicted measurements from the simulator are used to estimate the likelihood of actual measurements, which in turn reduces the uncertainty in the original sample space via a conditional probability method called Bayesian inferencing. This highly efficient, staged Metropolis-type search algorithm allows us to address extremely complex problems and opens the door to solving many data-driven, nonlinear, multidimensional problems. A key challenge has been developing representation methods that integrate the local details of real data with the global physics of the simulations, enabling supercomputers to efficiently solve the problem. Development focused on large-scale problems, and on examining the mathematical robustness of the approach in diverse applications. Multiple data types were combined with large-scale simulations to evaluate systems with {approx}{sup 10}20,000 possible states (detecting underground leaks at the Hanford waste tanks). The probable uses of chemical process facilities were assessed using an evidence-tree representation and in-process updating. Other applications included contaminant flow paths at the Savannah River Site, locating structural flaws in buildings, improving models for seismic travel times systems used to monitor nuclear proliferation, characterizing the source of indistinct atmospheric plumes, and improving flash radiography. In the course of developing these applications, we also developed new methods to cluster and analyze the results of the state-space searches, as well as a number of algorithms to improve the search speed and efficiency. Our generalized solution contributes both a means to make more informed predictions of the behavior of very complex systems, and to improve those predictions as events unfold, using new data in real time.
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
NSDL National Science Digital Library
2014-09-18
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, ?.
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.
Monte Carlo methods for TMD analyses
NASA Astrophysics Data System (ADS)
Schnell, Gunar
2015-01-01
Monte Carlo simulations are an indispensable tool in experimental high-energy physics. Indeed, many discoveries rely on realistic modeling of background processes. In the field of transverse-momentum-dependent parton distribution and fragmentation functions there is a clear lack of a reliable Monte Carlo physics generator that can be used in experimental and phenomenological analyses. The need for such Monte Carlo generators, the status of some solutions and prospects are discussed.
NASA Technical Reports Server (NTRS)
Bell, Thomas L.; Abdullah, A.; Martin, Russell L.; North, Gerald R.
1990-01-01
Estimates of monthly average rainfall based on satellite observations from a low earth orbit will differ from the true monthly average because the satellite observes a given area only intermittently. This sampling error inherent in satellite monitoring of rainfall would occur even if the satellite instruments could measure rainfall perfectly. The size of this error is estimated for a satellite system being studied at NASA, the Tropical Rainfall Measuring Mission (TRMM). First, the statistical description of rainfall on scales from 1 to 1000 km is examined in detail, based on rainfall data from the Global Atmospheric Research Project Atlantic Tropical Experiment (GATE). A TRMM-like satellite is flown over a two-dimensional time-evolving simulation of rainfall using a stochastic model with statistics tuned to agree with GATE statistics. The distribution of sampling errors found from many months of simulated observations is found to be nearly normal, even though the distribution of area-averaged rainfall is far from normal. For a range of orbits likely to be employed in TRMM, sampling error is found to be less than 10 percent of the mean for rainfall averaged over a 500 x 500 sq km area.
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.
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.
Dynamically stratified Monte Carlo forecasting
NASA Technical Reports Server (NTRS)
Schubert, Siegfried; Suarez, Max; Schemm, Jae-Kyung; Epstein, Edward
1992-01-01
A new method for performing Monte Carlo forecasts is introduced. The method, called dynamic stratification, selects initial perturbations based on a stratification of the error distribution. A simple implementation is presented in which the error distribution used for the stratification is estimated from a linear model derived from a large ensemble of 12-h forecasts with the full dynamic model. The stratification thus obtained is used to choose a small subsample of initial states with which to perform the dynamical Monte Carlo forecasts. Several test cases are studied using a simple two-level general circulation model with uncertain initial conditions. It is found that the method provides substantial reductions in the sampling error of the forecast mean and variance when compared to the more traditional approach of choosing the initial perturbations at random. The degree of improvement, however, is sensitive to the nature of the initial error distribution and to the base state. In practice the method may be viable only if the computational burden involved in obtaining an adequate estimate of the error distribution is shared with the data-assimilation procedure.
Sequential Monte Carlo multiple testing
Sandve, Geir Kjetil; Nygård, Ståle
2011-01-01
Motivation: In molecular biology, as in many other scientific fields, the scale of analyses is ever increasing. Often, complex Monte Carlo simulation is required, sometimes within a large-scale multiple testing setting. The resulting computational costs may be prohibitively high. Results: We here present MCFDR, a simple, novel algorithm for false discovery rate (FDR) modulated sequential Monte Carlo (MC) multiple hypothesis testing. The algorithm iterates between adding MC samples across tests and calculating intermediate FDR values for the collection of tests. MC sampling is stopped either by sequential MC or based on a threshold on FDR. An essential property of the algorithm is that it limits the total number of MC samples whatever the number of true null hypotheses. We show on both real and simulated data that the proposed algorithm provides large gains in computational efficiency. Availability: MCFDR is implemented in the Genomic HyperBrowser (http://hyperbrowser.uio.no/mcfdr), a web-based system for genome analysis. All input data and results are available and can be reproduced through a Galaxy Pages document at: http://hyperbrowser.uio.no/mcfdr/u/sandve/p/mcfdr. Contact: geirksa@ifi.uio.no PMID:21998154
Single scatter electron Monte Carlo
Svatos, M.M. [Lawrence Livermore National Lab., CA (United States)|Wisconsin Univ., Madison, WI (United States)
1997-03-01
A single scatter electron Monte Carlo code (SSMC), CREEP, has been written which bridges the gap between existing transport methods and modeling real physical processes. CREEP simulates ionization, elastic and bremsstrahlung events individually. Excitation events are treated with an excitation-only stopping power. The detailed nature of these simulations allows for calculation of backscatter and transmission coefficients, backscattered energy spectra, stopping powers, energy deposits, depth dose, and a variety of other associated quantities. Although computationally intense, the code relies on relatively few mathematical assumptions, unlike other charged particle Monte Carlo methods such as the commonly-used condensed history method. CREEP relies on sampling the Lawrence Livermore Evaluated Electron Data Library (EEDL) which has data for all elements with an atomic number between 1 and 100, over an energy range from approximately several eV (or the binding energy of the material) to 100 GeV. Compounds and mixtures may also be used by combining the appropriate element data via Bragg additivity.
Some Challenges for Monte Carlo Simulation
Jim Murtha
Although Monte Carlo simulation has become much more widely accepted in the past 10 years (Murtha 1997), its applications in the oil and gas industry often lack imagination, focusing on volumetric estimates of resources and reserves. Monte Carlo simulation is the principal analytical tool of risk analysis. Its direct objective is always to estimate the range of something (e.g., reserves,
What Monte Carlo methods cannot do
Scott Ferson
1996-01-01
Although extremely flexible and obviously useful for many risk assessment problems, Monte Carlo methods have four significant limitations that risk analysts should keep in mind. (1) Like most methods based on probability theory, Monte Carlo methods are data?intensive. Consequently, they usually cannot produce results unless a considerable body of empirical information has been collected, or unless the analyst is willing
Monte Carlo Methods in Geophysical Inverse Problems
Malcolm Sambridge; Klaus Mosegaard
2002-01-01
Monte Carlo inversion techniques were first used by Earthscientists more than 30 years ago. Since that time they havebeen applied to a wide range of problems, from the inversion offree oscillation data for whole Earth seismic structure tostudies at the meter-scale lengths encountered in explorationseismology. This paper traces the development and application ofMonte Carlo methods for inverse problems in the
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
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.
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],
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
STAN ULAM, JOHN VON NEUMANN, and the MONTE CARLO METHOD
STAN ULAM, JOHN VON NEUMANN, and the MONTE CARLO METHOD by Roger Eckhardt T he Monte Carlo method solitaire. "The first thoughts and attempts I made to practice [the Monte Carlo method] were suggested
Sequential Monte Carlo for Model Predictive N. Kantas, J.M. Maciejowski, and A. Lecchini-Visintini
Kantas, Nikolas
for general (non-convex) stochastic Model Predictive Control (MPC) problems. It shows how SMC methods canSequential Monte Carlo for Model Predictive Control N. Kantas, J.M. Maciejowski, and A. Lecchini optimisation, Stochastic MPC, Sequential Monte Carlo. 1 Introduction Nonlinear Model Predictive Control (MPC
Optimised Iteration in Coupled Monte Carlo - Thermal-Hydraulics Calculations
NASA Astrophysics Data System (ADS)
Hoogenboom, J. Eduard; Dufek, Jan
2014-06-01
This paper describes an optimised iteration scheme for the number of neutron histories and the relaxation factor in successive iterations of coupled Monte Carlo and thermal-hydraulic reactor calculations based on the stochastic iteration method. The scheme results in an increasing number of neutron histories for the Monte Carlo calculation in successive iteration steps and a decreasing relaxation factor for the spatial power distribution to be used as input to the thermal-hydraulics calculation. The theoretical basis is discussed in detail and practical consequences of the scheme are shown, among which a nearly linear increase per iteration of the number of cycles in the Monte Carlo calculation. The scheme is demonstrated for a full PWR type fuel assembly. Results are shown for the axial power distribution during several iteration steps. A few alternative iteration method are also tested and it is concluded that the presented iteration method is near optimal.
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.
Configuration Path Integral Monte Carlo
NASA Astrophysics Data System (ADS)
Bonitz, Michael; Schoof, Tim; Groth, Simon; Filinov, Alexei; Hochstuhl, David
2011-11-01
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) [1]. 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. [2], fails due to the fermion sign problem. [4pt] [1] T. Schoof, M. Bonitz, A. Filinov, D. Hochstuhl, and J.W. Dufty, Contrib. Plasma Phys. (2011), DOI 10.1002/ctpp.201100012;.[0pt] [2] ``Introduction to computational methods for many-body physics,'' M. Bonitz and D. Semkat (eds.). Rinton Press, Princeton 2006, chapter 4.
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.
Renormalization Group by Monte Carlo Methods
Shang-Keng Ma
1976-01-01
I discuss the basic ideas in applying the Monte Carlo methods to the renormalization-group study of static and dynamic critical phenomena within the framework of a kinetic Ising model. Simple calculations demonstrating these ideas are presented.
Machine Learning ! ! ! ! ! Srihari Markov Chain Monte Carlo
srihari@cedar.buffalo.edu #12;Machine Learning ! ! ! ! ! Srihari 2 Topics 1. Markov Chain Monte Carlo 2(t) and Â another candidate drawn from q(z|z(t+1)) Accepted steps in green Rejected steps in red = )z(~ *)z
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.
Extra Chance Generalized Hybrid Monte Carlo
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; Sanz-Serna, J. M.
2015-01-01
We study a method, Extra Chance Generalized Hybrid Monte Carlo, to avoid rejections in the Hybrid Monte Carlo method and related algorithms. In the spirit of delayed rejection, whenever a rejection would occur, extra work is done to find a fresh proposal that, hopefully, may be accepted. We present experiments that clearly indicate that the additional work per sample carried out in the extra chance approach clearly pays in terms of the quality of the samples generated.
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
Quantum Monte Carlo simulations of solids W. M. C. Foulkes
Wu, Zhigang
Quantum Monte Carlo simulations of solids W. M. C. Foulkes CMTH Group, Department of Physics and fixed-node diffusion quantum Monte Carlo methods and how they may be used to calculate the properties-functional theory 37 E. Quantum Monte Carlo methods 38 III. Monte Carlo Methods 39 A. Statistical foundations 39 B
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 nonÂoptimal solutions. The sequential Monte Carlo methods, or particle filters chose the number of particles. 2 Sequential Monte Carlo methods Monte Carlo techniques have been
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 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 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 Â· Monte-Carlo with He at STP. #12;Monte Carlo Scattering Algorithm* Â· Implemented a Monte Carlo scattering algorithm
The Monte-Carlo Revolution in Go Remi Coulom
Coulom, RÃ©mi - Groupe de Recherche sur l'Apprentissage Automatique, UniversitÃ© Charles de Gaulle
The Monte-Carlo Revolution in Go RÂ´emi Coulom UniversitÂ´e Charles de Gaulle, INRIA, CNRS, Lille, France January, 2009 JFFoS'2008: Japanese-French Frontiers of Science Symposium #12;Introduction Monte-Carlo configurations RÂ´emi Coulom The Monte Carlo Revolution in Go 2 / 12 #12;Introduction Monte-Carlo Tree Search
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
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
Monte Carlo Methods in Reactor Physics
Haghighat, Alireza
2001-06-17
Two approaches exist for particle transport simulation in reactor physics, deterministic and statistical Monte Carlo. The Monte Carlo and deterministic approaches are compared, and their advantages and disadvantages are discussed. Then different issues related to Monte Carlo simulations for solving different types of problems are described, along with methods to resolve some of the issues; these include variance-reduction techniques, automated variance techniques, and parallel computing. Then a few sample examples for real-life problems are presented. In the author's opinion, there are effective variance-reduction techniques and automation tools for the fixed-source simulations. This, however, is not true for the Monte Carlo eigenvalue calculations. The needs in this area are development of methods for determination of a ''good'' starting source and variance-reduction methods for effective sampling of source energies and regions. This is especially important because of emerging new applications including Monte Carlo depletion in general; Generation VI reactor design, which may involve irregular geometries and novel concepts; design and analyses for plutonium disposition; spent-fuel storage; radioactive waste disposal; and criticality safety evaluation of nuclear material handling facilities. The author believe that to make the Monte Carlo methods more effective and reliable, the use of deterministic methods is a must.
Multiple-time-stepping generalized hybrid Monte Carlo methods
NASA Astrophysics Data System (ADS)
Escribano, Bruno; Akhmatskaya, Elena; Reich, Sebastian; Azpiroz, Jon M.
2015-01-01
Performance of the generalized shadow hybrid Monte Carlo (GSHMC) method [1], which proved to be superior in sampling efficiency over its predecessors [2-4], molecular dynamics and hybrid Monte Carlo, can be further improved by combining it with multi-time-stepping (MTS) and mollification of slow forces. We demonstrate that the comparatively simple modifications of the method not only lead to better performance of GSHMC itself but also allow for beating the best performed methods, which use the similar force splitting schemes. In addition we show that the same ideas can be successfully applied to the conventional generalized hybrid Monte Carlo method (GHMC). The resulting methods, MTS-GHMC and MTS-GSHMC, provide accurate reproduction of thermodynamic and dynamical properties, exact temperature control during simulation and computational robustness and efficiency. MTS-GHMC uses a generalized momentum update to achieve weak stochastic stabilization to the molecular dynamics (MD) integrator. MTS-GSHMC adds the use of a shadow (modified) Hamiltonian to filter the MD trajectories in the HMC scheme. We introduce a new shadow Hamiltonian formulation adapted to force-splitting methods. The use of such Hamiltonians improves the acceptance rate of trajectories and has a strong impact on the sampling efficiency of the method. Both methods were implemented in the open-source MD package ProtoMol and were tested on a water and a protein systems. Results were compared to those obtained using a Langevin Molly (LM) method [5] on the same systems. The test results demonstrate the superiority of the new methods over LM in terms of stability, accuracy and sampling efficiency. This suggests that putting the MTS approach in the framework of hybrid Monte Carlo and using the natural stochasticity offered by the generalized hybrid Monte Carlo lead to improving stability of MTS and allow for achieving larger step sizes in the simulation of complex systems.
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
Improvements and Applications of Semistochastic Quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Holmes, Adam; Changlani, Hitesh; Morales, Miguel; Nightingale, M. P.; Umrigar, C. J.
2013-03-01
Fully stochastic quantum Monte Carlo (QMC) methods, such as the full configuration interaction quantum Monte Carlo (FCIQMC) [1,2] allow one to compute the ground state of a Hamiltonian in a far larger Hilbert space than is possible using deterministic iterative diagonalization techniques. However, QMC methods suffer from the sign problem and may have large statistical errors. Recently we have shown [3] that these problems can be greatly alleviated by using a semistochastic quantum Monte Carlo (SQMC) approach, wherein the iterative projector is applied deterministically for a small subset of the Hilbert space states and stochastically elsewhere. In addition, the initiator bias, which is introduced to tame the sign problem in FCIQMC, is often greatly reduced. We explore further improvements to SQMC and apply it to a subset of the G2 set of molecules [4]. [1] George Booth, Alex Thom, Ali Alavi. J Chem Phys 131, 050106, (2009). [2] Deidre Cleland, George Booth, and Ali Alavi. J Chem Phys 132, 041103 (2010). [3] F. R. Petruzielo, A. A. Holmes, Hitesh J. Changlani, M. P. Nightingale, and C. J. Umrigar. Phys Rev Lett (Accepted 5 Oct 2012). [4] L. A. Curtiss, K. Raghavachari, G. W. Trucks, and J. A. Pople, J Chem Phys 94, 7221 (1991).
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.
Diagrammatic Monte Carlo and Worm Algorithm Techniques
NASA Astrophysics Data System (ADS)
Prokof'ev, Nikolay
This chapter reviews basic principles of Diagrammatic Monte Carlo and Worm Algorithm techniques. Diagrammatic Monte Carlo establishes generic rules for unbiased sampling of well defined configuration spaces when the only source of errors is of statistical origin due to finite sampling time, no matter whether configuration parameters involve discrete, as in the Ising model, or continuous, as in Feynman diagrams or lattice path integrals, variables. Worm Algorithms allow one to sample efficiently configuration spaces with complex topology and non-local constraints which cause severe problems for Monte Carlo schemes based on local updates. They achieve this goal by working with the enlarged configuration space which includes configurations violating constraints present in the original formulation.
Fast quantum Monte Carlo on a GPU
NASA Astrophysics Data System (ADS)
Lutsyshyn, Y.
2015-02-01
We present a scheme for the parallelization of quantum Monte Carlo method on graphical processing units, focusing on variational Monte Carlo simulation of bosonic systems. We use asynchronous execution schemes with shared memory persistence, and obtain an excellent utilization of the accelerator. The CUDA code is provided along with a package that simulates liquid helium-4. The program was benchmarked on several models of Nvidia GPU, including Fermi GTX560 and M2090, and the Kepler architecture K20 GPU. Special optimization was developed for the Kepler cards, including placement of data structures in the register space of the Kepler GPUs. Kepler-specific optimization is discussed.
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.
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
Improved wave functions for quantum Monte Carlo
Seth, Priyanka
2013-02-05
Improved wave functions for quantum Monte Carlo Priyanka Seth Corpus Christi College, Cambridge Dissertation submitted for the degree of Doctor of Philosophy at the University of Cambridge August 2012 To mum, dad, ìÉìÉ and the memory of êÉ. Preface... been published or is to be published: Chapter 3: P. Seth, P. Lo´pez R?´os and R. J. Needs, “Quantum Monte Carlo study of the first-row atoms and ions”, J. Chem. Phys. 134, 084105 (2011). Chapter 4: P. Lo´pez R´?os, P. Seth, N. D. Drummond and R. J...
Paris-Sud XI, UniversitÃ© de
the evaporation of the drop formed by coalescence, the aerosol particle that remains will have the mass growth by stochastic coalescence L. Alfonso 1 , G. B. Raga 2 , and D. Baumgardner 2 1 Universidad Aut crystal habits, different types of soluble CCN, particle charging and drop breakup. 1 Introduction
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 Arithmetic: exploiting randomness in floating-point arithmetic
Parker, D. Stott
Monte Carlo Arithmetic: exploiting randomness in floating Abstract Monte Carlo Arithmetic (MCA) is an extension of standard floating-point * *arithmetic that exploits randomness in basic floating-point operations. MCA includes rando* *m rounding _ which
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 ...
Coded aperture optimization using Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Martineau, A.; Rocchisani, J. M.; Moretti, J. L.
2010-04-01
Coded apertures using Uniformly Redundant Arrays (URA) have been unsuccessfully evaluated for two-dimensional and three-dimensional imaging in Nuclear Medicine. The images reconstructed from coded projections contain artifacts and suffer from poor spatial resolution in the longitudinal direction. We introduce a Maximum-Likelihood Expectation-Maximization (MLEM) algorithm for three-dimensional coded aperture imaging which uses a projection matrix calculated by Monte Carlo simulations. The aim of the algorithm is to reduce artifacts and improve the three-dimensional spatial resolution in the reconstructed images. Firstly, we present the validation of GATE (Geant4 Application for Emission Tomography) for Monte Carlo simulations of a coded mask installed on a clinical gamma camera. The coded mask modelling was validated by comparison between experimental and simulated data in terms of energy spectra, sensitivity and spatial resolution. In the second part of the study, we use the validated model to calculate the projection matrix with Monte Carlo simulations. A three-dimensional thyroid phantom study was performed to compare the performance of the three-dimensional MLEM reconstruction with conventional correlation method. The results indicate that the artifacts are reduced and three-dimensional spatial resolution is improved with the Monte Carlo-based MLEM reconstruction.
Physically Based Rendering Monte Carlo Integration
Kazhdan, Michael
Computational Cost: 1. Russian Roulette 2. Splitting Reduce Variance: 1. Stratified sampling 2. Importance sampling #12;Russian Roulette Given a PDF p and a function f, the Monte- Carlo estimate of the integral is Roulette If f is expensive to evaluate and we know its value has to be small, we may want avoid calculating
HEURISTICS IN MONTE CARLO GO Peter Drake
Drake, Peter
, but smaller boards are sometimes used for teaching new players or for com- puter Go research. The two playersHEURISTICS IN MONTE CARLO GO Peter Drake Lewis & Clark College Department of Mathematical Sciences Asian game of Go is considered one of the grand challenges of artifi- cial intelligence. Traditional
Digital image inpainting using monte carlo method
Jianping Gu; Silong Peng; Xuelin Wang
2004-01-01
Image Inpainting refers to the ill-posed problem of filling in the missing data in digital images by interpolating from the vicinity. It is shown in this paper how inpainting can be performed by means of random simulation of boundary in- tegral, which we call the Monte Carlo method. Our method is computationally less taxing than the classical diffusion methods, and
Monte Carlo Generator for Muon Pair Production
Burkhardt, H; Kokoulin, R P
2002-01-01
A Monte Carlo Generator for the electromagnetic pair production of muon pairs by high-energy photons in matter is described. The computer code is designed as a standard electromagnetic process for GEANT4. The relevant formulas and algorithms are described and illustrated in detail.
Convergence of Sequential Monte Carlo Methods
Dan Crisan; Arnaud Doucet
2000-01-01
Bayesian estimation problems where the posterior distribution evolves over time through the accumulationof data arise in many applications in statistics and related fields. Recently, a large number of algorithmsand applications based on sequential Monte Carlo methods (also known as particle filtering methods) haveappeared in the literature to solve this class of problems; see (Doucet, de Freitas & Gordon, 2001) for
Monte Carlo Solution of Waiting Line Problems
Billy E. Goetz
1960-01-01
This presentation makes no pretense of original contribution to either Monte Carlo or waiting-line analysis. It is merely an attempt to explain an important application of an interesting technique to managers somewhat lacking in mathematical sophistication. My objective is to enable such managers: (1) to recognize situations in which the technique may be useful, (2) to select appropriate staff or
THE BEGINNING of the MONTE CARLO METHOD
its new name of the Monte Carlo method. This essay attempts to describe the de- tails that led a preliminary computational model of a thermonuclear reaction for the ENIAC. He felt he could convince different applications.) Our response to von Neumann's suggestion was enthusi- astic, and his heuristic
Monte Carlo simulation of polarization backscattering spectroscopy
NASA Astrophysics Data System (ADS)
Deng, Yong; Lu, Qiang; Luo, Qingming; Hu, Rui; Zhu, Dan
2004-08-01
In this paper, we have developed a Monte Carlo algorithm that simulates the wavelength dependent, elastic scattering spectroscopy of the polarization light in preinvasive cancer tissue. Using stokes vector formalism and scattering amplitudes calculated with Mie theory. The simulation results show the backscattering spectroscopy is sensitive to cellular and nuclear size.
Dosimetry, scattering theory, and Monte Carlo simulation
Gordon McCabe
2008-06-28
The purpose of this paper is to provide an introduction to the physics of scattering theory, to define the dosimetric concept of linear energy transfer in terms of scattering theory, and to provide an introduction to the concepts underlying Monte Carlo simulations.
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.
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
Exploring Probability and the Monte Carlo Method
NSDL National Science Digital Library
2012-08-02
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 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.
Robust Monte Carlo localization for mobile robots
Sebastian Thrun; Dieter Fox; Wolfram Burgard; Frank Dellaert
2001-01-01
Mobile robot localization is the problem of determining a robot's pose from sensor data. This article presents a family of probabilistic localization algorithms known as Monte Carlo Localization (MCL). MCL algorithms represent a robot's belief by a set of weighted hypotheses (samples), which approximate the posterior under a common Bayesian formulation of the localization problem. Building on the basic MCL
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 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 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 Simulation of Single Event Effects
Robert A. Weller; Marcus H. Mendenhall; Robert A. Reed; Ronald D. Schrimpf; Kevin M. Warren; Brian D. Sierawski; Lloyd W. Massengill
2010-01-01
In this paper, we describe a Monte Carlo approach for estimating the frequency and character of single event effects based on a combination of physical modeling of discrete radiation events, device simulations to estimate charge transport and collection, and circuit simulations to determine the effect of the collected charge. A mathematical analysis of the procedure reveals it to be closely
Edge diffraction in Monte Carlo ray tracing
Edward R. Freniere; G. Groot Gregory; Richard A. Hassler
1999-01-01
Monte Carlo ray tracing programs are now being used to solve many optical analysis problems in which the entire optomechanical system must be considered. In many analyses, it is desired to consider the effects of diffraction by mechanical edges. Smoothly melding the effects of diffraction, a wave phenomenon, into a ray-tracing program is a significant technical challenge. This paper discusses
Markov Chain Monte Carlo Method without Detailed Balance
Hidemaro Suwa; Synge Todo
2010-10-13
We present a specific algorithm that generally satisfies the balance condition without imposing the detailed balance in the Markov chain Monte Carlo. In our algorithm, the average rejection rate is minimized, and even reduced to zero in many relevant cases. The absence of the detailed balance also introduces a net stochastic flow in a configuration space, which further boosts up the convergence. We demonstrate that the autocorrelation time of the Potts model becomes more than 6 times shorter than that by the conventional Metropolis algorithm. Based on the same concept, a bounce-free worm algorithm for generic quantum spin models is formulated as well.
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
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
Variance Reduction Techniques for Implicit Monte Carlo Simulations
Landman, Jacob Taylor
2013-09-19
VARIANCE REDUCTION TECHNIQUES FOR IMPLICIT MONTE CARLO SIMULATIONS An Undergraduate Research Scholars Thesis by JACOB TAYLOR LANDMAN Submitted to Honors and Undergraduate Research Texas A&M University in partial fulfillment of the requirements... of Implicit Monte Carlo Simulations . . . . . . . . . . . . . . . . . . 4 A Brief Overview of Variance Reduction Techniques . . . . . . . . . . . . . . . . 5 II MONTE CARLO WEIGHTED SAMPLING . . . . . . . . . . . . . . . . . . . . 6 Explanation of Traditional...
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 procedure for protein design Anders Irback,* Carsten Peterson,
IrbÃ¤ck, Anders
Monte Carlo procedure for protein design Anders IrbaÂ¨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 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 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 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 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: Â· Natural variation. The only study to date
Monte Carlo modeling of optical coherence tomography systems
Monte Carlo modeling of optical coherence tomography systems Peter E. Andersen Optics and Fluid 2003 Outline Â· Motivation Â· Monte Carlo OCT Â use MC to model interference? Â· Results Â comparison Dynamics Department SFM'03 Â 7-10 October 2003 Motivation Â· Monte Carlo (MC) modeling of light propagation
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 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@eecs.berkeley.edu Kurt Keutzer University of California, Berkeley keutzer@eecs.berkeley.edu ABSTRACT The Monte Carlo for a particular data working set. This paper presents the Monte Carlo Methods software pro- gramming pattern
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 Tree Search in Crazy Stone Remi Coulom
Coulom, RÃ©mi - Groupe de Recherche sur l'Apprentissage Automatique, UniversitÃ© Charles de Gaulle
Monte-Carlo Tree Search in Crazy Stone RÂ´emi Coulom UniversitÂ´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 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
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
A New Highly Convergent Monte Carlo Method for Matrix Computations
Dimov, Ivan
A New Highly Convergent Monte Carlo Method for Matrix Computations I.T. Dimov 1 , V.N. Alexandrov 2 Abstract In this paper a second degree iterative Monte Carlo method for solving Systems of Linear be at least c2 N times less than the number of realizations Nc of the existing Monte Carlo method
Semistochastic Projector Monte Carlo Method F. R. Petruzielo1
Nightingale, Peter
Semistochastic Projector Monte Carlo Method F. R. Petruzielo1 , A. A. Holmes1 , Hitesh J. Changlani. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem, Monte Carlo methods can be used to represent stochas- tically both the vector and multiplication
Parallel Monte Carlo Driver (PMCD)—a software package for Monte Carlo simulations in parallel
NASA Astrophysics Data System (ADS)
Mendes, B.; Pereira, A.
2003-03-01
Thanks to the dramatic decrease of computer costs and the no less dramatic increase in those same computer's capabilities and also thanks to the availability of specific free software and libraries that allow the set up of small parallel computation installations the scientific community is now in a position where parallel computation is within easy reach even to moderately budgeted research groups. The software package PMCD (Parallel Monte Carlo Driver) was developed to drive the Monte Carlo simulation of a wide range of user supplied models in parallel computation environments. The typical Monte Carlo simulation involves using a software implementation of a function to repeatedly generate function values. Typically these software implementations were developed for sequential runs. Our driver was developed to enable the run in parallel of the Monte Carlo simulation, with minimum changes to the original code that implements the function of interest to the researcher. In this communication we present the main goals and characteristics of our software, together with a simple study its expected performance. Monte Carlo simulations are informally classified as "embarrassingly parallel", meaning that the gains in parallelizing a Monte Carlo run should be close to ideal, i.e. with speed ups close to linear. In this paper our simple study shows that without compromising the easiness of use and implementation, one can get performances very close to the ideal.
Lattice kinetic Monte Carlo simulations of convective-diffusive systems
Flamm, Matthew H.; Diamond, Scott L.; Sinno, Talid
2009-01-01
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
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.
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.
Monte Carlo simulation of gas Cerenkov detectors
Mack, J.M.; Jain, M.; Jordan, T.M.
1984-01-01
Theoretical study of selected gamma-ray and electron diagnostic necessitates coupling Cerenkov radiation to electron/photon cascades. A Cerenkov production model and its incorporation into a general geometry Monte Carlo coupled electron/photon transport code is discussed. A special optical photon ray-trace is implemented using bulk optical properties assigned to each Monte Carlo zone. Good agreement exists between experimental and calculated Cerenkov data in the case of a carbon-dioxide gas Cerenkov detector experiment. Cerenkov production and threshold data are presented for a typical carbon-dioxide gas detector that converts a 16.7 MeV photon source to Cerenkov light, which is collected by optics and detected by a photomultiplier.
Introduction to Multicanonical Monte Carlo Simulations
Bernd A. Berg
1999-09-15
Monte Carlo simulation with {\\it a-priori} unknown weights have attracted recent attention and progress has been made in understanding (i) the technical feasibility of such simulations and (ii) classes of systems for which such simulations lead to major improvements over conventional Monte Carlo simulations. After briefly sketching the history of multicanonical calculations and their range of application, a general introduction in the context of the statistical physics of the d-dimensional generalized Potts models is given. Multicanonical simulations yield canonical expectation values for a range of temperatures or any other parameter(s) for which appropriate weights can be constructed. We shall address in some details the question how the multicanonical weights are actually obtained. Subsequently miscellaneous topics related to the considered algorithms are reviewed. Then multicanonical studies of first order phase transitions are discussed and finally applications to complex systems such as spin glasses and proteins.
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.
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.
Monte Carlo Simulations of Star Clusters
Mirek Giersz
2000-06-30
A revision of Stod\\'o{\\l}kiewicz's Monte Carlo code is used to simulate evolution of large star clusters. The survey on the evolution of multi-mass N-body systems influenced by the tidal field of a parent galaxy and by stellar evolution is discussed. For the first time, the simulation on the "star-by-star" bases of evolution of 1,000,000 body star cluster is presented. \\
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 Approach to M-Theory
Werner Krauth; Hermann Nicolai; Matthias Staudacher
1998-04-01
We discuss supersymmetric Yang-Mills theory dimensionally reduced to zero dimensions and evaluate the SU(2) and SU(3) partition functions by Monte Carlo methods. The exactly known SU(2) results are reproduced to very high precision. Our calculations for SU(3) agree closely with an extension of a conjecture due to Green and Gutperle concerning the exact value of the SU(N) partition functions.
Monte Carlo approach to M-theory
Werner Krauth; Hermann Nicolai; Matthias Staudacher
1998-01-01
We discuss supersymmetric Yang-Mills theory dimensionally reduced to zero dimensions and evaluate the SU(2) and SU(3) partition functions by Monte Carlo methods. The exactly known SU(2) results are reproduced to very high precision. Our calculations for SU(3) agree closely with an extension of a conjecture due to Green and Gutperle concerning the exact value of the SU(N) partition functions.
Amalfi/Positano Monte CarloMarseille
Spence, Harlan Ernest
Florence Pisa Rome Amalfi/Positano Monte CarloMarseille Barcelona Taormina Kusadasi Santorini (Piraeus), Greece Embark 1:00 p.m. 8:00 p.m. Day 3 Santorini, Greece 8:00 a.m. 8:00 p.m. Day 4 Ephesus,099 PENTHOUSE SUITE $15,998 PH3 $6,999 $16,398 PH2 $7,199 $16,998 PH1 $7,499 #12;PORTS OF CALL SANTORINI
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.
Rapidity gaps and the PHOJET Monte Carlo
F. W. Bopp; R. Engel; J. Ranft
1998-01-01
A model for the production of large rapidity gaps being implemented in the Monte Carlo event generator PHOJET is discussed. In this model, high-mass diffraction dissociation exhibits properties similar to hadron production in non-diffractive hadronic collisions at high energies. Hard diffraction is described using leading-order QCD matrix elements together with a parton distribution function for the pomeron and pomeron-flux factorization.
Monte Carlo small-sample perturbation calculations
Feldman, U.; Gelbard, E.; Blomquist, R.
1983-01-01
Two different Monte Carlo methods have been developed for benchmark computations of small-sample-worths in simplified geometries. The first is basically a standard Monte Carlo perturbation method in which neutrons are steered towards the sample by roulette and splitting. One finds, however, that two variance reduction methods are required to make this sort of perturbation calculation feasible. First, neutrons that have passed through the sample must be exempted from roulette. Second, neutrons must be forced to undergo scattering collisions in the sample. Even when such methods are invoked, however, it is still necessary to exaggerate the volume fraction of the sample by drastically reducing the size of the core. The benchmark calculations are then used to test more approximate methods, and not directly to analyze experiments. In the second method the flux at the surface of the sample is assumed to be known. Neutrons entering the sample are drawn from this known flux and tracking by Monte Carlo. The effect of the sample or the fission rate is then inferred from the histories of these neutrons. The characteristics of both of these methods are explored empirically.
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)
Monte Carlo dose mapping on deforming anatomy
NASA Astrophysics Data System (ADS)
Zhong, Hualiang; Siebers, Jeffrey V.
2009-10-01
This paper proposes a Monte Carlo-based energy and mass congruent mapping (EMCM) method to calculate the dose on deforming anatomy. Different from dose interpolation methods, EMCM separately maps each voxel's deposited energy and mass from a source image to a reference image with a displacement vector field (DVF) generated by deformable image registration (DIR). EMCM was compared with other dose mapping methods: energy-based dose interpolation (EBDI) and trilinear dose interpolation (TDI). These methods were implemented in EGSnrc/DOSXYZnrc, validated using a numerical deformable phantom and compared for clinical CT images. On the numerical phantom with an analytically invertible deformation map, EMCM mapped the dose exactly the same as its analytic solution, while EBDI and TDI had average dose errors of 2.5% and 6.0%. For a lung patient's IMRT treatment plan, EBDI and TDI differed from EMCM by 1.96% and 7.3% in the lung patient's entire dose region, respectively. As a 4D Monte Carlo dose calculation technique, EMCM is accurate and its speed is comparable to 3D Monte Carlo simulation. This method may serve as a valuable tool for accurate dose accumulation as well as for 4D dosimetry QA.
Monte Carlo dose mapping on deforming anatomy
Zhong, Hualiang; Siebers, Jeffrey V
2010-01-01
This paper proposes a Monte Carlo-based energy and mass congruent mapping (EMCM) method to calculate the dose on deforming anatomy. Different from dose interpolation methods, EMCM separately maps each voxel’s deposited energy and mass from a source image to a reference image with a displacement vector field (DVF) generated by deformable image registration (DIR). EMCM was compared with other dose mapping methods: energy-based dose interpolation (EBDI) and trilinear dose interpolation (TDI). These methods were implemented in EGSnrc/DOSXYZnrc, validated using a numerical deformable phantom and compared for clinical CT images. On the numerical phantom with an analytically invertible deformation map, EMCM mapped the dose exactly the same as its analytic solution, while EBDI and TDI had average dose errors of 2.5% and 6.0%. For a lung patient’s IMRT treatment plan, EBDI and TDI differed from EMCM by 1.96% and 7.3% in the lung patient’s entire dose region, respectively. As a 4D Monte Carlo dose calculation technique, EMCM is accurate and its speed is comparable to 3D Monte Carlo simulation. This method may serve as a valuable tool for accurate dose accumulation as well as for 4D dosimetry QA. PMID:19741278
Randomized quasi-Monte Carlo simulation of fast-ion thermalization
NASA Astrophysics Data System (ADS)
Höök, L. J.; Johnson, T.; Hellsten, T.
2012-01-01
This work investigates the applicability of the randomized quasi-Monte Carlo method for simulation of fast-ion thermalization processes in fusion plasmas, e.g. for simulation of neutral beam injection and radio frequency heating. In contrast to the standard Monte Carlo method, the quasi-Monte Carlo method uses deterministic numbers instead of pseudo-random numbers and has a statistical weak convergence close to {O}(N^{-1}) , where N is the number of markers. We have compared different quasi-Monte Carlo methods for a neutral beam injection scenario, which is solved by many realizations of the associated stochastic differential equation, discretized with the Euler-Maruyama scheme. The statistical convergence of the methods is measured for time steps up to 214.
Monte Carlo techniques of simulation applied to a single item inventory system
Aldred, William Murray
1965-01-01
INTRODUCTION. II BASIC CONCEPTS OF INVENTORY CONTROL Page Deterministic Inventory Models (General) Stochastic Inventory Models (General) . Need for Simulation in Inventory Control (General) Monte Carlo Technique of Simulating a Sample From a Given... of the most widely used techniques are the deterministic and the stochastic methods of inventory control. Both are thoroughly explained by G. Hadley and T. Whitten in 1nuen*ozS and Pz'oductf on Contzoi [6] . Deterministic Inventory Models (General...
Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods
Philip D. ONeill; David J. Balding; Niels G. Becker; Mervi Eerola; Denis Mollison
2000-01-01
This paper exploresthe use of Markov chain Monte Carlo (MCMC) methods for the analysis ofinfectious disease data, with the hope that they will permit analyses to be madeunder more realistic assumptions. Two important kinds of data sets are considered,containing temporal and non-temporal information respectively, from outbreaks ofmeasles and influenza. Stochastic epidemic models are used to describe the processesthat generate the
Current status and new horizons in Monte Carlo simulation of X-ray CT scanners
Habib Zaidi; Mohammad Reza Ay
2007-01-01
With the advent of powerful computers and parallel processing including Grid technology, the use of Monte Carlo (MC) techniques for radiation transport simu- lation has become the most popular method for modeling radiological imaging systems and particularly X-ray com- puted tomography (CT). The stochastic nature of involved processes such as X-ray photons generation, interaction with matter and detection makes MC
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
A Monte Carlo Model Reveals Independent Signaling at Central Glutamatergic Synapses
Kevin M. Franks; Thomas M. Bartol; Terrence J. Sejnowski
2002-01-01
We have developed a biophysically realistic model of receptor activation at an idealized central glutamatergic synapse that uses Monte Carlo techniques to simulate the stochastic nature of transmission following release of a single synaptic vesicle. For the a synapse with 80 AMPA and 20 NMDA receptors, a single quantum, with 3000 glutamate molecules, opened approximately 3 NMDARs and 20 AMPARs.
State-of-the-art Monte Carlo 1988
Soran, P.D.
1988-06-28
Particle transport calculations in highly dimensional and physically complex geometries, such as detector calibration, radiation shielding, space reactors, and oil-well logging, generally require Monte Carlo transport techniques. Monte Carlo particle transport can be performed on a variety of computers ranging from APOLLOs to VAXs. Some of the hardware and software developments, which now permit Monte Carlo methods to be routinely used, are reviewed in this paper. The development of inexpensive, large, fast computer memory, coupled with fast central processing units, permits Monte Carlo calculations to be performed on workstations, minicomputers, and supercomputers. The Monte Carlo renaissance is further aided by innovations in computer architecture and software development. Advances in vectorization and parallelization architecture have resulted in the development of new algorithms which have greatly reduced processing times. Finally, the renewed interest in Monte Carlo has spawned new variance reduction techniques which are being implemented in large computer codes. 45 refs.
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.
Quantum Monte Carlo for vibrating molecules
Brown, W.R. [Univ. of California, Berkeley, CA (United States). Chemistry Dept.]|[Lawrence Berkeley National Lab., CA (United States). Chemical Sciences Div.
1996-08-01
Quantum Monte Carlo (QMC) has successfully computed the total electronic energies of atoms and molecules. The main goal of this work is to use correlation function quantum Monte Carlo (CFQMC) to compute the vibrational state energies of molecules given a potential energy surface (PES). In CFQMC, an ensemble of random walkers simulate the diffusion and branching processes of the imaginary-time time dependent Schroedinger equation in order to evaluate the matrix elements. The program QMCVIB was written to perform multi-state VMC and CFQMC calculations and employed for several calculations of the H{sub 2}O and C{sub 3} vibrational states, using 7 PES`s, 3 trial wavefunction forms, two methods of non-linear basis function parameter optimization, and on both serial and parallel computers. In order to construct accurate trial wavefunctions different wavefunctions forms were required for H{sub 2}O and C{sub 3}. In order to construct accurate trial wavefunctions for C{sub 3}, the non-linear parameters were optimized with respect to the sum of the energies of several low-lying vibrational states. In order to stabilize the statistical error estimates for C{sub 3} the Monte Carlo data was collected into blocks. Accurate vibrational state energies were computed using both serial and parallel QMCVIB programs. Comparison of vibrational state energies computed from the three C{sub 3} PES`s suggested that a non-linear equilibrium geometry PES is the most accurate and that discrete potential representations may be used to conveniently determine vibrational state energies.
Introduction to the Diffusion Monte Carlo Method
Ioan Kosztin; Byron Faber; Klaus Schulten
1997-02-20
A self-contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a numerical algorithm is formulated. The algorithm is applied to determine the ground state of the harmonic oscillator, the Morse oscillator, the hydrogen atom, and the electronic ground state of the H2+ ion and of the H2 molecule. A computer program on which the sample calculations are based is available upon request.
The Moment Guided Monte Carlo Method
Pierre Degond; Giacomo Dimarco; Lorenzo Pareschi
2009-08-03
In this work we propose a new approach for the numerical simulation of kinetic equations through Monte Carlo schemes. We introduce a new technique which permits to reduce the variance of particle methods through a matching with a set of suitable macroscopic moment equations. In order to guarantee that the moment equations provide the correct solutions, they are coupled to the kinetic equation through a non equilibrium term. The basic idea, on which the method relies, consists in guiding the particle positions and velocities through moment equations so that the concurrent solution of the moment and kinetic models furnishes the same macroscopic quantities.
Multiple quadrature by Monte Carlo techniques
Voss, John Dietrich
1966-01-01
(k) = x '=2 I I 3 3' f f(x)dx = ? = 9 0 3 0 Value computed by Monte Carlo (10, 000 points): 8. 99 Figure 1. Point Rejection Technique, Two Dimensions the probability of the point being in that area is numerically equal to the ratio of the area... was computed. Im ortance Sam lin In the above method we have used a technique of weighing the values of the function to approximate an average over a uniformly dis- tributed random set of points. We shall now introduce a technique called "importance...
SATMC: SED Analysis Through Monte Carlo
NASA Astrophysics Data System (ADS)
Johnson, Seth
2013-09-01
SATMC is a general purpose, MCMC-based SED fitting code written for IDL and Python. Following Bayesian statistics and Monte Carlo Markov Chain algorithms, SATMC derives the best fit parameter values and returns the sampling of parameter space used to construct confidence intervals and parameter-parameter confidence contours. The fitting may cover any range of wavelengths. The code is designed to incorporate any models (and potential priors) of the user's choice. The user's guide list all the relevant details for including observations, models and usage under both IDL and Python.
Score Bounded Monte-Carlo Tree Search
NASA Astrophysics Data System (ADS)
Cazenave, Tristan; Saffidine, Abdallah
Monte-Carlo Tree Search (MCTS) is a successful algorithm used in many state of the art game engines. We propose to improve a MCTS solver when a game has more than two outcomes. It is for example the case in games that can end in draw positions. In this case it improves significantly a MCTS solver to take into account bounds on the possible scores of a node in order to select the nodes to explore. We apply our algorithm to solving Seki in the game of Go and to Connect Four.
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.
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.
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.
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 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
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.
Dynamic Monte Carlo renormalization group. II
Moseley, L.L.; Gibbs, P.W. (Univ. of West Indies, St. Michael (Barbados)); Jan, N. (Univ. of West Indies, St. Michael (Barbardos) St. Francis Xavier Univ., Antigonish, Nova Scotia (Canada))
1989-10-01
The dynamic Monte Carlo Renormalization group method introduced by Jan, Moseley, and Stauffer is used to determine the dynamic exponent of the Ising model with conserved magnetization in two dimensions. The authors present an explicit theoretical basis for the method and expand on the original results for the Kawasaki model. The new result clearly demonstrates the validity of the method and the value of the dynamic exponent, z = 3.79 {plus minus} 0.05, supports the conclusion of Halperin, Hohenberg, and Ma.
Kinetic Monte Carlo simulations of proton conductivity.
Mas?owski, T; Drzewi?ski, A; Ulner, J; Wojtkiewicz, J; Zdanowska-Fr?czek, M; Nordlund, K; Kuronen, A
2014-07-01
The kinetic Monte Carlo method is used to model the dynamic properties of proton diffusion in anhydrous proton conductors. The results have been discussed with reference to a two-step process called the Grotthuss mechanism. There is a widespread belief that this mechanism is responsible for fast proton mobility. We showed in detail that the relative frequency of reorientation and diffusion processes is crucial for the conductivity. Moreover, the current dependence on proton concentration has been analyzed. In order to test our microscopic model the proton transport in polymer electrolyte membranes based on benzimidazole C(7)H(6)N(2) molecules is studied. PMID:25122279
Archimedes, the Free Monte Carlo simulator
Sellier, Jean Michel D
2012-01-01
Archimedes is the GNU package for Monte Carlo simulations of electron transport in semiconductor devices. The first release appeared in 2004 and since then it has been improved with many new features like quantum corrections, magnetic fields, new materials, GUI, etc. This document represents the first attempt to have a complete manual. Many of the Physics models implemented are described and a detailed description is presented to make the user able to write his/her own input deck. Please, feel free to contact the author if you want to contribute to the project.
Neutron transport calculations using Quasi-Monte Carlo methods
Moskowitz, B.S.
1997-07-01
This paper examines the use of quasirandom sequences of points in place of pseudorandom points in Monte Carlo neutron transport calculations. For two simple demonstration problems, the root mean square error, computed over a set of repeated runs, is found to be significantly less when quasirandom sequences are used ({open_quotes}Quasi-Monte Carlo Method{close_quotes}) than when a standard Monte Carlo calculation is performed using only pseudorandom points.
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.
Monte Carlo learning/biasing experiment with intelligent random numbers
Booth, T.E.
1985-01-01
A Monte Carlo learning and biasing technique is described that does its learning and biasing in the random number space rather than the physical phase-space. The technique is probably applicable to all linear Monte Carlo problems, but no proof is provided here. Instead, the technique is illustrated with a simple Monte Carlo transport problem. Problems encountered, problems solved, and speculations about future progress are discussed. 12 refs.
Monte Carlo techniques for analyzing deep-penetration problems
Cramer, S.N.; Gonnord, J.; Hendricks, J.S.
1986-02-01
Current methods and difficulties in Monte Carlo deep-penetration calculations are reviewed, including statistical uncertainty and recent adjoint optimization of splitting, Russian roulette, and exponential transformation biasing. Other aspects of the random walk and estimation processes are covered, including the relatively new DXANG angular biasing technique. Specific items summarized are albedo scattering, Monte Carlo coupling techniques with discrete ordinates and other methods, adjoint solutions, and multigroup Monte Carlo. The topic of code-generated biasing parameters is presented, including the creation of adjoint importance functions from forward calculations. Finally, current and future work in the area of computer learning and artificial intelligence is discussed in connection with Monte Carlo applications.
Monte Carlo modeling of spatial coherence: free-space diffraction
Fischer, David G.; Prahl, Scott A.; Duncan, Donald D.
2008-01-01
We present a Monte Carlo method for propagating partially coherent fields through complex deterministic optical systems. A Gaussian copula is used to synthesize a random source with an arbitrary spatial coherence function. Physical optics and Monte Carlo predictions of the first- and second-order statistics of the field are shown for coherent and partially coherent sources for free-space propagation, imaging using a binary Fresnel zone plate, and propagation through a limiting aperture. Excellent agreement between the physical optics and Monte Carlo predictions is demonstrated in all cases. Convergence criteria are presented for judging the quality of the Monte Carlo predictions. PMID:18830335
Kinetic Monte Carlo with fields: diffusion in heterogeneous systems
NASA Astrophysics Data System (ADS)
Alfredo Caro, Jose
2011-03-01
It is commonly perceived that to achieve breakthrough scientific discoveries in the 21^st century an integration of world leading experimental capabilities with theory, computational modeling and high performance computer simulations is necessary. Lying between the atomic and the macro scales, the meso scale is crucial for advancing materials research. Deterministic methods result computationally too heavy to cover length and time scales relevant for this scale. Therefore, stochastic approaches are one of the options of choice. In this talk I will describe recent progress in efficient parallelization schemes for Metropolis and kinetic Monte Carlo [1-2], and the combination of these ideas into a new hybrid Molecular Dynamics-kinetic Monte Carlo algorithm developed to study the basic mechanisms taking place in diffusion in concentrated alloys under the action of chemical and stress fields, incorporating in this way the actual driving force emerging from chemical potential gradients. Applications are shown on precipitation and segregation in nanostructured materials. Work in collaboration with E. Martinez, LANL, and with B. Sadigh, P. Erhart and A. Stukowsky, LLNL. Supported by the Center for Materials at Irradiation and Mechanical Extremes, an Energy Frontier Research Center funded by the U.S. Department of Energy (Award # 2008LANL1026) at Los Alamos National Laboratory [4pt] [1] B. Sadigh et al. to be published [2] E. Martinez et al. J. Comp. Phys. 227 (2008) 3804-3823
THE MCNPX MONTE CARLO RADIATION TRANSPORT CODE
WATERS, LAURIE S. [Los Alamos National Laboratory; MCKINNEY, GREGG W. [Los Alamos National Laboratory; DURKEE, JOE W. [Los Alamos National Laboratory; FENSIN, MICHAEL L. [Los Alamos National Laboratory; JAMES, MICHAEL R. [Los Alamos National Laboratory; JOHNS, RUSSELL C. [Los Alamos National Laboratory; PELOWITZ, DENISE B. [Los Alamos National Laboratory
2007-01-10
MCNPX (Monte Carlo N-Particle eXtended) is a general-purpose Monte Carlo radiation transport code with three-dimensional geometry and continuous-energy transport of 34 particles and light ions. It contains flexible source and tally options, interactive graphics, and support for both sequential and multi-processing computer platforms. MCNPX is based on MCNP4B, and has been upgraded to most MCNP5 capabilities. MCNP is a highly stable code tracking neutrons, photons and electrons, and using evaluated nuclear data libraries for low-energy interaction probabilities. MCNPX has extended this base to a comprehensive set of particles and light ions, with heavy ion transport in development. Models have been included to calculate interaction probabilities when libraries are not available. Recent additions focus on the time evolution of residual nuclei decay, allowing calculation of transmutation and delayed particle emission. MCNPX is now a code of great dynamic range, and the excellent neutronics capabilities allow new opportunities to simulate devices of interest to experimental particle physics; particularly calorimetry. This paper describes the capabilities of the current MCNPX version 2.6.C, and also discusses ongoing code development.
Phylogenetic inference via sequential Monte Carlo.
Bouchard-Côté, Alexandre; Sankararaman, Sriram; Jordan, Michael I
2012-07-01
Bayesian inference provides an appealing general framework for phylogenetic analysis, able to incorporate a wide variety of modeling assumptions and to provide a coherent treatment of uncertainty. Existing computational approaches to bayesian inference based on Markov chain Monte Carlo (MCMC) have not, however, kept pace with the scale of the data analysis problems in phylogenetics, and this has hindered the adoption of bayesian methods. In this paper, we present an alternative to MCMC based on Sequential Monte Carlo (SMC). We develop an extension of classical SMC based on partially ordered sets and show how to apply this framework--which we refer to as PosetSMC--to phylogenetic analysis. We provide a theoretical treatment of PosetSMC and also present experimental evaluation of PosetSMC on both synthetic and real data. The empirical results demonstrate that PosetSMC is a very promising alternative to MCMC, providing up to two orders of magnitude faster convergence. We discuss other factors favorable to the adoption of PosetSMC in phylogenetics, including its ability to estimate marginal likelihoods, its ready implementability on parallel and distributed computing platforms, and the possibility of combining with MCMC in hybrid MCMC-SMC schemes. Software for PosetSMC is available at http://www.stat.ubc.ca/ bouchard/PosetSMC. PMID:22223445
Discrete range clustering using Monte Carlo methods
NASA Technical Reports Server (NTRS)
Chatterji, G. B.; Sridhar, B.
1993-01-01
For automatic obstacle avoidance guidance during rotorcraft low altitude flight, a reliable model of the nearby environment is needed. Such a model may be constructed by applying surface fitting techniques to the dense range map obtained by active sensing using radars. However, for covertness, passive sensing techniques using electro-optic sensors are desirable. As opposed to the dense range map obtained via active sensing, passive sensing algorithms produce reliable range at sparse locations, and therefore, surface fitting techniques to fill the gaps in the range measurement are not directly applicable. Both for automatic guidance and as a display for aiding the pilot, these discrete ranges need to be grouped into sets which correspond to objects in the nearby environment. The focus of this paper is on using Monte Carlo methods for clustering range points into meaningful groups. One of the aims of the paper is to explore whether simulated annealing methods offer significant advantage over the basic Monte Carlo method for this class of problems. We compare three different approaches and present application results of these algorithms to a laboratory image sequence and a helicopter flight sequence.
Monte Carlo generators in ATLAS software
NASA Astrophysics Data System (ADS)
Ay, C.; Buckley, A.; Butterworth, J.; Ferland, J.; Hinchliffe, I.; Jinnouchi, O.; Katzy, J.; Kersevan, B.; Lobodzinska, E.; Monk, J.; Qin, Z.; Savinov, V.; Schumacher, J.
2010-04-01
This document describes how Monte Carlo (MC) generators can be used in the ATLAS software framework (Athena). The framework is written in C++ using Python scripts for job configuration. Monte Carlo generators that provide the four-vectors describing the results of LHC collisions are written in general by third parties and are not part of Athena. These libraries are linked from the LCG Generator Services (GENSER) distribution. Generators are run from within Athena and the generated event output is put into a transient store, in HepMC format, using StoreGate. A common interface, implemented via inheritance of a GeneratorModule class, guarantees common functionality for the basic generation steps. The generator information can be accessed and manipulated by helper packages like TruthHelper. The ATLAS detector simulation as well access the truth information from StoreGate1. Steering is done through specific interfaces to allow for flexible configuration using ATLAS Python scripts. Interfaces to most general purpose generators, including: Pythia6, Pythia8, Herwig, Herwig++ and Sherpa are provided, as well as to more specialized packages, for example Phojet and Cascade. A second type of interface exist for the so called Matrix Element generators that only generate the particles produced in the hard scattering process and write events in the Les Houches event format. A generic interface to pass these events to Pythia6 and Herwig for parton showering and hadronisation has been written.
Calculating Pi Using the Monte Carlo Method
NASA Astrophysics Data System (ADS)
Williamson, Timothy
2013-11-01
During the summer of 2012, I had the opportunity to participate in a research experience for teachers at the center for sustainable energy at Notre Dame University (RET @ cSEND) working with Professor John LoSecco on the problem of using antineutrino detection to accurately determine the fuel makeup and operating power of nuclear reactors. During full power operation, a reactor may produce 1021 antineutrinos per second with approximately 100 per day being detected. While becoming familiar with the design and operation of the detectors, and how total antineutrino flux could be obtained from such a small sample, I read about a simulation program called Monte Carlo. Further investigation led me to the Monte Carlo method page of Wikipedia2 where I saw an example of approximating pi using this simulation. Other examples where this method was applied were typically done with computer simulations2 or purely mathematical.3 It is my belief that this method may be easily related to the students by performing the simple activity of sprinkling rice on an arc drawn in a square. The activity that follows was inspired by those simulations and was used by my AP Physics class last year with very good results.
Monte Carlo simulation study of droplet nucleation
NASA Astrophysics Data System (ADS)
Neimark, Alexander V.; Vishnyakov, Aleksey
2005-05-01
A new rigorous Monte Carlo simulation approach is employed to study nucleation barriers for droplets in Lennard-Jones fluid. Using the gauge cell method we generate the excess isotherm of critical clusters in the size range from two to six molecular diameters. The ghost field method is employed to compute the cluster free energy and the nucleation barrier with desired precision of (1-2)kT. Based on quantitative results obtained by Monte Carlo simulations, we access the limits of applicability of the capillarity approximation of the classical nucleation theory and the Tolman equation. We show that the capillarity approximation corrected for vapor nonideality and liquid compressibility provides a reasonable assessment for the size of critical clusters in Lennard-Jones fluid; however, its accuracy is not sufficient to predict the nucleation barriers for making practical estimates of the rate of nucleation. The established dependence of the droplet surface tension on the droplet size cannot be approximated by the Tolman equation for small droplets of radius less than four molecular diameters. We confirm the conclusion of ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)] that integration of the normal component of the Irving-Kirkwood pressure tensor severely underestimates the nucleation barriers for small clusters.
Quantum Monte Carlo methods for nuclear physics
J. Carlson; S. Gandolfi; F. Pederiva; Steven C. Pieper; R. Schiavilla; K. E. Schmidt; R. B. Wiringa
2014-12-09
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 and transition moments 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.
Multilevel Monte Carlo simulation of Coulomb collisions
NASA Astrophysics Data System (ADS)
Rosin, M. S.; Ricketson, L. F.; Dimits, A. M.; Caflisch, R. E.; Cohen, B. I.
2014-10-01
We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the Langevin representation of the Landau-Fokker-Planck equation. It does so by combining multiple solutions to the underlying equations with varying numbers of timesteps. For a desired level of accuracy ?, the computational cost of the method is O(?-2) or O(?-2(), depending on the underlying discretization, Milstein or Euler-Maruyama respectively. This is to be contrasted with a cost of O(?-3) for direct simulation Monte Carlo or binary collision methods. We successfully demonstrate the method with a classic beam diffusion test case in 2D, making use of the Lévy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for ?=10-5. We discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.
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.
Monte Carlo simulation of semiconductor devices
NASA Astrophysics Data System (ADS)
Jensen, Geir U.; Lund, Bjørnar; Fjeldly, Tor A.; Shur, Michael
1991-08-01
This paper gives a review of applications of the Monte Carlo technique and recent literature on Monte Carlo modeling of semiconductor devices. The emphasis of the original research results reported in this paper is on self-consistent ensemble Monte Carlo simulation of GaAs/AlGaAs Heterostructure Field-Effect Transistors (HFETs) and novel HFET structures. We consider both electron and hole transport keeping in mind possible applications for complementary devices and circuits. Hole transport properties in GaAs are treated using corrected expressions for the scattering rates and a very accurate analytical description of the valence bands valid to about 1 eV. We review the corrected rates. Our simulations demonstrate superlinear behavior in the velocity-field relationship at low temperatures, and a temperature maximum is found in the low-field mobility between 40 K and 60 K at a doping density of 10 16 cm -3. We describe in detail our two-dimensional self-consistent Monte Carlo simulator and demostrrate the usefulness of Monte Carlo simulations for developing and validating simple device models utilized in computer-aided design tools for VLSI circuits. From this perspective, the unified charge-control model is also briefly outlined. Short-channel effects in self-aligned HFETs are shown to be caused by the injection of charge from the contact regions into the buffer beneath the device channel for gate lengths shorter than about 0.5 ?m, given an adequately large aspect ratio. For possible incorporation in charge-control models, the threshold voltage shift as well as the output conductance in saturation are found to be approximately inversely proportional to the gate length under the same conditions. Our simulations show that a p-i-p + buffer structure improves the carrier confinement to the channel, reducing the output conductance by about 80% in a 0.3 ?m device. Two device concepts recently proposed, aimed at increasing carrier velocities, are studied. The Variable Threshold HFET (VTHFET) as well as the Split-Gate HFET (SGHFET) utilize a gate voltage swing that is made to depend on lateral position. This position dependence raises the resistivity and thus the electric field and the velocity near the source contact. For a certain doping configuration, a p-type-like VTHFET is shown to exhibit a 78% increase in the current-gain cutoff frequency fT, a 59% increase in the maximum transconductance, and substantially higher K-factor compared with a conventional 0.5 ?m GaAs/AlGaAs HFET. In n-type VTHFETs, the only pronounced improvement is broader and flatter high gm region. The much larger improvement using p-type VTHFETs is shown to be associated withthe lower hole mobility, the absence of satellite valleys, and the smaller velocity overshoot. The n-VTHFET also suffer from a big shift in overall threshold voltage. The remarkable modulation of velocity and energy profiles achieved could in its own right warrant applications in other n-type devices, such as real-space transfer devices. Guidelines for succesful utilization of the VTHFET concept in other materials and for other device geometries are given.
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 Studies of Quantum Many-Body Systems
NASA Astrophysics Data System (ADS)
Zhang, Shiwei
1993-01-01
This thesis describes studies of the ground-state properties of quantum many-body systems by Monte Carlo techniques. In the first part, an algorithm is described to address the fundamental "sign problem" in quantum Monte Carlo when applied to fermion systems. Implementation of this algorithm in a parallel distributed environment is then discussed. The last part presents variational calculations of the ground states of ^4 He clusters. The sign problem prevents exact simulations of large many-fermion systems without uncontrolled approximations. It arises because of the antisymmetric nature of wavefunctions of fermion systems, and because of the use of random sampling. The proposed new algorithm is within the framework of the Green's function Monte Carlo method. To attack the difficulties associated with the sign problem, several new ideas are introduced to improve the Monte Carlo sampling techniques. As tests, the energies of an excited state of the He atom and of the ground states of the Li, Be, and N atoms are calculated. The algorithm remained stable and the results were in excellent agreement with the experimental values for the energies. The fermion algorithm was parallelized and implemented on a coupled cluster of workstations using a message-passing environment. The method of parallelization maintains large granularity and therefore low overhead. Despite the stochastic nature of the algorithm, good load-balancing can be accomplished and reproducibility is ensured. Droplets of ^4He atoms, as an example of simple inhomogeneous quantum many-body systems, are of interest to condensed-matter physics as well as nuclear physics. Previous variational studies of their ground states were unsatisfactory as unphysical one-body form factors had to be used to enforce a bound state. The new trial wavefunction, based on the shadow wavefunction for bulk helium, has a modified shadow-shadow correlation that reflects the varying local density in the system. A bound state is obtained without recourse to one-body form factors. The bulk wavefunction is naturally recovered as the system size is increased.
Variance and efficiency in Monte Carlo transport calculations
NASA Astrophysics Data System (ADS)
Lux, Iván
1980-09-01
Recent developments in Monte Carlo variance and efficiency analysis are summarized. Sufficient conditions are given under which the variance of a Monte Carlo game is less than that of another. The efficiencies of the ELP method and a game with survival biasing and Russian roulette are treated.
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
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
Sequential Monte Carlo Methods for Statistical Analysis of Tables
Liu, Jun
is a few orders of magnitude more efficient. In particular, compared with Markov chain Monte Carlo (MCMC)-based. Our method compares favorably with other existing Monte Carlo- based algorithms, and sometimes to achieve. KEY WORDS: Conditional inference; Contingency table; Counting problem; Exact test; Sequential
Monte Carlo methods in an introductory electromagnetic course
M. N. O. Sadiku
1990-01-01
Although the pedagogical value of introducing numerical methods such as finite-element methods, finite-difference methods, and moment methods in an introductory electromagnetics (EM) course has been recognized, no similar attempt has been made to introduce Monte Carlo methods. An attempt is made to fill this gap by presenting Monte Carlo procedures in simple terms that can be presented in an introductory
New sequential Monte Carlo methods for nonlinear dynamic systems
Dong Guo; Xiaodong Wang; Rong Chen
2005-01-01
In this paper we present several new sequential Monte Carlo (SMC) algorithms for online estimation (filtering) of nonlinear dynamic systems. SMC has been shown to be a powerful tool for dealing with complex dynamic systems. It sequentially generates Monte Carlo samples from a proposal distribution, adjusted by a set of importance weight with respect to a target distribution, to facilitate
Sequential Monte Carlo Methods to Train Neural Network Models
João F. G. De Freitas; Mahesan Niranjan; Andrew H. Gee; Arnaud Doucet
2000-01-01
We discuss a novel strategy for training neural networks using sequential Monte Carlo algorithms and propose a new hybrid gradient descent\\/sampling importance resampling algorithm (HySIR). In terms of computational time and accuracy, the hybrid SIR is a clear improvement over conventional sequential Monte Carlo techniques. The new algorithm may be viewed as a global optimization strategy that allows us to
Quantum Monte Carlo Method for Attractive Coulomb Potentials
J. S. Kole; H. De Raedt
2001-02-06
Starting from an exact lower bound on the imaginary-time propagator, we present a Path-Integral Quantum Monte Carlo method that can handle singular attractive potentials. We illustrate the basic ideas of this Quantum Monte Carlo algorithm by simulating the ground state of hydrogen and helium.
Quasi-Monte Carlo Methods in Numerical Finance
Corwin Joy; Phelim P. Boyle; Ken Seng Tan
1996-01-01
This paper introduces and illustrates a new version of the Monte Carlo method that has attractive properties for the numerical valuation of derivatives. The traditional Monte Carlo method has proven to be a powerful and flexible tool for many types of derivatives calculations. Under the conventional approach pseudo-random numbers are used to evaluate the expression of interest. Unfortunately, the use
Recent Advances in Randomized Quasi-Monte Carlo Methods
Pierre L’Ecuyer; Christiane Lemieux
We survey some of the recent developments on quasi-Monte Carlo (QMC) methods, which, in their basic form, are a deterministic counterpart to the Monte Carlo (MC) method. Our main focus is the applicability of these methods to practical problems that involve the estimation of a high-dimensional integral. We review several QMC constructions and different randomizations that have been proposed to
The Monte Carlo Method. Popular Lectures in Mathematics.
ERIC Educational Resources Information Center
Sobol', I. M.
The Monte Carlo Method is a method of approximately solving mathematical and physical problems by the simulation of random quantities. The principal goal of this booklet is to suggest to specialists in all areas that they will encounter problems which can be solved by the Monte Carlo Method. Part I of the booklet discusses the simulation of random…
Radiative heat transfer with quasi-monte carlo methods
A. Kersch; W. Morokoff; A. Schuster
1994-01-01
Monte Carlo simulation is often used to solve radiative transfer problems wherecomplex physical phenomena and geometries must be handled. Slow convergenceis a well known disadvantage of such methods. In this paper we demonstratethat a significant improvement in computation time can be achieved by usingQuasi-Monte Carlo methods to simulate Rapid Thermal Processing, which is animportant technique for the production of semiconductor
Cruising The Simplex: Hamiltonian Monte Carlo and the Dirichlet Distribution
Betancourt, M J
2010-01-01
Due to its constrained support, the Dirichlet distribution is uniquely suited to many applications. The constraints that make it powerful, however, can also hinder practical implementations, particularly those utilizing Markov Chain Monte Carlo (MCMC) techniques such as Hamiltonian Monte Carlo. I demonstrate a series of transformations that reshape the canonical Dirichlet distribution into a form much more amenable to MCMC algorithms.
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 rate function, yield to maturity, CMS, CMT, volatility, convexity adjustment, martingale Abstract This paper proposes a Monte Carlo technique for pricing the for- ward yield to maturity, when the volatility
Bayesian Inference in Econometric Models Using Monte Carlo Integration
John Geweke
1989-01-01
Methods for the systematic application of Monte Carlo integration with importance sampling to Bayesian inference are developed. Conditions under which the numerical approximation converges almost surely to the true value with the number of Monte Carlo replications, and its numerical accuracy may be assessed reliably, are given. Importance sampling densities are derived from multivariate normal or student approximations to the
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
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…
TOPICAL REVIEW Monte Carlo methods for phase equilibria of uids
by either Monte Carlo or molecular dynamics methods. Monte Carlo methods are based on generating con over time and length scales that are not directly accessible by molecular dynamics or simple constant techniques are described in detail. The Gibbs ensemble method is based on simulations of two regions coupled
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
Hybrid algorithms in quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Kim, Jeongnim; Esler, Kenneth P.; McMinis, Jeremy; Morales, Miguel A.; Clark, Bryan K.; Shulenburger, Luke; Ceperley, David M.
2012-12-01
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.
Monte Carlo simulation of modulated phases
NASA Technical Reports Server (NTRS)
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.
Monte Carlo stratified source-sampling
Blomquist, R.N.; Gelbard, E.M.
1997-09-01
In 1995, at a conference on criticality safety, a special session was devoted to the Monte Carlo {open_quotes}eigenvalue of the world{close_quotes} problem. Argonne presented a paper, at that session, in which the anomalies originally observed in that problem were reproduced in a much simplified model-problem configuration, and removed by a version of stratified source-sampling. The original test-problem was treated by a special code designed specifically for that purpose. Recently ANL started work on a method for dealing with more realistic eigenvalue of the world configurations, and has been incorporating this method into VIM. The original method has been modified to take into account real-world statistical noise sources not included in the model problem. This paper constitutes a status report on work still in progress.
Monte Carlo applications to acoustical field solutions
NASA Technical Reports Server (NTRS)
Haviland, J. K.; Thanedar, B. D.
1973-01-01
The Monte Carlo technique is proposed for the determination of the acoustical pressure-time history at chosen points in a partial enclosure, the central idea of this technique being the tracing of acoustical rays. A statistical model is formulated and an algorithm for pressure is developed, the conformity of which is examined by two approaches and is shown to give the known results. The concepts that are developed are applied to the determination of the transient field due to a sound source in a homogeneous medium in a rectangular enclosure with perfect reflecting walls, and the results are compared with those presented by Mintzer based on the Laplace transform approach, as well as with a normal mode solution.
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 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.
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.
Lunar Regolith Albedos Using Monte Carlos
NASA Technical Reports Server (NTRS)
Wilson, T. L.; Andersen, V.; Pinsky, L. S.
2003-01-01
The analysis of planetary regoliths for their backscatter albedos produced by cosmic rays (CRs) is important for space exploration and its potential contributions to science investigations in fundamental physics and astrophysics. Albedos affect all such experiments and the personnel that operate them. Groups have analyzed the production rates of various particles and elemental species by planetary surfaces when bombarded with Galactic CR fluxes, both theoretically and by means of various transport codes, some of which have emphasized neutrons. Here we report on the preliminary results of our current Monte Carlo investigation into the production of charged particles, neutrons, and neutrinos by the lunar surface using FLUKA. In contrast to previous work, the effects of charm are now included.
Monte Carlo Modeling of Luminescent Solar Concentrators
NASA Astrophysics Data System (ADS)
Mooney, Alex; Fontecchio, Paul; Wittmershaus, Bruce
2006-03-01
Luminescent Solar Concentrators (LSCs) offer an inexpensive alternative for solar power generation. A LSC is a flat, translucent plate that absorbs sunlight through embedded, highly fluorescent molecules. The emitted light is concentrated via total internal reflection at the edges of the LSC, where photovoltaic cells covert it into electricity. We've developed a Monte Carlo model that predicts the properties of LSCs by tracing individual light rays. The user controls the plate's geometry and spectral properties, along with the spectral profile of the excitation source. The user can include a specular or diffuse reflective background under the LSC. We've demonstrated the ability to predict the output of a LSC as a function of its optical density. Reabsorption distorts the profile of fluorescence as light propagates through a LSC, and the program can accurately reproduce the effect. The goal is to use the model as a predictive tool for improving the design of LSCs.
Green's function Monte Carlo in nuclear physics
Carlson, J.
1990-01-01
We review the status of Green's Function Monte Carlo (GFMC) methods as applied to problems in nuclear physics. New methods have been developed to handle the spin and isospin degrees of freedom that are a vital part of any realistic nuclear physics problem, whether at the level of quarks or nucleons. We discuss these methods and then summarize results obtained recently for light nuclei, including ground state energies, three-body forces, charge form factors and the coulomb sum. As an illustration of the applicability of GFMC to quark models, we also consider the possible existence of bound exotic multi-quark states within the framework of flux-tube quark models. 44 refs., 8 figs., 1 tab.
Quantum Monte Carlo Study of Sulfur
NASA Astrophysics Data System (ADS)
Suewattana, Malliga; Krakauer, Henry; Zhang, Shiwei
2004-03-01
We apply a recently developed quantum Monte Carlo (QMC) method (Shiwei Zhang, Henry Krakauer, Phys. Rev. Lett. 90). 136401 (2003). to calculate the atomization energy of sulfur molecule and the ionization energies of sulfur atom. The QMC method projects out the ground state by random walks in the space of Slater determinants, using auxiliary-fields to decouple the Coulomb interaction between electrons. A trial wave function |?_T> is used in the approximation to control the phase problem in QMC. We carry out Hartree-Fock (HF) and density functional theory (with the local density approximation (LDA)) calculations. The generated single Slater determinant wave functions are then used as |?_T> in QMC. The HF and LDA |?_T>'s lead to atomization energies in agreement with each other and the experimental value.
Methods for Monte Carlo simulations of biomacromolecules
Vitalis, Andreas; Pappu, Rohit V.
2010-01-01
The state-of-the-art for Monte Carlo (MC) simulations of biomacromolecules is reviewed. Available methodologies for sampling conformational equilibria and associations of biomacromolecules in the canonical ensemble, given a continuum description of the solvent environment, are reviewed. Detailed sections are provided dealing with the choice of degrees of freedom, the efficiencies of MC algorithms and algorithmic peculiarities, as well as the optimization of simple movesets. The issue of introducing correlations into elementary MC moves, and the applicability of such methods to simulations of biomacromolecules is discussed. A brief discussion of multicanonical methods and an overview of recent simulation work highlighting the potential of MC methods are also provided. It is argued that MC simulations, while underutilized biomacromolecular simulation community, hold promise for simulations of complex systems and phenomena that span multiple length scales, especially when used in conjunction with implicit solvation models or other coarse graining strategies. PMID:20428473
Quantum Ice : a quantum Monte Carlo study
Nic Shannon; Olga Sikora; Frank Pollmann; Karlo Penc; Peter Fulde
2011-12-13
Ice states, in which frustrated interactions lead to a macroscopic ground-state degeneracy, occur in water ice, in problems of frustrated charge order on the pyrochlore lattice, and in the family of rare-earth magnets collectively known as spin ice. Of particular interest at the moment are "quantum spin ice" materials, where large quantum fluctuations may permit tunnelling between a macroscopic number of different classical ground states. Here we use zero-temperature quantum Monte Carlo simulations to show how such tunnelling can lift the degeneracy of a spin or charge ice, stabilising a unique "quantum ice" ground state --- a quantum liquid with excitations described by the Maxwell action of 3+1-dimensional quantum electrodynamics. We further identify a competing ordered "squiggle" state, and show how both squiggle and quantum ice states might be distinguished in neutron scattering experiments on a spin ice material.
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.
Rapidity gaps and the PHOJET Monte Carlo
F. W. Bopp; R. Engel; J. Ranft
1998-03-24
A model for the production of large rapidity gaps being implemented in the Monte Carlo event generator PHOJET is discussed. In this model, high-mass diffraction dissociation exhibits properties similar to hadron production in non-diffractive hadronic collisions at high energies. Hard diffraction is described using leading-order QCD matrix elements together with a parton distribution function for the pomeron and pomeron-flux factorization. Since this factorization is imposed on Born graph level only, unitarity corrections lead to a non-factorizing flux function. Rapidity gaps between jets are obtained by soft color reconnection. It was previously shown that this model is able to describe data on diffractive hadron production from the CERN-SPS collider and from the HERA lepton-proton collider. In this work we focus on the model predictions for rapidity gap events in p-p collisions at \\sqrt{s} = 1800 GeV and compare to TEVATRON data.
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 modelling of TRIGA research reactor
NASA Astrophysics Data System (ADS)
El Bakkari, B.; Nacir, B.; El Bardouni, T.; El Younoussi, C.; Merroun, O.; Htet, A.; Boulaich, Y.; Zoubair, M.; Boukhal, H.; Chakir, M.
2010-10-01
The Moroccan 2 MW TRIGA MARK II research reactor at Centre des Etudes Nucléaires de la Maâmora (CENM) achieved initial criticality on May 2, 2007. The reactor is designed to effectively implement the various fields of basic nuclear research, manpower training, and production of radioisotopes for their use in agriculture, industry, and medicine. This study deals with the neutronic analysis of the 2-MW TRIGA MARK II research reactor at CENM and validation of the results by comparisons with the experimental, operational, and available final safety analysis report (FSAR) values. The study was prepared in collaboration between the Laboratory of Radiation and Nuclear Systems (ERSN-LMR) from Faculty of Sciences of Tetuan (Morocco) and CENM. The 3-D continuous energy Monte Carlo code MCNP (version 5) was used to develop a versatile and accurate full model of the TRIGA core. The model represents in detailed all components of the core with literally no physical approximation. Continuous energy cross-section data from the more recent nuclear data evaluations (ENDF/B-VI.8, ENDF/B-VII.0, JEFF-3.1, and JENDL-3.3) as well as S( ?, ?) thermal neutron scattering functions distributed with the MCNP code were used. The cross-section libraries were generated by using the NJOY99 system updated to its more recent patch file "up259". The consistency and accuracy of both the Monte Carlo simulation and neutron transport physics were established by benchmarking the TRIGA experiments. Core excess reactivity, total and integral control rods worth as well as power peaking factors were used in the validation process. Results of calculations are analysed and discussed.
Monte Carlo simulation of neutron detectors
NASA Astrophysics Data System (ADS)
Stephan, Andrew Curtis
2003-06-01
Neutron detectors are simulated using Monte Carlo methods in order to gain insight into how they work and optimize their performance. Simulated results for a Micromegas neutron beam monitor using a custom computer code are compared with published experimental data to verify the accuracy of the simulation. Different designs (e.g. neutron converter material, gas chamber width, gas pressure) are tested to assess their impact on detector performance. It is determined that a 10B converter foil and 1 mm drift gap width work best for a neutron beam monitor. The Micromegas neutron beam monitor neutronics are evaluated using the computer code MCNP. An optimized set of design criteria are determined that minimize neutron scattering probability in the device. In a best-case scenario, the thermal neutron scattering probability in the detector is 1.1*10-3. Lastly, composite neutron scintillators consisting of fluorescent dopant particles in a lithiated matrix material are simulated using a custom Monte Carlo code. The effects of design parameters such as dopant particle size, dopant volumetric concentration, and dopant and matrix material densities on scintillator characteristics are quantified. For ZnS:Ag particles in a lithiated glass matrix, it is found that dopant particle radii of 1 micron or less result in approximately Gaussian-shaped pulse height spectra and dopant particle radii of 5 microns or less result in practically all neutron absorption events producing scintillation light emission. Self-absorption of scintillation light is not treated in the simulation. Both the Micromegas and composite neutron scintillator simulations use the TRIM code as a heavy-charged particle transport engine.
Crossing the mesoscale no-mans land via parallel kinetic Monte Carlo.
Garcia Cardona, Cristina (San Diego State University); Webb, Edmund Blackburn, III; Wagner, Gregory John; Tikare, Veena; Holm, Elizabeth Ann; Plimpton, Steven James; Thompson, Aidan Patrick; Slepoy, Alexander (U. S. Department of Energy, NNSA); Zhou, Xiao Wang; Battaile, Corbett Chandler; Chandross, Michael Evan
2009-10-01
The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applying it to materials modeling problems of interest to Sandia. In this report we give an overview of the methods and algorithms developed, and describe our new open-source code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator. We also highlight the development of several Monte Carlo models in SPPARKS for specific materials modeling applications, including grain growth, bubble formation, diffusion in nanoporous materials, defect formation in erbium hydrides, and surface growth and evolution.
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.
Iterative acceleration methods for Monte Carlo and deterministic criticality calculations
Urbatsch, T.J.
1995-11-01
If you have ever given up on a nuclear criticality calculation and terminated it because it took so long to converge, you might find this thesis of interest. The author develops three methods for improving the fission source convergence in nuclear criticality calculations for physical systems with high dominance ratios for which convergence is slow. The Fission Matrix Acceleration Method and the Fission Diffusion Synthetic Acceleration (FDSA) Method are acceleration methods that speed fission source convergence for both Monte Carlo and deterministic methods. The third method is a hybrid Monte Carlo method that also converges for difficult problems where the unaccelerated Monte Carlo method fails. The author tested the feasibility of all three methods in a test bed consisting of idealized problems. He has successfully accelerated fission source convergence in both deterministic and Monte Carlo criticality calculations. By filtering statistical noise, he has incorporated deterministic attributes into the Monte Carlo calculations in order to speed their source convergence. He has used both the fission matrix and a diffusion approximation to perform unbiased accelerations. The Fission Matrix Acceleration method has been implemented in the production code MCNP and successfully applied to a real problem. When the unaccelerated calculations are unable to converge to the correct solution, they cannot be accelerated in an unbiased fashion. A Hybrid Monte Carlo method weds Monte Carlo and a modified diffusion calculation to overcome these deficiencies. The Hybrid method additionally possesses reduced statistical errors.
Spectral backward Monte Carlo method for surface infrared image simulation
NASA Astrophysics Data System (ADS)
Sun, Haifeng; Xia, Xinlin; Sun, Chuang; Chen, Xue
2014-11-01
The surface infrared radiation is an important part that contributes to the infrared image of the airplane. The Monte Carlo method for the infrared image calculation is suitable for the complex geometry of targets like airplanes. The backward Monte Carlo method is prior to the forward Monte Carlo method for the usually long distance between targets and the detector. Similar to the non-gray absorbing media, the random number relation is developed for the radiation of the spectral surface. In the backward Monte Carlo method, one random number that reverses the wave length (or wave number) may result deferent wave numbers for targets' surface elements on the track of a photon bundle. Through the manipulation of the densities of a photon bundles in arbitrary small intervals near wave numbers, all the wave lengths corresponding to one random number on the targets' surface elements on the track of the photon bundle are kept the same to keep the balance of the energy of the photon bundle. The model developed together with the energy partition model is incorporated into the backward Monte Carlo method to form the spectral backward Monte Carlo method. The developed backward Monte Carlo method is used to calculate the infrared images of a simple configuration with two gray spectral bands, and the efficiency of it is validated by compared the results of it to that of the non-spectral backward Monte Carlo method . Then the validated spectral backward Monte Carlo method is used to simulate the infrared image of the SDM airplane model with spectral surface, and the distribution of received infrared radiation flux of pixels in the detector is analyzed.
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.
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)
Monte Carlo dose calculation on deforming anatomy.
Peterhans, Matthias; Frei, Daniel; Manser, Peter; Aguirre, Mauricio Reyes; Fix, Michael K
2011-05-01
This article presents the implementation and validation of a dose calculation approach for deforming anatomical objects. Deformation is represented by deformation vector fields leading to deformed voxel grids representing the different deformation scenarios. Particle transport in the resulting deformed voxels is handled through the approximation of voxel surfaces by triangles in the geometry implementation of the Swiss Monte Carlo Plan framework. The focus lies on the validation methodology which uses computational phantoms representing the same physical object through regular and irregular voxel grids. These phantoms are chosen such that the new implementation for a deformed voxel grid can be compared directly with an established dose calculation algorithm for regular grids. Furthermore, separate validation of the aspects voxel geometry and the density changes resulting from deformation is achieved through suitable design of the validation phantom. We show that equivalent results are obtained with the proposed method and that no statistically significant errors are introduced through the implementation for irregular voxel geometries. This enables the use of the presented and validated implementation for further investigations of dose calculation on deforming anatomy. PMID:21247744
Biofilm growth: a lattice Monte Carlo model
NASA Astrophysics Data System (ADS)
Tao, Yuguo; Slater, Gary
2011-03-01
Biofilms are complex colonies of bacteria that grow in contact with a wall, often in the presence of a flow. In the current work, biofilm growth is investigated using a new two-dimensional lattice Monte Carlo algorithm based on the Bond-Fluctuation Algorithm (BFA). One of the distinguishing characteristics of biofilms, the synthesis and physical properties of the extracellular polymeric substance (EPS) in which the cells are embedded, is explicitly taken into account. Cells are modelled as autonomous closed loops with well-defined mechanical and thermodynamic properties, while the EPS is modelled as flexible polymeric chains. This BFA model allows us to add biologically relevant features such as: the uptake of nutrients; cell growth, division and death; the production of EPS; cell maintenance and hibernation; the generation of waste and the impact of toxic molecules; cell mutation and evolution; cell motility. By tuning the structural, interactional and morphologic parameters of the model, the cell shapes as well as the growth and maturation of various types of biofilm colonies can be controlled.
Quantum Ice : A Quantum Monte Carlo Study
NASA Astrophysics Data System (ADS)
Sikora, Olga; Benton, Owen; Shannon, Nic; Penc, Karlo; McClarty, Paul; Pollmann, Frank; Moessner, Roderich; Fulde, Peter
2012-02-01
The magnetic ``ice'' state found in spin ice materials has recently generated great excitement for its magnetic monopole excitations. However the deconfined nature of these monopoles depends crucially on the macroscopic degeneracy of the classical ice ground state. And at very low temperatures we might expect this degeneracy to be lifted by quantum tunneling between different ice configurations. Here we present the results of large-scale Green's function Monte Carlo simulation of ice-type models which include quantum tunneling. We find compelling evidence of an extended quantum U(1)-liquid ground state with deconfined monopole excitations in both the quantum dimer model [1,2] and the quantum ice model on the diamond lattice [3]. This quantum U(1) liquid proves to be remarkably robust against the inclusion of long range dipolar interactions. [0pt] [1] O. Sikora et al., Phys. Rev. Lett. 103, 247001 (2009) [2] O. Sikora et al., Phys. Rev. B 84, 115129 (2011) [3] N. Shannon et al., arXiv:1105.4196
The GENIE neutrino Monte Carlo generator
NASA Astrophysics Data System (ADS)
Andreopoulos, C.; Bell, A.; Bhattacharya, D.; Cavanna, F.; Dobson, J.; Dytman, S.; Gallagher, H.; Guzowski, P.; Hatcher, R.; Kehayias, P.; Meregaglia, A.; Naples, D.; Pearce, G.; Rubbia, A.; Whalley, M.; Yang, T.
2010-02-01
GENIE [1] is a new neutrino event generator for the experimental neutrino physics community. The goal of the project is to develop a 'canonical' neutrino interaction physics Monte Carlo whose validity extends to all nuclear targets and neutrino flavors from MeV to PeV energy scales. Currently, emphasis is on the few-GeV energy range, the challenging boundary between the non-perturbative and perturbative regimes, which is relevant for the current and near future long-baseline precision neutrino experiments using accelerator-made beams. The design of the package addresses many challenges unique to neutrino simulations and supports the full life-cycle of simulation and generator-related analysis tasks. GENIE is a large-scale software system, consisting of ˜120000 lines of C++ code, featuring a modern object-oriented design and extensively validated physics content. The first official physics release of GENIE was made available in August 2007, and at the time of the writing of this article, the latest available version was v2.4.4.
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
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).
Improved method for implicit Monte Carlo
Brown, F. B. (Forrest B.); Martin, W. R. (William R.)
2001-01-01
The Implicit Monte Carlo (IMC) method has been used for over 30 years to analyze radiative transfer problems, such as those encountered in stellar atmospheres or inertial confinement fusion. Reference [2] provided an exact error analysis of IMC for 0-D problems and demonstrated that IMC can exhibit substantial errors when timesteps are large. These temporal errors are inherent in the method and are in addition to spatial discretization errors and approximations that address nonlinearities (due to variation of physical constants). In Reference [3], IMC and four other methods were analyzed in detail and compared on both theoretical grounds and the accuracy of numerical tests. As discussed in, two alternative schemes for solving the radiative transfer equations, the Carter-Forest (C-F) method and the Ahrens-Larsen (A-L) method, do not exhibit the errors found in IMC; for 0-D, both of these methods are exact for all time, while for 3-D, A-L is exact for all time and C-F is exact within a timestep. These methods can yield substantially superior results to IMC.
The GENIE Neutrino Monte Carlo Generator
C. Andreopoulos; A. Bell; D. Bhattacharya; F. Cavanna; J. Dobson; S. Dytman; H. Gallagher; P. Guzowski; R. Hatcher; P. Kehayias; A. Meregaglia; D. Naples; G. Pearce; A. Rubbia; M. Whalley; T. Yang
2009-11-18
GENIE is a new neutrino event generator for the experimental neutrino physics community. The goal of the project is to develop a `canonical' neutrino interaction physics Monte Carlo whose validity extends to all nuclear targets and neutrino flavors from MeV to PeV energy scales. Currently, emphasis is on the few-GeV energy range, the challenging boundary between the non-perturbative and perturbative regimes, which is relevant for the current and near future long-baseline precision neutrino experiments using accelerator-made beams. The design of the package addresses many challenges unique to neutrino simulations and supports the full life-cycle of simulation and generator-related analysis tasks. GENIE is a large-scale software system, consisting of 120,000 lines of C++ code, featuring a modern object-oriented design and extensively validated physics content. The first official physics release of GENIE was made available in August 2007, and at the time of the writing of this article, the latest available version was v2.4.4.
Monte Carlo techniques for analyzing deep penetration problems
Cramer, S.N.; Gonnord, J.; Hendricks, J.S.
1985-01-01
A review of current methods and difficulties in Monte Carlo deep-penetration calculations is presented. Statistical uncertainty is discussed, and recent adjoint optimization of splitting, Russian roulette, and exponential transformation biasing is reviewed. Other aspects of the random walk and estimation processes are covered, including the relatively new DXANG angular biasing technique. Specific items summarized are albedo scattering, Monte Carlo coupling techniques with discrete ordinates and other methods, adjoint solutions, and multi-group Monte Carlo. The topic of code-generated biasing parameters is presented, including the creation of adjoint importance functions from forward calculations. Finally, current and future work in the area of computer learning and artificial intelligence is discussed in connection with Monte Carlo applications. 29 refs.
Library of anomalous ??? couplings for ? +? -(n?) Monte Carlo programs
NASA Astrophysics Data System (ADS)
Paul, T.; Swain, J.; Wa?, Z.
2000-02-01
We briefly describe a library that may be used with any e +e -?? +? -(n?) Monte Carlo program to account for the effects of anomalous ??? couplings. The implementation of this library in KORALZ version 4.04 is discussed.
Combinatorial nuclear level density by a Monte Carlo method
N. Cerf
1993-09-14
We present a new combinatorial method for the calculation of the nuclear level density. It is based on a Monte Carlo technique, in order to avoid a direct counting procedure which is generally impracticable for high-A nuclei. The Monte Carlo simulation, making use of the Metropolis sampling scheme, allows a computationally fast estimate of the level density for many fermion systems in large shell model spaces. We emphasize the advantages of this Monte Carlo approach, particularly concerning the prediction of the spin and parity distributions of the excited states, and compare our results with those derived from a traditional combinatorial or a statistical method. Such a Monte Carlo technique seems very promising to determine accurate level densities in a large energy range for nuclear reaction calculations.
MODELING LEACHING OF VIRUSES BY THE MONTE CARLO METHOD
A predictive screening model was developed for fate and transport of viruses in the unsaturated zone. A database of input parameters allowed Monte Carlo analysis with the model. The resulting kernel densities of predicted attenuation during percolation indicated very ...
Markovian Monte Carlo Solutions of the NLO QCD Evolution Equations
NASA Astrophysics Data System (ADS)
Golec-Biernat, K.; Jadach, S.; Placzek, W.; Skrzypek, M.
2006-06-01
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.
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.
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.
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...
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 ...
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 variance reduction approaches for non-Boltzmann tallies
Booth, T.E.
1992-12-01
Quantities that depend on the collective effects of groups of particles cannot be obtained from the standard Boltzmann transport equation. Monte Carlo estimates of these quantities are called non-Boltzmann tallies and have become increasingly important recently. Standard Monte Carlo variance reduction techniques were designed for tallies based on individual particles rather than groups of particles. Experience with non-Boltzmann tallies and analog Monte Carlo has demonstrated the severe limitations of analog Monte Carlo for many non-Boltzmann tallies. In fact, many calculations absolutely require variance reduction methods to achieve practical computation times. Three different approaches to variance reduction for non-Boltzmann tallies are described and shown to be unbiased. The advantages and disadvantages of each of the approaches are discussed.
Parallel Fission Bank Algorithms in Monte Carlo Criticality Calculations
Romano, Paul Kollath
In this work we describe a new method for parallelizing the source iterations in a Monte Carlo criticality calculation. Instead of having one global fission bank that needs to be synchronized, as is traditionally done, our ...
Kinetic Monte Carlo simulations of nanocrystalline film deposition
Ruan, Shiyun
A full diffusion kinetic Monte Carlo algorithm is used to model nanocrystalline film deposition, and study the mechanisms of grain nucleation and microstructure formation in such films. The major finding of this work is ...
A Particle Population Control Method for Dynamic Monte Carlo
NASA Astrophysics Data System (ADS)
Sweezy, Jeremy; Nolen, Steve; Adams, Terry; Zukaitis, Anthony
2014-06-01
A general particle population control method has been derived from splitting and Russian Roulette for dynamic Monte Carlo particle transport. A well-known particle population control method, known as the particle population comb, has been shown to be a special case of this general method. This general method has been incorporated in Los Alamos National Laboratory's Monte Carlo Application Toolkit (MCATK) and examples of it's use are shown for both super-critical and sub-critical systems.
Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms
Alan D. Sokal
1996-01-01
IntroductionThe goal of these lectures is to give an introduction to current research on MonteCarlo methods in statistical mechanics and quantum field theory, with an emphasis on:1) the conceptual foundations of the method, including the possible dangers andmisuses, and the correct use of statistical error analysis; and2) new Monte Carlo algorithms for problems in critical phenomena and quantumfield theory, aimed
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.
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.
Monte Carlo methods and applications in nuclear physics
Carlson, J.
1990-01-01
Monte Carlo methods for studying few- and many-body quantum systems are introduced, with special emphasis given to their applications in nuclear physics. Variational and Green's function Monte Carlo methods are presented in some detail. The status of calculations of light nuclei is reviewed, including discussions of the three-nucleon-interaction, charge and magnetic form factors, the coulomb sum rule, and studies of low-energy radiative transitions. 58 refs., 12 figs.
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.
PEPSI - a Monte Carlo generator for polarized leptoproduction
L. Mankiewicz; A. Schäfer; M. Veltri
1992-01-01
We describe PEPSI (Polarized Electron Proton Scattering Interactions), a Monte Carlo program for polarized deep inelastic leptoproduction mediated by electromagnetic interaction, and explain how to use it. The code is a modification of the LEPTO 4.3 Lund Monte Carlo for unpolarized scattering. The hard virtual gamma-parton scattering is generated according to the polarization-dependent QCD cross-section of the first order in
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
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 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 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
American Option Pricing on Reconfigurable Hardware Using Least-Squares Monte Carlo Method
Arslan, Tughrul
American Option Pricing on Reconfigurable Hardware Using Least-Squares Monte Carlo Method Xiang using the simple Monte Carlo method. A number of extended Monte Carlo methods have been published, the Quasi-Monte Carlo method is adopted for stock price paths generation. Our real FPGA hardware
4 Monte Carlo Methods in Classical Statistical Physics
Janke, Wolfhard
4 Monte Carlo Methods in Classical Statistical Physics Wolfhard Janke Institut fÂ¨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, 79Â140 (2008) DOI 10
Monte Carlo simulations for spinodal decomposition
Sander, E. [George Mason Univ., Fairfax, VA (United States). Dept. of Mathematical Sciences] [George Mason Univ., Fairfax, VA (United States). Dept. of Mathematical Sciences; Wanner, T. [Univ. of Maryland, Baltimore, MD (United States). Dept. of Mathematics and Statistics] [Univ. of Maryland, Baltimore, MD (United States). Dept. of Mathematics and Statistics
1999-06-01
This paper addresses the phenomenon of spinodal decomposition for the Cahn-Hilliard equation. Namely, the authors are interested in why most solutions to the Cahn-Hilliard equation which start near a homogeneous equilibrium u{sub 0} {equivalent_to} {mu} in the spinodal interval exhibit phase separation with a characteristic wavelength when exiting a ball of radius R in a Hilbert space centered at u{sub 0}. There are two mathematical explanations for spinodal decomposition, due to Grant and to Maier-Paape and Wanner. In this paper, the authors numerically compare these two mathematical approaches. In fact, they are able to synthesize the understanding they gain from the numerics with the approach of Maier-Paape and Wanner, leading to a better understanding of the underlying mechanism for this behavior. With this new approach, they can explain spinodal decomposition for a longer time and larger radius than either of the previous two approaches. A rigorous mathematical explanation is contained in a separate paper. The approach is to use Monte Carlo simulations to examine the dependence of R, the radius to which spinodal decomposition occurs, as a function of the parameter {var_epsilon} of the governing equation. The authors give a description of the dominating regions on the surface of the ball by estimating certain densities of the distributions of the exit points. They observe, and can show rigorously, that the behavior of most solutions originating near the equilibrium is determined completely by the linearization for an unexpectedly long time. They explain the mechanism for this unexpectedly linear behavior, and show that for some exceptional solutions this cannot be observed. They also describe the dynamics of these exceptional solutions.
kmos: A lattice kinetic Monte Carlo framework
NASA Astrophysics Data System (ADS)
Hoffmann, Max J.; Matera, Sebastian; Reuter, Karsten
2014-07-01
Kinetic Monte Carlo (kMC) simulations have emerged as a key tool for microkinetic modeling in heterogeneous catalysis and other materials applications. Systems, where site-specificity of all elementary reactions allows a mapping onto a lattice of discrete active sites, can be addressed within the particularly efficient lattice kMC approach. To this end we describe the versatile kmos software package, which offers a most user-friendly implementation, execution, and evaluation of lattice kMC models of arbitrary complexity in one- to three-dimensional lattice systems, involving multiple active sites in periodic or aperiodic arrangements, as well as site-resolved pairwise and higher-order lateral interactions. Conceptually, kmos achieves a maximum runtime performance which is essentially independent of lattice size by generating code for the efficiency-determining local update of available events that is optimized for a defined kMC model. For this model definition and the control of all runtime and evaluation aspects kmos offers a high-level application programming interface. Usage proceeds interactively, via scripts, or a graphical user interface, which visualizes the model geometry, the lattice occupations and rates of selected elementary reactions, while allowing on-the-fly changes of simulation parameters. We demonstrate the performance and scaling of kmos with the application to kMC models for surface catalytic processes, where for given operation conditions (temperature and partial pressures of all reactants) central simulation outcomes are catalytic activity and selectivities, surface composition, and mechanistic insight into the occurrence of individual elementary processes in the reaction network.
Monte Carlo simulation of large electron fields
Faddegon, Bruce A; Perl, Joseph; Asai, Makoto
2010-01-01
Two Monte Carlo systems, EGSnrc and Geant4, the latter with two different “physics lists,” were used to calculate dose distributions in large electron fields used in radiotherapy. Source and geometry parameters were adjusted to match calculated results to measurement. Both codes were capable of accurately reproducing the measured dose distributions of the 6 electron beams available on the accelerator. Depth penetration matched the average measured with a diode and parallel-plate chamber to 0.04 cm or better. Calculated depth dose curves agreed to 2% with diode measurements in the buildup region, although for the lower beam energies there was a discrepancy of up to 5% in this region when calculated results are compared to parallel-plate measurements. Dose profiles at the depth of maximum dose matched to 2-3% in the central 25 cm of the field, corresponding to the field size of the largest applicator. A 4% match was obtained outside the central region. The discrepancy observed in the bremsstrahlung tail in published results that used EGS4 is no longer evident. Simulations with the different codes and physics lists used different source energies, incident beam angles, thicknesses of the primary foils, and distance between the primary and secondary foil. The true source and geometry parameters were not known with sufficient accuracy to determine which parameter set, including the energy of the source, was closest to the truth. These results underscore the requirement for experimental benchmarks of depth penetration and electron scatter for beam energies and foils relevant to radiotherapy. PMID:18296775
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.
Quantum Monte Carlo Endstation for Petascale Computing
David Ceperley
2011-03-02
The major achievements enabled by QMC Endstation grant include * Performance improvement on clusters of x86 multi-core systems, especially on Cray XT systems * New and improved methods for the wavefunction optimizations * New forms of trial wavefunctions * Implementation of the full application on NVIDIA GPUs using CUDA The scaling studies of QMCPACK on large-scale systems show excellent parallel efficiency up to 216K cores on Jaguarpf (Cray XT5). The GPU implementation shows speedups of 10-15x over the CPU implementation on older generation of x86. We have implemented hybrid OpenMP/MPI scheme in QMC to take advantage of multi-core shared memory processors of petascale systems. Our hybrid scheme has several advantages over the standard MPI-only scheme. * Memory optimized: large read-only data to store one-body orbitals and other shared properties to represent the trial wave function and many-body Hamiltonian can be shared among threads, which reduces the memory footprint of a large-scale problem. * Cache optimized: the data associated with an active Walker are in cache during the compute-intensive drift-diffusion process and the operations on an Walker are optimized for cache reuse. Thread-local objects are used to ensure the data affinity to a thread. * Load balanced: Walkers in an ensemble are evenly distributed among threads and MPI tasks. The two-level parallelism reduces the population imbalance among MPI tasks and reduces the number of point-to-point communications of large messages (serialized objects) for the Walker exchange. * Communication optimized: the communication overhead, especially for the collective operations necessary to determine ET and measure the properties of an ensemble, is significantly lowered by using less MPI tasks. The multiple forms of parallelism afforded by QMC algorithms make them ideal candidates for acceleration in the many-core paradigm. We presented the results of our effort to port the QMCPACK simulation code to the NVIDIA CUDA GPU platform. We restructured the CPU algorithms to express additional parallelism, minimize GPU-CPU communication, and efficiently utilize the GPU memory hierarchy. Using mixed precision on GT200 GPUs and MPI for intercommunication and load balancing, we observe typical full-application speedups of approximately 10x to 15x relative to quad-core Xeon CPUs alone, while reproducing the double-precision CPU results within statistical error. We developed an all-electron quantum Monte Carlo (QMC) method for solids that does not rely on pseudopotentials, and used it to construct a primary ultra-high-pressure calibration based on the equation of state of cubic boron nitride. We computed the static contribution to the free energy with the QMC method and obtained the phonon contribution from density functional theory, yielding a high-accuracy calibration up to 900 GPa usable directly in experiment. We computed the anharmonic Raman frequency shift with QMC simulations as a function of pressure and temperature, allowing optical pressure calibration. In contrast to present experimental approaches, small systematic errors in the theoretical EOS do not increase with pressure, and no extrapolation is needed. This all-electron method is applicable to first-row solids, providing a new reference for ab initio calculations of solids and benchmarks for pseudopotential accuracy. We compared experimental and theoretical results on the momentum distribution and the quasiparticle renormalization factor in sodium. From an x-ray Compton-profile measurement of the valence-electron momentum density, we derived its discontinuity at the Fermi wavevector finding an accurate measure of the renormalization factor that we compared with quantum-Monte-Carlo and G0W0 calculations performed both on crystalline sodium and on the homogeneous electron gas. Our calculated results are in good agreement with the experiment. We have been studying the heat of formation for various Kubas complexes of molecular hydrogen on Ti(1,2)ethylene-nH2 using Diffusion Monte Carlo. This work has been started and is o
Growth of polymer films by driven deposition: Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Bentrem, Frank Wallace
Growth of polymer films continues to be of great interest to researchers both for the understanding of the underlying physics as well as the applications in developing new materials. Computer simulations have proven to be useful tools in the study of polymer systems, and stochastic (Monte Carlo) simulations are used here to investigate growing polymer films by deposition. The polymer chains move on a cubic lattice where each monomer unit can move according to a set of rules and are driven towards the substrate by an external field. We begin with the relatively slow (single-monomer) kink-jump dynamics, however, incorporation of faster modes such as crankshaft and reptation movements seems crucial in relaxing the interface width. The structure of the chains are analyzed by evaluating the conformation at the wall, in the bulk, at the interface, and in solution. The polymer density profile is also examined at the substrate, throughout the bulk, and at the interface. Growth and roughness of the interface for deposited polymer chains are studied by evaluating the interface width, its development over time, steady-state, and equilibrium values. The growth characteristics for the interface are compared to those using particle deposition models. Also, the dependence of the interface width on chain length, field strength, and temperature is investigated by varying these parameters in order to establish empirical laws and scaling relationships.
1/ 17 Monte Carlo Simulation of the Law of the Maximum of a LÂ´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 LÂ´evy Process Motivation #12;2/ 17 Monte Carlo Simulation of the Law of the Maximum of a LÂ´evy Process
Li, Yaohang
Monte Carlo Methods and Appl., Vol. 11, No. 1, pp. 39 Â 55 (2005) c VSP 2005 Grid-based Quasi-Monte -- In this paper, we extend the techniques used in Grid-based Monte Carlo appli- cations to Grid-based quasi-Monte in quasirandom sequences prevents us from applying many of our Grid-based Monte Carlo techniques to Grid- based
Electron energy loss modelling in small volumes: A Monte Carlo study
NASA Astrophysics Data System (ADS)
Chaoui, Zine-El-Abidine
2008-12-01
In thin target and sub-volumes, electronic energy losses in single collisions vary considerably for individual charged particles. These fluctuations resulting from the stochastic nature of the interactions can be described through a simulation with Monte Carlo calculations. Models used in the present simulations to describe the electron scattering processes are derived from quantum mechanics. The resulting cross sections for energies up to 200 keV are shown for both processes, i.e. elastic and inelastic interactions. Influence of the Monte Carlo strategy adopted to calculate energy loss spectra (straggling functions) is discussed. Straggling functions calculated from the general purpose Monte Carlo code Penelope and the convolution method of Bichsel are included for comparisons. The results are new. In fact, disagreements have been found in the calculated energy spectra when using different strategies. These deviations are explained in the present study by investigating the thickness dependence on the electron energy. As a central result, energy deposition in silicon detectors can be described accurately when event by event Monte Carlo strategy is used.
Lee, Anthony; Yau, Christopher; Giles, Michael B.; Doucet, Arnaud; Holmes, Christopher C.
2011-01-01
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
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.
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
An Asymptotic-Preserving Monte Carlo Method for the Boltzmann Equation$ , Hong Liua,
Jin, Shi
An Asymptotic-Preserving Monte Carlo Method for the Boltzmann Equation$ Wei Rena , Hong Liua, , Shi Carlo method for the Boltzmann equation that is more efficient than the currently available Monte Carlo of this method, and compare it with some other asymptotic-preserving Monte Carlo methods in terms of numerical
A New Monte Carlo Method and Its Implications for Generalized Cluster Algorithms
C. H. Mak; Arun K. Sharma
2007-04-12
We describe a novel switching algorithm based on a ``reverse'' Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of cluster-type Monte Carlo methods, and the generalization makes it possible to derive cluster algorithms for systems with both discrete and continuous degrees of freedom. The roughening transition in the sine-Gordon model has been studied with this method, and high-accuracy simulations for system sizes up to $1024^2$ were carried out to examine the logarithmic divergence of the surface roughness above the transition temperature, revealing clear evidence for universal scaling of the Kosterlitz-Thouless type.
Quantum Monte Carlo calculated potential energy curve for the helium dimer.
Wu, Xuebin; Hu, Xianru; Dai, Yunchuan; Du, Chenlei; Chu, Shibin; Hu, Leibo; Deng, Jianbo; Feng, Yuanping
2010-05-28
We report on the results of both the diffusion quantum Monte Carlo (DMC) and reptation quantum Monte Carlo (RMC) methods on the potential energy curve of the helium dimer. We show that it is possible to obtain a highly accurate description of the helium dimer. An improved stochastic reconfiguration technique is employed to optimize the many-body wave function, which is the starting point for highly accurate simulations based on the DMC and RMC methods. We find that the results of these methods are in excellent agreement with the best theoretical results at short range, especially the recently developed RMC method, yield particularly accurate results with reduced statistical error, which gives very excellent agreement across the whole potential curve. For the equilibrium internuclear distance of 5.6 bohrs, the calculated total energy with RMC method is -5.807 483 599+/-0.000 000 016 hartree and the corresponding well depth is -11.003+/-0.005 K. PMID:20515092
Study of nuclear pairing with Configuration-Space Monte-Carlo approach
Lingle, Mark
2015-01-01
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 non-constant pairing strengths, cases with nearly degenerate excited states, limits when pairing correlations in finite systems are weak, and pr...
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.
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.
Vectorizing and macrotasking Monte Carlo neutral particle algorithms
Heifetz, D.B.
1987-04-01
Monte Carlo algorithms for computing neutral particle transport in plasmas have been vectorized and macrotasked. The techniques used are directly applicable to Monte Carlo calculations of neutron and photon transport, and Monte Carlo integration schemes in general. A highly vectorized code was achieved by calculating test flight trajectories in loops over arrays of flight data, isolating the conditional branches to as few a number of loops as possible. A number of solutions are discussed to the problem of gaps appearing in the arrays due to completed flights, which impede vectorization. A simple and effective implementation of macrotasking is achieved by dividing the calculation of the test flight profile among several processors. A tree of random numbers is used to ensure reproducible results. The additional memory required for each task may preclude using a larger number of tasks. In future machines, the limit of macrotasking may be possible, with each test flight, and split test flight, being a separate task.
A Quantum Monte Carlo Method at Fixed Energy
Edward Farhi; Jeffrey Goldstone; David Gosset; Harvey B. Meyer
2009-12-21
In this paper we explore new ways to study the zero temperature limit of quantum statistical mechanics using Quantum Monte Carlo simulations. We develop a Quantum Monte Carlo method in which one fixes the ground state energy as a parameter. The Hamiltonians we consider are of the form $H=H_{0}+\\lambda V$ with ground state energy E. For fixed $H_{0}$ and V, one can view E as a function of $\\lambda$ whereas we view $\\lambda$ as a function of E. We fix E and define a path integral Quantum Monte Carlo method in which a path makes no reference to the times (discrete or continuous) at which transitions occur between states. For fixed E we can determine $\\lambda(E)$ and other ground state properties of H.
Rapid Monte Carlo Simulation of Gravitational Wave Galaxies
NASA Astrophysics Data System (ADS)
Breivik, Katelyn; Larson, Shane L.
2015-01-01
With the detection of gravitational waves on the horizon, astrophysical catalogs produced by gravitational wave observatories can be used to characterize the populations of sources and validate different galactic population models. Efforts to simulate gravitational wave catalogs and source populations generally focus on population synthesis models that require extensive time and computational power to produce a single simulated galaxy. Monte Carlo simulations of gravitational wave source populations can also be used to generate observation catalogs from the gravitational wave source population. Monte Carlo simulations have the advantes of flexibility and speed, enabling rapid galactic realizations as a function of galactic binary parameters with less time and compuational resources required. We present a Monte Carlo method for rapid galactic simulations of gravitational wave binary populations.
Monte Carlo simulation of laser attenuation characteristics in fog
NASA Astrophysics Data System (ADS)
Wang, Hong-Xia; Sun, Chao; Zhu, You-zhang; Sun, Hong-hui; Li, Pan-shi
2011-06-01
Based on the Mie scattering theory and the gamma size distribution model, the scattering extinction parameter of spherical fog-drop is calculated. For the transmission attenuation of the laser in the fog, a Monte Carlo simulation model is established, and the impact of attenuation ratio on visibility and field angle is computed and analysed using the program developed by MATLAB language. The results of the Monte Carlo method in this paper are compared with the results of single scattering method. The results show that the influence of multiple scattering need to be considered when the visibility is low, and single scattering calculations have larger errors. The phenomenon of multiple scattering can be interpreted more better when the Monte Carlo is used to calculate the attenuation ratio of the laser transmitting in the fog.
Efficient Monte Carlo characterization of quantum operations for qudits
NASA Astrophysics Data System (ADS)
Gualdi, Giulia; Licht, David; Reich, Daniel M.; Koch, Christiane P.
2014-09-01
For qubits, Monte Carlo estimation of the average fidelity of Clifford unitaries is efficient: it requires a number of experiments that is independent of the number n of qubits and classical computational resources that scale only polynomially in n. Here, we identify the requirements for efficient Monte Carlo estimation and the corresponding properties of the measurement operator basis when replacing two-level qubits by p-level qudits. Our analysis illuminates the intimate connection between mutually unbiased measurements and the existence of unitaries that can be characterized efficiently. It allows us to propose a "hierarchy" of generalizations of the standard Pauli basis from qubits to qudits according to the associated scaling of resources required in Monte Carlo estimation of the average fidelity.
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.
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.
Efficient Monte Carlo characterization of quantum operations for qudits
Giulia Gualdi; David Licht; Daniel M. Reich; Christiane P. Koch
2014-04-06
For qubits, Monte Carlo estimation of the average fidelity of Clifford unitaries is efficient -- it requires a number of experiments that is independent of the number $n$ of qubits and classical computational resources that scale only polynomially in $n$. Here, we identify the requirements for efficient Monte Carlo estimation and the corresponding properties of the measurement operator basis when replacing two-level qubits by $p$-level qudits. Our analysis illuminates the intimate connection between mutually unbiased measurements and the existence of unitaries that can be characterized efficiently. It allows us to propose a 'hierarchy' of generalizations of the standard Pauli basis from qubits to qudits according to the associated scaling of resources required in Monte Carlo estimation of the average fidelity.
Quantum Monte Carlo calculations of light nuclei using chiral potentials.
Lynn, J E; Carlson, J; Epelbaum, E; Gandolfi, S; Gezerlis, A; Schwenk, A
2014-11-01
We present the first Green's function Monte Carlo calculations of light nuclei with nuclear interactions derived from chiral effective field theory up to next-to-next-to-leading order. Up to this order, the interactions can be constructed in a local form and are therefore amenable to quantum Monte Carlo calculations. We demonstrate a systematic improvement with each order for the binding energies of A=3 and A=4 systems. We also carry out the first few-body tests to study perturbative expansions of chiral potentials at different orders, finding that higher-order corrections are more perturbative for softer interactions. Our results confirm the necessity of a three-body force for correct reproduction of experimental binding energies and radii, and pave the way for studying few- and many-nucleon systems using quantum Monte Carlo methods with chiral interactions. PMID:25415900
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.
A study of voltage contrast image using Monte Carlo simulation
NASA Astrophysics Data System (ADS)
Ota, T.; Koshiba, T.; Nakasugi, T.
2007-03-01
Using Monte Carlo simulation, we studied voltage contrast (VC) image caused by negative charging. In order to simulate the VC image, we have developed an electron scattering program based on a consideration of the spatial charge conduction model. Also we have established a cluster computing system of 60 CPUs to shorten the processing time. Using a Monte Carlo simulator, we succeeded in obtaining the simulated VC image. Comparison between simulated images and experimental images reveals that the simulated images are in good agreement with some experimental images.
Overview of the MCU Monte Carlo Software Package
NASA Astrophysics Data System (ADS)
Kalugin, M. A.; Oleynik, D. S.; Shkarovsky, D. A.
2014-06-01
MCU (Monte Carlo Universal) is a project on development and practical use of a universal computer code for simulation of particle transport (neutrons, photons, electrons, positrons) in three-dimensional systems by means of the Monte Carlo method. This paper provides the information on the current state of the project. The developed libraries of constants are briefly described, and the potentialities of the MCU-5 package modules and the executable codes compiled from them are characterized. Examples of important problems of reactor physics solved with the code are presented.
Tracking multiple interacting subcellular structure by sequential Monte Carlo method.
Wen, Quan; Luby-Phelps, Kate; Gao, Jean
2009-01-01
With the wide application of Green Fluorescent Proteins (GFP) in the study of live cells, there is a surging need for computer-aided analysis on the huge amount of image sequence data acquired by the advanced microscopy devices. In this paper, a framework based on Sequential Monte Carlo (SMC) is proposed for multiple interacting object tracking. The distribution of the dimension varying joint state is sampled efficiently by a Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm with a novel height swap move. Experimental results were performed on synthetic and real confocal microscopy image sequences. PMID:19623773
Precise Monte Carlo Simulation of Single-Photon Detectors
Mario Stip?evi?; Daniel J. Gauthier
2014-11-13
We demonstrate the importance and utility of Monte Carlo simulation of single-photon detectors. Devising an optimal simulation is strongly influenced by the particular application because of the complexity of modern, avalanche-diode-based single-photon detectors.. Using a simple yet very demanding example of random number generation via detection of Poissonian photons exiting a beam splitter, we present a Monte Carlo simulation that faithfully reproduces the serial autocorrelation of random bits as a function of detection frequency over four orders of magnitude of the incident photon flux. We conjecture that this simulation approach can be easily modified for use in many other applications.
Monte Carlo simulation of lattice systems with RKKY interaction
NASA Astrophysics Data System (ADS)
Nefedev, K. V.; Belokon, V. I.; Kapitan, V. Yu; Dyachenko, O. I.
2014-03-01
Numerical approaches to the study of the magnetic states, properties, and phase transitions in the Ising spin systems with the long-range exchange interaction is presented. The Monte Carlo calculations have been performed for a system of Ising spins on a square lattice with long-range RKKY interaction. It is shown that the Monte Carlo simulation systems RKKY interaction leads to the formation of a complex of the magnetic structure. We compared the results of simulation with experimental images of domain structure of garnet ferrite films.
PEPSI — a Monte Carlo generator for polarized leptoproduction
NASA Astrophysics Data System (ADS)
Mankiewicz, L.; Schäfer, A.; Veltri, M.
1992-09-01
We describe PEPSI (Polarized Electron Proton Scattering Interactions), a Monte Carlo program for polarized deep inelastic leptoproduction mediated by electromagnetic interaction, and explain how to use it. The code is a modification of the LEPTO 4.3 Lund Monte Carlo for unpolarized scattering. The hard virtual gamma-parton scattering is generated according to the polarization-dependent QCD cross-section of the first order in ? S. PEPSI requires the standard polarization-independent JETSET routines to simulate the fragmentation into final hadrons.
Monte Carlo evaluation of discrete electronic stopping powers
Venezia, V.C.; Ordonez, C.A.; Molina, M.I. [Univ. of North Texas, Denton, TX (United States)
1994-12-31
A Monte Carlo evaluation of discrete electronic stopping powers is presented. The method is based on the binary encounter approximation and considers projectile stopping which results from the cumulative loss of energy during successive, independent, binary, Coulomb collisions. For each collision with a target electron, both the binding energy and the velocity distribution of the electron are taken into account. Because discrete electronic energy losses are evaluated, the approach is ideally suited for incorporation into existing Monte Carlo codes such as TRIM and MARLOWE. Detailed calculations are presented for nitrogen along with a comparison with experimental data.
Anomalous diffusion of a tethered membrane: a Monte Carlo investigation.
Popova, Hristina; Milchev, Andrey
2008-04-01
Using a continuum bead-spring Monte Carlo model, we study the anomalous diffusion dynamics of a self-avoiding tethered membrane by means of extensive computer simulations. We focus on the subdiffusive stochastic motion of the membrane's central node in the regime of flat membranes at temperatures above the membrane folding transition. While at times, larger than the characteristic membrane relaxation time tau(R) , the mean-square displacement of the center of mass of the sheet,
A Monte Carlo model of auroral hydrogen emission line profiles
NASA Astrophysics Data System (ADS)
Gérard, J.-C.; Shematovich, V. I.; Bisikalo, D. V.; Lummerzheim, D.
2005-06-01
Hydrogen line profiles measured from space-borne or ground-based instruments provide useful information to study the physical processes occurring in the proton aurora and to estimate the proton flux characteristics. The line shape of the hydrogen lines is determined by the velocity distribution of H atoms along the line-of-sight of the instrument. Calculations of line profiles of auroral hydrogen emissions were obtained using a Monte Carlo kinetic model of proton precipitation into the auroral atmosphere. In this model both processes of energy degradation and scattering angle redistribution in momentum and charge transfer collisions of the high-energy proton/hydrogen flux with the ambient atmospheric gas are considered at the microphysical level. The model is based on measured cross sections and scattering angle distributions and on a stochastic interpretation of such collisions. Calculations show that collisional angular redistribution of the precipitating proton/hydrogen beam is the dominant process leading to the formation of extended wings and peak shifts in the hydrogen line profiles. All simulations produce a peak shift from the rest line wavelength decreasing with increasing proton energy. These model predictions are confirmed by analysis of ground-based H-? line observations from Poker Flat, showing an anti-correlation between the magnitude of the peak shift and the extent of the blue wing of the line. Our results also strongly suggest that the relative extension of the blue and red wings provides a much better indicator of the auroral proton characteristic energy than the position of the peak wavelength.
Monte Carlo Method for a Quantum Measurement Process by a Single-Electron Transistor
Hsi-Sheng Goan
2004-06-15
We derive the quantum trajectory or stochastic (conditional) master equation for a single superconducting Cooper-pair box (SCB) charge qubit measured by a single-electron transistor (SET) detector. This stochastic master equation describes the random evolution of the measured SCB qubit density matrix which both conditions and is conditioned on a particular realization of the measured electron tunneling events through the SET junctions. Hence it can be regarded as a Monte Carlo method that allows us to simulate the continuous quantum measurement process. We show that the master equation for the "partially" reduced density matrix [Y. Makhlin et.al., Phys. Rev. Lett. 85, 4578 (2000)] can be obtained when a "partial" average is taken on the stochastic master equation over the fine grained measurement records of the tunneling events in the SET. Finally, we present some Monte Carlo simulation results for the SCB/SET measurement process. We also analyze the probability distribution P(m,t) of finding m electrons that have tunneled into the drain of the SET in time t to demonstrate the connection between the quantum trajectory approach and the "partially" reduced density matrix approach.
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.
Romano, Paul K. (Paul Kollath)
2013-01-01
Monte Carlo particle transport methods are being considered as a viable option for high-fidelity simulation of nuclear reactors. While Monte Carlo methods offer several potential advantages over deterministic methods, there ...
Incorporation of Monte-Carlo Computer Techniques into Science and Mathematics Education.
ERIC Educational Resources Information Center
Danesh, Iraj
1987-01-01
Described is a Monte-Carlo method for modeling physical systems with a computer. Also discussed are ways to incorporate Monte-Carlo simulation techniques for introductory science and mathematics teaching and also for enriching computer and simulation courses. (RH)
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 ...
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
Numerical study of reflectance imaging using a parallel Monte Carlo method
Numerical study of reflectance imaging using a parallel Monte Carlo method Cheng Chen and Jun Q. Lu scattering in biological tissues of turbid nature. We present a parallel Monte Carlo method for accurate
Goddard III, William A.
Monte Carlo Method Derek A. Debe, Matt J. Carlson, Jiro Sadanobu, S. I. Chan,§ and W. A. Goddard III. The foundation of this hierarchy is the Restrained Generic Protein (RGP) Direct Monte Carlo method. The RGP
Blind Data Detection in the Presence of PLL Phase Noise by Sequential Monte Carlo Method
Noels, Nele
Blind Data Detection in the Presence of PLL Phase Noise by Sequential Monte Carlo Method Erdal Abstract-- In this paper, based on a sequential Monte Carlo method, a computationally efficient algorithm
Approximation spaces in off-policy Monte Carlo learning
James F. Peters; Christopher Henry
2007-01-01
This paper introduces an approach to off-policy Monte Carlo (MC) learning guided by behaviour patterns gleaned from approximation spaces and rough set theory introduced by Zdzis?aw Pawlak in 1981. During reinforcement learning, an agent makes action selections in an effort to maximize a reward signal obtained from the environment. The problem considered in this paper is how to estimate the
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 to thank my supervisors Adam Postula and Peter Sutton at UQ for allowing me to come all the way
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.
Monte Carlo shipping cask calculations using an automated biasing procedure
Tang, J.S.; Hoffman, T.J.; Childs, R.L.; Parks, C.V.
1983-01-01
This paper describes an automated biasing procedure for Monte Carlo shipping cask calculations within the SCALE system - a modular code system for Standardized Computer Analysis for Licensing Evaluation. The SCALE system was conceived and funded by the US Nuclear Regulatory Commission to satisfy a strong need for performing standardized criticality, shielding, and heat transfer analyses of nuclear systems.
Monte Carlo simulation of the shape space model of immunology
NASA Astrophysics Data System (ADS)
Dasgupta, Subinay
1992-11-01
The shape space model of de Boer, Segel and Perelson for the immune system is studied with a probabilistic updating rule by Monte Carlo simulation. A suitable mathematical form is chosen for the probability of increase of B-cell concentration depending on the concentration around the mirror image site. The results obtained agree reasonably with the results obtained by deterministic cellular automata.
Data Splitting for Parallel Linear Algebra Monte Carlo Algorithms
Christian Weihrauch
Many scientific and engineering applications involve the inversion of large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The com- putational complexity of the Monte Carlo methods depend only on the number of chains and the
Monte Carlo simulations of ferromagnetic{endash}antiferromagnetic grains
Heinonen, O.
2001-06-01
The effects of finite temperature on exchange bias are investigated using Monte Carlo simulations of model systems. Thermal effects may introduce phase slips of domain walls wound into the antiferromagnet. Furthermore, spin{endash}flop coupling may be unstable with respect to domain formation at the interface. {copyright} 2001 American Institute of Physics.
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.
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
Monte Carlo Modeling of Io's [OI] Aurora in Eclipse
NASA Astrophysics Data System (ADS)
Moore, C. H.; Goldstein, D. B.; Varghese, P. L.; Trafton, L. M.; Stapelfeldt, K.
2006-03-01
A 3D direct Monte Carlo simulation is used to simulate Io's atmospheric interaction (upon entering eclipse) with electrons from the plasma torus. It is found that the flux tube depletion across Io controls the latitude of the bright wake feature.
Bayesian Posterior Comprehension via Message from Monte Carlo
Allison, Lloyd
Bayesian Posterior Comprehension via Message from Monte Carlo Leigh J. Fitzgibbon, David L. Dowe an epitome, or brief summary, of a Bayesian posterior distribution - and then investigate a general solution comprehension, and fast approximation of posterior expectations. We call these the properties of Bayesian
Improved Monte-Carlo simulator of partial discharge
R. J. van Brunt; P. von Glahn
1996-01-01
A previously introduced Monte-Carlo simulator of partial discharge (PD) has been extended and made more versatile to allow simulation of a wider range of observed discharge behavior. The version of the simulator described here allows simulation of pulsating PD that can be represented as a point process and covers such properties as nonstationary behavior associated with PD-induced modifications of the
Optimized Monte Carlo Path Generation using Genetic Algorithms
F. Suykens; Y. D. Willems
In this technical report we present a new method for optimizing the generation of paths in Monte Carlo global illumination rendering algorithms. Ray tracing, particle tracing, and bidirectional ray tracing all use random walks to estimate various fluxes in the scene. The probability density functions neces- sary to generate these random walks are optimized using a genetic algorithm, such that
Improved geometry representations for Monte Carlo radiation transport.
Martin, Matthew Ryan (Cornell University)
2004-08-01
ITS (Integrated Tiger Series) permits a state-of-the-art Monte Carlo solution of linear time-integrated coupled electron/photon radiation transport problems with or without the presence of macroscopic electric and magnetic fields of arbitrary spatial dependence. ITS allows designers to predict product performance in radiation environments.
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
Nonlinear Acoustics in Diatomic Gases Using Direct Simulation Monte Carlo
Amanda L. Danforth; Lyle N. Long
2005-01-01
The Direct Simulation Monte Carlo (DSMC) method has been very successful for the study of many problems in rarefied gas dynamics and hypersonic flow. The extension to applications such as acoustics will provide a useful tool for capturing all physical properties of interest for nonlinear acoustic problems, such as dispersion, attenuation, harmonic generation and nonequilibrium effects. The validity of DSMC
A Monte Carlo method for high dimensional integration
Yosihiko Ogata
1989-01-01
Summary A new method for the numerical integration of very high dimensional functions is introduced and implemented based on the Metropolis' Monte Carlo algorithm. The logarithm of the high dimensional integral is reduced to a 1-dimensional integration of a certain statistical function with respect to a scale parameter over the range of the unit interval. The improvement in accuracy is
Sequential Monte Carlo Methods for Statistical Analysis of Tables
Yuguo CHEN; Susan P. HOLMES; Jun S. LIU
2003-01-01
We describe a sequential importance sampling (SIS) procedure for analyzing two-way zero-one or contingency tables with fixed marginal sums. An essential feature of the new method is that it samples the columns of the table progressively according to certain special distri- butions. Our method produces Monte Carlo samples that are remarkably close to the uniform distribution, enabling one to approximate
Calculation of canopy bidirectional reflectance using the Monte Carlo method
J. K. ROSS; A. L. MARSHAK
1988-01-01
For a calculation of the plant canopy bidirectional reflectance distribution function (BRDF) the Monte Carlo method is used. The plant architecture is given by a rather universal mathematical model which allows to consider such structural parameters as canopy density and height, the number of leaves per plant, distance between leaves, dimensions and orientations of leaves and stems, etc., and their
Smoothness and dimension reduction in Quasi-Monte Carlo methods
B. Moskowitz; R. E. Caflisch
1996-01-01
Monte Carlo integration using quasirandom sequences has theoretical error bounds of size O (N?1 logdN) in dimension d, as opposed to the error of size O (N?12) for random or pseudorandom sequences. In practice, however, this improved performance for quasirandom sequences is often not observed. The degradation of performance is due to discontinuity or lack of smoothness in the integrand
Systolic Matrix Inversion Using a Monte Carlo Method
Graham M. Megson; V. N. Aleksandrov; I. T. Dimov
1994-01-01
A systolic array for inverting an n × n matrix using a Monte Carlo method is proposed. The basic array computes a single row of the inverse in 3n + N + T steps ( including input and output time) and O( nNT) cells where N is the number of chains and T is the length of each chain in
A direct simulation Monte-Carlo method for cluster coagulation
Kurt Liffman
1992-01-01
The study presents a method for analyzing cluster coagulation which relies on a Monte Carlo analysis of individual particles as they interact and form clusters from a homogeneous, monodisperse medium. Four case studies are shown, three of which compare the results of the code to the known analytic solutions of the Smoluchowski equation, and the fourth considers the cluster size
On the Gap-Tooth direct simulation Monte Carlo method
Armour, Jessica D
2012-01-01
This thesis develops and evaluates Gap-tooth DSMC (GT-DSMC), a direct Monte Carlo simulation procedure for dilute gases combined with the Gap-tooth method of Gear, Li, and Kevrekidis. The latter was proposed as a means of ...
Multicanonical multigrid Monte Carlo method and effective autocorellation time
W. Janke; T. Sauer
1993-12-09
We report tests of the recently proposed multicanonical multigrid Monte Carlo method for the two-dimensional $\\Phi^4$ field theory. Defining an effective autocorrelation time we obtain real time improvement factors of about one order of magnitude compared with standard multicanonical simulations.
On Monte Carlo methods for estimating ratios of normalizing constants
Ming-Hui Chen; Qi-Man Shao
1997-01-01
Recently, estimating ratios of normalizing constants has played an important role in Bayesian computations. Applications of estimating ratios of normalizing constants arise in many aspects of Bayesian statistical inference. In this article, we present an overview and discuss the current Monte Carlo methods for estimating ratios of normalizing constants. Then we propose a new ratio importance sampling method and establish
Structure From Motion Using Sequential Monte Carlo Methods
Gang Qian; Rama Chellappa
2001-01-01
In this papel; the structure from motion (SfM) problem is addressed using sequential Monte Carlo methods. A new Sfn algorithm based on random sampling is derived to esti- mate the posterior distributions of camera motion and scene structure for the perspective projection camera model. Ex- perimental results show that challenging issues in solving the structure from motion problem including errors
Efficient Evaluation of System Reliability by Monte Carlo Method
Hiromitsu Kumamoto; Kazuo Tanaka; Koichi Inoue
1977-01-01
This paper presents a new Monte Carlo method to estimate the reliability of a large complex system represented by a reliability block diagram or by a fault tree. Two binary functions are introduced; one dominates the system structure function and the other is dominated by the structure function. These functions can be constructed easily by using part of path sets
Monte Carlo method for magnetic impurities in metals
NASA Technical Reports Server (NTRS)
Hirsch, J. E.; Fye, R. M.
1986-01-01
The paper discusses a Monte Carlo algorithm to study properties of dilute magnetic alloys; the method can treat a small number of magnetic impurities interacting wiith the conduction electrons in a metal. Results for the susceptibility of a single Anderson impurity in the symmetric case show the expected universal behavior at low temperatures. Some results for two Anderson impurities are also discussed.
Markov chain Monte Carlo method and its application
Stephen P. Brooks
1998-01-01
Summary. The Markov chain Monte Carlo (MCMC) method, as a computer-intensive statistical tool, has enjoyed an enormous upsurge in interest over the last few years. This paper provides a simple, comprehensive and tutorial review of some of the most common areas of research in this field. We begin by discussing how MCMC algorithms can be constructed from standard building- blocks
Testing Dependent Correlations with Nonoverlapping Variables: A Monte Carlo Simulation
ERIC Educational Resources Information Center
Silver, N. Clayton; Hittner, James B.; May, Kim
2004-01-01
The authors conducted a Monte Carlo simulation of 4 test statistics or comparing dependent correlations with no variables in common. Empirical Type 1 error rates and power estimates were determined for K. Pearson and L. N. G. Filon's (1898) z, O. J. Dunn and V. A. Clark's (1969) z, J. H. Steiger's (1980) original modification of Dunn and Clark's…
Monte Carlo Results from a Computer Program for Tailored Testing.
ERIC Educational Resources Information Center
Cudeck, Robert A.; And Others
INTERTAIL, the computer program which implements an approach to tailored testing outlined by Cliff (1975), was examined with errorless data in several Monte Carlo studies. Three replications of each cell of a 3 x 3 table with 10, 20 and 40 items and persons were analyzed. Mean rank correlation coefficients between the true order, specified by…
RADIATIVE HEAT TRANSFER WITH QUASI-MONTE CARLO METHODS
. The radiative heat exchange in such a reactor is a function of the geometry of the problem, the spectralRADIATIVE HEAT TRANSFER WITH QUASI-MONTE CARLO METHODS A. Kersch1 W. Moroko2 A. Schuster1 1Siemens wafers, as well as many other industrial processes. Several factors are considered including surface ab
Monte Carlo Algorithms for Hardy-Weinberg Proportions
West, Mike
Monte Carlo Algorithms for Hardy-Weinberg Proportions Mark Huber,1 Yuguo Chen,2 Ian Dinwoodie,2 Department of Mathematics, Duke University, Durham, NC 27708-0320, USA April 25, 2005 Summary The Hardy-Weinberg its importance, many tests have been devised to determine if a finite population follows Hardy-Weinberg
Monte Carlo algorithms for Hardy-Weinberg Proportions
West, Mike
Monte Carlo algorithms for Hardy-Weinberg Proportions #3; By MARK HUBER Department of Mathematics The Hardy-Weinberg law is of basic importance in studying biological systems, and it is important to be able to determine if a population is in Hardy-Weinberg equilibrium. For #12;nite populations, this means testing
Monte Carlo simulations of environmental degradation on polymer coatings
Brian Hinderliter; Stuart Croll
2003-01-01
The degradation of a polymer coating and predicting the coating lifetime, based on physica properties and distribution within the coating of the polymer binder, pigments, and fillers, are economically very important. As technologies advance, allowing control of coatings at the nanoscale level, methods such as Monte Carlo can be used not only to predict the behavior of a nanodesigned coating
Adaptive Mesh and Algorithm Refinement using Direct Simulation Monte Carlo
Bell, John B.
Simulation Monte Carlo (DSMC), at the finest grid scale. As an illustration, consider the flow of a gas examples are presented and compared with purely continuum calculations. \\Lambda Permanent address: Physics of scales must be spanned, computational fluid dynamics (CFD) calculations often employ local mesh
Monte Carlo simulations for quantum field theories involving fermions
M. Karowski; R. Schrader; H. J. Thun
1985-01-01
We present a new variant of a Monte Carlo procedure for euclidean quantum field theories with fermions. On a lattice every term contributing to the expansion of the fermion determinant is interpreted as a configuration of self-avoiding oriented closed loops which represent the fermionic vacuum fluctuations. These loops are related to Symanzik's polymer description of euclidean quantum field theory. The
Multiple Overlapping Tiles for Contextual Monte Carlo Tree Search
Paris-Sud XI, Université de
be described as a reinforcement learning algorithm. This algorithm is particularly interesting when the number or Havannah. But this algo- rithm was also successfully applied on one-player problems like the automatic to be automatically modified depending on the context: Contextual Monte Carlo (CMC) simulations. We show
Multiple Overlapping Tiles for Contextual Monte Carlo Tree Search
in a discrete, observable, uncertain environment with finite horizon that can be described as a reinforcement- rithm was also successfully applied on one-player problems like the automatic generation of libraries a modification of the Monte Carlo simulations that allows them to be automatically modified depending
A New Omnidirectional Vision Sensor for Monte-Carlo Localization
Menegatti, Emanuele
grabbed by the robot (without a map) [13, 7, 8]. In our approach we use an omnidirectional vision system the pose of the robot inside the environment. Several techniques based on the Monte-Carlo localization (MCL scans of the fix obstacles around the robot and the localization is calculates matching those scans
Image Segmentation by Data Driven Markov Chain Monte Carlo
Zhuowen Tu; Song-Chun Zhu; Heung-yeung Shum
2001-01-01
This 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 seymen- tation in three aspects. Firstly, it designs effective and well balanced Markov Chain dynamics to explore the solution space and makes the split and merge process reversible at a middle level vision
PENGHITUNGAN FAKTOR BUILDUP TITANIUM DENGAN MENGGUNAKAN METODA MONTE CARLO
Hengky Istianto Has; Andang Widi Harto
THE CALCULATION OF TITANIUM BUILDUP FACTOR BASED ON MONTE CARLO METHOD. The objective of radioactive -waste container is to reduce radiation emission to the environment. For that purpose, we need material with ability to shield that radiation and last for 10.000 years. Titanium is one of the materials that can be used to make containers. Unfortunately, its buildup factor, which
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 event generators for hadron-hadron collisions
Knowles, I.G. [Argonne National Lab., IL (United States). High Energy Physics Div.; Protopopescu, S.D. [Brookhaven National Lab., Upton, NY (United States)
1993-06-01
A brief review of Monte Carlo event generators for simulating hadron-hadron collisions is presented. Particular emphasis is placed on comparisons of the approaches used to describe physics elements and identifying their relative merits and weaknesses. This review summarizes a more detailed report.
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.
Ordering dynamics of nematic liquid crystals: Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Singh, Amrita; Ahmad, Shaista; Puri, Sanjay; Singh, Shri
2012-11-01
We present comprehensive results from Monte Carlo (MC) simulations of ordering dynamics in d = 2 nematic liquid crystals. We compare our MC results with an analytic form obtained for the correlation function of the liquid crystal order parameter. The numerical and analytical results are in excellent agreement. The domain growth law is consistent with L(t) ? (t/ln?t)1/2.
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.
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
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
Path Integral Monte-Carlo Calculations for Relativistic Oscillator
Alexandr Ivanov; Oleg Pavlovsky
2014-11-11
The problem of Relativistic Oscillator has been studied in the framework of Path Integral Monte-Carlo(PIMC) approach. Ultra-relativistic and non-relativistic limits have been discussed. We show that PIMC method can be effectively used for investigation of relativistic systems.
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
2014-10-02
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.
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...
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
An Improved Monte Carlo Algorithm for Elastic Electron Backscattering
Dimov, Ivan
of the backscattering of electrons from metal targets is subject of extensive theoreticel and experimental work in surAn Improved Monte Carlo Algorithm for Elastic Electron Backscattering from Surfaces Ivan T. Dimov- face analysis. We are interested in the angular distribution of the back- scattered electrons. The flow
Present Status and Extensions of the Monte Carlo Performance Benchmark
NASA Astrophysics Data System (ADS)
Hoogenboom, J. Eduard; Petrovic, Bojan; Martin, William R.
2014-06-01
The NEA Monte Carlo Performance benchmark started in 2011 aiming to monitor over the years the abilities to perform a full-size Monte Carlo reactor core calculation with a detailed power production for each fuel pin with axial distribution. This paper gives an overview of the contributed results thus far. It shows that reaching a statistical accuracy of 1 % for most of the small fuel zones requires about 100 billion neutron histories. The efficiency of parallel execution of Monte Carlo codes on a large number of processor cores shows clear limitations for computer clusters with common type computer nodes. However, using true supercomputers the speedup of parallel calculations is increasing up to large numbers of processor cores. More experience is needed from calculations on true supercomputers using large numbers of processors in order to predict if the requested calculations can be done in a short time. As the specifications of the reactor geometry for this benchmark test are well suited for further investigations of full-core Monte Carlo calculations and a need is felt for testing other issues than its computational performance, proposals are presented for extending the benchmark to a suite of benchmark problems for evaluating fission source convergence for a system with a high dominance ratio, for coupling with thermal-hydraulics calculations to evaluate the use of different temperatures and coolant densities and to study the correctness and effectiveness of burnup calculations. Moreover, other contemporary proposals for a full-core calculation with realistic geometry and material composition will be discussed.
Harnessing graphical structure in Markov chain Monte Carlo learning
Stolorz, P.E. [California Inst. of Technology, Pasadena, CA (United States); Chew P.C. [Univ. of Pennsylvania, Philadelphia, PA (United States)
1996-12-31
The Monte Carlo method is recognized as a useful tool in learning and probabilistic inference methods common to many datamining problems. Generalized Hidden Markov Models and Bayes nets are especially popular applications. However, the presence of multiple modes in many relevant integrands and summands often renders the method slow and cumbersome. Recent mean field alternatives designed to speed things up have been inspired by experience gleaned from physics. The current work adopts an approach very similar to this in spirit, but focusses instead upon dynamic programming notions as a basis for producing systematic Monte Carlo improvements. The idea is to approximate a given model by a dynamic programming-style decomposition, which then forms a scaffold upon which to build successively more accurate Monte Carlo approximations. Dynamic programming ideas alone fail to account for non-local structure, while standard Monte Carlo methods essentially ignore all structure. However, suitably-crafted hybrids can successfully exploit the strengths of each method, resulting in algorithms that combine speed with accuracy. The approach relies on the presence of significant {open_quotes}local{close_quotes} information in the problem at hand. This turns out to be a plausible assumption for many important applications. Example calculations are presented, and the overall strengths and weaknesses of the approach are discussed.
Automated variance reduction for Monte Carlo shielding analyses with MCNP
NASA Astrophysics Data System (ADS)
Radulescu, Georgeta
Variance reduction techniques are employed in Monte Carlo analyses to increase the number of particles in the space phase of interest and thereby lower the variance of statistical estimation. Variance reduction parameters are required to perform Monte Carlo calculations. It is well known that adjoint solutions, even approximate ones, are excellent biasing functions that can significantly increase the efficiency of a Monte Carlo calculation. In this study, an automated method of generating Monte Carlo variance reduction parameters, and of implementing the source energy biasing and the weight window technique in MCNP shielding calculations has been developed. The method is based on the approach used in the SAS4 module of the SCALE code system, which derives the biasing parameters from an adjoint one-dimensional Discrete Ordinates calculation. Unlike SAS4 that determines the radial and axial dose rates of a spent fuel cask in separate calculations, the present method provides energy and spatial biasing parameters for the entire system that optimize the simulation of particle transport towards all external surfaces of a spent fuel cask. The energy and spatial biasing parameters are synthesized from the adjoint fluxes of three one-dimensional Discrete Ordinates adjoint calculations. Additionally, the present method accommodates multiple source regions, such as the photon sources in light-water reactor spent nuclear fuel assemblies, in one calculation. With this automated method, detailed and accurate dose rate maps for photons, neutrons, and secondary photons outside spent fuel casks or other containers can be efficiently determined with minimal efforts.
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.…
Monte Carlo study of the atmospheric spread function
NASA Technical Reports Server (NTRS)
Pearce, W. A.
1986-01-01
Monte Carlo radiative transfer simulations are used to study the atmospheric spread function appropriate to satellite-based sensing of the earth's surface. The parameters which are explored include the nadir angle of view, the size distribution of the atmospheric aerosol, and the aerosol vertical profile.
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; JouleÂThomson coefficient; Speed of sound INTRODUCTION Simulation methods
PARALLEL IMPLEMENTATION OF A GLOBAL LINE MONTE CARLO RADIOSITY
Roel Mart; Ignacio Mart ´ in
Radiosity methods are known by their expensive computational cost. To compute high quality images with a lot of polygons or patches may take hours. For this reason parallel processing will be a good option in order to decrease the computational cost. On the other hand, Monte Carlo methods offer good alternatives for paral- lelization, given their intrinsic decomposition properties in
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
Creating an Inexpensive Grid for Monte Carlo Calculations
Sean Smith; Steve Alexander; Stephen Foster; Nathan Lindzey; Robert S. Potter; Walter M. Potter; Jon. T. Rogers; Carl West; R. L. Coldwell; S. Datta
2007-01-01
We have developed software that converts an unused PC into a workstation that accepts jobs from a server and sends all results back to this server. Using a grid of up to 100 machines, a set of explicitly correlated wavefunctions optimized by Filippi and Umrigar and variational Monte Carlo we have plotted the electron density, the intracule density, the extracule
Monte Carlo simulation of detecting space debris with lidar
Shengliang Fang; Yuhua Fu; Zhen Li
2010-01-01
On the basis of analysis and processing of space background radiation, the article gives the detection probability when the lidar detecting space debris, and compare the random variable which is produced by Monte Carlo method with the detection probability, then get the detection results. The results reveal that, the detection model can well reflect the impact of the random variable
The Use of Monte Carlo Techniques to Teach Probability.
ERIC Educational Resources Information Center
Newell, G. J.; MacFarlane, J. D.
1985-01-01
Presents sports-oriented examples (cricket and football) in which Monte Carlo methods are used on microcomputers to teach probability concepts. Both examples include computer programs (with listings) which utilize the microcomputer's random number generator. Instructional strategies, with further challenges to help students understand the role of…
Computer Monte Carlo simulation in quantitative resource estimation
David H. Root; W. David Menzie; William A. Scott
1992-01-01
The method of making quantitative assessments of mineral resources sufficiently detailed for economic analysis is outlined in three steps. The steps are (1) determination of types of deposits that may be present in an area, (2) estimation of the numbers of deposits of the permissible deposit types, and (3) combination by Monte Carlo simulation of the estimated numbers of deposits
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 SIMULATION OF ELECTROMAGNETIC CASCADES IN THE EXTRAGALACTIC INFRARED
Whiting, Matthew
nuclei in high energy gamma rays ahs sparked interest in high energy extragalactic gamma ray astronomy for high energy gamma ray astronomy. ii #12; Acknowledgements I would like to thank first of all my it absorbs gamma rays, and I develop a program that uses monte carlo techniques, as well as suitable
A Multi-scale Monte Carlo Method for Electrolytes
Yihao Liang; Zhenli Xu; Xiangjun Xing
2015-04-02
Artifacts arise in the simulations of electrolytes using periodic boundary conditions (PBC). We show the origin of these artifacts are the periodic image charges and the constraint of charge neutrality inside the simulation box, both of which are unphysical from the view point of real systems. To cure these problems, we introduce a multi-scale Monte Carlo method, where ions inside a spherical cavity are simulated explicitly, whilst ions outside are treated implicitly using continuum theory. Using the method of Debye charging, we explicitly derive the effective interactions between ions inside the cavity, arising due to the fluctuations of ions outside. We find that these effective interactions consist of two types: 1) a constant cavity potential due to the asymmetry of the electrolyte, and 2) a reaction potential that depends on the positions of all ions inside. Combining the Grand Canonical Monte Carlo (GCMC) with a recently developed fast algorithm based of image charge method, we perform a multi-scale Monte Carlo simulation of symmetric electrolytes, and compare it with other simulation methods, including PBC+GCMC method, as well as large scale Monte Carlo simulation. We demonstrate that our multi-scale MC method is capable of capturing the correct physics of a large system using a small scale simulation.
SABRINA: an interactive solid geometry modeling program for Monte Carlo
West, J.T.
1985-01-01
SABRINA is a fully interactive three-dimensional geometry modeling program for MCNP. In SABRINA, a user interactively constructs either body geometry, or surface geometry models, and interactively debugs spatial descriptions for the resulting objects. This enhanced capability significantly reduces the effort in constructing and debugging complicated three-dimensional geometry models for Monte Carlo Analysis.
Markov chain Monte Carlo and Rao--Blackwellization
McKeague, Ian
Markov chain Monte Carlo and Rao--Blackwellization Ian W. McKeague \\Lambda Florida State University Wolfgang Wefelmeyer University of Siegen Abstract We introduce a form of Rao--Blackwellization for Markov, this form of Rao--Blackwellization always reduces the asymptotic variance, and derive two explicit forms
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
-Carlo simulation for LÂ´evy processes Original WHMC method: Kuznetsov et al. (2011) #12;9/ 24 Multil-level Weiner-Hopf Monte-Carlo simulation for LÂ´evy processes Original WHMC method: Kuznetsov et al. (2011) Consider-level Weiner-Hopf Monte-Carlo simulation for LÂ´evy processes Original WHMC method: Kuznetsov
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
Fast Monte Carlo for radiation therapy: the PEREGRINE Project
Hartmann Siantar, C.L.; Bergstrom, P.M.; Chandler, W.P.; Cox, L.J.; Daly, T.P.; Garrett, D.; House, R.K.; Moses, E.I.; Powell, C.L.; Patterson, R.W.; Schach von Wittenau, A.E.
1997-11-11
The purpose of the PEREGRINE program is to bring high-speed, high- accuracy, high-resolution Monte Carlo dose calculations to the desktop in the radiation therapy clinic. PEREGRINE is a three- dimensional Monte Carlo dose calculation system designed specifically for radiation therapy planning. It provides dose distributions from external beams of photons, electrons, neutrons, and protons as well as from brachytherapy sources. Each external radiation source particle passes through collimator jaws and beam modifiers such as blocks, compensators, and wedges that are used to customize the treatment to maximize the dose to the tumor. Absorbed dose is tallied in the patient or phantom as Monte Carlo simulation particles are followed through a Cartesian transport mesh that has been manually specified or determined from a CT scan of the patient. This paper describes PEREGRINE capabilities, results of benchmark comparisons, calculation times and performance, and the significance of Monte Carlo calculations for photon teletherapy. PEREGRINE results show excellent agreement with a comprehensive set of measurements for a wide variety of clinical photon beam geometries, on both homogeneous and heterogeneous test samples or phantoms. PEREGRINE is capable of calculating >350 million histories per hour for a standard clinical treatment plan. This results in a dose distribution with voxel standard deviations of <2% of the maximum dose on 4 million voxels with 1 mm resolution in the CT-slice plane in under 20 minutes. Calculation times include tracking particles through all patient specific beam delivery components as well as the patient. Most importantly, comparison of Monte Carlo dose calculations with currently-used algorithms reveal significantly different dose distributions for a wide variety of treatment sites, due to the complex 3-D effects of missing tissue, tissue heterogeneities, and accurate modeling of the radiation source.
Reconstruction of Human Monte Carlo Geometry from Segmented Images
NASA Astrophysics Data System (ADS)
Zhao, Kai; Cheng, Mengyun; Fan, Yanchang; Wang, Wen; Long, Pengcheng; Wu, Yican
2014-06-01
Human computational phantoms have been used extensively for scientific experimental analysis and experimental simulation. This article presented a method for human geometry reconstruction from a series of segmented images of a Chinese visible human dataset. The phantom geometry could actually describe detailed structure of an organ and could be converted into the input file of the Monte Carlo codes for dose calculation. A whole-body computational phantom of Chinese adult female has been established by FDS Team which is named Rad-HUMAN with about 28.8 billion voxel number. For being processed conveniently, different organs on images were segmented with different RGB colors and the voxels were assigned with positions of the dataset. For refinement, the positions were first sampled. Secondly, the large sums of voxels inside the organ were three-dimensional adjacent, however, there were not thoroughly mergence methods to reduce the cell amounts for the description of the organ. In this study, the voxels on the organ surface were taken into consideration of the mergence which could produce fewer cells for the organs. At the same time, an indexed based sorting algorithm was put forward for enhancing the mergence speed. Finally, the Rad-HUMAN which included a total of 46 organs and tissues was described by the cuboids into the Monte Carlo Monte Carlo Geometry for the simulation. The Monte Carlo geometry was constructed directly from the segmented images and the voxels was merged exhaustively. Each organ geometry model was constructed without ambiguity and self-crossing, its geometry information could represent the accuracy appearance and precise interior structure of the organs. The constructed geometry largely retaining the original shape of organs could easily be described into different Monte Carlo codes input file such as MCNP. Its universal property was testified and high-performance was experimentally verified
Direct aperture optimization for IMRT using Monte Carlo generated beamlets.
Bergman, Alanah M; Bush, Karl; Milette, Marie-Pierre; Popescu, I Antoniu; Otto, Karl; Duzenli, Cheryl
2006-10-01
This work introduces an EGSnrc-based Monte Carlo (MC) beamlet does distribution matrix into a direct aperture optimization (DAO) algorithm for IMRT inverse planning. The technique is referred to as Monte Carlo-direct aperture optimization (MC-DAO). The goal is to assess if the combination of accurate Monte Carlo tissue inhomogeneity modeling and DAO inverse planning will improve the dose accuracy and treatment efficiency for treatment planning. Several authors have shown that the presence of small fields and/or inhomogeneous materials in IMRT treatment fields can cause dose calculation errors for algorithms that are unable to accurately model electronic disequilibrium. This issue may also affect the IMRT optimization process because the dose calculation algorithm may not properly model difficult geometries such as targets close to low-density regions (lung, air etc.). A clinical linear accelerator head is simulated using BEAMnrc (NRC, Canada). A novel in-house algorithm subdivides the resulting phase space into 2.5 X 5.0 mm2 beamlets. Each beamlet is projected onto a patient-specific phantom. The beamlet dose contribution to each voxel in a structure-of-interest is calculated using DOSXYZnrc. The multileaf collimator (MLC) leaf positions are linked to the location of the beamlet does distributions. The MLC shapes are optimized using direct aperture optimization (DAO). A final Monte Carlo calculation with MLC modeling is used to compute the final dose distribution. Monte Carlo simulation can generate accurate beamlet dose distributions for traditionally difficult-to-calculate geometries, particularly for small fields crossing regions of tissue inhomogeneity. The introduction of DAO results in an additional improvement by increasing the treatment delivery efficiency. For the examples presented in this paper the reduction in the total number of monitor units to deliver is approximately 33% compared to fluence-based optimization methods. PMID:17089832
Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference
Nicolas Chopin
2004-01-01
The term “sequential Monte Carlo methods” or, equivalently, “particle filters,” refers to a general class of iterative algorithms that performs Monte Carlo approximations of a given sequence of distributions of interest (?_{t<\\/sub>). We establish in this paper a central limit theorem for the Monte Carlo estimates produced by these computational methods. This result holds under minimal assumptions on the distributions}
Utah, University of
Sequential Monte Carlo Point Process Estimation of Kinematics from Neural Spiking Activity. We have also proposed a Sequential Monte Carlo estimation methodology to reconstruct the kinematic counterpart for point 1 #12;processes of the Kalman filter), our Sequential Monte Carlo Estimation methodology
MCNP–REN: a Monte Carlo tool for neutron detector design
Mark E Abhold; Michael C Baker
2002-01-01
The development of neutron detectors makes extensive use of the predictions of detector response through the use of Monte Carlo techniques in conjunction with the point reactor model. Unfortunately, the point reactor model fails to accurately predict detector response in common applications. For this reason, the general Monte Carlo code developed at Los Alamos National Laboratory, Monte Carlo N-Particle (MCNP),
MCNP-REN: a Monte Carlo tool for neutron detector design
Mark E. Abhold; Michael C. Baker
2002-01-01
The development of neutron detectors makes extensive use of the predictions of detector response through the use of Monte Carlo techniques in conjunction with the point reactor model. Unfortunately, the point reactor model fails to accurately predict detector response in common applications. For this reason, the general Monte Carlo code developed at Los Alamos National Laboratory, Monte Carlo N-Particle (MCNP),
Direct Monte Carlo simulation of chemical reaction systems: Dissociation and recombination
Anderson, James B.
Direct Monte Carlo simulation of chemical reaction systems: Dissociation and recombination Shannon of Physics. I. INTRODUCTION In earlier studies15 we have found the direct Monte Carlo simulation method6 Monte Carlo simulation of dissociation-recombination reac- tions of the type M AB M A B. These reactions
Direct Monte Carlo simulation of chemical reaction systems: Simple bimolecular reactions
Anderson, James B.
Direct Monte Carlo simulation of chemical reaction systems: Simple bimolecular reactions Shannon D and understanding the behavior of gas phase chemical reaction systems. This Monte Carlo method, originated by Bird useful, and the gas dynamics of many systems is more easily predicted and understood by using Monte Carlo
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
Quantum Monte Carlo: Direct calculation of corrections to trial wave functions and their energies
Anderson, James B.
ARTICLES Quantum Monte Carlo: Direct calculation of corrections to trial wave functions, Pennsylvania 16802 Received 4 January 2000; accepted 10 March 2000 We report an improved Monte Carlo method Monte Carlo QMC method for the direct calculation of corrections to trial wave functions.13 We report
Menut, Laurent
Bayesian Monte Carlo analysis applied to regional-scale inverse emission modeling for reactive. The inversion method is based on Bayesian Monte Carlo analysis applied to a regional-scale chemistry transport are attributed to individual Monte Carlo simulations by comparing them with observations from the AIRPARIF
Monte Carlo Methods for Pricing and Hedging American Options in High Dimension
Caramellino, Lucia
Monte Carlo Methods for Pricing and Hedging American Options in High Dimension Lucia Caramellino1.zanette@uniud.it Summary. We numerically compare some recent Monte Carlo algorithms devoted to the pricing and hedging with respect to other Monte Carlo methods in terms of computing time. Here, we propose to suitably combine
Monte Carlo Algorithms for Linear Problems Central Laboratory for Parallel Computing
Dimov, Ivan
Monte Carlo Algorithms for Linear Problems Ivan Dimov Central Laboratory for Parallel Computing@copern.acad.bg Web site: http://www.acad.bg/BulRTD/math/dimov2.html Key words: Monte Carlo algorithms, linear classification: 65 C 05, 65 U 05 C O N T E N T S ffl Introduction ffl Iterative Monte Carlo Algorithms ffl
Monte Carlo Methods for Exact & Efficient Solution of the Generalized Optimality Equations
Monte Carlo Methods for Exact & Efficient Solution of the Generalized Optimality Equations Pedro A to the complexity of planning. In this paper, we introduce Monte Carlo methods to solve the generalized optimality of Monte Carlo proposals. In particular, it is seen that the number of proposals is essentially independent
Monte Carlo method for determining earthquake recurrence parameters from short paleoseismic paleoseismic series. From repeated Monte Carlo draws, it becomes possible to quantitatively estimate most to an overestimate of the hazard should they be used in probability calculations. Therefore a Monte Carlo approach
Monte Carlo Hauser-Feshbach Modeling of Prompt Fission Neutrons and Gamma Rays
Danon, Yaron
Monte Carlo Hauser-Feshbach Modeling of Prompt Fission Neutrons and Gamma Rays Patrick Talou1,a, USA Abstract. The decay of fission fragments is studied through Monte Carlo Hauser-Feshbach model and correlations of quantities for which we knew only about averages. On the theoretical side, Monte Carlo
Zeiri, Yehuda
Monte Carlo simulation of laser induced chemical vapor deposition Yehuda Zeiri, Uzi Atzmony 21 September 1989; accepted for publication 30 November 1990) We have used a Monte Carlo method developed a Monte Carlo procedure which was used to simulate the LICVD process. The beam inten- sities used
MONTE CARLO APPROXIMATIONS OF AMERICAN OPTIONS THAT PRESERVE MONOTONICITY AND CONVEXITY
Paris-Sud XI, UniversitÃ© de
MONTE CARLO APPROXIMATIONS OF AMERICAN OPTIONS THAT PRESERVE MONOTONICITY AND CONVEXITY PIERRE DEL are satisfied. In such a case, all Monte Carlo methods proposed so far in the literature do not preserve Monte Carlo methods were proposed by Boyle (1977) for European options, it seems that the first
Monte Carlo simulation of solid-state thermionic energy conversion devices based on non-planar
Monte Carlo simulation of solid-state thermionic energy conversion devices based on non structures is analyzed using a Monte Carlo electron transport model. Compared to the planar structures, about a chance to pass over the barrier in a triangle region. 2 Monte Carlo Algorithms We used a simplified
Monte Carlo Simulations of Biomolecules: The MC Module AARON R. DINNER1,2,3,4
Dinner, Aaron
Monte Carlo Simulations of Biomolecules: The MC Module in CHARMM JIE HU,1,2 AO MA,1,2 AARON R and flexible Monte Carlo (MC) module for the program CHARMM, which is used widely for modeling biomolecular Wiley Periodicals, Inc. J Comput Chem 27: 203Â216, 2006 Key words: Monte Carlo simulations; biomolecules
Monte Carlo Simulations on Nanoparticles in Elastomers. Effects of the Particles on the
Mark, James E.
Monte Carlo Simulations on Nanoparticles in Elastomers. Effects of the Particles on the Dimensions. Sen,2,3 Andrzej Kloczkowski3 Summary: Reinforcement of elastomers is modeled using Monte Carlo of elastomers; Monte Carlo methods; reinforcing fillers; rotational isomeric state theory Introduction One
MONTE CARLO f SIMULATION OF NEOCLASSICAL PROCESSES IN A TOKAMAK WITH PERTURBED MAGNETIC EQUILIBRIUM
MONTE CARLO f SIMULATION OF NEOCLASSICAL PROCESSES IN A TOKAMAK WITH PERTURBED MAGNETIC EQUILIBRIUM are studied by means of Monte Carlo f simulations. The numerical code follows the motion of the ions in full with the Monte Carlo technique and implemented such that the (parallel) momentum is conserved. ITER and ASDEX Up
Monte Carlo simulations of an amphiphilic polymer at a hydrophobic/hydrophilic interface
Wilson, Mark R.
Monte Carlo simulations of an amphiphilic polymer at a hydrophobic/hydrophilic interface ALINE F of Durham, South Road, Durham DH1 3LE, UK (Received 4 September 2002; accepted 23 October 2002) Monte Carlo described here uses Monte Carlo simula- tions to investigate the polynorborneneÂPEO system of reference [15
Monte Carlo methods for short polypeptides Jeremy Schofield a) and Mark A. Ratner
Schofield, Jeremy
Monte Carlo methods for short polypeptides Jeremy Schofield a) and Mark A. Ratner Department! Nonphysical sampling Monte Carlo techniques that enable average structural properties of short in vacuo polypeptide chains to be calculated accurately are discussed. Updating algorithms developed for Monte Carlo
Monte-Carlo valorisation of American options: facts and new algorithms to improve existing methods
Boyer, Edmond
Monte-Carlo valorisation of American options: facts and new algorithms to improve existing methods is to discuss efficient algorithms for the pricing of American options by two recently proposed Monte-Carlo type the quantization approach, are performed. Key words: American Options, Monte Carlo methods. 1. Introduction
Monte Carlo Simulation of Radiation in Gases with a NarrowBand Model
Dufresne, Jean-Louis
Monte Carlo Simulation of Radiation in Gases with a NarrowÂBand Model and a Net, Germany. published in ASME Journal of Heat Transfer, May 1996, pp.401Â407 Abstract The Monte Carlo method with the Monte Carlo method : numerical efficiency becomes independent of optical thickness, strongly non uniform
A Monte-Carlo game theoretic approach for Multi-Criteria Decision Making under uncertainty
Pasternack, Gregory B.
A Monte-Carlo game theoretic approach for Multi-Criteria Decision Making under uncertainty Kaveh-Criteria Decision Making Game theory Conflict resolution Monte-Carlo Uncertainty Sacramento-San Joaquin Delta a b with the uncertainty in input variables a Monte-Carlo Game Theory (MCGT) approach is sug- gested which maps
Monte Carlo Sampling of Near-Native Structures of Proteins With Applications
Dai, Yang
Monte Carlo Sampling of Near-Native Structures of Proteins With Applications AQ6 Jinfeng Zhang,1 Wiley-Liss, Inc. Key words: near-native structures; sequential Monte Carlo; protein structure simulation dynamics (MD) simulations, Metropolis Monte Carlo,7 the Gaussian net- work or elastic network models,8
Monte Carlo analysis of conformational transitions in superhelical DNA Hongzhi Sun
Benham, Craig J.
Monte Carlo analysis of conformational transitions in superhelical DNA Hongzhi Sun Department August 1995 MetropolisÂMonte Carlo algorithms are developed to analyze the strand separation transition the results of Monte Carlo calculations that use shuffling operations are compared with those from statistical
Monte Carlo Sampling of Near-Native Structures of Proteins With Applications
Liu, Jun
Monte Carlo Sampling of Near-Native Structures of Proteins With Applications Jinfeng Zhang,1 Ming. Key words: near-native structures; sequential Monte Carlo; protein structure simulation; protein) simulations, Metropolis Monte Carlo,7 the Gaussian net- work or elastic network models,8Â10 and chain
Monte Carlo methods designed for parallel computation Sheldon B. Opps and Jeremy Scho eld
Schofield, Jeremy
Monte Carlo methods designed for parallel computation Sheldon B. Opps and Jeremy Scho#12;eld of these methods is that individual Monte Carlo chains, which are run on a separate nodes, are coupled together- rate calculation, for example to improve the statistics of a Monte Carlo simulation, one inherent bene
Monte Carlo simulation of electron transport in degenerate and inhomogeneous semiconductors
Monte Carlo simulation of electron transport in degenerate and inhomogeneous semiconductors Mona exclusion principle in Monte Carlo simulations. This algorithm has significant advantages to implement the scattering rate. The ensemble Monte Carlo MC simulation is accepted as a powerful numerical technique
A Monte Carlo demographic analysis of the silky shark (Carcharhinus falciformis)
168 A Monte Carlo demographic analysis of the silky shark (Carcharhinus falciformis): implications mortality have shown promise for States. Monte Carlo methods are used shark demographic analysis (CortÃ©s that reflect pos poration of Monte Carlo simulation in sible longline gear selectivity for silky demographic
Monte Carlo ray tracing in optical canopy reflectance modelling M. I. Disney1*
Jones, Peter JS
1 Monte Carlo ray tracing in optical canopy reflectance modelling M. I. Disney1* , P. Lewis1 , P. R. J. North2 Abstract This paper reviews the use of Monte Carlo methods in optical canopy reflectance modelling. Their utility, and, more specifically, Monte Carlo ray tracing for the numerical simulation
The impact of Monte Carlo simulation: a scientometric analysis of scholarly literature
Pia, Maria Grazia; Bell, Zane W; Dressendorfer, Paul V
2010-01-01
A scientometric analysis of Monte Carlo simulation and Monte Carlo codes has been performed over a set of representative scholarly journals related to radiation physics. The results of this study are reported and discussed. They document and quantitatively appraise the role of Monte Carlo methods and codes in scientific research and engineering applications.
DOES WASTE-RECYCLING REALLY IMPROVE THE MULTI-PROPOSAL METROPOLIS-HASTINGS MONTE CARLO
Boyer, Edmond
DOES WASTE-RECYCLING REALLY IMPROVE THE MULTI-PROPOSAL METROPOLIS-HASTINGS MONTE CARLO ALGORITHM? JEAN-FRANCÂ¸OIS DELMAS AND BENJAMIN JOURDAIN Abstract. The waste-recycling Monte Carlo (WR) algorithm is measured through the asymptotic variance of the estimator of , f . The waste-recycling Monte Carlo (WR
A Quasi-Monte Carlo Method for Integration with Improved Convergence
Karaivanova, Aneta
A Quasi-Monte Carlo Method for Integration with Improved Convergence Aneta Karaivanova, Ivan Dimov anet@copern.bas.bg, ivdimov@bas.bg, sofia@copern.bas.bg Abstract. Quasi-Monte Carlo methods are based of random numbers with a more uniformly distributed de- terministic sequence. Quasi-Monte Carlo methods
Article type: Opinion Article Why the Monte Carlo Method is so important
Kroese, Dirk P.
Article type: Opinion Article Why the Monte Carlo Method is so important today Article ID Dirk P of Queensland Zdravko I. Botev The University of New South Wales Keywords Monte Carlo method, simulation, MCMC an essential ingredient in many quantitative investigations. Why is the Monte Carlo method (MCM) so important
Bayesian Training of Backpropagation Networks by the Hybrid Monte Carlo Method
Neal, Radford M.
Bayesian Training of Backpropagation Networks by the Hybrid Monte Carlo Method Radford M. Neal of backpropagation neural networks can feasibly be performed by the ``Hybrid Monte Carlo'' method. This approach by a Gaussian. In this work, the Hybrid Monte Carlo method is implemented in conjunction with simulated
An Implicit Monte Carlo Method for Rarefied Gas Dynamics I: The Space Homogeneous Case.
Pareschi, Lorenzo
An Implicit Monte Carlo Method for Rarefied Gas Dynamics I: The Space Homogeneous Case. Lorenzo a hybrid Monte Carlo method that is robust in the fluid dynamic limit. This method is based on an analytic of the new method. Key Words: Boltzmann equation, MonteÂCarlo methods, fluid dyanmic limit, imÂ plicit time
A Parallel Quasi-Monte Carlo Method for Computing Extremal Eigenvalues
Mascagni, Michael
A Parallel Quasi-Monte Carlo Method for Computing Extremal Eigenvalues Michael Mascagni1 and Aneta The convergence of Monte Carlo methods for numerical integration can often be improved by replacing pseudorandom). In this paper the convergence of a Monte Carlo method for evaluating the extremal eigenvalues of a given matrix
A Monte Carlo Method for Obtaining the Null Distribution of Functionindexed Logrank Statistics
Kosorok, Michael R.
A Monte Carlo Method for Obtaining the Null Distribution of Functionindexed Logrank Statistics a Monte Carlo method for accurately obtaining pvalues for the functionindexed statistics described in Kosorok and Lin (1998), Sections 1 through 3, and Kosorok (1998), Section 4. 2. THE MONTE CARLO METHOD Let
A Bayesian Approach to Multiscale Inverse Problems Using Sequential Monte Carlo Method
Zabaras, Nicholas J.
A Bayesian Approach to Multiscale Inverse Problems Using Sequential Monte Carlo Method Nicholas-modal, sequential Monte Carlo method is employed. Materials Process Design and Control Laboratory Cornell University are of high dimension and multi-modal, sequential Monte Carlo method is employed. Materials Process Design
Monte Carlo Method for Calculating the Electrostatic Energy of a Molecule
Mascagni, Michael
Monte Carlo Method for Calculating the Electrostatic Energy of a Molecule Michael Mascagni1 ,2 describing Monte Carlo methods for solving boundary value problems for the heat, Laplace and other diffusion's function first passage Monte Carlo method is the natural extension of WOS. The simulation
A new optimal Monte Carlo method for calculating integrals of smooth functions #
Dimov, Ivan
A new optimal Monte Carlo method for calculating integrals of smooth functions # Emanouil I. Atanassov 1 , Ivan T. Dimov 1 , Abstract An optimal Monte Carlo method for numerical integration of multi#ciency of the algorithms are also given. Keywords: Monte Carlo method, optimal quadrature formula, rate of convergence. ASM
A Quasi-Monte Carlo Method for Elliptic Boundary Value Problems Michael Mascagni
Mascagni, Michael
A Quasi-Monte Carlo Method for Elliptic Boundary Value Problems Michael Mascagni Aneta Karaivanova Yaohang Li Abstract In this paper we present and analyze a quasi-Monte Carlo method for solving elliptic estimate the accuracy and the computational complexity of the quasi-Monte Carlo method. Finally, results
DOES WASTE-RECYCLING REALLY IMPROVE THE MULTI-PROPOSAL METROPOLIS-HASTINGS MONTE CARLO
Recanati, Catherine
DOES WASTE-RECYCLING REALLY IMPROVE THE MULTI-PROPOSAL METROPOLIS-HASTINGS MONTE CARLO ALGORITHM? JEAN-FRANC#24;OIS DELMAS AND BENJAMIN JOURDAIN Abstract. The waste-recycling Monte Carlo (WR) algorithm of the estimator of h#25;; fi. The waste-recycling Monte Carlo (WR) algorithm, introduced by physicists, is a modi
ForPeerReview Lattice Kinetic Monte Carlo modeling of germanium solid
Florida, University of
ForPeerReview Lattice Kinetic Monte Carlo modeling of germanium solid phase epitaxial growth phase epitaxial growth, Semiconductors, Lattice Kinetic Monte Carlo, Germanium Wiley-VCH physica status solidi #12;ForPeerReview physica status solidi Lattice Kinetic Monte Carlo modeling of germanium solid
A Fast Monte Carlo Simulation for the International Linear Collider Detector
Furse, D.; /Georgia Tech
2005-12-15
The following paper contains details concerning the motivation for, implementation and performance of a Java-based fast Monte Carlo simulation for a detector designed to be used in the International Linear Collider. This simulation, presently included in the SLAC ILC group's org.lcsim package, reads in standard model or SUSY events in STDHEP file format, stochastically simulates the blurring in physics measurements caused by intrinsic detector error, and writes out an LCIO format file containing a set of final particles statistically similar to those that would have found by a full Monte Carlo simulation. In addition to the reconstructed particles themselves, descriptions of the calorimeter hit clusters and tracks that these particles would have produced are also included in the LCIO output. These output files can then be put through various analysis codes in order to characterize the effectiveness of a hypothetical detector at extracting relevant physical information about an event. Such a tool is extremely useful in preliminary detector research and development, as full simulations are extremely cumbersome and taxing on processor resources; a fast, efficient Monte Carlo can facilitate and even make possible detector physics studies that would be very impractical with the full simulation by sacrificing what is in many cases inappropriate attention to detail for valuable gains in time required for results.
Land use change prediction of Wuhan City: a Markov-Monte Carlo approach
NASA Astrophysics Data System (ADS)
Xia, Huiqiong; Zheng, Chunyan; Liu, Hai
2013-10-01
Markov model is found to be beneficial in describing and analyzing land cover change process. The probability of transition between each pair of states is recorded as an element of a transition probability matrix, which is the key factor to obtain a higher precision of prediction in Markov model. In this study, a combined use of RS, GIS, Markov stochastic modeling and Monte Carlo simulating techniques are employed in analyzing and prediction land use/cover changes in Wuhan city. The results indicate that the transition probability matrix derived from Monte Carlo experiment is more accurate for land use prediction, and the prediction results of land use change show that there urban growth is has notable, area of forest land continued decreasing, and that the land use/cover change process would be stable in the future. The study demonstrates remote sensing image is an effective data source and statistical information of land use is a valid supplement for land use/land cover research. Integration of these two kinds of data in Markov - Monte Carlo method can adjust the basis of the same observation time when images are not available every year or at a constant time interval in LUCC modeling. Land use/land cover change information from the prediction results will be beneficial in describing, analyzing the change process of land structure in Wuhan city in next 20 years.
Zou, Yonghong; Christensen, Erik R; Zheng, Wei; Wei, Hua; Li, An
2014-11-01
A stochastic process was developed to simulate the stepwise debromination pathways for polybrominated diphenyl ethers (PBDEs). The stochastic process uses an analogue Markov Chain Monte Carlo (AMCMC) algorithm to generate PBDE debromination profiles. The acceptance or rejection of the randomly drawn stepwise debromination reactions was determined by a maximum likelihood function. The experimental observations at certain time points were used as target profiles; therefore, the stochastic processes are capable of presenting the effects of reaction conditions on the selection of debromination pathways. The application of the model is illustrated by adopting the experimental results of decabromodiphenyl ether (BDE209) in hexane exposed to sunlight. Inferences that were not obvious from experimental data were suggested by model simulations. For example, BDE206 has much higher accumulation at the first 30 min of sunlight exposure. By contrast, model simulation suggests that, BDE206 and BDE207 had comparable yields from BDE209. The reason for the higher BDE206 level is that BDE207 has the highest depletion in producing octa products. Compared to a previous version of the stochastic model based on stochastic reaction sequences (SRS), the AMCMC approach was determined to be more efficient and robust. Due to the feature of only requiring experimental observations as input, the AMCMC model is expected to be applicable to a wide range of PBDE debromination processes, e.g. microbial, photolytic, or joint effects in natural environments. PMID:25113201
Monte Carlo simulation of particle acceleration at astrophysical shocks
NASA Astrophysics Data System (ADS)
Campbell, Roy K.
1989-09-01
A Monte Carlo code was developed for the simulation of particle acceleration at astrophysical shocks. The code is implemented in Turbo Pascal on a PC. It is modularized and structured in such a way that modification and maintenance are relatively painless. Monte Carlo simulations of particle acceleration at shocks follow the trajectories of individual particles as they scatter repeatedly across the shock front, gaining energy with each crossing. The particles are assumed to scatter from magnetohydrodynamic (MHD) turbulence on both sides of the shock. A scattering law is used which is related to the assumed form of the turbulence, and the particle and shock parameters. High energy cosmic ray spectra derived from Monte Carlo simulations have observed power law behavior just as the spectra derived from analytic calculations based on a diffusion equation. This high energy behavior is not sensitive to the scattering law used. In contrast with Monte Carlo calculations diffusive calculations rely on the initial injection of supra-thermal particles into the shock environment. Monte Carlo simulations are the only known way to describe the extraction of particles directly from the thermal pool. This was the triumph of the Monte Carlo approach. The question of acceleration efficiency is an important one in the shock acceleration game. The efficiency of shock waves efficient to account for the observed flux of high energy galactic cosmic rays was examined. The efficiency of the acceleration process depends on the thermal particle pick-up and hence the low energy scattering in detail. One of the goals is the self-consistent derivation of the accelerated particle spectra and the MHD turbulence spectra. Presumably the upstream turbulence, which scatters the particles so they can be accelerated, is excited by the streaming accelerated particles and the needed downstream turbulence is convected from the upstream region. The present code is to be modified to include a better description of particle scattering (pitch-angle instead of hard-sphere) and as iterative procedure for treating the self-excitation of the MHD turbulence.
Müller, Florian, E-mail: florian.mueller@sam.math.ethz.ch; Jenny, Patrick, E-mail: jenny@ifd.mavt.ethz.ch; Meyer, Daniel W., E-mail: meyerda@ethz.ch
2013-10-01
Monte Carlo (MC) is a well known method for quantifying uncertainty arising for example in subsurface flow problems. Although robust and easy to implement, MC suffers from slow convergence. Extending MC by means of multigrid techniques yields the multilevel Monte Carlo (MLMC) method. MLMC has proven to greatly accelerate MC for several applications including stochastic ordinary differential equations in finance, elliptic stochastic partial differential equations and also hyperbolic problems. In this study, MLMC is combined with a streamline-based solver to assess uncertain two phase flow and Buckley–Leverett transport in random heterogeneous porous media. The performance of MLMC is compared to MC for a two dimensional reservoir with a multi-point Gaussian logarithmic permeability field. The influence of the variance and the correlation length of the logarithmic permeability on the MLMC performance is studied.
Non-equilibrium Monte Carlo simulation of decaying Navier-Stokes turbulence
NASA Astrophysics Data System (ADS)
Biechele, Peter; Breuer, Heinz-Peter; Petruccione, Francesco
1999-05-01
Recently a master equation for the three-dimensional Navier-Stokes equation in k-space has been proposed. It has been shown, that the Hopf-equation can be derived from the time evolution of the stochastic process given by the master equation. Therefore it reproduces exactly the correct turbulence moment hierarchy. Here we present the results of a Monte Carlo simulation of turbulence in three space dimensions using the proposed master equation. We simulate the underlying stochastic process defined by the master equation by producing realizations and calculating averages. The results of the simulation at a Taylor-Reynolds number R? of about 112 show a -5/3 scaling range for the energy spectrum and the Kolmogorov-constant is about 1.6.