Successful combination of the stochastic linearization and Monte Carlo methods
NASA Technical Reports Server (NTRS)
Elishakoff, I.; Colombi, P.
1993-01-01
A combination of a stochastic linearization and Monte Carlo techniques is presented for the first time in literature. A system with separable nonlinear damping and nonlinear restoring force is considered. The proposed combination of the energy-wise linearization with the Monte Carlo method yields an error under 5 percent, which corresponds to the error reduction associated with the conventional stochastic linearization by a factor of 4.6.
L'Ecuyer, Pierre
, in the context of a geometric Brownian motion model with stochastic volatitity. We consider lookback optionsVARIANCE REDUCTION OF MONTE CARLO AND RANDOMIZED QUASIMONTE CARLO ESTIMATORS FOR STOCHASTIC of the BlackScholes model, with stochastic volatility. These models are believed to describe in a more
Heermann, Dieter W.
Contents 1. Stochastic Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 #12;#12;1. Stochastic Methods This chapter is concerned with methods which use stochastic elements. However, there are also inherently stochastic methods, such as the Monte-Carlo technique. An application
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).
Franke, B. C.; Prinja, A. K.
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)
Longitudinal functional principal component modeling via Stochastic Approximation Monte Carlo
Martinez, Josue G.; Liang, Faming; Zhou, Lan; Carroll, Raymond J.
2010-01-01
The authors consider the analysis of hierarchical longitudinal functional data based upon a functional principal components approach. In contrast to standard frequentist approaches to selecting the number of principal components, the authors do model averaging using a Bayesian formulation. A relatively straightforward reversible jump Markov Chain Monte Carlo formulation has poor mixing properties and in simulated data often becomes trapped at the wrong number of principal components. In order to overcome this, the authors show how to apply Stochastic Approximation Monte Carlo (SAMC) to this problem, a method that has the potential to explore the entire space and does not become trapped in local extrema. The combination of reversible jump methods and SAMC in hierarchical longitudinal functional data is simplified by a polar coordinate representation of the principal components. The approach is easy to implement and does well in simulated data in determining the distribution of the number of principal components, and in terms of its frequentist estimation properties. Empirical applications are also presented. PMID:20689648
Fitting of Stochastic Telecommunication Network Models via Distance Measures and MonteCarlo Tests
Schmidt, Volker
Fitting of Stochastic Telecommunication Network Models via Distance Measures and MonteÂCarlo Tests telecommunication data describing the spatial geometrical structure of an urban region and we propose a modelÂgeometric telecommunication model and a detailed description of the model fitting algorithm, we verify the algorithm by using
Stochastic variability in effective dose tissue weighting factors: A Monte Carlo study
Leslie, W.D.
1994-07-01
Tissue-weighting factors used in the calculation of the effective dose have undergone revision in the light of new data from the atomic bomb survivors. A Monte Carlo simulation was designed to evaluate the magnitude of stochastic errors in the derived factors. Results demonstrate substantial variability in the suggested factors. 19 refs., 2 figs., 4 tabs.
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.
Lecchini-Visintini, A; Maciejowski, J
2009-01-01
We introduce bounds on the finite-time performance of random searches based on Markov chain Monte Carlo methods for approaching the global solution of stochastic optimization problems defined on continuous domains. In contrast to existing results these bounds can be used in practice as rigorous stopping criteria. Our results are inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory. A comparison with other state-of-the art methods having finite-time guarantees for solving stochastic programming problems is included.
NASA Astrophysics Data System (ADS)
Demir, Alper
2004-11-01
Stochastic ordinary and partial differential equations (SOPDEs) in various forms arise and are successfully utilized in the modeling of a variety of physical and engineered systems such as telecommunication systems, electronic circuits, cosmological systems, financial systems, meteorological and climate systems. While the theory of stochastic partial and especially ordinary differential equations is more or less well understood, there has been much less work on practical formulations and computational approaches to solving these equations. In this paper, we concentrate on the stochastic non-linear Schrödinger equation (SNLSE) that arises in the analysis of wave propagation phenomena, mainly motivated by its predominant role as a modeling tool in the design of optically amplified long distance fiber telecommunication systems. We present novel formulations and computational methods for the stochastic characterization of the solution of the SNLSE. Our formulations and techniques are not aimed at computing individual realizations, i.e., sample paths, for the solution of the SNLSE á la Monte Carlo. Instead, starting with the SNLSE, we derive new systems of differential equations and develop associated computational techniques. The numerical solutions of these new equations directly produce the ensemble-averaged stochastic characterization desired for the solution of the SNLSE, in a non-Monte Carlo manner without having to compute many realizations needed for ensemble-averaging.
Brantley, P S
2009-06-30
Particle transport through binary stochastic mixtures has received considerable research attention in the last two decades. Zimmerman and Adams proposed a Monte Carlo algorithm (Algorithm A) that solves the Levermore-Pomraning equations and another Monte Carlo algorithm (Algorithm B) that should be more accurate as a result of improved local material realization modeling. Zimmerman and Adams numerically confirmed these aspects of the Monte Carlo algorithms by comparing the reflection and transmission values computed using these algorithms to a standard suite of planar geometry binary stochastic mixture benchmark transport solutions. The benchmark transport problems are driven by an isotropic angular flux incident on one boundary of a binary Markovian statistical planar geometry medium. In a recent paper, we extended the benchmark comparisons of these Monte Carlo algorithms to include the scalar flux distributions produced. This comparison is important, because as demonstrated, an approximate model that gives accurate reflection and transmission probabilities can produce unphysical scalar flux distributions. Brantley and Palmer recently investigated the accuracy of the Levermore-Pomraning model using a new interior source binary stochastic medium benchmark problem suite. In this paper, we further investigate the accuracy of the Monte Carlo algorithms proposed by Zimmerman and Adams by comparing to the benchmark results from the interior source binary stochastic medium benchmark suite, including scalar flux distributions. Because the interior source scalar flux distributions are of an inherently different character than the distributions obtained for the incident angular flux benchmark problems, the present benchmark comparison extends the domain of problems for which the accuracy of these Monte Carlo algorithms has been investigated.
of protons and on interaction with an external static electric field. The polarization decay and response and with predictions of a microscopic ``bound charge carrier'' model. Studying the proton dynamics by a field coolingMonte Carlo stochastic-dynamics study of dielectric response and nonergodicity in proton glass
ERIC Educational Resources Information Center
Gold, Michael Steven; Bentler, Peter M.
2000-01-01
Describes a Monte Carlo investigation of four methods for treating incomplete data: (1) resemblance based hot-deck imputation (RBHDI); (2) iterated stochastic regression imputation; (3) structured model expectation maximization; and (4) saturated model expectation maximization. Results favored the expectation maximization methods. (SLD)
Monte Carlo simulations of H2 formation on stochastically heated grains
H. M. Cuppen; O. Morata; Eric Herbst
2006-01-24
Continuous-time, random-walk Monte Carlo simulations of H2 formation on grains have been performed for surfaces that are stochastically heated by photons. We have assumed diffuse cloud conditions and used a variety of grains of varying roughness and size based on olivine. The simulations were performed at different optical depths. We confirmed that small grains (r formation of molecular hydrogen. The grain size distribution highly favours small grains and therefore H2 formation on these particles makes a large contribution to the overall formation rate for all but the roughest surfaces. We find that at A_V=0 only the roughest surfaces can produce the required amount of molecular hydrogen, but by A_V=1, smoother surfaces are possible alternatives. Use of a larger value for the evaporation energy of atomic hydrogen, but one still consistent with experiment, allows smoother surfaces to produce more H2.
Combining Stochastics and Analytics for a Fast Monte Carlo Decay Chain Generator
Kareem Kazkaz; Nick Walsh
2011-04-14
Various Monte Carlo programs, developed either by small groups or widely available, have been used to calculate the effects of decays of radioactive chains, from the original parent nucleus to the final stable isotopes. These chains include uranium, thorium, radon, and others, and generally have long-lived parent nuclei. Generating decays within these chains requires a certain amount of computing overhead related to simulating unnecessary decays, time-ordering the final results in post-processing, or both. We present a combination analytic/stochastic algorithm for creating a time-ordered set of decays with position and time correlations, and starting with an arbitrary source age. Thus the simulation costs are greatly reduced, while at the same time avoiding chronological post-processing. We discuss optimization methods within the approach to minimize calculation time.
A Monte Carlo simulation based inverse propagation method for stochastic model updating
NASA Astrophysics Data System (ADS)
Bao, Nuo; Wang, Chunjie
2015-08-01
This paper presents an efficient stochastic model updating method based on statistical theory. Significant parameters have been selected implementing the F-test evaluation and design of experiments, and then the incomplete fourth-order polynomial response surface model (RSM) has been developed. Exploiting of the RSM combined with Monte Carlo simulation (MCS), reduces the calculation amount and the rapid random sampling becomes possible. The inverse uncertainty propagation is given by the equally weighted sum of mean and covariance matrix objective functions. The mean and covariance of parameters are estimated synchronously by minimizing the weighted objective function through hybrid of particle-swarm and Nelder-Mead simplex optimization method, thus the better correlation between simulation and test is achieved. Numerical examples of a three degree-of-freedom mass-spring system under different conditions and GARTEUR assembly structure validated the feasibility and effectiveness of the proposed method.
Stochastic Monte-Carlo Markov Chain Inversions on Models Regionalized Using Receiver Functions
NASA Astrophysics Data System (ADS)
Larmat, C. S.; Maceira, M.; Kato, Y.; Bodin, T.; Calo, M.; Romanowicz, B. A.; Chai, C.; Ammon, C. J.
2014-12-01
There is currently a strong interest in stochastic approaches to seismic modeling - versus deterministic methods such as gradient methods - due to the ability of these methods to better deal with highly non-linear problems. Another advantage of stochastic methods is that they allow the estimation of the a posteriori probability distribution of the derived parameters, meaning the envisioned Bayesian inversion of Tarantola allowing the quantification of the solution error. The cost to pay of stochastic methods is that they require testing thousands of variations of each unknown parameter and their associated weights to ensure reliable probabilistic inferences. Even with the best High-Performance Computing resources available, 3D stochastic full waveform modeling at the regional scale still remains out-of-reach. We are exploring regionalization as one way to reduce the dimension of the parameter space, allowing the identification of areas in the models that can be treated as one block in a subsequent stochastic inversion. Regionalization is classically performed through the identification of tectonic or structural elements. Lekic & Romanowicz (2011) proposed a new approach with a cluster analysis of the tomographic velocity models instead. Here we present the results of a clustering analysis on the P-wave receiver-functions used in the subsequent inversion. Different clustering algorithms and quality of clustering are tested for different datasets of North America and China. Preliminary results with the kmean clustering algorithm show that an interpolated receiver function wavefield (Chai et al., GRL, in review) improve the agreement with the geological and tectonic regions of North America compared to the traditional approach of stacked receiver functions. After regionalization, 1D profile for each region is stochastically inferred using a parallelized code based on Monte-Carlo Markov Chains (MCMC), and modeling surfacewave-dispersion and receiver-functions observations. The parameters of the inversion are the elastic properties, the thickness and the number of isotropic layers. We will present preliminary results and compare them to results obtained from a different regionalizationbased on a tomographic model (Calo et al., 2013).
Practical Markov Chain Monte Carlo
Charles J. Geyer
1992-01-01
Markov chain Monte Carlo using the Metropolis-Hastings algorithm is a general method for the simulation of stochastic processes having probability densities known up to a constant of proportionality. Despite recent advances in its theory, the practice has remained controversial. This article makes the case for basing all inference on one long run of the Markov chain and estimating the Monte
Monte Carlo methods on advanced computer architectures
Martin, W.R. [Univ. of Michigan, Ann Arbor, MI (United States)
1991-12-31
Monte Carlo methods describe a wide class of computational methods that utilize random numbers to perform a statistical simulation of a physical problem, which itself need not be a stochastic process. For example, Monte Carlo can be used to evaluate definite integrals, which are not stochastic processes, or may be used to simulate the transport of electrons in a space vehicle, which is a stochastic process. The name Monte Carlo came about during the Manhattan Project to describe the new mathematical methods being developed which had some similarity to the games of chance played in the casinos of Monte Carlo. Particle transport Monte Carlo is just one application of Monte Carlo methods, and will be the subject of this review paper. Other applications of Monte Carlo, such as reliability studies, classical queueing theory, molecular structure, the study of phase transitions, or quantum chromodynamics calculations for basic research in particle physics, are not included in this review. The reference by Kalos is an introduction to general Monte Carlo methods and references to other applications of Monte Carlo can be found in this excellent book. For the remainder of this paper, the term Monte Carlo will be synonymous to particle transport Monte Carlo, unless otherwise noted. 60 refs., 14 figs., 4 tabs.
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.
Assaraf, Roland; Caffarel, Michel; Kollias, A C
2011-04-15
We present a method to efficiently evaluate small energy differences of two close N-body systems by employing stochastic processes having a stability versus chaos property. By using the same random noise, energy differences are computed from close trajectories without reweighting procedures. The approach is presented for quantum systems but can be applied to classical N-body systems as well. It is exemplified with diffusion Monte Carlo simulations for long chains of hydrogen atoms and molecules for which it is shown that the long-standing problem of computing energy derivatives is solved. PMID:21568537
Stochastic method for accommodation of equilibrating basins in kinetic Monte Carlo simulations.
Siclen, Clinton Dew Van
2007-02-21
A computationally simple way to accommodate 'basins' of trapping states in standard kinetic Monte Carlo simulations is presented. By assuming that the system is effectively equilibrated in the basin, the residence time (time spent in the basin before escape) and the probabilities for transitions to states outside the basin may be calculated. This is demonstrated for point defect diffusion over a periodic grid of sites containing a complex basin. PMID:22251579
Stochastic method for accommodation of equilibrating basins in kinetic Monte Carlo simulations
Van Siclen, Clinton D
2007-02-01
A computationally simple way to accommodate "basins" of trapping states in standard kinetic Monte Carlo simulations is presented. By assuming the system is effectively equilibrated in the basin, the residence time (time spent in the basin before escape) and the probabilities for transition to states outside the basin may be calculated. This is demonstrated for point defect diffusion over a periodic grid of sites containing a complex basin.
Ceperley, D; Alder, B
1986-02-01
An outline of a random walk computational method for solving the Schrödinger equation for many interacting particles is given, together with a survey of results achieved so far and of applications that remain to be explored. Monte Carlo simulations can be used to calculate accurately the bulk properties of the light elements hydrogen, helium, and lithium as well as the properties of the isolated atoms and of molecules made up from these elements. It is now possible to make reliable predictions of the behavior of these substances under experimentally difficult conditions, such as high pressure, and of properties that are difficult to measure experimentally, such as the momentum distribution in superfluid helium. For chemical systems, the stochastic method has a number of advantages over the widely used variational approach to determine ground-state properties, namely fast convergence to the exact result within objectively established error bounds. PMID:17750966
NASA Astrophysics Data System (ADS)
Jin, Shengye; Tamura, Masayuki
2013-10-01
Monte Carlo Ray Tracing (MCRT) method is a versatile application for simulating radiative transfer regime of the Solar - Atmosphere - Landscape system. Moreover, it can be used to compute the radiation distribution over a complex landscape configuration, as an example like a forest area. Due to its robustness to the complexity of the 3-D scene altering, MCRT method is also employed for simulating canopy radiative transfer regime as the validation source of other radiative transfer models. In MCRT modeling within vegetation, one basic step is the canopy scene set up. 3-D scanning application was used for representing canopy structure as accurately as possible, but it is time consuming. Botanical growth function can be used to model the single tree growth, but cannot be used to express the impaction among trees. L-System is also a functional controlled tree growth simulation model, but it costs large computing memory. Additionally, it only models the current tree patterns rather than tree growth during we simulate the radiative transfer regime. Therefore, it is much more constructive to use regular solid pattern like ellipsoidal, cone, cylinder etc. to indicate single canopy. Considering the allelopathy phenomenon in some open forest optical images, each tree in its own `domain' repels other trees. According to this assumption a stochastic circle packing algorithm is developed to generate the 3-D canopy scene in this study. The canopy coverage (%) and the tree amount (N) of the 3-D scene are declared at first, similar to the random open forest image. Accordingly, we randomly generate each canopy radius (rc). Then we set the circle central coordinate on XY-plane as well as to keep circles separate from each other by the circle packing algorithm. To model the individual tree, we employ the Ishikawa's tree growth regressive model to set the tree parameters including DBH (dt), tree height (H). However, the relationship between canopy height (Hc) and trunk height (Ht) is unclear to us. We assume the proportion between Hc and Ht as a random number in the interval from 2.0 to 3.0. De Wit's sphere leaf angle distribution function was used within the canopy for acceleration. Finally, we simulate the open forest albedo using MCRT method. The MCRT algorithm of this study is summarized as follows (1) Initialize the photon with a position (r0), source direction (?0) and intensity (I0), respectively. (2) Simulate the free path (s) of a photon under the condition of (r', ?, I') in the canopy. (3) Calculate the new position of the photon r=r +s?'. (4) Determine the new scattering direction (?)after collision at, r and then calculate the new intensity I = ?L(?L,?'-->?)I'.(5) Accumulate the intensity I of a photon escaping from the top boundary of the 3-D Scene, otherwise redo from step (2), until I is smaller than a threshold. (6) Repeat from step (1), for each photon. We testify the model on four different simulated open forests and the effectiveness of the model is demonstrated in details.
D. D. Ferrante; J. Doll; G. S. Guralnik; D. Sabo
2002-09-04
Using a common technique for approximating distributions [generalized functions], we are able to use standard Monte Carlo methods to compute QFT quantities in Minkowski spacetime, under phase transitions, or when dealing with coalescing stationary points.
Subhadip Raychaudhuri; Eric Willgohs; Thuc-Nghi Nguyen; Elaine M. Khan; Tzipora Goldkorn
2008-01-01
Apoptosis, or genetically programmed cell death, is a crucial cellular process that maintains the balance between life and death in cells. The precise molecular mechanism of apoptosis signaling and the manner in which type 1 and type 2 pathways of the apoptosis signaling network are differentially activated under distinct apoptotic stimuli is poorly understood. Based on Monte Carlo stochastic simulations,
Semistochastic Projector Monte Carlo Method
NASA Astrophysics Data System (ADS)
Petruzielo, F. R.; Holmes, A. A.; Changlani, Hitesh J.; Nightingale, M. P.; Umrigar, C. J.
2012-12-01
We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially stochastically with respect to expectation values only. Compared to a fully stochastic method, the semistochastic approach significantly reduces the computational time required to obtain the eigenvalue to a specified statistical uncertainty. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem: the fermion Hubbard model and the carbon dimer.
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.
Comparative Monte Carlo efficiency by Monte Carlo analysis
NASA Astrophysics Data System (ADS)
Rubenstein, B. M.; Gubernatis, J. E.; Doll, J. D.
2010-09-01
We propose a modified power method for computing the subdominant eigenvalue ?2 of a matrix or continuous operator. While useful both deterministically and stochastically, we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers of mixed signs to represent the subdominant eigenfunction. Accordingly, the methods must cancel these signs properly in order to sample this eigenfunction faithfully. We present a simple procedure to solve this sign problem and then test our Monte Carlo methods by computing ?2 of various Markov chain transition matrices. As |?2| of this matrix controls the rate at which Monte Carlo sampling relaxes to a stationary condition, its computation also enabled us to compare efficiencies of several Monte Carlo algorithms as applied to two quite different types of problems. We first computed ?2 for several one- and two-dimensional Ising models, which have a discrete phase space, and compared the relative efficiencies of the Metropolis and heat-bath algorithms as functions of temperature and applied magnetic field. Next, we computed ?2 for a model of an interacting gas trapped by a harmonic potential, which has a mutidimensional continuous phase space, and studied the efficiency of the Metropolis algorithm as a function of temperature and the maximum allowable step size ? . Based on the ?2 criterion, we found for the Ising models that small lattices appear to give an adequate picture of comparative efficiency and that the heat-bath algorithm is more efficient than the Metropolis algorithm only at low temperatures where both algorithms are inefficient. For the harmonic trap problem, we found that the traditional rule of thumb of adjusting ? so that the Metropolis acceptance rate is around 50% is often suboptimal. In general, as a function of temperature or ? , ?2 for this model displayed trends defining optimal efficiency that the acceptance ratio does not. The cases studied also suggested that Monte Carlo simulations for a continuum model are likely more efficient than those for a discretized version of the model.
Markov Chain Monte Carlo Methods Markov Chain Monte Carlo Methods
Robert, Christian P.
Markov Chain Monte Carlo Methods Markov Chain Monte Carlo Methods Christian P. Robert Universit´e Paris-Dauphine, IuF, & CRESt http://www.ceremade.dauphine.fr/~xian October 16, 2013 #12;Markov Chain 2011] #12;Markov Chain Monte Carlo Methods Outline Motivations, Random Variable Generation Chapters 1
ON SEQUENTIAL MONTE CARLO SAMPLING OF DISCRETELY OBSERVED STOCHASTIC DIFFERENTIAL EQUATIONS
Del Moral , Pierre
importance resampling (i.e., particle filtering) are presented. The methods are based on transformations, that is, the Radon-Nikodym derivative of the measure of the stochastic process with respect to the measure particle systems [11], which are particle based solutions to nonlinear filtering problems also in the con
Comparative Monte Carlo efficiency by Monte Carlo analysis.
Rubenstein, B M; Gubernatis, J E; Doll, J D
2010-09-01
We propose a modified power method for computing the subdominant eigenvalue ?{2} of a matrix or continuous operator. While useful both deterministically and stochastically, we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers of mixed signs to represent the subdominant eigenfunction. Accordingly, the methods must cancel these signs properly in order to sample this eigenfunction faithfully. We present a simple procedure to solve this sign problem and then test our Monte Carlo methods by computing ?{2} of various Markov chain transition matrices. As |?{2}| of this matrix controls the rate at which Monte Carlo sampling relaxes to a stationary condition, its computation also enabled us to compare efficiencies of several Monte Carlo algorithms as applied to two quite different types of problems. We first computed ?{2} for several one- and two-dimensional Ising models, which have a discrete phase space, and compared the relative efficiencies of the Metropolis and heat-bath algorithms as functions of temperature and applied magnetic field. Next, we computed ?{2} for a model of an interacting gas trapped by a harmonic potential, which has a mutidimensional continuous phase space, and studied the efficiency of the Metropolis algorithm as a function of temperature and the maximum allowable step size ?. Based on the ?{2} criterion, we found for the Ising models that small lattices appear to give an adequate picture of comparative efficiency and that the heat-bath algorithm is more efficient than the Metropolis algorithm only at low temperatures where both algorithms are inefficient. For the harmonic trap problem, we found that the traditional rule of thumb of adjusting ? so that the Metropolis acceptance rate is around 50% is often suboptimal. In general, as a function of temperature or ? , ?{2} for this model displayed trends defining optimal efficiency that the acceptance ratio does not. The cases studied also suggested that Monte Carlo simulations for a continuum model are likely more efficient than those for a discretized version of the model. PMID:21230207
Markov Chain Monte Carlo Methods Markov Chain Monte Carlo Methods
Robert, Christian P.
Markov Chain Monte Carlo Methods Markov Chain Monte Carlo Methods Christian P. Robert Universit´e Paris Dauphine and CREST-INSEE http://www.ceremade.dauphine.fr/~xian 3-6 Mayo 2005 #12;Markov Chain Integration Notions on Markov Chains The Metropolis-Hastings Algorithm The Gibbs Sampler MCMC tools
Parallel Markov chain Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Ren, Ruichao; Orkoulas, G.
2007-06-01
With strict detailed balance, parallel Monte Carlo simulation through domain decomposition cannot be validated with conventional Markov chain theory, which describes an intrinsically serial stochastic process. In this work, the parallel version of Markov chain theory and its role in accelerating Monte Carlo simulations via cluster computing is explored. It is shown that sequential updating is the key to improving efficiency in parallel simulations through domain decomposition. A parallel scheme is proposed to reduce interprocessor communication or synchronization, which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time for systems of moderate and large size.
Marcus, Ryan C.
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.
Markov Chain Monte Carlo Usher's Algorithm
Bremen, UniversitÃ¤t
Concepts Markov Chain Monte Carlo Usher's Algorithm Markov Chain Monte Carlo for Parameter Optimization Holger Schultheis 18.11.2013 1 / 27 #12;Concepts Markov Chain Monte Carlo Usher's Algorithm Topics 1 Concepts 2 Markov Chain Monte Carlo Basics Example Metropolis and Simulated Annealing 3 Usher
Markov Chain Monte Carlo Usher's Algorithm
Bremen, UniversitÃ¤t
Concepts Markov Chain Monte Carlo Usher's Algorithm Markov Chain Monte Carlo for Parameter Optimization Holger Schultheis 19.11.2012 1 / 27 #12;Concepts Markov Chain Monte Carlo Usher's Algorithm Topics 1 Concepts 2 Markov Chain Monte Carlo Basics Example Metropolis and Simulated Annealing 3 Usher
1 Simulation Monte Carlo methods
Verschelde, Jan
Outline 1 Simulation Monte Carlo methods random numbers 2 Repeat Until binary expansion break Intro to Computer Science (MCS 260) running simulations L-12 9 February 2015 1 / 30 #12;Simulation Monte. Simulation consists in the repeated drawing of samples according to a probability distribution. We count
Monte Carlo reconstruction of the inflationary potential
Richard Easther; William H. Kinney
2002-11-07
We present Monte Carlo reconstruction, a new method for ``inverting'' observational data to constrain the form of the scalar field potential responsible for inflation. This stochastic technique is based on the flow equation formalism and has distinct advantages over reconstruction methods based on a Taylor expansion of the potential. The primary ansatz required for Monte Carlo reconstruction is simply that inflation is driven by a single scalar field. We also require a very mild slow roll constraint, which can be made arbitrarily weak since Monte Carlo reconstruction is implemented at arbitrary order in the slow roll expansion. While our method cannot evade fundamental limits on the accuracy of reconstruction, it can be simply and consistently applied to poor data sets, and it takes advantage of the attractor properties of single-field inflation models to constrain the potential outside the small region directly probed by observations. We show examples of Monte Carlo reconstruction for data sets similar to that expected from the Planck satellite, and for a hypothetical measurement with a factor of five better parameter discrimination than Planck.
Monte Carlo integration on GPU
J. Kanzaki
2010-10-11
We use a graphics processing unit (GPU) for fast computations of Monte Carlo integrations. Two widely used Monte Carlo integration programs, VEGAS and BASES, are parallelized on GPU. By using $W^{+}$ plus multi-gluon production processes at LHC, we test integrated cross sections and execution time for programs in FORTRAN and C on CPU and those on GPU. Integrated results agree with each other within statistical errors. Execution time of programs on GPU run about 50 times faster than those in C, and more than 60 times faster than the original FORTRAN programs.
Proton Upset Monte Carlo Simulation
NASA Technical Reports Server (NTRS)
O'Neill, Patrick M.; Kouba, Coy K.; Foster, Charles C.
2009-01-01
The Proton Upset Monte Carlo Simulation (PROPSET) program calculates the frequency of on-orbit upsets in computer chips (for given orbits such as Low Earth Orbit, Lunar Orbit, and the like) from proton bombardment based on the results of heavy ion testing alone. The software simulates the bombardment of modern microelectronic components (computer chips) with high-energy (.200 MeV) protons. The nuclear interaction of the proton with the silicon of the chip is modeled and nuclear fragments from this interaction are tracked using Monte Carlo techniques to produce statistically accurate predictions.
33. Monte Carlo techniques 1 33. MONTE CARLO TECHNIQUES
Masci, Frank
distribution function F(x). For a discrete distribution, F(x) will have a discontinuous jump of size f distribution Most Monte Carlo sampling or integration techniques assume a "random number generator," which - distribution function (expressing the probability that x a) is given by Eq
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
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.
Monte Carlo Integration with Subtraction
Rudy Arthur; A. D. Kennedy
2012-09-04
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 \\chi-squared 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.
NSDL National Science Digital Library
McGath, Gary
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.
Markov Chain Monte Carlo and Gibbs Sampling
Walsh, Bruce
Appendix 3 Markov Chain Monte Carlo and Gibbs Sampling Far better an approximate answer development of Markov Chain Monte Carlo (MCMC) meth uses the previous sample value to randomly generate the next sample value, generating a Markov chain
Optimizing Efficiency of Perturbative Monte Carlo Method
Truong, Thanh N.
-- --Method TOM J. EVANS, THANH N. TRUONG 1998 ABSTRACT: We introduce error weighting functions into the perturbative Monte Carlo method for use andror MM regions. 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1632 1638, 1998 Keywords: Monte Carlo
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.
Krylov-Projected Quantum Monte Carlo Method
NASA Astrophysics Data System (ADS)
Blunt, N. S.; Alavi, Ali; Booth, George H.
2015-07-01
We present an approach to the calculation of arbitrary spectral, thermal, and excited state properties within the full configuration interaction quzantum Monte Carlo framework. This is achieved via an unbiased projection of the Hamiltonian eigenvalue problem into a space of stochastically sampled Krylov vectors, thus, enabling the calculation of real-frequency spectral and thermal properties and avoiding explicit analytic continuation. We use this approach to calculate temperature-dependent properties and one- and two-body spectral functions for various Hubbard models, as well as isolated excited states in ab initio systems.
Efficient Monte Carlo sampling by parallel marginalization
Weare, Jonathan
2007-01-01
Markov chain Monte Carlo sampling methods often suffer from long correlation times. Consequently, these methods must be run for many steps to generate an independent sample. In this paper, a method is proposed to overcome this difficulty. The method utilizes information from rapidly equilibrating coarse Markov chains that sample marginal distributions of the full system. This is accomplished through exchanges between the full chain and the auxiliary coarse chains. Results of numerical tests on the bridge sampling and filtering/smoothing problems for a stochastic differential equation are presented. PMID:17640896
Quantum Monte Carlo with short directed loops
NASA Astrophysics Data System (ADS)
Kao, Ying-Jer
2007-03-01
We introduce a new type of directed loop algorithm with short-loop generation for the stochastic series expansion quantum Monte Carlo method[1]. Short-loop algorithms have been shown to greatly improve the dynamics at low temperature in studies of classical spin ice models[2]. We will discuss the framework of this algorithm and make comparisons to the conventional directed loop algorithm in a specific quantum spin model. [1]O.Suljuasen and A. W. Sandvik, Phys. Rev. E66, 046701 (2002). [2]R. Melko et al., Phys. Rev. Lett. 87, 067203 (2001).
Markov Chain Monte Carlo Usher's Algorithm
Bremen, UniversitÃ¤t
Metropolis & SA Markov Chain Properties irreducibility: i, j , k such that p (k) ij > 0 at each pointConcepts Markov Chain Monte Carlo Usher's Algorithm Markov Chain Monte Carlo for Parameter Optimization Holger Schultheis 04.11.2014 1 / 27 #12;Concepts Markov Chain Monte Carlo Usher's Algorithm Topics
MARKOV CHAIN MONTE CARLO MATTHEW JOSEPH
May, J. Peter
MARKOV CHAIN MONTE CARLO MATTHEW JOSEPH Abstract. Markov chain Monte Carlo is an umbrella term for algorithms that use Markov chains to sample from a given probability distribution. This paper is a brief examination of Markov chain Monte Carlo and its usage. We begin by discussing Markov chains and the ergodicity
Monte Carlo Experiments: Design and Implementation.
ERIC Educational Resources Information Center
Paxton, Pamela; Curran, Patrick J.; Bollen, Kenneth A.; Kirby, Jim; Chen, Feinian
2001-01-01
Illustrates the design and planning of Monte Carlo simulations, presenting nine steps in planning and performing a Monte Carlo analysis from developing a theoretically derived question of interest through summarizing the results. Uses a Monte Carlo simulation to illustrate many of the relevant points. (SLD)
Comparative Monte Carlo Efficiency by Monte Carlo Analysis
Rubenstein, B M; Doll, J D
2010-01-01
We propose a modified power method for computing the subdominant eigenvalue $\\lambda_2$ of a matrix or continuous operator. Here we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers of mixed signs to represent the subdominant eigenfuction. Accordingly, the methods must cancel these signs properly in order to sample this eigenfunction faithfully. We present a simple procedure to solve this sign problem and then test our Monte Carlo methods by computing the $\\lambda_2$ of various Markov chain transition matrices. We first computed ${\\lambda_2}$ for several one and two dimensional Ising models, which have a discrete phase space, and compared the relative efficiencies of the Metropolis and heat-bath algorithms as a function of temperature and applied magnetic field. Next, we computed $\\lambda_2$ for a model of an interacting gas trapped by a harmonic potential, which has a mutidimensional continuous phase space, and studied the efficiency of the Metropolis ...
Danon, Yaron
in the literature because of its relative simplicity and applicability to a number of physical problems-phase coolant, or fractured geological material.5 The statistical nature of the geometry of a stochastic mixture stochastic mixture with Markovian mixing statistics. Markovian mixing statistics are defined by P~i r j! ds
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.
An Introduction to Multilevel Monte Carlo for Option Valuation
Higham, Desmond J
2015-01-01
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation. In 2008, Giles proposed a remarkable improvement to the approach of discretizing with a numerical method and applying standard Monte Carlo. His multilevel Monte Carlo method offers an order of speed up given by the inverse of epsilon, where epsilon is the required accuracy. So computations can run 100 times more quickly when two digits of accuracy are required. The multilevel philosophy has since been adopted by a range of researchers and a wealth of practically significant results has arisen, most of which have yet to make their way into the expository literature. In this work, we give a brief, accessible, introduction to multilevel Monte Carlo and summarize recent results applicable to the task of option evaluation.
Present status of vectorized Monte Carlo
Brown, F.B.
1987-01-01
Monte Carlo applications have traditionally been limited by the large amounts of computer time required to produce acceptably small statistical uncertainties, so the immediate benefit of vectorization is an increase in either the number of jobs completed or the number of particles processed per job, typically by one order of magnitude or more. This results directly in improved engineering design analyses, since Monte Carlo methods are used as standards for correcting more approximate methods. The relatively small number of vectorized programs is a consequence of the newness of vectorized Monte Carlo, the difficulties of nonportability, and the very large development effort required to rewrite or restructure Monte Carlo codes for vectorization. Based on the successful efforts to date, it may be concluded that Monte Carlo vectorization will spread to increasing numbers of codes and applications. The possibility of multitasking provides even further motivation for vectorizing Monte Carlo, since the step from vector to multitasked vector is relatively straightforward.
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.
Dimensional reduction by Monte Carlo
NASA Astrophysics Data System (ADS)
Callaway, David J. E.; Petronzio, Roberto
1984-12-01
A Monte Carlo method for mapping a field theoretical or statistical system to a new theory embedded in a space-time of lesser dimensionality is presented. Typically, the critical properties of the dimensionally reduced system depend upon the details of the mapping. As an example, the two-dimensional Ising model is mapped to a one-dimensional Ising model with long-range forces and a phase transition. Systems with long-range interactions and known exponents can thus be constructed with this procedure.
NSDL National Science Digital Library
AMPS GK-12 Program,
At its core, the LEGO® MINDSTORMS® NXT product provides a programmable microprocessor. Students use the NXT processor to simulate an experiment involving thousands of uniformly random points placed within a unit square. Using the underlying geometry of the experimental model, as well as the geometric definition of the constant ? (pi), students form an empirical ratio of areas to estimate a numerical value of ?. Although typically used for numerical integration of irregular shapes, in this activity, students use a Monte Carlo simulation to estimate a common but rather complex analytical form—the numerical value of the most famous irrational number, ?.
Monte Carlo approach to turbulence
P. Düben; D. Homeier; K. Jansen; D. Mesterhazy; G. Münster
2009-11-03
The behavior of the one-dimensional random-force-driven Burgers equation is investigated in the path integral formalism on a discrete space-time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as structure functions, as ensemble averages over different field realizations. The regularization of shock solutions to the zero-viscosity limit (Hopf-equation) eventually leads to constraints on lattice parameters required for the stability of the simulations. Insight into the formation of localized structures (shocks) and their dynamics is obtained.
NASA Technical Reports Server (NTRS)
Parrish, R. V.; Dieudonne, J. E.; Filippas, T. A.
1971-01-01
An algorithm employing a modified sequential random perturbation, or creeping random search, was applied to the problem of optimizing the parameters of a high-energy beam transport system. The stochastic solution of the mathematical model for first-order magnetic-field expansion allows the inclusion of state-variable constraints, and the inclusion of parameter constraints allowed by the method of algorithm application eliminates the possibility of infeasible solutions. The mathematical model and the algorithm were programmed for a real-time simulation facility; thus, two important features are provided to the beam designer: (1) a strong degree of man-machine communication (even to the extent of bypassing the algorithm and applying analog-matching techniques), and (2) extensive graphics for displaying information concerning both algorithm operation and transport-system behavior. Chromatic aberration was also included in the mathematical model and in the optimization process. Results presented show this method as yielding better solutions (in terms of resolutions) to the particular problem than those of a standard analog program as well as demonstrating flexibility, in terms of elements, constraints, and chromatic aberration, allowed by user interaction with both the algorithm and the stochastic model. Example of slit usage and a limited comparison of predicted results and actual results obtained with a 600 MeV cyclotron are given.
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.
Tom Kennedy
2003-02-05
Simulations of the self-avoiding walk (SAW) are performed in a half-plane and a cut-plane (the complex plane with the positive real axis removed) using the pivot algorithm. We test the conjecture of Lawler, Schramm and Werner that the scaling limit of the two-dimensional SAW is given by Schramm's Stochastic Loewner Evolution (SLE). The agreement is found to be excellent. The simulations also test the conformal invariance of the SAW since conformal invariance would imply that if we map the walks in the cut-plane into the half plane using the conformal map z -> sqrt(z), then the resulting walks will have the same distribution as the SAW in the half plane. The simulations show excellent agreement between the distributions.
Monte Carlo surface flux tallies
Favorite, Jeffrey A
2010-11-19
Particle fluxes on surfaces are difficult to calculate with Monte Carlo codes because the score requires a division by the surface-crossing angle cosine, and grazing angles lead to inaccuracies. We revisit the standard practice of dividing by half of a cosine 'cutoff' for particles whose surface-crossing cosines are below the cutoff. The theory behind this approximation is sound, but the application of the theory to all possible situations does not account for two implicit assumptions: (1) the grazing band must be symmetric about 0, and (2) a single linear expansion for the angular flux must be applied in the entire grazing band. These assumptions are violated in common circumstances; for example, for separate in-going and out-going flux tallies on internal surfaces, and for out-going flux tallies on external surfaces. In some situations, dividing by two-thirds of the cosine cutoff is more appropriate. If users were able to control both the cosine cutoff and the substitute value, they could use these parameters to make accurate surface flux tallies. The procedure is demonstrated in a test problem in which Monte Carlo surface fluxes in cosine bins are converted to angular fluxes and compared with the results of a discrete ordinates calculation.
Bilinear diffusion quantum Monte Carlo methods
NASA Astrophysics Data System (ADS)
Arias de Saavedra, F.; Kalos, M. H.
2003-02-01
The standard method of quantum Monte Carlo for the solution of the Schrödinger equation in configuration space can be described quite generally as devising a random walk that generates—at least asymptotically—populations of random walkers whose probability density is proportional to the wave function of the system being studied. While, in principle, the energy eigenvalue of the Hamiltonian can be calculated with high accuracy, estimators of operators that do not commute the Hamiltonian cannot. Bilinear quantum Monte Carlo (BQMC) is an alternative in which the square of the wave function is sampled in a somewhat indirect way. More specifically, one uses a pair of walkers at positions x and y and introduces stochastic dynamics to sample ?i(x)t(x,y)?j(y), where ?i(x) and ?j(y) are eigenfunctions of (possibly different) Hamiltonians, and t(x,y) is a kernel that correlates positions x and y. Using different Hamiltonians permits the accurate computation of small energy differences. We review the conceptual basis of BQMC, discuss qualitatively and analytically the problem of the fluctuations in the branching, and present partial solutions to that problem. Finally we exhibit numerical results for some model systems including harmonic oscillators and the hydrogen and helium atoms. Further research will be necessary to make this a practical and generally applicable scheme.
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.
Chemical application of diffusion quantum Monte Carlo
NASA Technical Reports Server (NTRS)
Reynolds, P. J.; Lester, W. A., Jr.
1984-01-01
The diffusion quantum Monte Carlo (QMC) method gives a stochastic solution to the Schroedinger equation. This approach is receiving increasing attention in chemical applications as a result of its high accuracy. However, reducing statistical uncertainty remains a priority because chemical effects are often obtained as small differences of large numbers. As an example, the single-triplet splitting of the energy of the methylene molecule CH sub 2 is given. The QMC algorithm was implemented on the CYBER 205, first as a direct transcription of the algorithm running on the VAX 11/780, and second by explicitly writing vector code for all loops longer than a crossover length C. The speed of the codes relative to one another as a function of C, and relative to the VAX, are discussed. The computational time dependence obtained versus the number of basis functions is discussed and this is compared with that obtained from traditional quantum chemistry codes and that obtained from traditional computer architectures.
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.
Machine Learning ! ! ! ! ! Srihari Markov Chain Monte Carlo
Machine Learning ! ! ! ! ! Srihari 1 Markov Chain Monte Carlo Sampling Methods Sargur Srihari srihari@cedar.buffalo.edu #12;Machine Learning ! ! ! ! ! Srihari 2 Topics 1. Markov Chain Monte Carlo 2. Basic Metropolis Algorithm 3. Markov Chains 4. Metropolis-Hastings Algorithm 5. Gibbs Sampling 6. Slice
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.
Markov Chain Monte Carlo and Gibbs Sampling
Walsh, Bruce
Appendix 3 Markov Chain Monte Carlo and Gibbs Sampling A constant them in the development of Markov Chain Monte Carlo (MCMC) methods, that has made computation of very complex posteriors rather easy to randomly generate the next sample value, generating a Markov chain (as the transition probabilities between
Fission Matrix Capability for MCNP Monte Carlo
Carney, Sean E.; Brown, Forrest B.; Kiedrowski, Brian C.; Martin, William R.
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],
Quantum Monte Carlo calculations of the potential energy curve of the helium dimer
Xuebin Wu; Chenlei Du; Yunchuan Dai; Shibin Chu; Leibo Hu; Jianbo Deng; Yuanping Feng
2010-01-01
We report 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
The MC21 Monte Carlo Transport Code
Sutton TM, Donovan TJ, Trumbull TH, Dobreff PS, Caro E, Griesheimer DP, Tyburski LJ, Carpenter DC, Joo H
2007-01-09
MC21 is a new Monte Carlo neutron and photon transport code currently under joint development at the Knolls Atomic Power Laboratory and the Bettis Atomic Power Laboratory. MC21 is the Monte Carlo transport kernel of the broader Common Monte Carlo Design Tool (CMCDT), which is also currently under development. The vision for CMCDT is to provide an automated, computer-aided modeling and post-processing environment integrated with a Monte Carlo solver that is optimized for reactor analysis. CMCDT represents a strategy to push the Monte Carlo method beyond its traditional role as a benchmarking tool or ''tool of last resort'' and into a dominant design role. This paper describes various aspects of the code, including the neutron physics and nuclear data treatments, the geometry representation, and the tally and depletion capabilities.
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.
Quantum Monte Carlo Calculations of Light Nuclei
Steven C. Pieper
2007-11-09
During the last 15 years, there has been much progress in defining the nuclear Hamiltonian and applying quantum Monte Carlo methods to the calculation of light nuclei. I describe both aspects of this work and some recent results.
Analytical Applications of Monte Carlo Techniques.
ERIC Educational Resources Information Center
Guell, Oscar A.; Holcombe, James A.
1990-01-01
Described are analytical applications of the theory of random processes, in particular solutions obtained by using statistical procedures known as Monte Carlo techniques. Supercomputer simulations, sampling, integration, ensemble, annealing, and explicit simulation are discussed. (CW)
P. Bartalini; L. Dudko; A. Kryukov; I. Seluzhenkov; A. Sherstnev; A. Vologdin
2004-04-27
We present the Monte-Carlo events Data Base (MCDB) project and its development plans. MCDB facilitates communication between authors of Monte-Carlo generators and experimental users. It also provides a convenient book-keeping and an easy access to generator level samples. The first release of MCDB is now operational for the CMS collaboration. In this paper we review the main ideas behind MCDB and discuss future plans to develop this Data Base further within the CERN LCG framework.
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.
Monte-Carlo Go Reinforcement Learning Experiments Bruno Bouzy
Bouzy, Bruno
Monte-Carlo Go Reinforcement Learning Experiments Bruno Bouzy Universit´e Ren´e Descartes UFR de during simulations performed in a Monte-Carlo Go archi- tecture. Currently, Monte-Carlo is a popular technique for computer Go. In a previous study, Monte-Carlo was associated with domain-dependent knowledge
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.
Multiple-time-stepping generalized hybrid Monte Carlo methods
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.
Das Ising-Modell und Monte-Carlo-Simulation Das Ising-Modell und Monte-Carlo-Simulation
Das Ising-Modell und Monte-Carlo-Simulation Das Ising-Modell und Monte-Carlo-Simulation Aljoscha Rheinwalt 14. Januar 2009 Betreuender Professor: Prof. M. MÂ¨uller-PreuÃ?ker #12;Das Ising-Modell und Monte-Carlo-Simulation #12;Das Ising-Modell und Monte-Carlo-Simulation Gliederung Gliederung Ising-Modell Definition
NASA Astrophysics Data System (ADS)
Morales-Casique, E.; Briseño-Ruiz, J. V.; Hernández, A. F.; Herrera, G. S.; Escolero-Fuentes, O.
2014-12-01
We present a comparison of three stochastic approaches for estimating log hydraulic conductivity (Y) and predicting steady-state groundwater flow. Two of the approaches are based on the data assimilation technique known as ensemble Kalman filter (EnKF) and differ in the way prior statistical moment estimates (PSME) (required to build the Kalman gain matrix) are obtained. In the first approach, the Monte Carlo method is employed to compute PSME of the variables and parameters; we denote this approach by EnKFMC. In the second approach PSME are computed through the direct solution of approximate nonlocal (integrodifferential) equations that govern the spatial conditional ensemble means (statistical expectations) and covariances of hydraulic head (h) and fluxes; we denote this approach by EnKFME. The third approach consists of geostatistical stochastic inversion of the same nonlocal moment equations; we denote this approach by IME. In addition to testing the EnKFMC and EnKFME methods in the traditional manner that estimate Y over the entire grid, we propose novel corresponding algorithms that estimate Y at a few selected locations and then interpolate over all grid elements via kriging as done in the IME method. We tested these methods to estimate Y and h in steady-state groundwater flow in a synthetic two-dimensional domain with a well pumping at a constant rate, located at the center of the domain. In addition, to evaluate the performance of the estimation methods, we generated four unconditional different realizations that served as "true" fields. The results of our numerical experiments indicate that the three methods were effective in estimating h, reaching at least 80% of predictive coverage, although both EnKF were superior to the IME method. With respect to estimating Y, the three methods reached similar accuracy in terms of the mean absolute value error. Coupling the EnKF methods with kriging to estimate Y reduces to one fourth the CPU time required for data assimilation while both estimation accuracy and uncertainty do not deteriorate significantly.
Monte Carlo simulations of cold atom ratchets
NASA Astrophysics Data System (ADS)
Brown, Martin
This thesis reports the theoretical study of several cold atom ratchet systems. In particular the focus of the work is the determination of the ratchet current as a function of the ratchet parameters through analysis of the system symmetries and through numerical simulation. Ratchets are devices that exhibit directed motion in the absence of net forces. It is necessary to drive them away from thermal equilibrium so as to not violate the second law of thermodynamics. Currents are generated when the symmetries of the ratchet do not forbid it, a consequence of Curie's principle. An analysis of the symmetries will help determine for what parameters currents will be generated we perform such analyses in our investigations. The ratchets studied are modelled on the experimentally realised implementation of cold atoms in a driven optical lattice. Through the parameters of the driving and the optical lattice itself, we control the breaking of the symmetries and thus the generation of atomic currents. The precise relationship between current and ratchet parameters is explored by numerical simulation. In experiments the driving is achieved through a phase-modulation of the optical lattice beams. In numerical simulations we include the driving force directly in the equations of motion. We verify theoretically and numerically that the two approaches are equivalent. We have modelled the dynamics of atoms in light-fields through semiclassical and quantum treatments. The semiclassical treatment results in stochastic differential equations for the external degrees of freedom. These are simulated using the Monte-Carlo technique. For the fully quantum treatment we apply a stochastic trajectory method to simulate the master equation. We perform a comparison between different treatments for an over-damped ratchet.
Shell model the Monte Carlo way
Ormand, W.E.
1995-03-01
The formalism for the auxiliary-field Monte Carlo approach to the nuclear shell model is presented. The method is based on a linearization of the two-body part of the Hamiltonian in an imaginary-time propagator using the Hubbard-Stratonovich transformation. The foundation of the method, as applied to the nuclear many-body problem, is discussed. Topics presented in detail include: (1) the density-density formulation of the method, (2) computation of the overlaps, (3) the sign of the Monte Carlo weight function, (4) techniques for performing Monte Carlo sampling, and (5) the reconstruction of response functions from an imaginary-time auto-correlation function using MaxEnt techniques. Results obtained using schematic interactions, which have no sign problem, are presented to demonstrate the feasibility of the method, while an extrapolation method for realistic Hamiltonians is presented. In addition, applications at finite temperature are outlined.
Quantum speedup of Monte Carlo methods
Ashley Montanaro
2015-07-29
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomised or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.
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.
Relevance of accurate Monte Carlo modeling in nuclear medical imaging
Zaidi, H
1999-01-01
Monte Carlo techniques have become popular in different areas of medical physics with advantage of powerful computing systems. In particular, they have been extensively applied to simulate processes involving random behavior and to quantify physical parameters that are difficult or even impossible to calculate by experimental measurements. Recent nuclear medical imaging innovations such as single-photon emission computed tomography (SPECT), positron emission tomography (PET), and multiple emission tomography (MET) are ideal for Monte Carlo modeling techniques because of the stochastic nature of radiation emission, transport and detection processes. Factors which have contributed to the wider use include improved models of radiation transport processes, the practicality of application with the development of acceleration schemes and the improved speed of computers. This paper presents derivation and methodological basis for this approach and critically reviews their areas of application in nuclear imaging. An ...
Monte Carlo evaluation of thermal desorption rates
Adams, J.E.; Doll, J.D.
1981-05-01
The recently reported method for computing thermal desorption rates via a Monte Carlo evaluation of the appropriate transition state theory expression (J. E. Adams and J. D. Doll, J. Chem. Phys. 74, 1467 (1980)) is extended, by the use of importance sampling, so as to generate the complete temperature dependence in a single calculation. We also describe a straightforward means of calculating the activation energy for the desorption process within the same Monte Carlo framework. The result obtained in this way represents, for the case of a simple desorptive event, an upper bound to the true value.
Multiple quadrature by Monte Carlo techniques
Voss, John Dietrich
1966-01-01
10 Importance Sampling 27 Error in Evaluating 4. 1 vs. Number of Points of Evaluation at Intergrand 30 Non-Central Case 33 Needle and Parallel Lines Sample Space . . 43 CHAPTER I INTRODUCTION Monte Carlo was the code name given to a method... (around 30). The results are checked against a table of known values. The table may then be extended for higher degrees of free- dom by the Monte Carlo technique used. The non-central cumulative Chi-square distribution is also obtained by integration...
Monte Carlo electron/photon transport
Mack, J.M.; Morel, J.E.; Hughes, H.G.
1985-01-01
A review of nonplasma coupled electron/photon transport using Monte Carlo method is presented. Remarks are mainly restricted to linerarized formalisms at electron energies from 1 keV to 1000 MeV. Applications involving pulse-height estimation, transport in external magnetic fields, and optical Cerenkov production are discussed to underscore the importance of this branch of computational physics. Advances in electron multigroup cross-section generation is reported, and its impact on future code development assessed. Progress toward the transformation of MCNP into a generalized neutral/charged-particle Monte Carlo code is described. 48 refs.
Geodesic Monte Carlo on Embedded Manifolds.
Byrne, Simon; Girolami, Mark
2013-12-01
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
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.
Order N cluster Monte Carlo method for spin systems with long-range interactions
Kouki Fukui; Synge Todo
2009-01-01
An efficient O(N) cluster Monte Carlo method for Ising models with long-range interactions is presented. Our novel algorithm does not introduce any cutoff for interaction range and thus it strictly fulfills the detailed balance. The realized stochastic dynamics is equivalent to that of the conventional Swendsen–Wang algorithm, which requires O(N2) operations per Monte Carlo sweep if applied to long-range interacting
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.
A Monte Carlo Application to Approximate Pi.
ERIC Educational Resources Information Center
Easterday, Kenneth; Smith, Tommy
1991-01-01
The Monte Carlo procedure of generating random points that lie within the unit square is used to approximate pi, as the ratio of points within the first quadrant of the unit circle to the total number of randomly generated points. A BASIC computer program for this method is included. (JJK)
Descriptions and Comparisons of Monte Carlo Algorithms
Larry Engelhardt
2009-01-01
Complex and highly interdisciplinary by nature, MC methods have been written about extensively over the years. This review of Jun S. Liu's book, Monte Carlo Strategies in Scientific Computing (Springer, 2nd printing, 2008), notes that it focuses heavily on theory, but also describes a wide variety of algorithms.
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 Simulations of Model Nonionic Surfactants
Monte Carlo Simulations of Model Nonionic Surfactants A.P. Chatterjee and A.Z. Panagiotopoulos surfactants. Formation of micellar aggregates as a function of temperature and surfactant chemical potential the dependence of micellar size on surfactant chemical potential. The observed dependence of the CMC
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.
Markov Chain Monte Carlo Prof. David Page
Page Jr., C. David
Markov Chain Monte Carlo Prof. David Page transcribed by Matthew G. Lee #12;Markov Chain · A Markov from state s to state s' · For any time t, T(s s') is the probability of the Markov process being in state s' at time t+1 given that it is in state s at time t #12;Some Properties of Markov Chains (Some we
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.
Monte Carlo sampling for visual pose tracking
Jehoon Lee; Romeil Sandhu; Allen Tannenbaum
2011-01-01
In this paper, we present a visual pose tracking algorithm based on Monte Carlo sampling of special Euclidean group SE(3) and knowledge of a 3D model. In general, the relative pose of an object in 3D space can be described by sequential transformation matrices at each time step. Thus, the objective of this work is to find a transformation matrix
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 Renormalization Group: a review
Gupta, R.
1985-01-01
The logic and the methods of Monte Carlo Renormalization Group (MCRG) are reviewed. A status report of results for 4-dimensional lattice gauge theories derived using MCRG is presented. Existing methods for calculating the improved action are reviewed and evaluated. The Gupta-Cordery improved MCRG method is described and compared with the standard one. 71 refs., 8 figs.
Monte Carlo simulation of osmotic equilibria
NASA Astrophysics Data System (ADS)
Schreiber, Sebastian; Hentschke, Reinhard
2011-10-01
We present a Metropolis Monte Carlo simulation algorithm for the Tp?-ensemble, where T is the temperature, p is the overall external pressure, and ? is the osmotic pressure across the membrane. The algorithm, which can be applied to small molecules or sorption of small molecules in polymer networks, is tested for the case of Lennard-Jones interactions.
Monte Carlo simulations of lattice gauge theories
Rebbi, C
1980-02-01
Monte Carlo simulations done for four-dimensional lattice gauge systems are described, where the gauge group is one of the following: U(1); SU(2); Z/sub N/, i.e., the subgroup of U(1) consisting of the elements e 2..pi..in/N with integer n and N; the eight-element group of quaternions, Q; the 24- and 48-element subgroups of SU(2), denoted by T and O, which reduce to the rotation groups of the tetrahedron and the octahedron when their centers Z/sub 2/, are factored out. All of these groups can be considered subgroups of SU(2) and a common normalization was used for the action. The following types of Monte Carlo experiments are considered: simulations of a thermal cycle, where the temperature of the system is varied slightly every few Monte Carlo iterations and the internal energy is measured; mixed-phase runs, where several Monte Carlo iterations are done at a few temperatures near a phase transition starting with a lattice which is half ordered and half disordered; measurements of averages of Wilson factors for loops of different shape. 5 figures, 1 table. (RWR)
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 of the microcanonical ensemble
Creutz, M.
1984-04-05
We consider simulating statistical systems with a random walk on a constant energy surface. This combines features of deterministic molecular dynamics techniques and conventional Monte Carlo simulations. For discrete systems the method can be programmed to run an order of magnitude faster than other approaches. It does not require high quality random numbers and may also be useful for nonequilibrium studies. 10 references.
Structural Reliability and Monte Carlo Simulation.
ERIC Educational Resources Information Center
Laumakis, P. J.; Harlow, G.
2002-01-01
Analyzes a simple boom structure and assesses its reliability using elementary engineering mechanics. Demonstrates the power and utility of Monte-Carlo simulation by showing that such a simulation can be implemented more readily with results that compare favorably to the theoretical calculations. (Author/MM)
Parallel Monte-Carlo Tree Search with Simulation Servers
Hideki Kato; Ikuo Takeuchi
2010-01-01
Monte-Carlo tree search is a new best-first tree search algorithm that triggered a revolution in the computer Go world. Developing good parallel Monte-Carlo tree search algorithms is importan because single processor's performance cannot be expected to increase as used to. A novel parallel Monte-Carlo tree search algorithm is proposed. A tree searcher runs on a client computer and multiple Monte-Carlo
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.
Deterministic Simulation for Risk Management Quasi-Monte Carlo beats
Papageorgiou, Anargyros
1 Deterministic Simulation for Risk Management Quasi-Monte Carlo beats Monte Carlo for Value are widely used in pricing and risk management of complex financial instruments. Recently, quasi-Monte Carlo and accuracy. In this paper we address the application of these deterministic methods to risk management. Our
Deterministic Simulation for Risk Management QuasiMonte Carlo beats
Papageorgiou, Anargyros
1 Deterministic Simulation for Risk Management QuasiMonte Carlo beats Monte Carlo for Value are widely used in pricing and risk management of complex financial instruments. Recently, quasiMonte Carlo and accuracy. In this paper we address the application of these deterministic methods to risk management. Our
SMC for Bayesian Computation 1 Sequential Monte Carlo for Bayesian
Del Moral , Pierre
SMC for Bayesian Computation 1 Sequential Monte Carlo for Bayesian Computation Pierre Del Moral University of Cambridge, UK Summary Sequential Monte Carlo (SMC) methods are a class of importance sampling.g. Doucet et al. 2001). However, in comparison to Markov chain Monte Carlo (MCMC), the applica- tion of SMC
Parallel computing and Monte Carlo algorithms Jeffrey S. Rosenthal*
Rosenthal, Jeffrey S.
Parallel computing and Monte Carlo algorithms by Jeffrey S. Rosenthal* [Far East Journal to parallel computing, and that "parallel Monte Carlo" should be more widely used. We consider a number of parallel Markov chain Monte Carlo. We illustrate our results with actual computer experiments. Keywords
Parallel computing and Monte Carlo algorithms Je rey S. Rosenthal*
Rosenthal, Jeffrey S.
Parallel computing and Monte Carlo algorithms by Je#11;rey S. Rosenthal* [Far East Journal to parallel computing, and that \\parallel Monte Carlo" should be more widely used. We consider a number of parallel Markov chain Monte Carlo. We illustrate our results with actual computer experiments. Keywords
Monte Carlo Analysis of Security Protocols: Needham-Schroeder Revisited
Grosu, Radu
Monte Carlo Analysis of Security Protocols: Needham-Schroeder Revisited R. Grosu, X. Huang, S,xhuang,sas,pyang@cs.sunysb.edu Abstract We apply Monte Carlo model checking to the Needham-Schroeder public key authentication protocol that Monte Carlo model checking can find attacks in security protocols like Needham-Schroeder when
Monte Carlo Methods for the Linearized Poisson-Boltzmann Equation
Mascagni, Michael
the LPBE by a Monte Carlo method is to randomize a finite-difference algorithm. When applied to the LPBE algo- rithm, another, related, Monte Carlo algorithm is presented. This modified Monte Carlo method probability. It is then shown that this method is mathematically equivalent to the previous modified WOS
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)
Mizusaki, Takahiro; Shimizu, Noritaka
2012-02-01
We propose a new variational Monte Carlo (VMC) method with an energy variance extrapolation for large-scale shell-model calculations. This variational Monte Carlo is a stochastic optimization method with a projected correlated condensed pair state as a trial wave function, and is formulated with the M-scheme representation of projection operators, the Pfaffian and the Markov-chain Monte Carlo. Using this method, we can stochastically calculate approximated yrast energies and electromagnetic transition strengths. Furthermore, by combining this VMC method with energy variance extrapolation, we can estimate exact shell-model energies.
Optimizing large parameter sets in variational quantum Monte Carlo
Neuscamman, Eric; Chan, Garnet Kin-Lic
2011-01-01
We present a technique for optimizing hundreds of thousands of variational parameters in variational quantum Monte Carlo. By introducing iterative Krylov subspace solvers and by multiplying by the Hamiltonian and overlap matrices as they are sampled, we remove the need to construct and store these matrices and thus bypass the most expensive steps of the stochastic reconfiguration and linear method optimization techniques. We demonstrate the effectiveness of this approach by using stochastic reconfiguration to optimize a correlator product state wavefunction with a pfaffian reference for four example systems. In two examples on the two dimensional Hubbard model, we study 16 and 64 site lattices, recovering energies accurate to 1% in the smaller lattice and predicting particle-hole phase separation in the larger. In two examples involving an ab initio Hamiltonian, we investigate the potential energy curve of a symmetrically dissociated 4x4 hydrogen lattice as well as the singlet-triplet gap in free base porphin...
Monte Carlo simulations of fluid vesicles.
Sreeja, K K; Ipsen, John H; Sunil Kumar, P B
2015-07-15
Lipid vesicles are closed two dimensional fluid surfaces that are studied extensively as model systems for understanding the physical properties of biological membranes. Here we review the recent developments in the Monte Carlo techniques for simulating fluid vesicles and discuss some of their applications. The technique, which treats the membrane as an elastic sheet, is most suitable for the study of large scale conformations of membranes. The model can be used to study vesicles with fixed and varying topologies. Here we focus on the case of multi-component membranes with the local lipid and protein composition coupled to the membrane curvature leading to a variety of shapes. The phase diagram is more intriguing in the case of fluid vesicles having an in-plane orientational order that induce anisotropic directional curvatures. Methods to explore the steady state morphological structures due to active flux of materials have also been described in the context of Monte Carlo simulations. PMID:26087479
PHOTOS Monte Carlo and its theoretical accuracy
Z. Was; P. Golonka; G. Nanava
2008-07-17
Because of properties of QED, the bremsstrahlung corrections to decays of particles or resonances can be calculated, with a good precision, separately from other effects. Thanks to the widespread use of event records such calculations can be embodied into a separate module of Monte Carlo simulation chains, as used in High Energy Experiments of today. The PHOTOS Monte Carlo program is used for this purpose since nearly 20 years now. In the following talk let us review the main ideas and constraints which shaped the program version of today and enabled it widespread use. Finally, we will underline importance of aspects related to reliability of program results: event record contents and implementation of channel specific matrix elements.
An enhanced Monte Carlo outlier detection method.
Zhang, Liangxiao; Li, Peiwu; Mao, Jin; Ma, Fei; Ding, Xiaoxia; Zhang, Qi
2015-09-30
Outlier detection is crucial in building a highly predictive model. In this study, we proposed an enhanced Monte Carlo outlier detection method by establishing cross-prediction models based on determinate normal samples and analyzing the distribution of prediction errors individually for dubious samples. One simulated and three real datasets were used to illustrate and validate the performance of our method, and the results indicated that this method outperformed Monte Carlo outlier detection in outlier diagnosis. After these outliers were removed, the value of validation by Kovats retention indices and the root mean square error of prediction decreased from 3.195 to 1.655, and the average cross-validation prediction error decreased from 2.0341 to 1.2780. This method helps establish a good model by eliminating outliers. © 2015 Wiley Periodicals, Inc. PMID:26226927
Random number stride in Monte Carlo calculations
Hendricks, J.S.
1990-01-01
Monte Carlo radiation transport codes use a sequence of pseudorandom numbers to sample from probability distributions. A common practice is to start each source particle a predetermined number of random numbers up the pseudorandom number sequence. This number of random numbers skipped between each source particles the random number stride, S. Consequently, the jth source particle always starts with the j{center dot}Sth random number providing correlated sampling'' between similar calculations. A new machine-portable random number generator has been written for the Monte Carlo radiation transport code MCNP providing user's control of the random number stride. First the new MCNP random number generator algorithm will be described and then the effects of varying the stride will be presented. 2 refs., 1 fig.
Evaluation Function Based Monte-Carlo LOA
NASA Astrophysics Data System (ADS)
Winands, Mark H. M.; Björnsson, Yngvi
Recently, Monte-Carlo Tree Search (MCTS) has advanced the field of computer Go substantially. Also in the game of Lines of Action (LOA), which has been dominated so far by ??, MCTS is making an inroad. In this paper we investigate how to use a positional evaluation function in a Monte-Carlo simulation-based LOA program (MC-LOA). Four different simulation strategies are designed, called Evaluation Cut-Off, Corrective, Greedy, and Mixed. They use an evaluation function in several ways. Experimental results reveal that the Mixed strategy is the best among them. This strategy draws the moves randomly based on their transition probabilities in the first part of a simulation, but selects them based on their evaluation score in the second part of a simulation. Using this simulation strategy the MC-LOA program plays at the same level as the ?? program MIA, the best LOA-playing entity in the world.
Monte Carlo simulation of Touschek effect.
Xiao, A.; Borland, M.; Accelerator Systems Division
2010-07-30
We present a Monte Carlo method implementation in the code elegant for simulating Touschek scattering effects in a linac beam. The local scattering rate and the distribution of scattered electrons can be obtained from the code either for a Gaussian-distributed beam or for a general beam whose distribution function is given. In addition, scattered electrons can be tracked through the beam line and the local beam-loss rate and beam halo information recorded.
Canonical Demon Monte Carlo Renormalization Group
M. Hasenbusch; K. Pinn; C. Wieczerkowski
1994-11-23
We describe a method to compute renormalized coupling constants in a Monte Carlo renormalization group calculation. It can be used, e.g., for lattice spin or gauge models. The basic idea is to simulate a joint system of block spins and canonical demons. Unlike the Microcanonical Renormalization Group of Creutz et al. it avoids systematical errors in small volumes. We present numerical results for the O(3) nonlinear sigma-model.
Monte Carlo simulation of Alaska wolf survival
NASA Astrophysics Data System (ADS)
Feingold, S. J.
1996-02-01
Alaskan wolves live in a harsh climate and are hunted intensively. Penna's biological aging code, using Monte Carlo methods, has been adapted to simulate wolf survival. It was run on the case in which hunting causes the disruption of wolves' social structure. Social disruption was shown to increase the number of deaths occurring at a given level of hunting. For high levels of social disruption, the population did not survive.
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.
Seismic Tomography by Monte Carlo Sampling
NASA Astrophysics Data System (ADS)
D?bski, Wojciech
2010-02-01
The paper discusses the performance and robustness of the Bayesian (probabilistic) approach to seismic tomography enhanced by the numerical Monte Carlo sampling technique. The approach is compared with two other popular techniques, namely the damped least-squares (LSQR) method and the general optimization approach. The theoretical considerations are illustrated by an analysis of seismic data from the Rudna (Poland) copper mine. Contrary to the LSQR and optimization techniques the Bayesian approach allows for construction of not only the "best-fitting" model of the sought velocity distribution but also other estimators, for example the average model which is often expected to be a more robust estimator than the maximum likelihood solution. We demonstrate that using the Markov Chain Monte Carlo sampling technique within the Bayesian approach opens up the possibility of analyzing tomography imaging uncertainties with minimal additional computational effort compared to the robust optimization approach. On the basis of the considered example it is concluded that the Monte Carlo based Bayesian approach offers new possibilities of robust and reliable tomography imaging.
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.
Evaluation of expectation values in full configuration interaction quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Spencer, J. S.; Foulkes, W. M. C.
2013-03-01
The full configuration interaction quantum Monte Carlo (FCIQMC) method provides access to the exact ground state energy. However, like diffusion Monte Carlo, it is hard to precisely calculate expectation values of operators which do not commute with the Hamiltonian due to the stochastic representation of the wavefunction. Following related work on diffusion Monte Carlo, we have formulated an approach to stochastically sample additional operators in FCIQMC by using the Hellmann-Feynman theorem and sampling pumped equations of motion coupled to the standard equation of motion used to evolve the wavefunction. Our approach requires only minor modifications to existing FCIQMC programs and can be used to evaluate expectation values of arbitrary operators. We will present example calculations on the Hubbard model and molecular systems.
Sabelfeld, Karl
2015-01-01
A stochastic algorithm for simulation of fluctuation-induced kinetics of H$_2$ formation on grain surfaces is suggested as a generalization of the technique developed in our recent studies where this method was developed to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. The stochastic model is based on the spatially inhomogeneous, nonlinear integro-differential Smoluchowski equations with random source term. In this paper we derive the general system of Smoluchowski type equations for the formation of H$_2$ from two hydrogen atoms on the surface of interstellar dust grains with physisorption and chemisorption sites. We focus in this study on the spatial distribution, and numerically investigate the segregation in the case of a source with a continuous generation in time and randomly distributed in space. The stochastic particle method presented is based on a probabilistic interpretation of the underlying process as a stochastic Markov process of interacting ...
Simulation Studies of Phase Inversion in Agitated Vessels Using a Monte Carlo Technique
Leslie Y. Yeo; Omar K. Matar; E. Susana Perez de Ortiz; Geoffrey F. Hewitt
2002-01-01
A speculative study on the conditions under which phase inversion occurs in agitated liquid–liquid dispersions is conducted using a Monte Carlo technique. The simulation is based on a stochastic model, which accounts for fundamental physical processes such as drop deformation, breakup, and coalescence, and utilizes the minimization of interfacial energy as a criterion for phase inversion. Profiles of the interfacial
Paris-Sud XI, Université de
contamination by metals. This paper describes a method for the stochastic analysis of the effects network, Monte Carlo simulation, Soil contamination, Copper, Bean leaves, Soil factors variability. 1 with various soil amendments, may affect trace metal mobility (Goovaerts, 2001; Broos et al., 1999, Schnabel et
Particle Monte Carlo methods in statistical learning and rare event simulation
Del Moral , Pierre
Particle Monte Carlo methods in statistical learning and rare event simulation P. Del Moral (INRIA Some hyper-refs Feynman-Kac formulae, Genealogical & Interacting Particle Systems with appl., Springer/delmoral/index.html [+ Links] #12;Stochastic particle sampling methods Interacting jumps models Genetic type interacting
Status of Monte-Carlo Event Generators
Hoeche, Stefan; /SLAC
2011-08-11
Recent progress on general-purpose Monte-Carlo event generators is reviewed with emphasis on the simulation of hard QCD processes and subsequent parton cascades. Describing full final states of high-energy particle collisions in contemporary experiments is an intricate task. Hundreds of particles are typically produced, and the reactions involve both large and small momentum transfer. The high-dimensional phase space makes an exact solution of the problem impossible. Instead, one typically resorts to regarding events as factorized into different steps, ordered descending in the mass scales or invariant momentum transfers which are involved. In this picture, a hard interaction, described through fixed-order perturbation theory, is followed by multiple Bremsstrahlung emissions off initial- and final-state and, finally, by the hadronization process, which binds QCD partons into color-neutral hadrons. Each of these steps can be treated independently, which is the basic concept inherent to general-purpose event generators. Their development is nowadays often focused on an improved description of radiative corrections to hard processes through perturbative QCD. In this context, the concept of jets is introduced, which allows to relate sprays of hadronic particles in detectors to the partons in perturbation theory. In this talk, we briefly review recent progress on perturbative QCD in event generation. The main focus lies on the general-purpose Monte-Carlo programs HERWIG, PYTHIA and SHERPA, which will be the workhorses for LHC phenomenology. A detailed description of the physics models included in these generators can be found in [8]. We also discuss matrix-element generators, which provide the parton-level input for general-purpose Monte Carlo.
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.
Improved wave functions for quantum Monte Carlo
Seth, Priyanka
2013-02-05
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. Needs, “Framework for constructing... and a pedant when it comes to indentation. I thank Neil Drummond and John Trail for helpful discussions. I am indebted to Tracey Ingham, Michael Rutter, David Taylor and Helen Verrechia for keeping TCM running smoothly. This work would not have been...
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.
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.
Monte Carlo algorithm for free energy calculation
NASA Astrophysics Data System (ADS)
Bi, Sheng; Tong, Ning-Hua
2015-07-01
We propose a Monte Carlo algorithm for the free energy calculation based on configuration space sampling. An upward or downward temperature scan can be used to produce F (T ) . We implement this algorithm for the Ising model on a square lattice and triangular lattice. Comparison with the exact free energy shows an excellent agreement. We analyze the properties of this algorithm and compare it with the Wang-Landau algorithm, which samples in energy space. This method is applicable to general classical statistical models. The possibility of extending it to quantum systems is discussed.
Reverse Monte Carlo modelling of crystalline disorder
NASA Astrophysics Data System (ADS)
Keen, D. A.; Tucker, M. G.; Dove, M. T.
2005-02-01
The reverse Monte Carlo (RMC) modelling method, although initially developed for interpreting structural data from liquids and amorphous materials, has been extensively applied to similar data from crystalline systems. This has been especially beneficial for materials which display a large amount of disorder. The work in this area will be briefly reviewed here, including a summary of the range of crystalline materials which have been studied using RMC modelling. Recent developments made specifically to improve the RMC modelling method for crystalline systems will also be described.
A Monte Carlo algorithm for degenerate plasmas
Turrell, A.E., E-mail: a.turrell09@imperial.ac.uk; Sherlock, M.; Rose, S.J.
2013-09-15
A procedure for performing Monte Carlo calculations of plasmas with an arbitrary level of degeneracy is outlined. It has possible applications in inertial confinement fusion and astrophysics. Degenerate particles are initialised according to the Fermi–Dirac distribution function, and scattering is via a Pauli blocked binary collision approximation. The algorithm is tested against degenerate electron–ion equilibration, and the degenerate resistivity transport coefficient from unmagnetised first order transport theory. The code is applied to the cold fuel shell and alpha particle equilibration problem of inertial confinement fusion.
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.
Improvement of a quantum monte carlo method
NASA Astrophysics Data System (ADS)
Marcu, Mihail; Müller, Jürgen; Schmatzer, Franz-Karl
1986-07-01
Quantum Monte Carlo simulations based on the Trotter formula exp(- ?H)= lim M?? [exp(- gbA/ M)exp(- gbB/ M)] M, H= A+ B, involve extrapolating the finite M results to the M=? limit. New ways to perform this extrapolation are discussed. Data from an older simulation are reanalysed with the new method. For the one-dimensional isotropic ferromagnet our results now agree with other results in the literature. For the one-dimensional isotropic antiferromagnet, the critical exponent of the staggered susceptibility is consistent with 1.
Canonical Demon Monte Carlo Renormalization Group
M. Hasenbusch; K. Pinn; C. Wieczerkowski
1994-06-27
We describe a new method to compute renormalized coupling constants in a Monte Carlo renormalization group calculation. The method can be used for a general class of models, e.g., lattice spin or gauge models. The basic idea is to simulate a joint system of block spins and canonical demons. In contrast to the Microcanonical Renormalization Group invented by Creutz et al. our method does not suffer from systematical errors stemming from a simultaneous use of two different ensembles. We present numerical results for the $O(3)$ nonlinear $\\sigma$-model.
Monte Carlo simulation of the enantioseparation process
NASA Astrophysics Data System (ADS)
Bustos, V. A.; Acosta, G.; Gomez, M. R.; Pereyra, V. D.
2012-09-01
By means of Monte Carlo simulation, a study of enantioseparation by capillary electrophoresis has been carried out. A simplified system consisting of two enantiomers S (R) and a selector chiral C, which reacts with the enantiomers to form complexes RC (SC), has been considered. The dependence of ?? (enantioseparation) with the concentration of chiral selector and with temperature have been analyzed by simulation. The effect of the binding constant and the charge of the complexes are also analyzed. The results are qualitatively satisfactory, despite the simplicity of the model.
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
Diffusion quantum Monte Carlo for molecules
Lester, W.A. Jr.
1986-07-01
A quantum mechanical Monte Carlo method has been used for the treatment of molecular problems. The imaginary-time Schroedinger equation written with a shift in zero energy (E/sub T/ - V(R)) can be interpreted as a generalized diffusion equation with a position-dependent rate or branching term. Since diffusion is the continuum limit of a random walk, one may simulate the Schroedinger equation with a function psi (note, not psi/sup 2/) as a density of ''walks.'' The walks undergo an exponential birth and death as given by the rate term. 16 refs., 2 tabs.
Monte Carlo simulation study of liquid crystals
NASA Astrophysics Data System (ADS)
Xu, Jianling
Using Monte Carlo simulation methods, we investigate the physical properties of nematic and smectic liquid crystals, including effects due to electric fields, chirality, and anisotropic confining boundaries. Simulation studies include off-lattice molecular scale models and on-lattice mesoscale models. First, we present a Monte Carlo simulation study of the electroclinic effect in smectic A liquid crystals, at the molecular scale in three dimensions. We find that collective intermolecular properties like molecular tilt and transition temperatures are quite sensitive to slight details of molecular shape. In the SmA phase we find evidence of vortex-like point defects. We also observe a field-induced nematic-smectic phase transition. In a chiral Sm A material, an applied electric field can induce, not only molecular tilt, but also a periodic modulation in the director. Using a coarse-grained two-dimensional mesoscale model based on a continuum elastic free energy functional, we carry out Monte Carlo simulation of a "spin lattice" model with free energy minimized by the simulated-annealing method. The phase diagram is in close agreement with the predictions of continuum elastic theory, but shows that the modulation is not always sinusoidal as assumed. We also observe effects of chiral fluctuations, including incipient chiral stripes and localized chiral vortices. Working again at the molecular scale, we use Monte Carlo simulation methods to study the interaction of a nematic liquid crystal with an anisotropic substrate composed of a flat wall decorated with a pattern of parallel ridges, to see how the pattern on the substrate influences the state of nematic order. We find that ridges on the substrate suppress director fluctuations and thus enhance the nematic order parameter, with the most narrowly spaced ridges giving the greatest enhancement. However, the correlation length associated with the drop-off of nematic order from the substrate appears to be independent of ridge spacing. Lastly, we describe some preliminary investigations of chiral symmetry-breaking in bent-core liquid crystals. In molecular scale simulation, we found evidence of chiral symmetry breaking in a crystalline phase. Thus we demonstrated that chiral excited states do not play an essential role in chiral symmetry breaking.
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.
NASA Astrophysics Data System (ADS)
Sabelfeld, K. K.
2015-09-01
A stochastic algorithm for simulation of fluctuation-induced kinetics of H2 formation on grain surfaces is suggested as a generalization of the technique developed in our recent studies [1] where this method was developed to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. The stochastic model is based on the spatially inhomogeneous, nonlinear integro-differential Smoluchowski equations with random source term. In this paper we derive the general system of Smoluchowski type equations for the formation of H2 from two hydrogen atoms on the surface of interstellar dust grains with physisorption and chemisorption sites. We focus in this study on the spatial distribution, and numerically investigate the segregation in the case of a source with a continuous generation in time and randomly distributed in space. The stochastic particle method presented is based on a probabilistic interpretation of the underlying process as a stochastic Markov process of interacting particle system in discrete but randomly progressed time instances. The segregation is analyzed through the correlation analysis of the vector random field of concentrations which appears to be isotropic in space and stationary in time.
THE MCNPX MONTE CARLO RADIATION TRANSPORT CODE
WATERS, LAURIE S.; MCKINNEY, GREGG W.; DURKEE, JOE W.; FENSIN, MICHAEL L.; JAMES, MICHAEL R.; JOHNS, RUSSELL C.; PELOWITZ, DENISE B.
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.
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.
Reverse Monte Carlo modeling in confined systems
NASA Astrophysics Data System (ADS)
Sánchez-Gil, V.; Noya, E. G.; Lomba, E.
2014-01-01
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 36Ar 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.
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.
Quantum Monte Carlo methods for nuclear physics
Carlson, Joseph A.; Gandolfi, Stefano; Pederiva, Francesco; Pieper, Steven C.; Schiavilla, Rocco; Schmidt, K. E,; Wiringa, Robert B.
2014-10-19
Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-bodymore »interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.« less
Scalar QED, NLO and PHOTOS Monte Carlo
G. Nanava; Z. Was
2007-03-26
Recently, QED bremsstrahlung in $B$-meson decays into pair of scalars (\\pi's and/or K's) is of interest. If experimental acceptance must be taken into account, PHOTOS Monte Carlo is often used in experimental simulations. We will use scalar QED to benchmark PHOTOS, even though this theory is of limited use for complex objects. We present the analytical form of the kernel used in the older versions of PHOTOS, and the new, exact (scalar QED) one. Matrix element and phase-space Jacobians are separated in the final weight and future extensions based on measurable electromagnetic form-factors are thus possible. The massive phase-space is controlled in the the program with no approximations. Thanks to the iterative solution all leading and next to leading logarithmic terms are properly reproduced by the Monte Carlo simulation. Simultaneously, full differential distributions over complete multiple body phase-space are provided. An agreement of better than 0.01% with independent calculations of scalar QED is demonstrated.
A local superbasin kinetic Monte Carlo method.
Fichthorn, Kristen A; Lin, Yangzheng
2013-04-28
We present a local superbasin kinetic Monte Carlo (LSKMC) method that efficiently treats multiple-time-scale problems in kinetic Monte Carlo (KMC). The method is designed to solve the small-barrier problem created by groups of recurrent free-energy minima connected by low free-energy barriers and separated from the full phase space of the system by high barriers. We propose an algorithm to detect, on the fly, groups of recurrent free-energy minima connected by low free-energy barriers and to consolidate them into "superbasins," which we treat with rate equations and/or absorbing Markov chains. We discuss various issues involved with implementing LSKMC simulations that contain local superbasins and non-superbasin events concurrently. These issues include the time distribution of superbasin escapes and interactions between superbasin and non-superbasin states. The LSKMC method is exact, as it introduces no new approximations into conventional KMC simulations. We demonstrate various aspects of LSKMC in several examples, which indicate that significant increases in computational efficiency can be achieved using this method. PMID:23635108
Monte Carlo modeling for perfusion monitoring
NASA Astrophysics Data System (ADS)
Dixon, Brandon; Ibey, Bennett L.; Ericson, M. Nance; Wilson, Mark A.; Cote, Gerard L.
2003-07-01
A Monte Carlo method was developed to model light transport through multi-layered tissue with the application focused on the development of an implantable perfusion monitor. The model was developed and then verified experimentally with a micro perfusion phantom. The program modeled a three-layer (tissue, capillary bed, tissue) scenario to investigate the source-detector separation effects for an implantable sensor. The Monte Carlo code was used specifically to model the effects of absorption and scattering properties of the surrounding tissue, the hemoglobin concentration in the middle layer, the ratio of thickness of the capillary layer to the first layer, and the probe-source separation distance on the propagation of the light through the tissue. The model was verified experimentally, using a simple in vitro system with optical source and detector fibers separated at various distances. The model was also used to investigate fluctuations in luminance as a result of hemoglobin concentrations and the response of the system to various wavelengths. The model was helpful for an ongoing project to develop an implantable perfusion monitor for transplanted organs or skin flaps.
Convergence acceleration of neutronic Monte Carlo calculations
Jehouani; Ichaoui; Boulkheir
2000-10-01
Often neutrons are produced in nuclear reactors with high energies, but they are needed at low energies for uses like activation analysis and neutron capture therapy. The evaluation of the slowed down neutron amount by using the Monte Carlo method is very expensive in computation time and the variance is large for natural simulation. In order to reduce the variance and the computation time, we used two biasing techniques to accelerate the calculation convergence. We have used the adjoint flux in the considered system as an importance function in the neutron slowing down equation. In this study, we have considered a homogeneous medium that contains a mixture of U238 (absorber) and hydrogen (scatterer). By handling the adjoint slowing down equation, we have used an analytical approximation of the fine structure of the adjoint flux, as a neutron importance function in the Monte Carlo simulation, for selecting the nuclide with which neutrons interact during their slowing down without absorption. For the second method, we modified the neutron slowing down equation by multiplying it by the adjoint flux. This allowed us to select neutron energies after collision and to avoid the energies corresponding to the absorption resonance. In fact, this was accomplished by assigning an appropriate statistical weight to the neutron, since its birth. For the two methods, a correction in the statistical weight was made after each neutron collision and a Fortran program was used to perform these calculations. PMID:11003538
Parallel and Portable Monte Carlo Particle Transport
NASA Astrophysics Data System (ADS)
Lee, S. R.; Cummings, J. C.; Nolen, S. D.; Keen, N. D.
1997-08-01
We have developed a multi-group, Monte Carlo neutron transport code in C++ using object-oriented methods and the Parallel Object-Oriented Methods and Applications (POOMA) class library. This transport code, called MC++, currently computes k and ? eigenvalues of the neutron transport equation on a rectilinear computational mesh. It is portable to and runs in parallel on a wide variety of platforms, including MPPs, clustered SMPs, and individual workstations. It contains appropriate classes and abstractions for particle transport and, through the use of POOMA, for portable parallelism. Current capabilities are discussed, along with physics and performance results for several test problems on a variety of hardware, including all three Accelerated Strategic Computing Initiative (ASCI) platforms. Current parallel performance indicates the ability to compute ?-eigenvalues in seconds or minutes rather than days or weeks. Current and future work on the implementation of a general transport physics framework (TPF) is also described. This TPF employs modern C++ programming techniques to provide simplified user interfaces, generic STL-style programming, and compile-time performance optimization. Physics capabilities of the TPF will be extended to include continuous energy treatments, implicit Monte Carlo algorithms, and a variety of convergence acceleration techniques such as importance combing.
Quantum Monte Carlo methods for nuclear physics
NASA Astrophysics Data System (ADS)
Carlson, J.; Gandolfi, S.; Pederiva, F.; Pieper, Steven C.; Schiavilla, R.; Schmidt, K. E.; Wiringa, R. B.
2015-07-01
Quantum Monte Carlo methods have proved valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab initio calculations reproduce many low-lying states, moments, and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. The nuclear interactions and currents are reviewed along with a description of 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. A variety of results are presented, including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. 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 are also described. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.
Scalable Domain Decomposed Monte Carlo Particle Transport
NASA Astrophysics Data System (ADS)
O'Brien, Matthew Joseph
In this dissertation, we present the parallel algorithms necessary to run domain decomposed Monte Carlo particle transport on large numbers of processors (millions of processors). Previous algorithms were not scalable, and the parallel overhead became more computationally costly than the numerical simulation. The main algorithms we consider are: • Domain decomposition of constructive solid geometry: enables extremely large calculations in which the background geometry is too large to fit in the memory of a single computational node. • Load Balancing: keeps the workload per processor as even as possible so the calculation runs efficiently. • Global Particle Find: if particles are on the wrong processor, globally resolve their locations to the correct processor based on particle coordinate and background domain. • Visualizing constructive solid geometry, sourcing particles, deciding that particle streaming communication is completed and spatial redecomposition. These algorithms are some of the most important parallel algorithms required for domain decomposed Monte Carlo particle transport. We demonstrate that our previous algorithms were not scalable, prove that our new algorithms are scalable, and run some of the algorithms up to 2 million MPI processes on the Sequoia supercomputer.
Multilevel Monte Carlo simulation of Coulomb collisions
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(?{sup ?2}) or O(?{sup ?2}(ln?){sup 2}), depending on the underlying discretization, Milstein or Euler–Maruyama respectively. This is to be contrasted with a cost of O(?{sup ?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{sup ?5}. We discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.
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.
Simple Monte Carlo model for crowd dynamics
NASA Astrophysics Data System (ADS)
Piazza, Francesco
2010-08-01
In this paper, we introduce a simple Monte Carlo method for simulating the dynamics of a crowd. Within our model a collection of hard-disk agents is subjected to a series of two-stage steps, implying (i) the displacement of one specific agent followed by (ii) a rearrangement of the rest of the group through a Monte Carlo dynamics. The rules for the combined steps are determined by the specific setting of the granular flow, so that our scheme should be easily adapted to describe crowd dynamics issues of many sorts, from stampedes in panic scenarios to organized flow around obstacles or through bottlenecks. We validate our scheme by computing the serving times statistics of a group of agents crowding to be served around a desk. In the case of a size homogeneous crowd, we recover intuitive results prompted by physical sense. However, as a further illustration of our theoretical framework, we show that heterogeneous systems display a less obvious behavior, as smaller agents feature shorter serving times. Finally, we analyze our results in the light of known properties of nonequilibrium hard-disk fluids and discuss general implications of our model.
Quantum Monte Carlo methods for nuclear physics
J. Carlson; S. Gandolfi; F. Pederiva; Steven C. Pieper; R. Schiavilla; K. E. Schmidt; R. B. Wiringa
2015-04-29
Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.
Metallic lithium by quantum Monte Carlo
Sugiyama, G.; Zerah, G.; Alder, B.J.
1986-12-01
Lithium was chosen as the simplest known metal for the first application of quantum Monte Carlo methods in order to evaluate the accuracy of conventional one-electron band theories. Lithium has been extensively studied using such techniques. Band theory calculations have certain limitations in general and specifically in their application to lithium. Results depend on such factors as charge shape approximations (muffin tins), pseudopotentials (a special problem for lithium where the lack of rho core states requires a strong pseudopotential), and the form and parameters chosen for the exchange potential. The calculations are all one-electron methods in which the correlation effects are included in an ad hoc manner. This approximation may be particularly poor in the high compression regime, where the core states become delocalized. Furthermore, band theory provides only self-consistent results rather than strict limits on the energies. The quantum Monte Carlo method is a totally different technique using a many-body rather than a mean field approach which yields an upper bound on the energies. 18 refs., 4 figs., 1 tab.
Normality of Monte Carlo criticality eigenfunction decomposition coefficients
Toth, B. E.; Martin, W. R.; Griesheimer, D. P.
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 solution of a semi-discrete transport equation
Urbatsch, T.J.; Morel, J.E.; Gulick, J.C.
1999-09-01
The authors present the S{sub {infinity}} method, a hybrid neutron transport method in which Monte Carlo particles traverse discrete space. The goal of any deterministic/stochastic hybrid method is to couple selected characters from each of the methods in hopes of producing a better method. The S{sub {infinity}} method has the features of the lumped, linear-discontinuous (LLD) spatial discretization, yet it has no ray-effects because of the continuous angular variable. They derive the S{sub {infinity}} method for the solid-state, mono-energetic transport equation in one-dimensional slab geometry with isotropic scattering and an isotropic internal source. They demonstrate the viability of the S{sub {infinity}} method by comparing their results favorably to analytic and deterministic results.
CERN-TH.6275/91 Monte Carlo Event Generation
Sjöstrand, Torbjörn
CERN-TH.6275/91 Monte Carlo Event Generation for LHC T. Sj¨ostrand CERN -- Geneva Abstract The necessity of event generators for LHC physics studies is illustrated, and the Monte Carlo approach is outlined. A survey is presented of existing event generators, followed by a more detailed study
An Improved Monte Carlo Algorithm for Elastic Electron Backscattering
Dimov, Ivan
is the initial angle). Such an equation may be transformed into an integral equation of the form = K + 0, as one- face analysis. We are interested in the angular distribution of the back- scattered electrons. The flow of electrons satisfies an integral equation, which might be solved by Monte Carlo methods. The Monte Carlo ap
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…
Monte Carlo Simulation of Sintering on Multiprocessor Systems
Maguire Jr., Gerald Q.
great time and memory constraints. A metallurgy process called sintering, by which powders are formedMonte Carlo Simulation of Sintering on Multiprocessor Systems Jens R. Lind Master of Science Thesis storage and parallel execution for simulation of an atomic process #12;ii #12;iii Monte Carlo Simulation
Metodos de Monte Carlo Paulo Roberto de Carvalho Junior
M´etodos de Monte Carlo Paulo Roberto de Carvalho J´unior prcjunior@inf.ufpr.br VRI Vis~ao Rob´otica e Imagem Universidade Federal do Paran´a Paulo Roberto de Carvalho J´unior M´etodos de Monte Carlo a quantidade de amostras, maior a probabilidade de se aproximar do resultado correto Paulo Roberto de Carvalho
Multiscale kinetic Monte Carlo algorithm for simulating epitaxial growth
Jason P. Devita; Leonard M. Sander; Peter Smereka
2005-01-01
We present a fast Monte Carlo algorithm for simulating epitaxial surface growth, based on the continuous-time Monte Carlo algorithm of Bortz, Kalos, and Lebowitz. When simulating realistic growth regimes, much computational time is consumed by the relatively fast dynamics of the adatoms. Continuum and continuum-discrete hybrid methods have been developed to approach this issue; however, in many situations, the density
MCMs: Early History and The Basics Monte Carlo Methods
Mascagni, Michael
The Problems The People The Technology Monte Carlo Methods The Birth General Concepts of the Monte Carlo Method. The Technology: Massive human computers using hand calculators, the Fermiac, access to early digital computers Simulation of neutron histories (neutronics) 1. Given neutron positions/momenta, geometry 2. Compute flux
Economic Risk Analysis: Using Analytical and Monte Carlo Techniques.
ERIC Educational Resources Information Center
O'Donnell, Brendan R.; Hickner, Michael A.; Barna, Bruce A.
2002-01-01
Describes the development and instructional use of a Microsoft Excel spreadsheet template that facilitates analytical and Monte Carlo risk analysis of investment decisions. Discusses a variety of risk assessment methods followed by applications of the analytical and Monte Carlo methods. Uses a case study to illustrate use of the spreadsheet tool…
Rare-event Probability Estimation with Conditional Monte Carlo
Kroese, Dirk P.
Rare-event Probability Estimation with Conditional Monte Carlo Joshua C. C. Chan Dirk P. Kroese April, 2009 Abstract Estimation of rare-event probabilities in high-dimensional settings via importance. In view of this, we develop efficient algorithms based on conditional Monte Carlo to estimate rare
Simulated Annealing: A Monte Carlo Method for GPS Surveying
Fidanova, Stefka
Simulated Annealing: A Monte Carlo Method for GPS Surveying Stefka Fidanova IPP -- BAS, Acad. G annealing technique,which is a Monte Carlo method, to analyze and improve the e#ciency of the de sign which can be coupled with the simulated annealing technique. 1 Introduction The GPS is a satellite
Monte Carlo Test Assembly for Item Pool Analysis and Extension
ERIC Educational Resources Information Center
Belov, Dmitry I.; Armstrong, Ronald D.
2005-01-01
A new test assembly algorithm based on a Monte Carlo random search is presented in this article. A major advantage of the Monte Carlo test assembly over other approaches (integer programming or enumerative heuristics) is that it performs a uniform sampling from the item pool, which provides every feasible item combination (test) with an equal…
Kinetic Monte Carlo Simulations of dislocations in heteroepitaxial growth
Biehl, Michael
Kinetic Monte Carlo Simulations of dislocations in heteroepitaxial growth F. Much #3; , M. Ahr, M the lattice constants of the substrate and the adsorbate from Kinetic Monte Carlo (KMC) simulations for the appearance of mis#12;t dislocations, or self-assembled island formation. The only parameters of the model
O -lattice Kinetic Monte Carlo simulations of strained heteroepitaxial growth
Biehl, Michael
O#11;-lattice Kinetic Monte Carlo simulations of strained heteroepitaxial growth Michael Biehl, Florian Much, and Christian Vey Abstract. An o#11;-lattice, continuous space Kinetic Monte Carlo (KMC. As a starting point, we study a simplifying (1+1)-dimensional situation with inter-atomic interactions given
Markov Chain Monte Carlo and Related Topics Department of Statistics
Liu, Jun
Markov Chain Monte Carlo and Related Topics Jun S. Liu Department of Statistics Stanford University), economics and finance, engineering (Geman and Geman 1984), material science (Frenkel and Smit 1996), physics (Metropolis et al. 1953; Goodman and Sokal 1989), to statistics. Among all simulation methods, Monte Carlo
Nonlocal Monte Carlo algorithms for statistical physics applications
Janke, Wolfhard
Nonlocal Monte Carlo algorithms for statistical physics applications Wolfhard Janke1 Institut fu of Monte Carlo computer simulations in statistical physics, special emphasis is placed on applications phenomena 1. Introduction Statistical physics of complex systems pose many hard problems which can often
Adjoint electron-photon transport Monte Carlo calculations with ITS
Lorence, L.J.; Kensek, R.P.; Halbleib, J.A.; Morel, J.E.
1995-02-01
A general adjoint coupled electron-photon Monte Carlo code for solving the Boltzmann-Fokker-Planck equation has recently been created. It is a modified version of ITS 3.0, a coupled electronphoton Monte Carlo code that has world-wide distribution. The applicability of the new code to radiation-interaction problems of the type found in space environments is demonstrated.
Optimization, Estimation, and Control for Kinetic Monte Carlo Simulations
Gallivan, Martha A.
to be beneficial [15]. The mathematical framework of control theory provides a systematic alternative for thin filmOptimization, Estimation, and Control for Kinetic Monte Carlo Simulations of Thin Film Deposition strategy is applied to an atomic scale kinetic Monte Carlo simulation of thin film deposition. A model
MONTE CARLO SIMULATION FOR AMERICAN Russel E. Caflisch
Caflisch, Russel
- plementary to the trivial lower bound. The Least Squares Monte Carlo (LSM) provides a direct method for pricing American options. Quasi- random sequences have been used to improve performance of LSM; a brief. The third (Section 6) is the Least Squares Monte Carlo (LSM) method derived by Longstaff and Schwartz [19
Vectorized Monte Carlo methods for reactor lattice analysis
Brown, F.B.
1984-03-01
Some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-energy Monte Carlo code for use on the CYBER-205 computer are discussed. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. For background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed.
Vectorized Monte Carlo methods for reactor lattice analysis
Brown, F.B.
1982-11-01
This report details some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-energy Monte Carlo code for use on the CYBER-205 computer. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. for background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed.
Tunneling hybrid Monte-Carlo algorithm
Golterman, Maarten [Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132 (United States); Shamir, Yigal [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Ramat Aviv, 69978 (Israel)
2007-11-01
The Hermitian Wilson kernel used in the construction of the domain-wall and overlap Dirac operators has exceptionally small eigenvalues that make it expensive to reach high-quality chiral symmetry for domain-wall fermions, or high precision in the case of the overlap operator. An efficient way of suppressing such eigenmodes consists of including a positive power of the determinant of the Wilson kernel in the Boltzmann weight, but doing this also suppresses tunneling between topological sectors. Here we propose a modification of the hybrid Monte-Carlo algorithm which aims to restore tunneling between topological sectors by excluding the lowest eigenmodes of the Wilson kernel from the molecular-dynamics evolution, and correcting for this at the accept/reject step. We discuss the implications of this modification for the acceptance rate.
Parallel implicit Monte Carlo in C++
Urbatsch, T.J.; Evans, T.M.
1998-12-31
The authors are developing a parallel C++ Implicit Monte Carlo code in the Draco framework. As a background and motivation for the parallelization strategy, they first present three basic parallelization schemes. They use three hypothetical examples, mimicking the memory constraints of the real world, to examine characteristics of the basic schemes. Next, they present a two-step scheme proposed by Lawrence Livermore National Laboratory (LLNL). The two-step parallelization scheme they develop is based upon LLNL`s two-step scheme. The two-step scheme appears to have greater potential compared to the basic schemes and LLNL`s two-step scheme. Lastly, they explain the code design and describe how the functionality of C++ and the Draco framework assist the development of a parallel code.
Correlations in the Monte Carlo Glauber model
Jean-Paul Blaizot; Wojciech Broniowski; Jean-Yves Ollitrault
2014-09-12
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 RHIC and LHC 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 radiating reentry flows
NASA Technical Reports Server (NTRS)
Taylor, Jeff C.; Carlson, Ann B.; Hassan, H. A.
1993-01-01
The Direct Simulation Monte Carlo (DSMC) method is applied to a radiating, hypersonic, axisymmetric flow over a blunt body in the near continuum regime. The ability of the method to predict the flowfield radiation and the radiative heating is investigated for flow over the Project Fire II configuration at 11.36 kilometers per second at an altitude of 76.42 kilometers. Two methods that differ in the manner in which they treat ionization and estimate electronic excitation are employed. The calculated results are presented and compared with both experimental data and solutions where radiation effects were not included. Differences in the results are discussed. Both methods ignore self absorption and, as a result, overpredict measured radiative heating.
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.
Exploring theory space with Monte Carlo reweighting
Gainer, James S.; Lykken, Joseph; Matchev, Konstantin T.; Mrenna, Stephen; Park, Myeonghun
2014-10-13
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.
RMCProfile: reverse Monte Carlo for polycrystalline materials
NASA Astrophysics Data System (ADS)
Tucker, Matthew G.; Keen, David A.; Dove, Martin T.; Goodwin, Andrew L.; Hui, Qun
2007-08-01
A new approach to the reverse Monte Carlo analysis of total scattering data from polycrystalline materials is presented. The essential new feature is the incorporation of an explicit analysis of the Bragg peaks using a profile refinement, taking account of the instrument resolution function. Other new features including fitting data from magnetic materials, modelling lattice site disorder and new restraint and constraint options. The new method is demonstrated by a brief review of studies carried out during its development. The new program RMCProfile represents a significant advance in the analysis of polycrystalline total scattering data, especially where the local structure is to be explored within the true constraints of the long-range average structure.
Radiation Modeling with Direct Simulation Monte Carlo
NASA Technical Reports Server (NTRS)
Carlson, Ann B.; Hassan, H. A.
1991-01-01
Improvements in the modeling of radiation in low density shock waves with direct simulation Monte Carlo (DSMC) are the subject of this study. A new scheme to determine the relaxation collision numbers for excitation of electronic states is proposed. This scheme attempts to move the DSMC programs toward a more detailed modeling of the physics and more reliance on available rate data. The new method is compared with the current modeling technique and both techniques are compared with available experimental data. The differences in the results are evaluated. The test case is based on experimental measurements from the AVCO-Everett Research Laboratory electric arc-driven shock tube of a normal shock wave in air at 10 km/s and .1 Torr. The new method agrees with the available data as well as the results from the earlier scheme and is more easily extrapolated to di erent ow conditions.
Parallel tempering Monte Carlo in LAMMPS.
Rintoul, Mark Daniel; Plimpton, Steven James; Sears, Mark P.
2003-11-01
We present here the details of the implementation of the parallel tempering Monte Carlo technique into a LAMMPS, a heavily used massively parallel molecular dynamics code at Sandia. This technique allows for many replicas of a system to be run at different simulation temperatures. At various points in the simulation, configurations can be swapped between different temperature environments and then continued. This allows for large regions of energy space to be sampled very quickly, and allows for minimum energy configurations to emerge in very complex systems, such as large biomolecular systems. By including this algorithm into an existing code, we immediately gain all of the previous work that had been put into LAMMPS, and allow this technique to quickly be available to the entire Sandia and international LAMMPS community. Finally, we present an example of this code applied to folding a small protein.
Exploring theory space with Monte Carlo reweighting
Gainer, James S.; Lykken, Joseph; Matchev, Konstantin T.; Mrenna, Stephen; Park, Myeonghun
2014-10-01
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 theoristsmore »and experimentalists in exploring large theory parameter spaces in a rigorous way at the LHC.« less
Angular biasing in implicit Monte-Carlo
Zimmerman, G.B.
1994-10-20
Calculations of indirect drive Inertial Confinement Fusion target experiments require an integrated approach in which laser irradiation and radiation transport in the hohlraum are solved simultaneously with the symmetry, implosion and burn of the fuel capsule. The Implicit Monte Carlo method has proved to be a valuable tool for the two dimensional radiation transport within the hohlraum, but the impact of statistical noise on the symmetric implosion of the small fuel capsule is difficult to overcome. We present an angular biasing technique in which an increased number of low weight photons are directed at the imploding capsule. For typical parameters this reduces the required computer time for an integrated calculation by a factor of 10. An additional factor of 5 can also be achieved by directing even smaller weight photons at the polar regions of the capsule where small mass zones are most sensitive to statistical noise.
Monte Carlo simulations in Nuclear Medicine
NASA Astrophysics Data System (ADS)
Loudos, George K.
2007-11-01
Molecular imaging technologies provide unique abilities to localise signs of disease before symptoms appear, assist in drug testing, optimize and personalize therapy, and assess the efficacy of treatment regimes for different types of cancer. Monte Carlo simulation packages are used as an important tool for the optimal design of detector systems. In addition they have demonstrated potential to improve image quality and acquisition protocols. Many general purpose (MCNP, Geant4, etc) or dedicated codes (SimSET etc) have been developed aiming to provide accurate and fast results. Special emphasis will be given to GATE toolkit. The GATE code currently under development by the OpenGATE collaboration is the most accurate and promising code for performing realistic simulations. The purpose of this article is to introduce the non expert reader to the current status of MC simulations in nuclear medicine and briefly provide examples of current simulated systems, and present future challenges that include simulation of clinical studies and dosimetry applications.
Monte Carlo Exploration of Warped Higgsless Models
Hewett, J
2004-07-06
We have performed a detailed Monte Carlo exploration of the parameter space for a warped Higgsless model of electroweak symmetry breaking in 5 dimensions. This model is based on the SU(2)L x SU(2){sub R} x U(1){sub B-L} gauge group in an AdS{sub 5} bulk with arbitrary gauge kinetic terms on both the Planck and TeV branes. Constraints arising from precision electroweak measurements and collider data are found to be relatively easy to satisfy. We show, however, that the additional requirement of perturbative unitarity up to the cut-off, {approx} 10 TeV, in W{sub L}{sup +}W{sub L}{sup -} elastic scattering in the absence of dangerous tachyons eliminates all models. If successful models of this class exist, they must be highly fine-tuned.
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.
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 simulations of biomolecular binding
NASA Astrophysics Data System (ADS)
Verkhivker, Gennady
2003-03-01
The intrinsic plasticity and functional disorder-order folding transitions upon binding can provide an important prerequisite in effective molecular recognition of unstructured proteins, including the ability to bind with several targets and the increased rates of specific macromolecular association. A microscopic study of coupling between folding and binding is conducted for the p27 protein which derives a kinetic advantage from its intrinsically disordered unbound form during binding to the tertiary complex. Hierarchy of structural loss during p27 protein coupled unfolding and unbinding is simulated using high--temperature Monte Carlo simulations initiated from the crystal structure of the tertiary complex. Subsequent determination of the transition state ensemble leads to an atomic picture of the binding mechanism in agreement with the experimental data. We show that a functionally important disorder-order folding transition coupled to binding is largely determined by the intermolecular requirements to form a specific complex that ultimately dictates the folding mechanism.
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.
Monte Carlo techniques for neutron capture therapy
Wheeler, F.J. (Idaho National Engineering Lab., Idaho Falls (United States))
1991-01-01
At the Idaho National Engineering Laboratory, the current emphasis in neutron capture therapy (NCT) research is on treatment of glioblastoma multiforme using an administered {sup 10}B-containing drug followed by irradiation in an epithermal neutron beam. in appropriate subjects, the brain tumor selectively uptakes the {sup 10}B, and thermal-neutron flux generated in the tissue causes destruction of tumor cells via {sup 10}B (n,{alpha}){sup 7}Li reactions. Unlike applications of conventional photon therapy where simple methods can be used to calculate absorbed dose, NCT requires a rigorous three-dimensional solution of the Boltzmann transport equation for each unique application. This paper outlines new methods developed for the rtt-MC Monte Carlo code to address the unique requirements of NCT.
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.
Stanford University
Alamos National Laboratory in the early years after World War II. The first electronic computer useful in computer graphics. Good references on Monte Carlo methods include Kalos & Whitlock [1986 [1987], and Kuipers & Niederreiter [1974]. 2.1 A brief history Monte Carlo methods originated at the Los
A hybrid Monte Carlo and response matrix Monte Carlo method in criticality calculation
Li, Z.; Wang, K.
2012-07-01
Full core calculations are very useful and important in reactor physics analysis, especially in computing the full core power distributions, optimizing the refueling strategies and analyzing the depletion of fuels. To reduce the computing time and accelerate the convergence, a method named Response Matrix Monte Carlo (RMMC) method based on analog Monte Carlo simulation was used to calculate the fixed source neutron transport problems in repeated structures. To make more accurate calculations, we put forward the RMMC method based on non-analog Monte Carlo simulation and investigate the way to use RMMC method in criticality calculations. Then a new hybrid RMMC and MC (RMMC+MC) method is put forward to solve the criticality problems with combined repeated and flexible geometries. This new RMMC+MC method, having the advantages of both MC method and RMMC method, can not only increase the efficiency of calculations, also simulate more complex geometries rather than repeated structures. Several 1-D numerical problems are constructed to test the new RMMC and RMMC+MC method. The results show that RMMC method and RMMC+MC method can efficiently reduce the computing time and variations in the calculations. Finally, the future research directions are mentioned and discussed at the end of this paper to make RMMC method and RMMC+MC method more powerful. (authors)
Crossing the mesoscale no-mans land via parallel kinetic Monte Carlo.
Garcia Cardona, Cristina; Webb, Edmund Blackburn, III; Wagner, Gregory John; Tikare, Veena; Holm, Elizabeth Ann; Plimpton, Steven James; Thompson, Aidan Patrick; Slepoy, Alexander; 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.
Optimizing large parameter sets in variational quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Neuscamman, Eric; Umrigar, C. J.; Chan, Garnet Kin-Lic
2012-01-01
We present a technique for optimizing hundreds of thousands of variational parameters in variational quantum Monte Carlo. By introducing iterative Krylov subspace solvers and by multiplying by the Hamiltonian and overlap matrices as they are sampled, we remove the need to construct and store these matrices and thus bypass the most expensive steps of the stochastic reconfiguration and linear method optimization techniques. We demonstrate the effectiveness of this approach by using stochastic reconfiguration to optimize a correlator product state wave function with a Pfaffian reference for four example systems. In two examples on the two dimensional Fermionic Hubbard model, we study 16 and 64 site lattices, recovering energies accurate to 1% in the smaller lattice and predicting particle-hole phase separation in the larger. In two examples involving an ab initio Hamiltonian, we investigate the potential energy curve of a symmetrically dissociated 4×4 hydrogen lattice as well as the singlet-triplet gap in free base porphin. In the hydrogen system we recover 98% or more of the correlation energy at all geometries, while for porphin we compute the gap in a 24 orbital active space to within 0.02 eV of the exact result. The number of variational parameters in these examples ranges from 4×103 to 5×105.
Bold diagrammatic Monte Carlo study of ?4 theory
NASA Astrophysics Data System (ADS)
Davody, Ali
2013-12-01
By incorporating renormalization procedure into bold diagrammatic Monte Carlo, we propose a method for studying quantum field theories in the strong coupling regime. Bold diagrammatic Monte Carlo essentially samples Feynman diagrams using local Metropolis-type updates. Applying the method to three-dimensional ?4 theory, we analyze the strong coupling limit of the theory and confirm the existence of a nontrivial IR fixed point in agreement with prior studies. Interestingly, we find that working with bold correlation functions as building blocks of the Monte Carlo procedure renders the scheme convergent, and no further resummation method is needed.
Intrinsic Auger signal profiles derived by Monte Carlo analysis
NASA Astrophysics Data System (ADS)
Ding, Z.-J.; Shimizu, R.; Goto, K.
1996-07-01
A Monte Carlo simulation with cascade secondary electron generation has recently enabled us to obtain the background formed by backscattered electrons in Auger spectra. Applying this approach to experimentalEN(E)-spectrameasured by Goto et al. with a novel CMA, we have derived the Cu-LMM spectrum with the background fully subtracted. Further Monte Carlo calculation of the response function for Auger electrons has then yielded the background due to inelastically scattered Auger electrons. Compared to Tougaard's background subtraction method, the intrinsic Auger signal profile obtained by the present Monte Carlo analysis shows stronger Auger electron intensities at the lower energy side and describes much better the experimental spectrum.
The Monte Carlo method improves physician practice valuation.
Grayson, James M; Rutsohn, Phil; Jackson, Pamela Z
2006-01-01
This article demonstrates the use of the Monte Carlo simulation method in physician practice valuation. The Monte Carlo method allows the valuator to incorporate probability ranges into the discounted cash flow model and obtain an output indicating the probability for specified ranges of practice valuation. Given the high level of uncertainty in projected cash flows associated with physician practices, the value of this kind of information in a practice valuation decision would quite obviously be superior to any single point estimate generated by a traditional discounted cash flow model. It is postulated that virtually all hospitals support an information system that can easily accommodate a Monte Carlo simulation. PMID:16906001
Monte Carlo Simulations for Future Geoneutrino Detectors
NASA Astrophysics Data System (ADS)
Askins, Morgan
2010-11-01
The main contribution of heat in the earth's mantle is thought to be the radioactive decays of 238U, 232Th, and 40K. A precise measurement of the levels of 238U and 232Th can be determined by measuring the flux of electron anti-neutrinos (geoneutrinos) emitted from their decay chains. Although detectors such as kamLAND and Borexino have detected few geoneutrinos, a new cost effective geoneutrino detector is proposed which takes advantage of the total internal reflection within a long rectangular prism acrylic container of liquid scintillator having a single photomultiplier tube (PMT) on each end. An array of these containers would allow for a large scintillator volume relative to the number of PMTs, but could have a lower radio-purity. The event signatures of these decays were compared to those from neutrino interactions using Monte Carlo simulation software based upon GEANT4. In this poster I will discuss the limitations which arise from this design such as, the thickness of the acrylic container which causes high loss of optical photons due to scattering and absorption, rod length which results in higher scattering rates within the scintillator, and size of the array.
Monte Carlo Simulations for Future Geoneutrino Detectors
NASA Astrophysics Data System (ADS)
Askins, Morgan
2010-10-01
The main contribution of heat in the earth's mantle is thought to be the radioactive decays of 238U, 232Th, and 40K. A precise measurement of the levels of 238U and 232Th can be determined by measuring the flux of electron anti-neutrinos (geoneutrinos) emitted from their decay chains. Although detectors such as kamLAND and Borexino have detected few geoneutrinos, a new cost effective geoneutrino detector is proposed which takes advantage of the total internal reflection within a long rectangular prism acrylic container of liquid scintillator having a single photomultiplier tube (PMT) on each end. An array of these containers would allow for a large scintillator volume relative to the number of PMTs, but could have a lower radio-purity. The event signatures of these decays were compared to those from neutrino interactions using Monte Carlo simulation software based upon GEANT4. In this poster I will discuss the limitations which arise from this design such as, the thickness of the acrylic container which causes high loss of optical photons due to scattering and absorption, rod length which results in higher scattering rates within the scintillator, and size of the array.
Monte Carlo simulation studies of neurofilament brushes
NASA Astrophysics Data System (ADS)
Kwak, Yongkyu; Chang, Rakwoo; Gebremichael, Yeshitila
2012-12-01
We have studied the intermolecular interaction between neurofilaments (NFs) using Monte Carlo simulation methods. NFs are assembled from three distinct molecular weight proteins (NF-L, NF-M, NF-H) that are bound to each other laterally forming 10 nm diameter Þlamentous rods along with side-arm extensions. The molecular model consists of two neuroÞlament backbones along with sidearm extensions that are distributed according to the stoichiometry of the three subunits. The side arms are modeled at amino acid resolution with each amino acid represented by a hard sphere along with the corresponding charge valence. In our previous studies of a single NF brush, we have found that NF-M is most responsible for the neurofilament protrusion. In this study, we discuss the structural properties such as density profiles and mean-square radius of gyration of each type of side arms as a function of the inter-filament distance. Unlike conventional belief that crossbridging by NF-H side chains between the neurofilaments would be formed, we have only found repulsive interaction between the two neurofilaments.
La modélisation par Reverse Monte Carlo (RMC)
NASA Astrophysics Data System (ADS)
McGreevy, R. L.
2003-09-01
La technique de modélisation par Reverse Monte Carlo (RMC) est une méthode générale de modélisation structurale à partir d'un ensemble de données expérimentales. Cette méthode étant très souple, elle peut s'appliquer à de nombreux types de données. Jusqu'à présent ces applications comprennent : la diffraction des neutrons (y compris la substitution isotopique), la diffraction des rayons X (y compris la diffusion anomale), la diffraction des électrons, la RMN (les techniques d'angle magique et de 2ème moment) et l'EXAFS. Les systèmes étudiés sont également d'une grande variété : liquides, verres, polymères, cristaux et matériaux magnétiques, par exemple. Ce cours présente les bases de la méthode RMC en signalant certaines des idées fausses répandues. L'accent sera mis sur le fait que les modèles structuraux obtenus par RMC ne sont ni'uniques' ni 'exacts' ; cependant ils sont souvent utiles à la compréhension soit de la structure du système, soit des relations entre structure et autres propriétés physiques.
Replica exchange statistical temperature Monte Carlo
Kim, Jaegil; Keyes, Thomas; Straub, John E.
2009-01-01
The replica exchange statistical temperature Monte Carlo algorithm (RESTMC) is presented, extending the single-replica STMC algorithm [J. Kim, J. E. Straub, and T. Keyes, Phys. Rev. Lett. 97, 050601 (2006)] to alleviate the slow convergence of the conventional temperature replica exchange method (t-REM) with increasing system size. In contrast to the Gibbs–Boltzmann sampling at a specific temperature characteristic of the standard t-REM, RESTMC samples a range of temperatures in each replica and achieves a flat energy sampling employing the generalized sampling weight, which is automatically determined via the dynamic modification of the replica-dependent statistical temperature. Faster weight determination, through the dynamic update of the statistical temperature, and the flat energy sampling, maximizing energy overlaps between neighboring replicas, lead to a considerable acceleration in the convergence of simulations even while employing significantly fewer replicas. The performance of RESTMC is demonstrated and quantitatively compared with that of the conventional t-REM under varying simulation conditions for Lennard-Jones 19, 31, and 55 atomic clusters, exhibiting single- and double-funneled energy landscapes. PMID:19334813
Accelerated Monte Carlo Methods for Coulomb Collisions
NASA Astrophysics Data System (ADS)
Rosin, Mark; Ricketson, Lee; Dimits, Andris; Caflisch, Russel; Cohen, Bruce
2014-03-01
We present a new highly efficient multi-level Monte Carlo (MLMC) simulation algorithm for Coulomb collisions in a plasma. The scheme, initially developed and used successfully for applications in financial mathematics, is applied here to kinetic plasmas for the first time. The method is based on a Langevin treatment of the Landau-Fokker-Planck equation and has a rich history derived from the works of Einstein and Chandrasekhar. The MLMC scheme successfully reduces the computational cost of achieving an RMS error ? in the numerical solution to collisional plasma problems from (?-3) - for the standard state-of-the-art Langevin and binary collision algorithms - to a theoretically optimal (?-2) scaling, when used in conjunction with an underlying Milstein discretization to the Langevin equation. In the test case presented here, the method accelerates simulations by factors of up to 100. We summarize the scheme, present some tricks for improving its efficiency yet further, and discuss the method's range of applicability. Work performed for US DOE by LLNL under contract DE-AC52- 07NA27344 and by UCLA under grant DE-FG02-05ER25710.
Monte Carlo simulations of Protein Adsorption
NASA Astrophysics Data System (ADS)
Sharma, Sumit; Kumar, Sanat K.; Belfort, Georges
2008-03-01
Amyloidogenic diseases, such as, Alzheimer's are caused by adsorption and aggregation of partially unfolded proteins. Adsorption of proteins is a concern in design of biomedical devices, such as dialysis membranes. Protein adsorption is often accompanied by conformational rearrangements in protein molecules. Such conformational rearrangements are thought to affect many properties of adsorbed protein molecules such as their adhesion strength to the surface, biological activity, and aggregation tendency. It has been experimentally shown that many naturally occurring proteins, upon adsorption to hydrophobic surfaces, undergo a helix to sheet or random coil secondary structural rearrangement. However, to better understand the equilibrium structural complexities of this phenomenon, we have performed Monte Carlo (MC) simulations of adsorption of a four helix bundle, modeled as a lattice protein, and studied the adsorption behavior and equilibrium protein conformations at different temperatures and degrees of surface hydrophobicity. To study the free energy and entropic effects on adsorption, Canonical ensemble MC simulations have been combined with Weighted Histogram Analysis Method(WHAM). Conformational transitions of proteins on surfaces will be discussed as a function of surface hydrophobicity and compared to analogous bulk transitions.
Realistic Monte Carlo Simulation of PEN Apparatus
NASA Astrophysics Data System (ADS)
Glaser, Charles; PEN Collaboration
2015-04-01
The PEN collaboration undertook to measure the ?+ -->e+?e(?) branching ratio with a relative uncertainty of 5 ×10-4 or less at the Paul Scherrer Institute. This observable is highly susceptible to small non V - A contributions, i.e, non-Standard Model physics. The detector system included a beam counter, mini TPC for beam tracking, an active degrader and stopping target, MWPCs and a plastic scintillator hodoscope for particle tracking and identification, and a spherical CsI EM calorimeter. GEANT 4 Monte Carlo simulation is integral to the analysis as it is used to generate fully realistic events for all pion and muon decay channels. The simulated events are constructed so as to match the pion beam profiles, divergence, and momentum distribution. Ensuring the placement of individual detector components at the sub-millimeter level and proper construction of active target waveforms and associated noise, enables us to more fully understand temporal and geometrical acceptances as well as energy, time, and positional resolutions and calibrations in the detector system. This ultimately leads to reliable discrimination of background events, thereby improving cut based or multivariate branching ratio extraction. Work supported by NSF Grants PHY-0970013, 1307328, and others.
Classical Trajectory and Monte Carlo Techniques
NASA Astrophysics Data System (ADS)
Olson, Ronald
The classical trajectory Monte Carlo (CTMC) method originated with Hirschfelder, who studied the H + D2 exchange reaction using a mechanical calculator [58.1]. With the availability of computers, the CTMC method was actively applied to a large number of chemical systems to determine reaction rates, and final state vibrational and rotational populations (see, e.g., Karplus et al. [58.2]). For atomic physics problems, a major step was introduced by Abrines and Percival [58.3] who employed Kepler's equations and the Bohr-Sommerfield model for atomic hydrogen to investigate electron capture and ionization for intermediate velocity collisions of H+ + H. An excellent description is given by Percival and Richards [58.4]. The CTMC method has a wide range of applicability to strongly-coupled systems, such as collisions by multiply-charged ions [58.5]. In such systems, perturbation methods fail, and basis set limitations of coupled-channel molecular- and atomic-orbital techniques have difficulty in representing the multitude of activeexcitation, electron capture, and ionization channels. Vector- and parallel-processors now allow increasingly detailed study of the dynamics of the heavy projectile and target, along with the active electrons.
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 simulation of chromatin stretching
NASA Astrophysics Data System (ADS)
Aumann, Frank; Lankas, Filip; Caudron, Maïwen; Langowski, Jörg
2006-04-01
We present Monte Carlo (MC) simulations of the stretching of a single 30nm chromatin fiber. The model approximates the DNA by a flexible polymer chain with Debye-Hückel electrostatics and uses a two-angle zigzag model for the geometry of the linker DNA connecting the nucleosomes. The latter are represented by flat disks interacting via an attractive Gay-Berne potential. Our results show that the stiffness of the chromatin fiber strongly depends on the linker DNA length. Furthermore, changing the twisting angle between nucleosomes from 90° to 130° increases the stiffness significantly. An increase in the opening angle from 22° to 34° leads to softer fibers for small linker lengths. We observe that fibers containing a linker histone at each nucleosome are stiffer compared to those without the linker histone. The simulated persistence lengths and elastic moduli agree with experimental data. Finally, we show that the chromatin fiber does not behave as an isotropic elastic rod, but its rigidity depends on the direction of deformation: Chromatin is much more resistant to stretching than to bending.
Monte Carlo simulation of stoquastic Hamiltonians
Sergey Bravyi
2015-01-08
Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field Ising Model (TIM), the Heisenberg model on bipartite graphs, and the bosonic Hubbard model. Here we consider the problem of estimating the ground state energy of a local stoquastic Hamiltonian $H$ with a promise that the ground state of $H$ has a non-negligible correlation with some `guiding' state that admits a concise classical description. A formalized version of this problem called Guided Stoquastic Hamiltonian is shown to be complete for the complexity class MA (a probabilistic analogue of NP). To prove this result we employ the Projection Monte Carlo algorithm with a variable number of walkers. Secondly, we show that the ground state and thermal equilibrium properties of the ferromagnetic TIM can be simulated in polynomial time on a classical probabilistic computer. This result is based on the approximation algorithm for the classical ferromagnetic Ising model due to Jerrrum and Sinclair (1993).
Monte Carlo shower counter studies. Progress report
Snyder, H.D.
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.
Monte Carlo simulations of image stacking
NASA Astrophysics Data System (ADS)
Sahin, Mesut; Wilson, David L.
1993-09-01
In image stacking, we combine multiple x-ray angiography images with incomplete arterial filling into a single output image with more completely filled arteries. Among other applications, image stacking is useful in neuroangiography embolization and in CO2 angiography. Using Monte Carlo simulations and tests on clinical image sequences, we compare three methods: (1) traditional extreme-intensity (EI) which consists of a max-dark or max-light operation on the sequence, (2) matched filtering (MF) with spatially varying parameters, and (3) a new algorithm, trimmed-extreme-intensity (TEI). In the simulations, we use Poisson noise and model the time-course of the arterial contrast signal with a gamma variate curve. The figure of merit for comparisons is the contrast-to-noise (CNR) ratio. We find that our spatially-dependent MF method works well with image which have a well-defined direction of flow as in the legs, but not with more complex flow patterns as in neuroangiography. On clinical images, TEI gives good results and is more robust than MF.
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.
Monte Carlo Simulations for RHIC Spin Physics
S. Guellenstern; P. Gornicki; L. Mankiewicz; A. Schaefer
1994-10-05
Direct photon production in longitudinally polarised proton-proton collisions offers the most direct and unproblematic possibility to determine the polarised gluon distribution of a proton. This information could play a major role for improving our understanding of the nucleon structure and QCD in general. It is hoped that such experiments will be done at RHIC. We present results of detailed Monte Carlo simulations using a code called {\\sc SPHINX}. We find that for RHIC energies and large gluon polarisation the Compton graph dominates allowing for a direct test of $\\Delta g$. Triggering on away-side jets with the envisaged jet-criteria should allow to obtain more detailed information on $\\Delta g(x)$. The photon asymmetry resulting from the asymmetry of produced $\\pi^0$'s provides an additional signal, which is complementary to the other two. For small gluon polarisation, i.e. $\\Delta g \\le 0.5$ or very soft polarised gluon-distributions the envisaged experiments will require a highly sophisticated simulation and large statistics to extract more than upper bounds for $|\\Delta g(x)|$.}
Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth
Tim P. Schulze; Peter Smereka; Weinan E
2003-01-01
We present a hybrid method for simulating epitaxial growth that combines kinetic Monte-Carlo (KMC) simulations with the Burton–Cabrera–Frank model for crystal growth. This involves partitioning the computational domain into KMC regions and regions where we time-step a discretized diffusion equation. Computational speed and accuracy are discussed. We find that the method is significantly faster than KMC while accounting for stochastic
NASA Technical Reports Server (NTRS)
Queen, Eric M.; Omara, Thomas M.
1990-01-01
A realization of a stochastic atmosphere model for use in simulations is presented. The model provides pressure, density, temperature, and wind velocity as a function of latitude, longitude, and altitude, and is implemented in a three degree of freedom simulation package. This implementation is used in the Monte Carlo simulation of an aeroassisted orbital transfer maneuver and results are compared to those of a more traditional approach.
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 ...
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 ...
Variance Reduction Techniques for Implicit Monte Carlo Simulations
Landman, Jacob Taylor
2013-09-19
The Implicit Monte Carlo (IMC) method is widely used for simulating thermal radiative transfer and solving the radiation transport equation. During an IMC run a grid network is constructed and particles are sourced into the problem to simulate...
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)
COMPARISON OF MONTE CARLO METHODS FOR NONLINEAR RADIATION TRANSPORT
W. R. MARTIN; F. B. BROWN
2001-03-01
Five Monte Carlo methods for solving the nonlinear thermal radiation transport equations are compared. The methods include the well-known Implicit Monte Carlo method (IMC) developed by Fleck and Cummings, an alternative to IMC developed by Carter and Forest, an ''exact'' method recently developed by Ahrens and Larsen, and two methods recently proposed by Martin and Brown. The five Monte Carlo methods are developed and applied to the radiation transport equation in a medium assuming local thermodynamic equilibrium. Conservation of energy is derived and used to define appropriate material energy update equations for each of the methods. Details of the Monte Carlo implementation are presented, both for the random walk simulation and the material energy update. Simulation results for all five methods are obtained for two infinite medium test problems and a 1-D test problem, all of which have analytical solutions. Conclusions regarding the relative merits of the various schemes are presented.
A Theory of Monte Carlo Visibility Sampling RAVI RAMAMOORTHI
Toronto, University of
inspiring early discussions with Rob Cook, espe- cially on formulating the pixel-light 2D frequency domain provided input for the discussion of blue noise and quasi-Monte Carlo meth- ods respectively in Sec. 8
OBJECT KINETIC MONTE CARLO SIMULATIONS OF CASCADE ANNEALING IN TUNGSTEN
Nandipati, Giridhar; Setyawan, Wahyu; Heinisch, Howard L.; Roche, Kenneth J.; Kurtz, Richard J.; Wirth, Brian D.
2014-03-31
The objective of this work is to study the annealing of primary cascade damage created by primary knock-on atoms (PKAs) of various energies, at various temperatures in bulk tungsten using the object kinetic Monte Carlo (OKMC) method.
A Monte Carlo tool for multi-node reliability evaluation
Thalasila, Chander Pravin
1993-01-01
the development of a Monte Carlo program (MACS) which can generate contingencies and their probabilities and frequencies including common mode and dependent failures. This program has been further extended to perform the reliability analysis of interconnected...
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...
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.
Particle Physics Phenomenology 1. Introduction and Monte Carlo techniques
Sjöstrand, Torbjörn
/81 #12;A tour to Monte Carlo . . . because Einstein was wrong: God does throw dice! Quantum mechanics, . . . p p/p Incoming beams: parton densities Torbj¨orn Sj¨ostrand PPP 1: Introduction and MC techniques
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 ...
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.
Monte Carlo study of a Cyberknife stereotactic radiosurgery system
Fujio Araki; Fujio
2006-01-01
This study investigated small-field dosimetry for a Cyberknife stereotactic radiosurgery system using Monte Carlo simulations. The EGSnrc\\/BEAMnrc Monte Carlo code was used to simulate the Cyberknife treatment head, and the DOSXYZnrc code was implemented to calculate central axis depth-dose curves, off-axis dose profiles, and relative output factors for various circular collimator sizes of 5 to 60 mm. Water-to-air stopping power
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.
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.
Shift: A Massively Parallel Monte Carlo Radiation Transport Package
Pandya, Tara M [ORNL; Johnson, Seth R [ORNL; Davidson, Gregory G [ORNL; Evans, Thomas M [ORNL; Hamilton, Steven P [ORNL
2015-01-01
This paper discusses the massively-parallel Monte Carlo radiation transport package, Shift, de- veloped at Oak Ridge National Laboratory. It reviews the capabilities, implementation, and parallel performance of this code package. Scaling results demonstrate very good strong and weak scaling behavior of the implemented algorithms. Benchmark results from various reactor problems show that Shift results compare well to other contemporary Monte Carlo codes and experimental results.
Quasi-Monte Carlo integration over ? for migration ? inversion
Maarten V. de Hoop; Carl Spencer
1996-01-01
In this paper, we analyse the discretization of the generalized radon transform\\/amplitude versus scattering angles (GRT\\/AVA) migration - inversion formula by means of quasi-Monte Carlo methods. These methods are efficient, in the sense that they require sparsely sampled measurements only, and accurate, which we have shown by theory and examples. Another feature of Monte Carlo methods is their ability to
Development of Monte Carlo Capability for Orion Parachute Simulations
NASA Technical Reports Server (NTRS)
Moore, James W.
2011-01-01
Parachute test programs employ Monte Carlo simulation techniques to plan testing and make critical decisions related to parachute loads, rate-of-descent, or other parameters. This paper describes the development and use of a MATLAB-based Monte Carlo tool for three parachute drop test simulations currently used by NASA. The Decelerator System Simulation (DSS) is a legacy 6 Degree-of-Freedom (DOF) simulation used to predict parachute loads and descent trajectories. The Decelerator System Simulation Application (DSSA) is a 6-DOF simulation that is well suited for modeling aircraft extraction and descent of pallet-like test vehicles. The Drop Test Vehicle Simulation (DTVSim) is a 2-DOF trajectory simulation that is convenient for quick turn-around analysis tasks. These three tools have significantly different software architectures and do not share common input files or output data structures. Separate Monte Carlo tools were initially developed for each simulation. A recently-developed simulation output structure enables the use of the more sophisticated DSSA Monte Carlo tool with any of the core-simulations. The task of configuring the inputs for the nominal simulation is left to the existing tools. Once the nominal simulation is configured, the Monte Carlo tool perturbs the input set according to dispersion rules created by the analyst. These rules define the statistical distribution and parameters to be applied to each simulation input. Individual dispersed parameters are combined to create a dispersed set of simulation inputs. The Monte Carlo tool repeatedly executes the core-simulation with the dispersed inputs and stores the results for analysis. The analyst may define conditions on one or more output parameters at which to collect data slices. The tool provides a versatile interface for reviewing output of large Monte Carlo data sets while preserving the capability for detailed examination of individual dispersed trajectories. The Monte Carlo tool described in this paper has proven useful in planning several Crew Exploration Vehicle parachute tests.
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.
Methods for calculating forces within quantum Monte Carlo simulations.
Badinski, A; Haynes, P D; Trail, J R; Needs, R J
2010-02-24
Atomic force calculations within the variational and diffusion quantum Monte Carlo methods are described. The advantages of calculating diffusion quantum Monte Carlo forces with the 'pure' rather than the 'mixed' probability distribution are discussed. An accurate and practical method for calculating forces using the pure distribution is presented and tested for the SiH molecule. The statistics of force estimators are explored and violations of the central limit theorem are found in some cases. PMID:21386380
Benchmarking Monte Carlo Codes for Criticality Safety Using Subcritical Measurements
NASA Astrophysics Data System (ADS)
Valentine, T.
Monte Carlo codes that are used for criticality safety evaluations are typically validated using critical experiments in which the neutron multiplication factor is unity. However, the conditions for most fissile material operations do not coincide to those of the critical experiments. This paper demonstrates that Monte Carlo methods and nuclear data can be validated using subcritical measurements whose conditions may coincide more closely to actual configurations of fissile material.
Perturbation Monte Carlo methods for tissue structure alterations.
Nguyen, Jennifer; Hayakawa, Carole K; Mourant, Judith R; Spanier, Jerome
2013-01-01
This paper describes an extension of the perturbation Monte Carlo method to model light transport when the phase function is arbitrarily perturbed. Current perturbation Monte Carlo methods allow perturbation of both the scattering and absorption coefficients, however, the phase function can not be varied. The more complex method we develop and test here is not limited in this way. We derive a rigorous perturbation Monte Carlo extension that can be applied to a large family of important biomedical light transport problems and demonstrate its greater computational efficiency compared with using conventional Monte Carlo simulations to produce forward transport problem solutions. The gains of the perturbation method occur because only a single baseline Monte Carlo simulation is needed to obtain forward solutions to other closely related problems whose input is described by perturbing one or more parameters from the input of the baseline problem. The new perturbation Monte Carlo methods are tested using tissue light scattering parameters relevant to epithelia where many tumors originate. The tissue model has parameters for the number density and average size of three classes of scatterers; whole nuclei, organelles such as lysosomes and mitochondria, and small particles such as ribosomes or large protein complexes. When these parameters or the wavelength is varied the scattering coefficient and the phase function vary. Perturbation calculations give accurate results over variations of ?15-25% of the scattering parameters. PMID:24156056
An improved method for treating Monte Carlo-diffusion interfaces
Densmore, J. D. (Jeffery D.)
2004-01-01
Discrete Diffusion Monte Carlo (DDMC) has been suggested as a technique for increasing the efficiency of Monte Carlo simulations in diffusive media. In this technique, Monte Carlo particles travel discrete steps between spatial cells according to a discretized diffusion equation. An important part of the DDMC method is the treatment of the interface between a transport region, where standard Monte Carlo is used, and a diffusive region, where DDMC is employed. Previously developed DDMC methods use the Marshak boundary condition at transport diffusion-interfaces, and thus produce incorrect results if the Monte Carlo-calculated angular flux incident on the interface surface is anisotropic. In this summary we present a new interface method based on the asymptotic diffusion-limit boundary condition, which is able to produce accurate solutions if the incident angular flux is anisotropic. We show that this new interface technique has a simple Monte Carlo interpretation, and can be used in conjunction with the existing DDMC method. With a set of numerical simulations, we demonstrate that this asymptotic interface method is much more accurate than the previously developed Marshak interface method.
Implications of Monte Carlo Statistical Errors in Criticality Safety Assessments
Pevey, Ronald E.
2005-09-15
Most criticality safety calculations are performed using Monte Carlo techniques because of Monte Carlo's ability to handle complex three-dimensional geometries. For Monte Carlo calculations, the more histories sampled, the lower the standard deviation of the resulting estimates. The common intuition is, therefore, that the more histories, the better; as a result, analysts tend to run Monte Carlo analyses as long as possible (or at least to a minimum acceptable uncertainty). For Monte Carlo criticality safety analyses, however, the optimization situation is complicated by the fact that procedures usually require that an extra margin of safety be added because of the statistical uncertainty of the Monte Carlo calculations. This additional safety margin affects the impact of the choice of the calculational standard deviation, both on production and on safety. This paper shows that, under the assumptions of normally distributed benchmarking calculational errors and exact compliance with the upper subcritical limit (USL), the standard deviation that optimizes production is zero, but there is a non-zero value of the calculational standard deviation that minimizes the risk of inadvertently labeling a supercritical configuration as subcritical. Furthermore, this value is shown to be a simple function of the typical benchmarking step outcomes--the bias, the standard deviation of the bias, the upper subcritical limit, and the number of standard deviations added to calculated k-effectives before comparison to the USL.
DPEMC: A Monte Carlo for double diffraction
NASA Astrophysics Data System (ADS)
Boonekamp, M.; Kúcs, T.
2005-05-01
We extend the POMWIG Monte Carlo generator developed by B. Cox and J. Forshaw, to include new models of central production through inclusive and exclusive double Pomeron exchange in proton-proton collisions. Double photon exchange processes are described as well, both in proton-proton and heavy-ion collisions. In all contexts, various models have been implemented, allowing for comparisons and uncertainty evaluation and enabling detailed experimental simulations. Program summaryTitle of the program:DPEMC, version 2.4 Catalogue identifier: ADVF Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVF Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer: any computer with the FORTRAN 77 compiler under the UNIX or Linux operating systems Operating system: UNIX; Linux Programming language used: FORTRAN 77 High speed storage required:<25 MB No. of lines in distributed program, including test data, etc.: 71 399 No. of bytes in distributed program, including test data, etc.: 639 950 Distribution format: tar.gz Nature of the physical problem: Proton diffraction at hadron colliders can manifest itself in many forms, and a variety of models exist that attempt to describe it [A. Bialas, P.V. Landshoff, Phys. Lett. B 256 (1991) 540; A. Bialas, W. Szeremeta, Phys. Lett. B 296 (1992) 191; A. Bialas, R.A. Janik, Z. Phys. C 62 (1994) 487; M. Boonekamp, R. Peschanski, C. Royon, Phys. Rev. Lett. 87 (2001) 251806; Nucl. Phys. B 669 (2003) 277; R. Enberg, G. Ingelman, A. Kissavos, N. Timneanu, Phys. Rev. Lett. 89 (2002) 081801; R. Enberg, G. Ingelman, L. Motyka, Phys. Lett. B 524 (2002) 273; R. Enberg, G. Ingelman, N. Timneanu, Phys. Rev. D 67 (2003) 011301; B. Cox, J. Forshaw, Comput. Phys. Comm. 144 (2002) 104; B. Cox, J. Forshaw, B. Heinemann, Phys. Lett. B 540 (2002) 26; V. Khoze, A. Martin, M. Ryskin, Phys. Lett. B 401 (1997) 330; Eur. Phys. J. C 14 (2000) 525; Eur. Phys. J. C 19 (2001) 477; Erratum, Eur. Phys. J. C 20 (2001) 599; Eur. Phys. J. C 23 (2002) 311]. This program implements some of the more significant ones, enabling the simulation of central particle production through color singlet exchange between interacting protons or antiprotons. Method of solution: The Monte Carlo method is used to simulate all elementary 2?2 and 2?1 processes available in HERWIG. The color singlet exchanges implemented in DPEMC are implemented as functions reweighting the photon flux already present in HERWIG. Restriction on the complexity of the problem: The program relying extensively on HERWIG, the limitations are the same as in [G. Marchesini, B.R. Webber, G. Abbiendi, I.G. Knowles, M.H. Seymour, L. Stanco, Comput. Phys. Comm. 67 (1992) 465; G. Corcella, I.G. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M. Seymour, B. Webber, JHEP 0101 (2001) 010]. Typical running time: Approximate times on a 800 MHz Pentium III: 5-20 min per 10 000 unweighted events, depending on the process under consideration.
Monte Carlo study of microdosimetric diamond detectors.
Solevi, Paola; Magrin, Giulio; Moro, Davide; Mayer, Ramona
2015-09-21
Ion-beam therapy provides a high dose conformity and increased radiobiological effectiveness with respect to conventional radiation-therapy. Strict constraints on the maximum uncertainty on the biological weighted dose and consequently on the biological weighting factor require the determination of the radiation quality, defined as the types and energy spectra of the radiation at a specific point. However the experimental determination of radiation quality, in particular for an internal target, is not simple and the features of ion interactions and treatment delivery require dedicated and optimized detectors. Recently chemical vapor deposition (CVD) diamond detectors have been suggested as ion-beam therapy microdosimeters. Diamond detectors can be manufactured with small cross sections and thin shapes, ideal to cope with the high fluence rate. However the sensitive volume of solid state detectors significantly deviates from conventional microdosimeters, with a diameter that can be up to 1000 times the height. This difference requires a redefinition of the concept of sensitive thickness and a deep study of the secondary to primary radiation, of the wall effects and of the impact of the orientation of the detector with respect to the radiation field. The present work intends to study through Monte Carlo simulations the impact of the detector geometry on the determination of radiation quality quantities, in particular on the relative contribution of primary and secondary radiation. The dependence of microdosimetric quantities such as the unrestricted linear energy L and the lineal energy y are investigated for different detector cross sections, by varying the particle type (carbon ions and protons) and its energy. PMID:26309235
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.
a Monte Carlo Simulation of Water Clusters.
NASA Astrophysics Data System (ADS)
Kemper, Paul Joseph, Jr.
1990-01-01
A Bennett NVT (constant number, N, volume, V, and temperature, T) Metropolis Monte Carlo method and the Stillinger-Rahman revised central force potentials (RSL2) are used to calculate Helmholtz free energy differences for small n and n-1 rigid molecule clusters at T = 263 K. From the slope and intercept (at n = infty ) of the free energy differences for n = 2, 3, 4, 5, 6, 13, 18, 24, 40, and 60 (plotted versus n ^{2over 3} - (n-1)^{2over 3}) an effective surface tension for the small water clusters and an equilibrium vapor pressure, P_{ rm o}, are extracted. Assuming simple scaled forms for the reduced vapor pressure (ln (P _{rm c}/P_ {rm o}) ~ W_{rm o} (T _{rm c}/T-1)) and for the effective surface tension /kT per surface molecule ( sigma/ (kT_rho_ {rm b}^{2over 3} ) ~ Omega (T_{rm c}/T -1), rho_{rm b} is bulk liquid density) this data gives T_ {rm c} = 650 +/- 10 K and an effective excess surface entropy per surface molecule, Omega ~ 1.7 +/- 0.1. The latter quantity (a fundamental parameter in the scaled formalism for homogeneous and heterogeneous water nucleation) is 13% larger than the experimental bulk liquid value of 1.5. Small cluster density profiles, dipole moment distributions, heat capacity and root mean squared displacements of oxygen atoms are also presented. The small water clusters are shown to be liquid-like at T/T_{rm c} ~ 0.4 and to have "surface" water molecules with average dipole moments oriented parallel to a surface of constant radius. It is suggested that the latter effect increases the excess surface entropy for these potentials and produces the comparatively large value of Omega.
Monte Carlo study of microdosimetric diamond detectors
NASA Astrophysics Data System (ADS)
Solevi, Paola; Magrin, Giulio; Moro, Davide; Mayer, Ramona
2015-09-01
Ion-beam therapy provides a high dose conformity and increased radiobiological effectiveness with respect to conventional radiation-therapy. Strict constraints on the maximum uncertainty on the biological weighted dose and consequently on the biological weighting factor require the determination of the radiation quality, defined as the types and energy spectra of the radiation at a specific point. However the experimental determination of radiation quality, in particular for an internal target, is not simple and the features of ion interactions and treatment delivery require dedicated and optimized detectors. Recently chemical vapor deposition (CVD) diamond detectors have been suggested as ion-beam therapy microdosimeters. Diamond detectors can be manufactured with small cross sections and thin shapes, ideal to cope with the high fluence rate. However the sensitive volume of solid state detectors significantly deviates from conventional microdosimeters, with a diameter that can be up to 1000 times the height. This difference requires a redefinition of the concept of sensitive thickness and a deep study of the secondary to primary radiation, of the wall effects and of the impact of the orientation of the detector with respect to the radiation field. The present work intends to study through Monte Carlo simulations the impact of the detector geometry on the determination of radiation quality quantities, in particular on the relative contribution of primary and secondary radiation. The dependence of microdosimetric quantities such as the unrestricted linear energy L and the lineal energy y are investigated for different detector cross sections, by varying the particle type (carbon ions and protons) and its energy.
Lattice Monte Carlo simulations of polymer melts
NASA Astrophysics Data System (ADS)
Hsu, Hsiao-Ping
2014-12-01
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 Sc(q) [minimum in the Kratky-plot] found by Wittmer et al. [EPL 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.
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
2008-03-01
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 six 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 build-up 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
Monte Carlo simulation of large electron fields
NASA Astrophysics Data System (ADS)
Faddegon, Bruce A.; Perl, Joseph; Asai, Makoto
2008-03-01
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 six 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 build-up 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.
Thermally driven atmospheric escape: Monte Carlo simulations for Titan's atmosphere
Zhigilei, Leonid V.
Thermally driven atmospheric escape: Monte Carlo simulations for Titan's atmosphere Orenthal J Carlo simulations a b s t r a c t Recent models of Titan's upper atmosphere were used to reproduce of Titan's atmosphere where the gas changes from being dominated by collisions to being dominated
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
Lattice Monte Carlo simulation of Galilei variant anomalous diffusion
NASA Astrophysics Data System (ADS)
Guo, Gang; Bittig, Arne; Uhrmacher, Adelinde
2015-05-01
The observation of an increasing number of anomalous diffusion phenomena motivates the study to reveal the actual reason for such stochastic processes. When it is difficult to get analytical solutions or necessary to track the trajectory of particles, lattice Monte Carlo (LMC) simulation has been shown to be particularly useful. To develop such an LMC simulation algorithm for the Galilei variant anomalous diffusion, we derive explicit solutions for the conditional and unconditional first passage time (FPT) distributions with double absorbing barriers. According to the theory of random walks on lattices and the FPT distributions, we propose an LMC simulation algorithm and prove that such LMC simulation can reproduce both the mean and the mean square displacement exactly in the long-time limit. However, the error introduced in the second moment of the displacement diverges according to a power law as the simulation time progresses. We give an explicit criterion for choosing a small enough lattice step to limit the error within the specified tolerance. We further validate the LMC simulation algorithm and confirm the theoretical error analysis through numerical simulations. The numerical results agree with our theoretical predictions very well.
Temporal acceleration of spatially distributed kinetic Monte Carlo simulations
Chatterjee, Abhijit [Department of Chemical Engineering and Center for Catalytic Science and Technology (CCST), University of Delaware, Newark, DE 19716-3110, (United States); Vlachos, Dionisios G. [Department of Chemical Engineering and Center for Catalytic Science and Technology (CCST), University of Delaware, Newark, DE 19716-3110, (United States)]. E-mail: vlachos@che.udel.edu
2006-01-20
The computational intensity of kinetic Monte Carlo (KMC) simulation is a major impediment in simulating large length and time scales. In recent work, an approximate method for KMC simulation of spatially uniform systems, termed the binomial {tau}-leap method, was introduced [A. Chatterjee, D.G. Vlachos, M.A. Katsoulakis, Binomial distribution based {tau}-leap accelerated stochastic simulation, J. Chem. Phys. 122 (2005) 024112], where molecular bundles instead of individual processes are executed over coarse-grained time increments. This temporal coarse-graining can lead to significant computational savings but its generalization to spatially lattice KMC simulation has not been realized yet. Here we extend the binomial {tau}-leap method to lattice KMC simulations by combining it with spatially adaptive coarse-graining. Absolute stability and computational speed-up analyses for spatial systems along with simulations provide insights into the conditions where accuracy and substantial acceleration of the new spatio-temporal coarse-graining method are ensured. Model systems demonstrate that the r-time increment criterion of Chatterjee et al. obeys the absolute stability limit for values of r up to near 1.
Monte Carlo role in radiobiological modelling of radiotherapy outcomes
NASA Astrophysics Data System (ADS)
El Naqa, Issam; Pater, Piotr; Seuntjens, Jan
2012-06-01
Radiobiological models are essential components of modern radiotherapy. They are increasingly applied to optimize and evaluate the quality of different treatment planning modalities. They are frequently used in designing new radiotherapy clinical trials by estimating the expected therapeutic ratio of new protocols. In radiobiology, the therapeutic ratio is estimated from the expected gain in tumour control probability (TCP) to the risk of normal tissue complication probability (NTCP). However, estimates of TCP/NTCP are currently based on the deterministic and simplistic linear-quadratic formalism with limited prediction power when applied prospectively. Given the complex and stochastic nature of the physical, chemical and biological interactions associated with spatial and temporal radiation induced effects in living tissues, it is conjectured that methods based on Monte Carlo (MC) analysis may provide better estimates of TCP/NTCP for radiotherapy treatment planning and trial design. Indeed, over the past few decades, methods based on MC have demonstrated superior performance for accurate simulation of radiation transport, tumour growth and particle track structures; however, successful application of modelling radiobiological response and outcomes in radiotherapy is still hampered with several challenges. In this review, we provide an overview of some of the main techniques used in radiobiological modelling for radiotherapy, with focus on the MC role as a promising computational vehicle. We highlight the current challenges, issues and future potentials of the MC approach towards a comprehensive systems-based framework in radiobiological modelling for radiotherapy.
Temporal acceleration of spatially distributed kinetic Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Chatterjee, Abhijit; Vlachos, Dionisios G.
2006-01-01
The computational intensity of kinetic Monte Carlo (KMC) simulation is a major impediment in simulating large length and time scales. In recent work, an approximate method for KMC simulation of spatially uniform systems, termed the binomial ?-leap method, was introduced [A. Chatterjee, D.G. Vlachos, M.A. Katsoulakis, Binomial distribution based ?-leap accelerated stochastic simulation, J. Chem. Phys. 122 (2005) 024112], where molecular bundles instead of individual processes are executed over coarse-grained time increments. This temporal coarse-graining can lead to significant computational savings but its generalization to spatially lattice KMC simulation has not been realized yet. Here we extend the binomial ?-leap method to lattice KMC simulations by combining it with spatially adaptive coarse-graining. Absolute stability and computational speed-up analyses for spatial systems along with simulations provide insights into the conditions where accuracy and substantial acceleration of the new spatio-temporal coarse-graining method are ensured. Model systems demonstrate that the r-time increment criterion of Chatterjee et al. obeys the absolute stability limit for values of r up to near 1.
Advances in quantum Monte Carlo for quantum critical systems
NASA Astrophysics Data System (ADS)
Sandvik, Anders
2000-03-01
During the past few years, there has been significant progress in efficient quantum Monte Carlo methods for certain classes of spin systems and other lattice many-body problems. Cluster updates have been developed that speed up the sampling by several orders of magnitude, and schemes to avoid the systematic errors of the traditionally used Trotter decomposition have been deviced. Thanks to these developments, quantum critical phenomena (for systems where there are no sign problems) can now be investigated to a level of accuracy approaching classical simulation studies. I will discuss an approach to quantum simulations which is particularly efficient for (unfrustrated) S=1/2 Heisenberg models; the stochastic series expansion (SSE) method incorporating a cluster update for sampling the power series expansion of exp(-? H) to all contributing orders [A. W. Sandvik, Phys. Rev. B 59 R14157 (1999)]. I will also discuss high-precision calculations using the SSE algorithm for the Heisenberg antiferromagnet on a bilayer. This model can be tuned through a quantum critical point by varying the ratio of the inter-plane (J_?) to in-plane interaction (J), and has been very useful for testing predictions for quantum critical behavior in two-dimensional antiferromagnets. I will discuss finite-size scaling of ground state data, as well as the finite-temperature quantum critical behavior.
Finding organic vapors - a Monte Carlo approach
NASA Astrophysics Data System (ADS)
Vuollekoski, Henri; Boy, Michael; Kerminen, Veli-Matti; Kulmala, Markku
2010-05-01
Aerosols have an important role in regulating the climate both directly by absorbing and scattering solar radiation, as well as indirectly by acting as cloud condensation nuclei. While it is known that their net effect on radiative forcing is negative, several key aspects remain mysterious. There exist plenty of known primary sources of particles due to both natural and man-made origin - for example desert dust, volcanic activity and tire debris. On the other hand, it has been shown that the formation of secondary particles, by nucleation from precursor vapors, is a frequent, global phenomenon. However, the very earliest steps in new particle formation - nucleation and early growth by condensation - have many big question marks on them. While several studies have indicated the importance of a sufficient concentration of sulphuric acid vapor for the process, it has also been noted that this is usually not enough. Heads have therefore turned to organic vapors, which in their multitude could explain various observed characteristics of new particle formation. But alas, the vast number of organic compounds, their complex chemistry and properties that make them difficult to measure, have complicated the quantifying task. Nevertheless, evidence of organic contribution in particles of all size classes has been found. In particular, a significant organic constituent in the very finest particles suggests the presence of a high concentration of very low-volatile organic vapors. In this study, new particle formation in the boreal forest environment of Hyytiälä, Finland, is investigated in a process model. Our goal is to quantify the concentration, to find the diurnal profile and to get hints of the identity of some organic vapors taking part in new particle formation. Previous studies on the subject have relied on data analysis of the growth rate of the observed particles. However, due to the coarse nature of the methods used to calculate growth rates, this approach has its drawbacks in accuracy, the inability to find diurnal variation and the lack of size resolution. Here, we aim to shed some light onto the problem by applying an ad hoc Monte Carlo algorithm to a well established aerosol dynamical model, the University of Helsinki Multicomponent Aerosol model (UHMA). By performing a side-by-side comparison with measurement data within the algorithm, this approach has the significant advantage of decreasing the amount of manual labor. But more importantly, by basing the comparison on particle number size distribution data - a quantity that can be quite reliably measured - the accuracy of the results is good.
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.
NASA Astrophysics Data System (ADS)
Khrushcheva, O.; Zhurkin, E. E.; Malerba, L.; Becquart, C. S.; Domain, C.; Hou, M.
2003-04-01
Several variants are possible in the suite of programs forming multiscale predictive tools to estimate the yield strength increase caused by irradiation in RPV steels. For instance, at the atomic scale, both the Metropolis and the lattice kinetic Monte Carlo methods (MMC and LKMC respectively) allow predicting copper precipitation under irradiation conditions. Since these methods are based on different physical models, the present contribution discusses their consistency on the basis of a realistic case study. A cascade debris in iron containing 0.2% of copper was modelled by molecular dynamics with the DYMOKA code, which is part of the REVE suite. We use this debris as input for both the MMC and the LKMC simulations. Thermal motion and lattice relaxation can be avoided in the MMC, making the model closer to the LKMC (LMMC method). The predictions and the complementarity of the three methods for modelling the same phenomenon are then discussed.
Monte Carlo studies of field theory and quantum gravity
NASA Astrophysics Data System (ADS)
Gregory, Eric Brittain
In this dissertation I describe three main research projects in which I have participated as a graduate student. They share the common theme of using Monte Carlo computer simulation to investigate quantum field theories. I begin by giving a brief review of Monte Carlo simulation as a discrete path integral approach to a quantum theory. Two of the projects involve tests of the Monte Carlo renormalization group method, a systematic way of integrating out short distance features of a physical system in order to gain insight about its critical behavior, and hence its continuum limit. After a review of the ideas of the renormalization group, I discuss our thorough investigation of Monte Carlo renormalization of ?4 field theory on a two-dimensional square lattice. The second renormalization project overlaps with the other main thrust of my research, studying quantum gravity as the continuum limit of a sum over all possible ways of piecing together discrete simplices, or simplicial quantum gravity. I describe a unique Monte Carlo renormalization group study of scalar fields coupled to two-dimensional quantum gravity, where we were able to extract the anomalous field dimension for a case inaccessible to analytic methods. Finally I discuss a study of four-dimensional quantum gravity coupled to gauge fields and special concerns one must be aware of when measuring connected correlators in fluctuating geometry.
An unbiased Hessian representation for Monte Carlo PDFs
NASA Astrophysics Data System (ADS)
Carrazza, Stefano; Forte, Stefano; Kassabov, Zahari; Latorre, José Ignacio; Rojo, Juan
2015-08-01
We develop a methodology for the construction of a Hessian representation of Monte Carlo sets of parton distributions, based on the use of a subset of the Monte Carlo PDF replicas as an unbiased linear basis, and of a genetic algorithm for the determination of the optimal basis. We validate the methodology by first showing that it faithfully reproduces a native Monte Carlo PDF set (NNPDF3.0), and then, that if applied to Hessian PDF set (MMHT14) which was transformed into a Monte Carlo set, it gives back the starting PDFs with minimal information loss. We then show that, when applied to a large Monte Carlo PDF set obtained as combination of several underlying sets, the methodology leads to a Hessian representation in terms of a rather smaller set of parameters (MC-H PDFs), thereby providing an alternative implementation of the recently suggested Meta-PDF idea and a Hessian version of the recently suggested PDF compression algorithm (CMC-PDFs). The mc2hessian conversion code is made publicly available together with (through LHAPDF6) a Hessian representations of the NNPDF3.0 set, and the MC-H PDF set.
A novel Kinetic Monte Carlo algorithm for Non-Equilibrium Simulations
NASA Astrophysics Data System (ADS)
Jha, Prateek; Kuzovkov, Vladimir; Grzybowski, Bartosz; Olvera de La Cruz, Monica
2012-02-01
We have developed an off-lattice kinetic Monte Carlo simulation scheme for reaction-diffusion problems in soft matter systems. The definition of transition probabilities in the Monte Carlo scheme are taken identical to the transition rates in a renormalized master equation of the diffusion process and match that of the Glauber dynamics of Ising model. Our scheme provides several advantages over the Brownian dynamics technique for non-equilibrium simulations. Since particle displacements are accepted/rejected in a Monte Carlo fashion as opposed to moving particles following a stochastic equation of motion, nonphysical movements (e.g., violation of a hard core assumption) are not possible (these moves have zero acceptance). Further, the absence of a stochastic ``noise'' term resolves the computational difficulties associated with generating statistically independent trajectories with definitive mean properties. Finally, since the timestep is independent of the magnitude of the interaction forces, much longer time-steps can be employed than Brownian dynamics. We discuss the applications of this scheme for dynamic self-assembly of photo-switchable nanoparticles and dynamical problems in polymeric systems.
Applications of the Fixed-Node Quantum Monte Carlo Method
NASA Astrophysics Data System (ADS)
Kulahlioglu, Adem Halil
Quantum Monte Carlo (QMC) is a highly sophisticated quantum many-body method. Diffusion Monte Carlo (DMC), a projected QMC method, is a stochastic solution of the stationary Schrodinger's equation. It is, in principle, an exact method. However, in dealing with fermions, since trial wave functions meet the antisymmetric condition of the many-body fermionic systems, it inevitably encounters the fermion sign problem. One of the ways to circumvent the sign problem is by imposing the so-called fixed-node approximation. The fixed-node DMC (FN-DMC), a highly promising method, is emerging as the method of choice for correlated treatment of many-body electronic structure problems since it is much more accurate than Khon-Sham DFT and has a competitive accuracy with CCSD(T) but scales better with system size than CCSD(T). An important drawback in FN-DMC is the fixed-node bias introduced by the approximate nature of the trial wave function nodes. In this dissertation, we examine the fixed-node bias and its restrictive impact on the accuracy of FN-DMC. Also, electron density dependence of the fixed-node bias is discussed by taking a relatively small atomic system. In our dissertation, we also applied FN-DMC in a relatively large molecular system with a transition metal, Zinc-porphyrin, to calculate the excitation energy in an adiabatic limit (vertical excitation). We found that FN-DMC results agree well with experimental values as well as with results obtained by some other correlated ab initio methods such as CCSD. In addition, we used FN-DMC to study a transition metal dimer, Mo 2, which is a challenging system for theoretical studies since there is large amount of many-body correlation effects. We constructed the antisymmetric part (Slater part) of the trial wave function by means of the Selected-CI method. Moreover, we carried out CCSD(T) calculations in order to be able to compare FN-DMC energies with another correlated method energies. FN-DMC and CCSD(T) calculations in Mo2, which is dominant with d-d bondings, enabled us to make comparisons between these two competitive methods and investigate the limitations impairing FN-DMC accuracy.
Monte Carlo dose calculations in advanced radiotherapy
NASA Astrophysics Data System (ADS)
Bush, Karl Kenneth
The remarkable accuracy of Monte Carlo (MC) dose calculation algorithms has led to the widely accepted view that these methods should and will play a central role in the radiotherapy treatment verification and planning of the future. The advantages of using MC clinically are particularly evident for radiation fields passing through inhomogeneities, such as lung and air cavities, and for small fields, including those used in today's advanced intensity modulated radiotherapy techniques. Many investigators have reported significant dosimetric differences between MC and conventional dose calculations in such complex situations, and have demonstrated experimentally the unmatched ability of MC calculations in modeling charged particle disequilibrium. The advantages of using MC dose calculations do come at a cost. The nature of MC dose calculations require a highly detailed, in-depth representation of the physical system (accelerator head geometry/composition, anatomical patient geometry/composition and particle interaction physics) to allow accurate modeling of external beam radiation therapy treatments. To perform such simulations is computationally demanding and has only recently become feasible within mainstream radiotherapy practices. In addition, the output of the accelerator head simulation can be highly sensitive to inaccuracies within a model that may not be known with sufficient detail. The goal of this dissertation is to both improve and advance the implementation of MC dose calculations in modern external beam radiotherapy. To begin, a novel method is proposed to fine-tune the output of an accelerator model to better represent the measured output. In this method an intensity distribution of the electron beam incident on the model is inferred by employing a simulated annealing algorithm. The method allows an investigation of arbitrary electron beam intensity distributions and is not restricted to the commonly assumed Gaussian intensity. In a second component of this dissertation the design, implementation and evaluation of a technique for reducing a latent variance inherent from the recycling of phase space particle tracks in a simulation is presented. In the technique a random azimuthal rotation about the beam's central axis is applied to each recycled particle, achieving a significant reduction of the latent variance. In a third component, the dissertation presents the first MC modeling of Varian's new RapidArc delivery system and a comparison of dose calculations with the Eclipse treatment planning system. A total of four arc plans are compared including an oropharynx patient phantom containing tissue inhomogeneities. Finally, in a step toward introducing MC dose calculation into the planning of treatments such as RapidArc, a technique is presented to feasibly generate and store a large set of MC calculated dose distributions. A novel 3-D dyadic multi-resolution (MR) decomposition algorithm is presented and the compressibility of the dose data using this algorithm is investigated. The presented MC beamlet generation method, in conjunction with the presented 3-D data MR decomposition, represents a viable means to introduce MC dose calculation in the planning and optimization stages of advanced radiotherapy.
Introduction to the variational and diffusion Monte Carlo methods
Toulouse, Julien; Umrigar, C J
2015-01-01
We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on the subject, we review in depth the Metropolis-Hastings algorithm used in VMC for sampling the square of an approximate wave function, discussing details important for applications to electronic systems. We also review in detail the more sophisticated DMC algorithm within the fixed-node approximation, introduced to avoid the infamous Fermionic sign problem, which allows one to sample a more accurate approximation to the ground-state wave function. Throughout this review, we discuss the statistical methods used for evaluating expectation values and statistical uncertainties. In particular, we show how to estimate nonlinear functions of expectation values and their statistical uncertainties.
A new estimator for nuclear forces in Quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Chiesa, Simone; Ceperley, David; Zhang, Shiwei
2004-03-01
The computation of ionic forces in Quantum Monte Carlo methods with a straightforward use of the Hellman-Feynman theorem has infinite variance. We introduce two new estimators based on the observation that the s-wave component of the density, responsible for the divergent variance, gives a null contribution and can be therefore excluded. The resulting estimators are very simple to apply to many-body systems. For variational Monte Carlo, this leads to a straightforward way to calculate all components of ionic forces at once, with very modest additional programming or computational cost. In diffusion Monte Carlo, since the force is calculated using the electronic density, forward walking or reptation QMC is needed for unbiased results. Applications to simple molecular systems are presented.
Optimum and efficient sampling for variational quantum Monte Carlo
Trail, John Robert; 10.1063/1.3488651
2010-01-01
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial wavefunctions, that is to Variational quantum Monte Carlo. Almost all previous implementations employ samples distributed as the physical probability density of the trial wavefunction, and assume the Central Limit Theorem to be valid. In this paper we provide an analysis of random error in estimation and optimisation that leads naturally to new sampling strategies with improved computational and statistical properties. A rigorous lower limit to the random error is derived, and an efficient sampling strategy presented that significantly increases computational efficiency. In addition the infinite variance heavy tailed random errors of optimum parameters in conventional methods are replaced with a Normal random error, strengthening the theoretical basis of optimisation. The method is ...
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.
Efficiency of Monte Carlo sampling in chaotic systems
NASA Astrophysics Data System (ADS)
Leitão, Jorge C.; Lopes, J. M. Viana Parente; Altmann, Eduardo G.
2014-11-01
In this paper we investigate how the complexity of chaotic phase spaces affect the efficiency of importance sampling Monte Carlo simulations. We focus on flat-histogram simulations of the distribution of finite-time Lyapunov exponent in a simple chaotic system and obtain analytically that the computational effort: (i) scales polynomially with the finite time, a tremendous improvement over the exponential scaling obtained in uniform sampling simulations; and (ii) the polynomial scaling is suboptimal, a phenomenon known as critical slowing down. We show that critical slowing down appears because of the limited possibilities to issue a local proposal in the Monte Carlo procedure when it is applied to chaotic systems. These results show how generic properties of chaotic systems limit the efficiency of Monte Carlo simulations.
A Quantum Monte Carlo investigation of dispersion interactions in graphite
NASA Astrophysics Data System (ADS)
Spanu, Leonardo; Galli, Giulia; Sorella, Sandro
2009-03-01
We present a series of Quantum Monte Carlo (QMC) calculations of graphite, aimed at describing on the same footing the strong C-C covalent bonds and the weaker interlayer interactions. In particular, we carried out calculations of binding energies, bond lengths and compressibility by using the Variational Monte Carlo and Lattice Regularized Diffusion Monte Carlo techniques [1]. We use as a variational ansatz the Jastrow Antisymmetrical Wave function, including a pairing determinant and a Jastrow correlation factor [2]. Our results allow for a detailed analysis of dispersion forces between graphite layers, including their behavior at long distances, and yield a quantitative estimate of the layer binding energy. 0.3cm [1] Casula M. et al. Phys. Rev. Lett. 95 100201 (2005) [2] Casula M. et al. J. Chem. Phys. 119, 6500 (2003)
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.
Skin image reconstruction using Monte Carlo based color generation
NASA Astrophysics Data System (ADS)
Aizu, Yoshihisa; Maeda, Takaaki; Kuwahara, Tomohiro; Hirao, Tetsuji
2010-11-01
We propose a novel method of skin image reconstruction based on color generation using Monte Carlo simulation of spectral reflectance in the nine-layered skin tissue model. The RGB image and spectral reflectance of human skin are obtained by RGB camera and spectrophotometer, respectively. The skin image is separated into the color component and texture component. The measured spectral reflectance is used to evaluate scattering and absorption coefficients in each of the nine layers which are necessary for Monte Carlo simulation. Various skin colors are generated by Monte Carlo simulation of spectral reflectance in given conditions for the nine-layered skin tissue model. The new color component is synthesized to the original texture component to reconstruct the skin image. The method is promising for applications in the fields of dermatology and cosmetics.
Monte Carlo Methods for Tempo Tracking and Rhythm Quantization
Cemgil, A T; 10.1613/jair.1121
2011-01-01
We present a probabilistic generative model for timing deviations in expressive music performance. The structure of the proposed model is equivalent to a switching state space model. The switch variables correspond to discrete note locations as in a musical score. The continuous hidden variables denote the tempo. We formulate two well known music recognition problems, namely tempo tracking and automatic transcription (rhythm quantization) as filtering and maximum a posteriori (MAP) state estimation tasks. Exact computation of posterior features such as the MAP state is intractable in this model class, so we introduce Monte Carlo methods for integration and optimization. We compare Markov Chain Monte Carlo (MCMC) methods (such as Gibbs sampling, simulated annealing and iterative improvement) and sequential Monte Carlo methods (particle filters). Our simulation results suggest better results with sequential methods. The methods can be applied in both online and batch scenarios such as tempo tracking and transcr...
The Monte Carlo method in quantum field theory
Colin Morningstar
2007-02-20
This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo method with Markov-chain based importance sampling is presented. Properties of Markov chains are discussed in detail and several proofs are presented, culminating in the fundamental limit theorem for irreducible Markov chains. The example of a real scalar field theory is used to illustrate the Metropolis-Hastings method and to demonstrate the effectiveness of an action-preserving (microcanonical) local updating algorithm in reducing autocorrelations. The goal of these lectures is to provide the beginner with the basic skills needed to start carrying out Monte Carlo studies in quantum field theories, as well as to present the underlying theoretical foundations of the method.
Coupled Electron-Ion Monte Carlo Calculations of Dense Metallic Hydrogen Carlo Pierleoni,1
Coupled Electron-Ion Monte Carlo Calculations of Dense Metallic Hydrogen Carlo Pierleoni,1 David M electrons, and we apply it to metallic hydrogen for pressures beyond molecular dissociation. We report data structure and higher melting temperatures of the proton crystal than do Car-Parrinello molecular dynamics
Coupled Electron Ion Monte Carlo Calculations of Atomic Markus Holzmann a, Carlo Pierleoni b
Coupled Electron Ion Monte Carlo Calculations of Atomic Hydrogen Markus Holzmann a, Carlo Pierleoni state electrons, and we apply it to metallic hydrogen for pressures beyond molecular dissociation crystal than Car-Parrinello Molecular Dynamics results using LDA. We further discuss the quantum motion
Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
Stephan Humeniuk; Tommaso Roscilde
2012-03-26
We present a general scheme for the calculation of the Renyi entropy of a subsystem in quantum many-body models that can be efficiently simulated via quantum Monte Carlo. When the simulation is performed at very low temperature, the above approach delivers the entanglement Renyi entropy of the subsystem, and it allows to explore the crossover to the thermal Renyi entropy as the temperature is increased. We implement this scheme explicitly within the Stochastic Series expansion as well as within path-integral Monte Carlo, and apply it to quantum spin and quantum rotor models. In the case of quantum spins, we show that relevant models in two dimensions with reduced symmetry (XX model or hardcore bosons, transverse-field Ising model at the quantum critical point) exhibit an area law for the scaling of the entanglement entropy.
Willert, Jeffrey Park, H.
2014-11-01
In this article we explore the possibility of replacing Standard Monte Carlo (SMC) transport sweeps within a Moment-Based Accelerated Thermal Radiative Transfer (TRT) algorithm with a Residual Monte Carlo (RMC) formulation. Previous Moment-Based Accelerated TRT implementations have encountered trouble when stochastic noise from SMC transport sweeps accumulates over several iterations and pollutes the low-order system. With RMC we hope to significantly lower the build-up of statistical error at a much lower cost. First, we display encouraging results for a zero-dimensional test problem. Then, we demonstrate that we can achieve a lower degree of error in two one-dimensional test problems by employing an RMC transport sweep with multiple orders of magnitude fewer particles per sweep. We find that by reformulating the high-order problem, we can compute more accurate solutions at a fraction of the cost.
Order-N cluster Monte Carlo method for spin systems with long-range interactions
Fukui, Kouki [Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Tokyo 113-8656 (Japan); Todo, Synge [Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Tokyo 113-8656 (Japan); CREST, Japan Science and Technology Agency, Kawaguchi 332-0012 (Japan)], E-mail: wistaria@ap.t.u-tokyo.ac.jp
2009-04-20
An efficient O(N) cluster Monte Carlo method for Ising models with long-range interactions is presented. Our novel algorithm does not introduce any cutoff for interaction range and thus it strictly fulfills the detailed balance. The realized stochastic dynamics is equivalent to that of the conventional Swendsen-Wang algorithm, which requires O(N{sup 2}) operations per Monte Carlo sweep if applied to long-range interacting models. In addition, it is shown that the total energy and the specific heat can also be measured in O(N) time. We demonstrate the efficiency of our algorithm over the conventional method and the O(NlogN) algorithm by Luijten and Bloete. We also apply our algorithm to the classical and quantum Ising chains with inverse-square ferromagnetic interactions, and confirm in a high accuracy that a Kosterlitz-Thouless phase transition, associated with a universal jump in the magnetization, occurs in both cases.
Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
Humeniuk, Stephan
2012-01-01
We present a general scheme for the calculation of the Renyi entropy of a subsystem in quantum many-body models that can be efficiently simulated via quantum Monte Carlo. When the simulation is performed at very low temperature, the above approach delivers the entanglement Renyi entropy of the subsystem, and it allows to explore the crossover to the thermal Renyi entropy as the temperature is increased. We implement this scheme explicitly within the Stochastic Series expansion as well as within path-integral Monte Carlo, and apply it to quantum spin and quantum rotor models. In the case of quantum spins, we show that relevant models in two dimensions with reduced symmetry (XX model or hardcore bosons, transverse-field Ising model at the quantum critical point) exhibit an area law for the scaling of the entanglement entropy.
Energies of the first row atoms from quantum Monte Carlo
Brown, Matthew; Rios, Pablo Lopez; Needs, Richard; 10.1063/1.2743972
2010-01-01
All-electron variational and diffusion quantum Monte Carlo calculations of the ground state energies of the first row atoms (Li to Ne) are reported. We use trial wavefunctions of four types: single determinant Slater-Jastrow wavefunctions; multi-determinant Slater-Jastrow wavefunctions; single determinant Slater-Jastrow wavefunctions with backflow transformations; multi-determinant Slater-Jastrow wavefunctions with backflow transformations. At the diffusion quantum Monte Carlo level and using our best trial wavefunctions we recover 99% or more of the correlation energy for Li, Be, B, C, N, and Ne, 97% for O, and 98% for F.
A Monte Carlo method for combined segregation and linkage analysis
Guo, S.W. (Univ. of Michigan, Ann Arbor, MI (United States)); Thompson, E.A. (Univ. of Washington, Seattle, WA (United States))
1992-11-01
The authors introduce a Monte Carlo approach to combined segregation and linkage analysis of a quantitative trait observed in an extended pedigree. In conjunction with the Monte Carlo method of likelihood-ratio evaluation proposed by Thompson and Guo, the method provides for estimation and hypothesis testing. The greatest attraction of this approach is its ability to handle complex genetic models and large pedigrees. Two examples illustrate the practicality of the method. One is of simulated data on a large pedigree; the other is a reanalysis of published data previously analyzed by other methods. 40 refs, 5 figs., 5 tabs.
Multiscale Kinetic Monte-Carlo for Simulating Epitaxial Growth
Jason P. DeVita; Leonard M. Sander; Peter Smereka
2005-01-01
We present a fast Monte-Carlo algorithm for simulating epitaxial surface\\u000agrowth, based on the continuous-time Monte-Carlo algorithm of Bortz, Kalos and\\u000aLebowitz. When simulating realistic growth regimes, much computational time is\\u000aconsumed by the relatively fast dynamics of the adatoms. Continuum and\\u000acontinuum-discrete hybrid methods have been developed to approach this issue;\\u000ahowever in many situations, the density of adatoms
Modelling hadronic interactions in cosmic ray Monte Carlo generators
NASA Astrophysics Data System (ADS)
Pierog, Tanguy
2015-08-01
Currently the uncertainty in the prediction of shower observables for different primary particles and energies is dominated by differences between hadronic interaction models. The LHC data on minimum bias measurements can be used to test Monte Carlo generators and these new constraints will help to reduce the uncertainties in air shower predictions. In this article, after a short introduction on air showers and Monte Carlo generators, we will show the results of the comparison between the updated version of high energy hadronic interaction models EPOS LHC and QGSJETII-04 with LHC data. Results for air shower simulations and their consequences on comparisons with air shower data will be discussed.
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.
Monte Carlo Simulations of Phosphate Polyhedron Connectivity in Glasses
ALAM,TODD M.
1999-12-21
Monte Carlo simulations of phosphate tetrahedron connectivity distributions in alkali and alkaline earth phosphate glasses are reported. By utilizing a discrete bond model, the distribution of next-nearest neighbor connectivities between phosphate polyhedron for random, alternating and clustering bonding scenarios was evaluated as a function of the relative bond energy difference. The simulated distributions are compared to experimentally observed connectivities reported for solid-state two-dimensional exchange and double-quantum NMR experiments of phosphate glasses. These Monte Carlo simulations demonstrate that the polyhedron connectivity is best described by a random distribution in lithium phosphate and calcium phosphate glasses.
Monte Carlo simulations of phosphate polyhedron connectivity in glasses
ALAM,TODD M.
2000-01-01
Monte Carlo simulations of phosphate tetrahedron connectivity distributions in alkali and alkaline earth phosphate glasses are reported. By utilizing a discrete bond model, the distribution of next-nearest neighbor connectivities between phosphate polyhedron for random, alternating and clustering bonding scenarios was evaluated as a function of the relative bond energy difference. The simulated distributions are compared to experimentally observed connectivities reported for solid-state two-dimensional exchange and double-quantum NMR experiments of phosphate glasses. These Monte Carlo simulations demonstrate that the polyhedron connectivity is best described by a random distribution in lithium phosphate and calcium phosphate glasses.
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
Monte Carlo calculation of monitor unit for electron arc therapy
Chow, James C. L.; Jiang Runqing
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.
Monte Carlo simulation of electrons in dense gases
NASA Astrophysics Data System (ADS)
Tattersall, Wade; Boyle, Greg; Cocks, Daniel; Buckman, Stephen; White, Ron
2014-10-01
We implement a Monte-Carlo simulation modelling the transport of electrons and positrons in dense gases and liquids, by using a dynamic structure factor that allows us to construct structure-modified effective cross sections. These account for the coherent effects caused by interactions with the relatively dense medium. The dynamic structure factor also allows us to model thermal gases in the same manner, without needing to directly sample the velocities of the neutral particles. We present the results of a series of Monte Carlo simulations that verify and apply this new technique, and make comparisons with macroscopic predictions and Boltzmann equation solutions. Financial support of the Australian Research Council.
Beyond the Born-Oppenheimer approximation with quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Tubman, Norm; Kylanpaa, Ilkka; Hammes-Schiffer, Sharon; Ceperley, David
2015-03-01
We develop tools that enable the study of non-adiabatic effects with variational and diffusion Monte Carlo methods. We introduce a highly accurate wave function ansatz for electron-ion systems that can involve a combination of both clamped ions and quantum nuclei. We explicitly calculate the ground state energies of H2, LiH, H2O and FHF- using fixed-node quantum Monte Carlo with wave function nodes that explicitly depend on the ion positions. The obtained energies implicitly include the effects arising from quantum nuclei and electron-nucleus coupling. We compare our results to the best theoretical and experimental results available and find excellent agreement.
Monte Carlo simulations of imprint behavior in ferroelectrics
NASA Astrophysics Data System (ADS)
Schorn, Peter J.; Böttger, Ulrich; Waser, Rainer
2005-12-01
In this letter, Monte Carlo simulation methods were used to investigate the influence of the defect orientation and concentration on the hysteresis loop in ferroelectric thin films. The hysteresis loops were calculated by an existing Monte Carlo model. For a certain type of defect orientation, the simulations revealed an asymmetric hysteresis loop behavior, similar to hysteresis curves recorded by imprint measurements. Though these results may not directly offer a new explanation for the imprint mechanism in ferroelectric thin films, they still provide insight information about the often observed phenomenon of imprinted hysteresis loops of as-prepared thin-film capacitors.
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.
Directed loop algorithm for quantum Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Sandvik, Anders
2003-03-01
Loop algorithms [1] have dramatically improved the performance of world-line quantum Monte Carlo simulations of a wide range of models. However, the method is restricted to certain regions of parameter space. In particular, the presence of external fields (chemical potential or magnetic field) can typically not be taken into account in the loop construction. Two other methods were developed that do not have this restriction; the worm algorithm [2] for world-lines in continuous imaginary time and the operator-loop algorithm for stochastic series expansion [3]. Here there is a greater freedom in the loop-building process (the loops can be self-intersecting and also, in some cases, back-tracking) and all interactions can therefore be taken into account. Recently a framework was developed [4] within which these more general algorithms emerge as natural generalizations of the original loop algorithm. In this "directed loop" approach, the detailed balance condition leads to a set of coupled equations for the probabilities of the various loop-building steps. The directed loop equations often have an infinite number of solutions, and the probabilities should hence be optimized for the most efficient simulations. I will discuss an algorithm for the S=1/2 XXZ model [4], where the optimization criterion is the minimization of the back-tracking probability. [1] H. G. Evertz, G. Lana, and M. Marcu, Phys. Rev. Lett. 70, 875 (1993). [2] N. V. Prokofev, B. V. Svistunov, and I. S. Tupitsyn, Phys. Lett A238, 253 (1998). [3] A. W. Sandvik, Phys. Rev. B59, R14157 (1999). [4] O.Suljuasen and A. W. Sandvik, Phys. Rev. E66, 046701 (2002).
ITER Neutronics Modeling Using Hybrid Monte Carlo/Deterministic and CAD-Based Monte Carlo Methods
Ibrahim, A.; Mosher, Scott W; Evans, Thomas M; Peplow, Douglas E.; Sawan, M.; Wilson, P.; Wagner, John C; Heltemes, Thad
2011-01-01
The immense size and complex geometry of the ITER experimental fusion reactor require the development of special techniques that can accurately and efficiently perform neutronics simulations with minimal human effort. This paper shows the effect of the hybrid Monte Carlo (MC)/deterministic techniques - Consistent Adjoint Driven Importance Sampling (CADIS) and Forward-Weighted CADIS (FW-CADIS) - in enhancing the efficiency of the neutronics modeling of ITER and demonstrates the applicability of coupling these methods with computer-aided-design-based MC. Three quantities were calculated in this analysis: the total nuclear heating in the inboard leg of the toroidal field coils (TFCs), the prompt dose outside the biological shield, and the total neutron and gamma fluxes over a mesh tally covering the entire reactor. The use of FW-CADIS in estimating the nuclear heating in the inboard TFCs resulted in a factor of ~ 275 increase in the MC figure of merit (FOM) compared with analog MC and a factor of ~ 9 compared with the traditional methods of variance reduction. By providing a factor of ~ 21 000 increase in the MC FOM, the radiation dose calculation showed how the CADIS method can be effectively used in the simulation of problems that are practically impossible using analog MC. The total flux calculation demonstrated the ability of FW-CADIS to simultaneously enhance the MC statistical precision throughout the entire ITER geometry. Collectively, these calculations demonstrate the ability of the hybrid techniques to accurately model very challenging shielding problems in reasonable execution times.
Monte Carlo sampling from the quantum state space. II
Yi-Lin Seah; Jiangwei Shang; Hui Khoon Ng; David John Nott; Berthold-Georg Englert
2015-04-27
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local maxima or evaluating an integral over a region in the quantum state space are but two exemplary applications of many. These tasks can only be performed reliably and efficiently with Monte Carlo methods, which involve good samplings of the parameter space in accordance with the relevant target distribution. We show how the Markov-chain Monte Carlo method known as Hamiltonian Monte Carlo, or hybrid Monte Carlo, can be adapted to this context. It is applicable when an efficient parameterization of the state space is available. The resulting random walk is entirely inside the physical parameter space, and the Hamiltonian dynamics enable us to take big steps, thereby avoiding strong correlations between successive sample points while enjoying a high acceptance rate. We use examples of single and double qubit measurements for illustration.
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.
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…
Impact of random numbers on parallel Monte Carlo application
Pandey, Ras B.
2002-10-22
A number of graduate students are involved at various level of research in this project. We investigate the basic issues in materials using Monte Carlo simulations with specific interest in heterogeneous materials. Attempts have been made to seek collaborations with the DOE laboratories. Specific details are given.
Monte Carlo method of solving heat conduction problems
S. K. Fraley; T. J. Hoffman; P. N. Stevens
1977-01-01
An innovative approach in the use of Monte Carlo to solve heat conduction problems was developed using a transport equation approximation to the heat conduction equation. The method was shown to be applicable to the solution of multimedia problems in complex geometries with no inherent limitations as to the geometric complexity of problems which can be solved. Nuclear radiation transport
On Monte Carlo simulations of the LAser RElativity Satellite experiment
NASA Astrophysics Data System (ADS)
Renzetti, G.
2015-05-01
I offer some critical reflections on recent Monte Carlo simulations of the Lageos-LARES experiment which aims to measure Earth×³s frame-dragging to percent level. I demonstrate that, in fact, they did not add anything new in support of this goal, being essentially affected by some of the issues already found in past analyses. I suggest some possible ameliorations.
Replica Exchange for Reactive Monte Carlo Simulations C. Heath Turner*
Lisal, Martin
Replica Exchange for Reactive Monte Carlo Simulations C. Heath Turner* Department of Chemical Research Laboratory, Weapons and Materials Research Directorate, Aberdeen ProVing Ground, Maryland 21005-5066 Martin Li´sal E. Ha´la Laboratory of Thermodynamics, Institute of Chemical Process Fundamentals, Academy
Monte Carlo simulation of neutron transport in intense neutron fields
W. K. Matthes
2008-01-01
Common Monte Carlo (MC) codes for neutron transport are usually applied to neutron fields of low density under the assumption that the isotopic composition of the structure materials will not be changed in neutron reactions. This assumption is no longer valid in intense neutron fields, where an appreciable number of nuclei of the structural material may get transformed into other
Quasicontinuum Monte Carlo: A method for surface growth simulations
G. Russo; L. M. Sander; P. Smereka
2004-01-01
We introduce an algorithm for treating growth on surfaces which combines important features of continuum methods (such as the level-set method) and kinetic Monte Carlo (KMC) simulations. We treat the motion of adatoms in continuum theory, but attach them to islands one atom at a time. The technique is borrowed from the dielectric breakdown model. Our method allows us to
A multilayer Monte Carlo method with free phase function choice
NASA Astrophysics Data System (ADS)
Watté, R.; Aernouts, B.; Saeys, W.
2012-06-01
This paper presents an adaptation of the widely accepted Monte Carlo method for Multi-layered media (MCML). Its original Henyey-Greenstein phase function is an interesting approach for describing how light scattering inside biological tissues occurs. It has the important advantage of generating deflection angles in an efficient - and therefore computationally fast- manner. However, in order to allow the fast generation of the phase function, the MCML code generates a distribution for the cosine of the deflection angle instead of generating a distribution for the deflection angle, causing a bias in the phase function. Moreover, other, more elaborate phase functions are not available in the MCML code. To overcome these limitations of MCML, it was adapted to allow the use of any discretized phase function. An additional tool allows generating a numerical approximation for the phase function for every layer. This could either be a discretized version of (1) the Henyey-Greenstein phase function, (2) a modified Henyey-Greenstein phase function or (3) a phase function generated from the Mie theory. These discretized phase functions are then stored in a look-up table, which can be used by the adapted Monte Carlo code. The Monte Carlo code with flexible phase function choice (fpf-MC) was compared and validated with the original MCML code. The novelty of the developed program is the generation of a user-friendly algorithm, which allows several types of phase functions to be generated and applied into a Monte Carlo method, without compromising the computational performance.
A Monte Carlo Approach for Football Play Generation Kennard Laviers
Sukthankar, Gita Reese
A Monte Carlo Approach for Football Play Generation Kennard Laviers School of EECS U. of Central, adversarial games and demonstrate its utility at gen- erating American football plays for Rush Football 2008. In football, like in many other multi-agent games, the actions of all of the agents are not equally crucial
MONTE CARLO EXPLORATIONS OF POLYGONAL KNOT SPACES KENNETH C. MILLETT
California at Santa Barbara, University of
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
Force induced melting of DNA hairpin: A Monte Carlo study
NASA Astrophysics Data System (ADS)
Kalyan, M. Suman; Murthy, K. P. N.
2013-02-01
In this paper we present the thermodynamic properties of DNA hairpin studied by using non-Boltzmann Monte Carlo methods. The force-temperature phase diagram and Landau free energy near and at critical temperatures are obtained. From free energy curves it is observed that the transition from closed loop state to open state is of first order.
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.
Exploring Mass Perception with Markov Chain Monte Carlo
ERIC Educational Resources Information Center
Cohen, Andrew L.; Ross, Michael G.
2009-01-01
Several previous studies have examined the ability to judge the relative mass of objects in idealized collisions. With a newly developed technique of psychological Markov chain Monte Carlo sampling (A. N. Sanborn & T. L. Griffiths, 2008), this work explores participants; perceptions of different collision mass ratios. The results reveal…
A separable shadow Hamiltonian hybrid Monte Carlo method
NASA Astrophysics Data System (ADS)
Sweet, Christopher R.; Hampton, Scott S.; Skeel, Robert D.; Izaguirre, Jesús A.
2009-11-01
Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The shadow hybrid Monte Carlo (SHMC) was previously introduced to reduce this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. SHMC's performance is limited by the need to generate momenta for the MD step from a nonseparable shadow Hamiltonian. We introduce the separable shadow Hamiltonian hybrid Monte Carlo (S2HMC) method based on a formulation of the leapfrog/Verlet integrator that corresponds to a separable shadow Hamiltonian, which allows efficient generation of momenta. S2HMC gives the acceptance rate of a fourth order integrator at the cost of a second-order integrator. Through numerical experiments we show that S2HMC consistently gives a speedup greater than two over HMC for systems with more than 4000 atoms for the same variance. By comparison, SHMC gave a maximum speedup of only 1.6 over HMC. S2HMC has the additional advantage of not requiring any user parameters beyond those of HMC. S2HMC is available in the program PROTOMOL 2.1. A Python version, adequate for didactic purposes, is also in MDL (http://mdlab.sourceforge.net/s2hmc).
Markov chain Monte Carlo Lecture 3 Markov Chain: Definition
Liang, Faming
Markov chain Monte Carlo Lecture 3 Markov Chain: Definition A Markov chain, named after Andrey Markov, is a sequence of ran- dom variables {Xi : i = 0, 1, 2, ...} with the Markov property that given A|X0 = x0, ..., Xt = xt) = Pr (Xt+1 A|Xt = xt) (1) holds for time t = 0, 1, ... #12;Markov chain
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
Systemic risk in banking networks without Monte Carlo simulation
Hurd, Thomas R.
Systemic risk in banking networks without Monte Carlo simulation James P. Gleeson1 , T. R. Hurd2 An analytical approach to calculating the expected size of contagion events in models of banking networks to be initiated by the default of one or more banks, and includes liquidity risk effects. Theoretical results
Applying Monte Carlo Techniques to the Capacitated Vehicle Routing Problem
Kosters, Walter
Applying Monte Carlo Techniques to the Capacitated Vehicle Routing Problem Frank W. Takes Walter A This paper describes a new method for solving the Capacitated Vehicle Routing Problem (CVRP). The CVRP-of-the-art methods based on metaheuristics. 1 Introduction The Vehicle Routing Problem (VRP) is a widely studied [17
Quasi-Newton Methods for Markov Chain Monte Carlo
Kaski, Samuel
Quasi-Newton Methods for Markov Chain Monte Carlo Yichuan Zhang and Charles Sutton School or infeasible. In this paper we propose MCMC samplers that make use of quasi- Newton approximations, which not valid. We address this problem by using limited memory quasi-Newton methods, which depend only
Monte Carlo simulation of entry in the Martian atmosphere
NASA Technical Reports Server (NTRS)
Hash, David B.; Hassan, H. A.
1992-01-01
The Direct Simulation Monte Carlo method of Bird is used to investigate the characteristics of low density hypersonic flowfields for typical aerobrakes during Martian atmospheric entry. The method allows for both thermal and chemical nonequilibrium. Results are presented for a sixty-degree spherically blunt cone for various nose radii and altitudes.
A separable shadow Hamiltonian hybrid Monte Carlo method
Sweet, Christopher R.; Hampton, Scott S.; Skeel, Robert D.; Izaguirre, Jesús A.
2009-01-01
Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The shadow hybrid Monte Carlo (SHMC) was previously introduced to reduce this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. SHMC’s performance is limited by the need to generate momenta for the MD step from a nonseparable shadow Hamiltonian. We introduce the separable shadow Hamiltonian hybrid Monte Carlo (S2HMC) method based on a formulation of the leapfrog?Verlet integrator that corresponds to a separable shadow Hamiltonian, which allows efficient generation of momenta. S2HMC gives the acceptance rate of a fourth order integrator at the cost of a second-order integrator. Through numerical experiments we show that S2HMC consistently gives a speedup greater than two over HMC for systems with more than 4000 atoms for the same variance. By comparison, SHMC gave a maximum speedup of only 1.6 over HMC. S2HMC has the additional advantage of not requiring any user parameters beyond those of HMC. S2HMC is available in the program PROTOMOL 2.1. A Python version, adequate for didactic purposes, is also in MDL (http:??mdlab.sourceforge.net?s2hmc). PMID:19894997
Modeling granular phosphor screens by Monte Carlo methods
Panagiotis F. Liaparinos; Ioannis S. Kandarakis; Dionisis A. Cavouras; Harry B. Delis; George S. Panayiotakisa
2006-01-01
The intrinsic phosphor properties are of significant importance for the performance of phosphor screens used in medical imaging systems. In previous analytical-theoretical and Monte Carlo studies on granular phosphor materials, values of optical properties, and light interaction cross sections were found by fitting to experimental data. These values were then employed for the assessment of phosphor screen imaging performance. However,
Bayesian Monte Carlo for the Global Optimization of Expensive Functions
Groot, Perry
representing environmental variables. Typ- ically, xc needs to be optimised, whereas xe are uncontrollable Bayesian Monte Carlo to obtain the objective function by integrating out environmental variables- istic case (i.e., no environmental variables) and show that the ALC criterion appears significantly
Applications of the Monte Carlo radiation transport toolkit at LLNL
NASA Astrophysics Data System (ADS)
Sale, Kenneth E.; Bergstrom, Paul M., Jr.; Buck, Richard M.; Cullen, Dermot; Fujino, D.; Hartmann-Siantar, Christine
1999-09-01
Modern Monte Carlo radiation transport codes can be applied to model most applications of radiation, from optical to TeV photons, from thermal neutrons to heavy ions. Simulations can include any desired level of detail in three-dimensional geometries using the right level of detail in the reaction physics. The technology areas to which we have applied these codes include medical applications, defense, safety and security programs, nuclear safeguards and industrial and research system design and control. The main reason such applications are interesting is that by using these tools substantial savings of time and effort (i.e. money) can be realized. In addition it is possible to separate out and investigate computationally effects which can not be isolated and studied in experiments. In model calculations, just as in real life, one must take care in order to get the correct answer to the right question. Advancing computing technology allows extensions of Monte Carlo applications in two directions. First, as computers become more powerful more problems can be accurately modeled. Second, as computing power becomes cheaper Monte Carlo methods become accessible more widely. An overview of the set of Monte Carlo radiation transport tools in use a LLNL will be presented along with a few examples of applications and future directions.
Monte Carlo Radiation Analysis of a Spacecraft Radioisotope Power System
NASA Technical Reports Server (NTRS)
Wallace, M.
1994-01-01
A Monte Carlo statistical computer analysis was used to create neutron and photon radiation predictions for the General Purpose Heat Source Radioisotope Thermoelectric Generator (GPHS RTG). The GPHS RTG is being used on several NASA planetary missions. Analytical results were validated using measured health physics data.
Cool Walking: A New Markov Chain Monte Carlo Sampling Method
Head-Gordon, Teresa L.
Cool Walking: A New Markov Chain Monte Carlo Sampling Method SCOTT BROWN, TERESA HEAD for overcoming quasi-ergodicity problems such as Jump Walking (J-Walking), Smart Walking (S-Walking), Smart Darting, and Parallel Tempering. We present an alternative to these approaches that we call Cool Walking
Monte Carlo Simulations of Light Propagation in Apples
Technology Transfer Automated Retrieval System (TEKTRAN)
This paper reports on the investigation of light propagation in fresh apples in the visible and short-wave near-infrared region using Monte Carlo simulations. Optical properties of ‘Golden Delicious’ apples were determined over the spectral range of 500-1100 nm using a hyperspectral imaging method, ...
Monte Carlo calculations of the vacuum Compton detector sensitivities
Hsu- Hsiao-Hua; Lee, Huan
1989-01-01
Monte Carlo simulations have been carried out to compute the static sensitivity of the vacuum Compton detector for monoenergetic gamma rays and electrons. A similar calculation using /sup 60/Co spectrum as input is found in good agreement with measurements. We also calculate the detector sensitivities for bremsstrahlung spectra produced by monoenergetic e-beam and compare with experimental data. 8 refs., 6 figs.
Monte Carlo variance reduction using finite element adjoint weight windows
Shahdatullah, M. S.; Ziver, K.; Eaton, M. D.; Pain, C. C.; Goddard, A. J. H.
2006-07-01
The use of Monte Carlo variance reduction techniques is unavoidable on present day computers in obtaining numerical solutions in complex shielding, deep penetration or other radiation transport problems such as nuclear well logging and ex-core reactor core modeling etc. A deterministic variance reduction technique based on the finite element adjoint weight window (FEAWW) scheme is developed and applied in the well-known and widely used Monte Carlo radiation transport code MCNP. The scheme involves generating importance maps from the adjoint deterministic EVENT transport calculations which are then extracted and used as 'weight window lower bounds' suitable for acceleration of the forward Monte Carlo radiation transport calculations. The 'holy grail' of an automatic variance reduction technique is to provide a single method which provides systematic or nearly systematic ways to eliminate much of the user's intervention. The proposed method employs the adjoint solutions to the problem of interest which has been folded into the MCNP weight window scheme. The FEAWW method is tested on a number of complex deep penetration and neutron streaming problems and compared against the standard Monte Carlo generated variance reduction techniques with encouraging results. (authors)
Reagents for Electrophilic Amination: A Quantum Monte CarloStudy
Amador-Bedolla, Carlos; Salomon-Ferrer, Romelia; Lester Jr.,William A.; Vazquez-Martinez, Jose A.; Aspuru-Guzik, Alan
2006-11-01
Electroamination is an appealing synthetic strategy toconstruct carbon-nitrogen bonds. We explore the use of the quantum MonteCarlo method and a proposed variant of the electron-pair localizationfunction--the electron-pair localization function density--as a measureof the nucleophilicity of nitrogen lone-pairs as a possible screeningprocedure for electrophilic reagents.
BROWNIAN PROCESSES FOR MONTE CARLO INTEGRATION ON COMPACT LIE GROUPS
Manton, Jonathan
BROWNIAN PROCESSES FOR MONTE CARLO INTEGRATION ON COMPACT LIE GROUPS S. SAID, The University for the evaluation of integrals of smooth functions defined on compact Lie groups. The approach is based on the ergodic property of Brownian processes in compact Lie groups. The paper provides an elementary proof
PATH INTEGRAL MONTE CARLO SIMULATIONS OF HOT DENSE BURKHARD MILITZER
Militzer, Burkhard
, PIMC has been applied to study the equilibrium properties of hot, dense hydrogen in the temperature thermodynamic properties. The modi#12;ca- tions are particularly signi#12;cant at low temperature and highPATH INTEGRAL MONTE CARLO SIMULATIONS OF HOT DENSE HYDROGEN BY BURKHARD MILITZER Diplom, Humboldt
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.
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…
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.
I. QUANTUM MONTE CARLO METHODS: INTRODUCTION AND BASICS Markus Holzmann
, 2012) I will provide a rough overview of zero temperature Quantum Monte Carlo calculations in electronic structure or chemical physics. Ideally, one would like to know the eigen values parameters which are then optimized to lower the energy. However, already the evaluation of the wavefunction
Bayesian internal dosimetry calculations using Markov Chain Monte Carlo.
Miller, G; Martz, H F; Little, T T; Guilmette, R
2002-01-01
A new numerical method for solving the inverse problem of internal dosimetry is described. The new method uses Markov Chain Monte Carlo and the Metropolis algorithm. Multiple intake amounts, biokinetic types, and times of intake are determined from bioassay data by integrating over the Bayesian posterior distribution. The method appears definitive, but its application requires a large amount of computing time. PMID:11926369
Titrating Polyelectrolytes --Variational Calculations and Monte Carlo Simulations
Söderberg, Bo
LU TP 951 May 1995 Titrating Polyelectrolytes -- Variational Calculations and Monte Carlo properties of a titrating polyelectrolyte in a discrete representation. In the variational treatment.e. titratable groups in a polymer will exchange protons with the solution and the polymer net charge will vary
Bold Diagrammatic Monte Carlo for Fermionic and Fermionized Systems
NASA Astrophysics Data System (ADS)
Svistunov, Boris
2013-03-01
In three different fermionic cases--repulsive Hubbard model, resonant fermions, and fermionized spins-1/2 (on triangular lattice)--we observe the phenomenon of sign blessing: Feynman diagrammatic series features finite convergence radius despite factorial growth of the number of diagrams with diagram order. Bold diagrammatic Monte Carlo technique allows us to sample millions of skeleton Feynman diagrams. With the universal fermionization trick we can fermionize essentially any (bosonic, spin, mixed, etc.) lattice system. The combination of fermionization and Bold diagrammatic Monte Carlo yields a universal first-principle approach to strongly correlated lattice systems, provided the sign blessing is a generic fermionic phenomenon. In three different fermionic cases--repulsive Hubbard model, resonant fermions, and fermionized spins-1/2 (on triangular lattice)--we observe the phenomenon of sign blessing: Feynman diagrammatic series features finite convergence radius despite factorial growth of the number of diagrams with diagram order. Bold diagrammatic Monte Carlo technique allows us to sample millions of skeleton Feynman diagrams. With the universal fermionization trick we can fermionize essentially any (bosonic, spin, mixed, etc.) lattice system. The combination of fermionization and Bold diagrammatic Monte Carlo yields a universal first-principle approach to strongly correlated lattice systems, provided the sign blessing is a generic fermionic phenomenon. Supported by NSF and DARPA
A Monte Carlo simulation of nucleation in amphiphilic solution
Isamu Kusaka; David W. Oxtoby
2001-01-01
We study nucleation of amphiphilic molecules in a solvent-amphiphile binary solution by Monte Carlo simulation. The method provides detailed information on the free energetics of micelle formation. Our model, despite its simplicity, captures various aspects of real amphiphilic solutions. For example, the density profiles exhibit typical micelle structure. The free energy surface for micelle formation is in line with recent
Criticality: a Monte-Carlo Heuristic for Go Remi Coulom
Coulom, Rémi - Groupe de Recherche sur l'Apprentissage Automatique, Université Charles de Gaulle
Criticality: a Monte-Carlo Heuristic for Go Programs R´emi Coulom Universit´e Charles de Gaulle for Go Programs 2 / 9 #12;Introduction Criticality Heuristic Experiments with Crazy Stone Conclusion´emi Coulom Criticality: a MC Heuristic for Go Programs 3 / 9 #12;Introduction Criticality Heuristic
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 of solids and clusters. CONTENTS I. Introduction 34 II. Interacting Electrons in Solids 35 A. The many to Ground States 55 A. Cohesive energies of solids 55 B. Phases of the electron gas 55 C. Static response
Monte Carlo event generators for hadron-hadron collisions
Knowles, I.G.; Protopopescu, S.D.
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 CALCULATIONS OF LR115 DETECTOR RESPONSE TO 222
Yu, Peter K.N.
Paper MONTE CARLO CALCULATIONS OF LR115 DETECTOR RESPONSE TO 222 Rn IN THE PRESENCE OF 220 Rn D. Nikezic´* and K. N. Yu* Abstract--The sensitivities (in m) of bare LR115 detectors and detectors for the LR115 detector. However, the total sensitiv- ities are approximately equal because 220 Rn is always
Noninvasive glucose monitoring in vivo based on Monte Carlo modeling
Li Xia Yu; Ji Liu
2010-01-01
Non-invasive glucose monitoring is one of the most active areas in biomedical research. A novel method for blood glucose measurement is presented. The measuring system consists of modulated laser, polarizer, photodiode and the lock-in amplifier. To study the light propagation and distribution in skin, the tissues model is established by using Monte Carlo Method. The results demonstrate that linear relationship
A Monte Carlo method for exponential hedging of contingent claims
Hurd, Thomas R.
of Black, Scholes, Merton and others, #12;- nancial assets in complete markets can be priced uniquely theoretically con- sistent approach to pricing and hedging of securities in incomplete #12;nancial markets on simulated Monte Carlo data. It shares with the LS framework intuitivity, simplicity and ex- ibility. #3
Optimising Monte Carlo Search Strategies for Automated Pattern Detection
Rosenthal, Jeffrey S.
a ``face'' (two eyes and a nose) from a sea of pixels. We describe an interactive patterndetection Java object detection models ``as simple as possible''). We assume that we seek some object (e.g., a faceOptimising Monte Carlo Search Strategies for Automated Pattern Detection by Je#rey S. Rosenthal
Optimising Monte Carlo Search Strategies for Automated Pattern Detection
Rosenthal, Jeffrey S.
a "face" (two eyes and a nose) from a sea of pixels. We describe an interactive pattern-detection Java detection models "as simple as possible"). We assume that we seek some object (e.g., a faceOptimising Monte Carlo Search Strategies for Automated Pattern Detection by Jeffrey S. Rosenthal
Monte Carlo simulation of ?-scattering for density variation measurement
NASA Astrophysics Data System (ADS)
Khiem, L. H.; Trong, T. D.
2015-05-01
This report studies the possibility of using backscattered ?-radiation for checking the density fluctuations of concrete thickness of newly constructed highways by means of Monte Carlo simulation. A computer program named NUCLGAUGE has been written in Visual Basics language. It should be useful for designing a device for density variation measurement of concrete layer of newly constructed highways using backscattered ?-radiation.
Modele Dayali Pekistirme ile grenme iin Ardisik Monte Carlo rnekleyicileri
Cemgil, A. Taylan
vd. [7] ise tersinir atlama Markov zinciri Monte Carlo kullanarak yakla¸sik olarak çikarim yapmi¸slardir. Biz ise, peki¸stime ile ögrenme probleminin çözümü için türetilmi¸s bu beklenti sunuyoruz. Son olarak ise, IV. bölümde yön- temimizi ölçüt bir problem üzerinde gerçekledigimiz deneyi ve
On Generating Monte Carlo Samples of Continuous Diffusion Bridges
Mykland, Per A.
On Generating Monte Carlo Samples of Continuous Diffusion Bridges Ming LIN, Rong CHEN, and Per, it is often useful to impute continuous-time bridge samples that follow the diffusion dynamics and connect for generating the intermediate paths of the bridge. The paths often are generated forward from the starting
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 ...
A Monte Carlo method for calculating orbits of comets
J. Q. Zheng; M. J. Valtonen; S. Mikkola; J. J. Matese; P. G. Whitman; H. Rickman
1994-01-01
The present work is divided into two stages: 1. By using large numbers (several millions) of accurate orbit integrations with the K-S regularization, probability distributions for changes in the orbital elements of comets during encounters with planets are evaluated. 2. These distributions are used in a Monte Carlo simulation scheme which follows the evolution of orbits under repeated close encounters.
Optical Monte Carlo modeling of a true portwine stain anatomy
Jennifer K. Barton; T. Joshua Pfefer; Ashley J. Welch; Derek J. Smithies; Jerry Nelson; Martin J. van Gemert
1998-01-01
A unique Monte Carlo program capable of accommodating an arbitrarily complex geometry was used to determine the energy deposition in a true port wine stain anatomy. Serial histologic sections taken from a biopsy of a dark red, laser therapy resistant stain were digitized and used to create the program input for simulation at wavelengths of 532 and 585 nm. At
Status of Vectorized Monte Carlo for Particle Transport Analysis
William R. Martin; Forrest B. Brown
1987-01-01
The conventional particle transport Monte Carlo algorithm is ill suited for modem vector supercomputers because the random nature of the particle transport process in the history based algorithm in hibits construction of vectors. An alterna tive, event-based algorithm is suitable for vectorization and has been used recently to achieve impressive gains in perfor mance on vector supercomputers. This re view
Parallel Monte Carlo Ion Recombination Simulation in Orca
Seinstra, Frank J.
Parallel Monte Carlo Ion Recombination Simulation in Orca Frank J. Seinstra Department of Mathematics and Computer Science Vrije Universiteit Amsterdam, The Netherlands August 1996 Abstract: Orca in most languages for dis tributed programming is based on message passing. In Orca, however, a shared
Monte Carlo Simulation of the Strength of Hybrid Composites
Hiroshi Fukuda; Tsu-Wei Chou
1982-01-01
This paper first deals with the stress concentration factors for a general fiber breakage model. The knowledge of stress redistribution at fiber fracture is then used for a Monte Carlo simulation of composite strength. The theoretical analysis has predicted the multiple fracture pattern of the low elongation fibers and the progressive nature of failure of hybrid composites. The enhanced ultimate
Ballistic target tracking based on quasi-Monte Carlo filtering
Hui Zhang; Chongzhao Han; Xiao Wang
2010-01-01
In this paper, we propose a new sequential quasi-Monte Carlo (SQMC) filtering algorithm for ballistic target tracking in the reentry phase. The central idea of the new algorithm is to apply number theoretic sampling method to SQMC. The point set of uniform distribution generated by cyclotomic field can construct more uniform scattered points in unit cube. Therefore, random samples generated
A Monte Carlo Approach for Adaptive Testing with Content Constraints
ERIC Educational Resources Information Center
Belov, Dmitry I.; Armstrong, Ronald D.; Weissman, Alexander
2008-01-01
This article presents a new algorithm for computerized adaptive testing (CAT) when content constraints are present. The algorithm is based on shadow CAT methodology to meet content constraints but applies Monte Carlo methods and provides the following advantages over shadow CAT: (a) lower maximum item exposure rates, (b) higher utilization of the…
Thermal Properties of Supercritical Carbon Dioxide by Monte Carlo Simulations
Lisal, Martin
Thermal Properties of Supercritical Carbon Dioxide by Monte Carlo Simulations C.M. COLINAa,b, *, C and speed of sound for carbon dioxide (CO2) in the supercritical region, using the fluctuation method based: Fluctuations; Carbon dioxide; 2CLJQ; JouleThomson coefficient; Speed of sound INTRODUCTION Simulation methods
Monte Carlo determination of the critical coupling in ?24 theory
NASA Astrophysics Data System (ADS)
Bosetti, Paolo; De Palma, Barbara; Guagnelli, Marco
2015-08-01
We use lattice formulation of ?4 theory in order to investigate nonperturbative features of its continuum limit in two dimensions. In particular, by means of Monte Carlo calculations, we obtain the critical coupling constant g /?2 in the continuum, where g is the unrenormalized coupling. Our final result is g /?2=11.15 ±0.0 6stat±0.0 3syst .
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 ...
Addendum to “Event-chain Monte Carlo algorithms for hard-sphere systems”
Bernard, Etienne
We extend the event-chain Monte Carlo algorithm from hard-sphere interactions to general potentials. This event-driven Monte Carlo algorithm is nonlocal and rejection free and allows for the breaking of detailed balance. ...
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
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.
Variational Quantum MonteCarlo Simulations with Tensor-Network States
NASA Astrophysics Data System (ADS)
Sandvik, A. W.; Vidal, G.
2007-11-01
We show that the formalism of tensor-network states, such as the matrix-product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of this approach by explicit MPS calculations for the transverse Ising chain with up to N=256 spins at criticality, using periodic boundary conditions and D×D matrices with D up to 48. The computational cost of our scheme formally scales as ND3, whereas standard MPS approaches and the related density matrix renormalization group method scale as ND5 and ND6, respectively, for periodic systems.
Monte Carlo Tests of SLE Predictions for the 2D Self-Avoiding Walk
Tom Kennedy
2001-12-21
The conjecture that the scaling limit of the two-dimensional self-avoiding walk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE) with $\\kappa=8/3$ leads to explicit predictions about the SAW. A remarkable feature of these predictions is that they yield not just critical exponents, but probability distributions for certain random variables associated with the self-avoiding walk. We test two of these predictions with Monte Carlo simulations and find excellent agreement, thus providing numerical support to the conjecture that the scaling limit of the SAW is SLE$_{8/3}$.
NASA Astrophysics Data System (ADS)
Shimizu, Keiichi; Genji, Takamu
The situation in which the plan of a new distribution network system should be examined as an electric power company approaches by the multi-machine interconnection of the distributed generators that will be expected in the near future. Then, the authors assumed applying the distribution system which may be adopted as the near future to a system and equipment of the Kansai Electric Power Company, and executed the reliability evaluation concerning the outage energy and voltage sag power that used the real scale model of distribution system by the stochastic reliability evaluation that used the Monte Carlo method.
Population Monte Carlo algorithms Yukito Iba The Institute of Statistical Mathematics
Iba, Yukito
279 ¤ Population Monte Carlo algorithms Yukito Iba The Institute of Statistical Mathematics iba algorithm Summary We give a cross-disciplinary survey on "population" Monte Carlo algorithms-disciplinary survey on "population" Monte Carlo algorithms. These al- gorithms, which are developed in various fields
A Markov-Chain Monte Carlo Approach to Simultaneous Localization and Mapping
Szepesvari, Csaba
A Markov-Chain Monte Carlo Approach to Simultaneous Localization and Mapping P´eter Torma Andr. of Computing Sciences University of Alberta, Canada Abstract A Markov-chain Monte Carlo based algo- rithm a so- lution to this problem based on a Markov-chain Monte Carlo (see, e.g., Andrieu et al., 2003
Open source software for electric field Monte Carlo simulation of coherent
Ottino, Julio M.
Open source software for electric field Monte Carlo simulation of coherent backscattering/14/2013 Terms of Use: http://spiedl.org/terms #12;Open source software for electric field Monte Carlo simulation present an open source electric field tracking Monte Carlo program to model backscattering in biological
Open source software for electric field Monte Carlo simulation of coherent
Pradhan, Prabhakar
Open source software for electric field Monte Carlo simulation of coherent backscattering/26/2012 Terms of Use: http://spiedl.org/terms #12;Open source software for electric field Monte Carlo simulation present an open source electric field tracking Monte Carlo program to model backscattering in biological
Resonance fluorescence near a photonic band edge: Dressedstate Monte Carlo wavefunction approach
John, Sajeev
Resonance fluorescence near a photonic band edge: DressedÂstate Monte Carlo waveÂfunction approach, Ontario, Canada M5S 1A7 ~Received 2 June 1997! We introduce a dressedÂstate Monte Carlo waveÂfunction frequencies. In this paper we introduce a dressedÂstate Monte Carlo waveÂfunction ~MCWF! technique @26
NASA Astrophysics Data System (ADS)
Armas-Pérez, Julio C.; Londono-Hurtado, Alejandro; Guzmán, Orlando; Hernández-Ortiz, Juan P.; de Pablo, Juan J.
2015-07-01
A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.
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.
Accelerated rescaling of single Monte Carlo simulation runs with the Graphics Processing Unit (GPU).
Yang, Owen; Choi, Bernard
2013-01-01
To interpret fiber-based and camera-based measurements of remitted light from biological tissues, researchers typically use analytical models, such as the diffusion approximation to light transport theory, or stochastic models, such as Monte Carlo modeling. To achieve rapid (ideally real-time) measurement of tissue optical properties, especially in clinical situations, there is a critical need to accelerate Monte Carlo simulation runs. In this manuscript, we report on our approach using the Graphics Processing Unit (GPU) to accelerate rescaling of single Monte Carlo runs to calculate rapidly diffuse reflectance values for different sets of tissue optical properties. We selected MATLAB to enable non-specialists in C and CUDA-based programming to use the generated open-source code. We developed a software package with four abstraction layers. To calculate a set of diffuse reflectance values from a simulated tissue with homogeneous optical properties, our rescaling GPU-based approach achieves a reduction in computation time of several orders of magnitude as compared to other GPU-based approaches. Specifically, our GPU-based approach generated a diffuse reflectance value in 0.08ms. The transfer time from CPU to GPU memory currently is a limiting factor with GPU-based calculations. However, for calculation of multiple diffuse reflectance values, our GPU-based approach still can lead to processing that is ~3400 times faster than other GPU-based approaches. PMID:24298424
Armas-Pérez, Julio C; Londono-Hurtado, Alejandro; Guzmán, Orlando; Hernández-Ortiz, Juan P; de Pablo, Juan J
2015-07-28
A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate. PMID:26233107
GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA
NASA Astrophysics Data System (ADS)
Spiechowicz, J.; Kostur, M.; Machura, L.
2015-06-01
This work presents an updated and extended guide on methods of a proper acceleration of the Monte Carlo integration of stochastic differential equations with the commonly available NVIDIA Graphics Processing Units using the CUDA programming environment. We outline the general aspects of the scientific computing on graphics cards and demonstrate them with two models of a well known phenomenon of the noise induced transport of Brownian motors in periodic structures. As a source of fluctuations in the considered systems we selected the three most commonly occurring noises: the Gaussian white noise, the white Poissonian noise and the dichotomous process also known as a random telegraph signal. The detailed discussion on various aspects of the applied numerical schemes is also presented. The measured speedup can be of the astonishing order of about 3000 when compared to a typical CPU. This number significantly expands the range of problems solvable by use of stochastic simulations, allowing even an interactive research in some cases.
Fast Monte Carlo-assisted simulation of cloudy Earth backgrounds
NASA Astrophysics Data System (ADS)
Adler-Golden, Steven; Richtsmeier, Steven C.; Berk, Alexander; Duff, James W.
2012-11-01
A calculation method has been developed for rapidly synthesizing radiometrically accurate ultraviolet through longwavelengthinfrared spectral imagery of the Earth for arbitrary locations and cloud fields. The method combines cloudfree surface reflectance imagery with cloud radiance images calculated from a first-principles 3-D radiation transport model. The MCScene Monte Carlo code [1-4] is used to build a cloud image library; a data fusion method is incorporated to speed convergence. The surface and cloud images are combined with an upper atmospheric description with the aid of solar and thermal radiation transport equations that account for atmospheric inhomogeneity. The method enables a wide variety of sensor and sun locations, cloud fields, and surfaces to be combined on-the-fly, and provides hyperspectral wavelength resolution with minimal computational effort. The simulations agree very well with much more time-consuming direct Monte Carlo calculations of the same scene.
Fixed-node diffusion Monte Carlo method for lithium systems
NASA Astrophysics Data System (ADS)
Rasch, K. M.; Mitas, L.
2015-07-01
We study lithium systems over a range of a number of atoms, specifically atomic anion, dimer, metallic cluster, and body-centered-cubic crystal, using the fixed-node diffusion Monte Carlo method. The focus is on analysis of the fixed-node errors of each system, and for that purpose we test several orbital sets in order to provide the most accurate nodal hypersurfaces. The calculations include both core and valence electrons in order to avoid any possible impact by pseudopotentials. To quantify the fixed-node errors, we compare our results to other highly accurate calculations, and wherever available, to experimental observations. The results for these Li systems show that the fixed-node diffusion Monte Carlo method achieves accurate total energies, recovers 96 -99 % of the correlation energy, and estimates binding energies with errors bounded by 0.1 eV /at .
Estimation of beryllium ground state energy by Monte Carlo simulation
NASA Astrophysics Data System (ADS)
Kabir, K. M. Ariful; Halder, Amal
2015-05-01
Quantum Monte Carlo method represent a powerful and broadly applicable computational tool for finding very accurate solution of the stationary Schrödinger equation for atoms, molecules, solids and a variety of model systems. Using variational Monte Carlo method we have calculated the ground state energy of the Beryllium atom. Our calculation are based on using a modified four parameters trial wave function which leads to good result comparing with the few parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Beryllium. Our calculation gives good estimation for the ground state energy of the Beryllium atom comparing with the corresponding exact data.
Monte Carlo Integration Using Spatial Structure of Markov Random Field
NASA Astrophysics Data System (ADS)
Yasuda, Muneki
2015-03-01
Monte Carlo integration (MCI) techniques are important in various fields. In this study, a new MCI technique for Markov random fields (MRFs) is proposed. MCI consists of two successive parts: the first involves sampling using a technique such as the Markov chain Monte Carlo method, and the second involves an averaging operation using the obtained sample points. In the averaging operation, a simple sample averaging technique is often employed. The method proposed in this paper improves the averaging operation by addressing the spatial structure of the MRF and is mathematically guaranteed to statistically outperform standard MCI using the simple sample averaging operation. Moreover, the proposed method can be improved in a systematic manner and is numerically verified by numerical simulations using planar Ising models. In the latter part of this paper, the proposed method is applied to the inverse Ising problem and we observe that it outperforms the maximum pseudo-likelihood estimation.
Interfacial properties of cyclic hydrocarbons: a Monte Carlo study.
Janecek, Jirí; Krienke, Hartmut; Schmeer, Georg
2006-04-01
The Monte Carlo technique is used to study the vapor-liquid interface of cyclopentane, cyclohexane, and benzene. The OPLS and TraPPE potential fields are compared in the temperature range from 298.15 to 348.15 K (273.15-298.15 K for C5H10). A new method for the treatment of the long-range interactions in inhomogeneous simulations is used. When this new method is employed, the obtained values of saturated liquid density and of enthalpy of vaporization are equal to those obtained using the bulk isothermal-isobaric Monte Carlo technique. The values of surface tension become independent of the cutoff distance and they are significantly larger than those when only simple spherical truncation of intermolecular interactions is used. PMID:16571003
Monte Carlo simulations of fermion systems: the determinant method
Gubernatis, J.E.
1985-01-01
Described are the details for performing Monte Carlo simulations on systems of fermions at finite temperatures by use of a technique called the Determinant Method. This method is based on a functional integral formulation of the fermion problem (Blankenbecler et al., Phys. Rev D 24, 2278 (1981)) in which the quartic fermion-fermion interactions that exist for certain models are transformed into bilinear ones by the introduction (J. Hirsch, Phys. Rev. B 28, 4059 (1983)) of Ising-like variables and an additional finite dimension. It is on the transformed problem the Monte Carlo simulations are performed. A brief summary of research on two such model problems, the spinless fermion lattice gas and the Anderson impurity problem, is also given.
Scalability and Parallelization of Monte-Carlo Tree Search
NASA Astrophysics Data System (ADS)
Bourki, Amine; Chaslot, Guillaume; Coulm, Matthieu; Danjean, Vincent; Doghmen, Hassen; Hoock, Jean-Baptiste; Hérault, Thomas; Rimmel, Arpad; Teytaud, Fabien; Teytaud, Olivier; Vayssière, Paul; Yu, Ziqin
Monte-Carlo Tree Search is now a well established algorithm, in games and beyond. We analyze its scalability, and in particular its limitations and the implications in terms of parallelization. We focus on our Go program MoGo and our Havannah program Shakti. We use multicore machines and message-passing machines. For both games and on both type of machines we achieve adequate efficiency for the parallel version. However, in spite of promising results in self-play there are situations for which increasing the time per move does not solve anything. Therefore parallelization is not a solution to all our problems. Nonetheless, for problems where the Monte-Carlo part is less biased than in the game of Go, parallelization should be quite efficient, even without shared memory.
Visibility assessment : Monte Carlo characterization of temporal variability.
Laulainen, N.; Shannon, J.; Trexler, E. C., Jr.
1997-12-12
Current techniques for assessing the benefits of certain anthropogenic emission reductions are largely influenced by limitations in emissions data and atmospheric modeling capability and by the highly variant nature of meteorology. These data and modeling limitations are likely to continue for the foreseeable future, during which time important strategic decisions need to be made. Statistical atmospheric quality data and apportionment techniques are used in Monte-Carlo models to offset serious shortfalls in emissions, entrainment, topography, statistical meteorology data and atmospheric modeling. This paper describes the evolution of Department of Energy (DOE) Monte-Carlo based assessment models and the development of statistical inputs. A companion paper describes techniques which are used to develop the apportionment factors used in the assessment models.
Research on GPU Acceleration for Monte Carlo Criticality Calculation
NASA Astrophysics Data System (ADS)
Xu, Qi; Yu, Ganglin; Wang, Kan
2014-06-01
The Monte Carlo neutron transport method can be naturally parallelized by multi-core architectures due to the dependency between particles during the simulation. The GPU+CPU heterogeneous parallel mode has become an increasingly popular way of parallelism in the field of scientific supercomputing. Thus, this work focuses on the GPU acceleration method for the Monte Carlo criticality simulation, as well as the computational efficiency that GPUs can bring. The "neutron transport step" is introduced to increase the GPU thread occupancy. In order to test the sensitivity of the MC code's complexity, a 1D one-group code and a 3D multi-group general purpose code are respectively transplanted to GPUs, and the acceleration effects are compared. The result of numerical experiments shows considerable acceleration effect of the "neutron transport step" strategy. However, the performance comparison between the 1D code and the 3D code indicates the poor scalability of MC codes on GPUs.
Quasi-Monte Carlo integration over ? for migration ? inversion
NASA Astrophysics Data System (ADS)
de Hoop, Maarten V.; Spencer, Carl
1996-06-01
In this paper, we analyse the discretization of the generalized radon transform/amplitude versus scattering angles (GRT/AVA) migration - inversion formula by means of quasi-Monte Carlo methods. These methods are efficient, in the sense that they require sparsely sampled measurements only, and accurate, which we have shown by theory and examples. Another feature of Monte Carlo methods is their ability to suppress effectively coherent noise associated with undesired wave phenomena in the inversion procedure. As examples, we carried out the associated integrations over 0266-5611/12/3/004/img3 and 0266-5611/12/3/004/img4, and consistently found that quasi-random sequences achieve a prescribed accuracy with significantly fewer nodes.
Monte Carlo Strategies for Selecting Parameter Values in Simulation Experiments.
Leigh, Jessica W; Bryant, David
2015-09-01
Simulation experiments are used widely throughout evolutionary biology and bioinformatics to compare models, promote methods, and test hypotheses. The biggest practical constraint on simulation experiments is the computational demand, particularly as the number of parameters increases. Given the extraordinary success of Monte Carlo methods for conducting inference in phylogenetics, and indeed throughout the sciences, we investigate ways in which Monte Carlo framework can be used to carry out simulation experiments more efficiently. The key idea is to sample parameter values for the experiments, rather than iterate through them exhaustively. Exhaustive analyses become completely infeasible when the number of parameters gets too large, whereas sampled approaches can fare better in higher dimensions. We illustrate the framework with applications to phylogenetics and genetic archaeology. PMID:26012871
Monte Carlo simulation of a mammographic test phantom.
Hunt, R A; Dance, D R; Pachoud, M; Alm Carlsson, G; Sandborg, M; Ullman, G; Verdun, F R
2005-01-01
A test phantom, including a wide range of mammographic tissue equivalent materials and test details, was imaged on a digital mammographic system. In order to quantify the effect of scatter on the contrast obtained for the test details, calculations of the scatter-to-primary ratio (S/P) have been made using a Monte Carlo simulation of the digital mammographic imaging chain, grid and test phantom. The results show that the S/P values corresponding to the imaging conditions used were in the range 0.084-0.126. Calculated and measured pixel values in different regions of the image were compared as a validation of the model and showed excellent agreement. The results indicate the potential of Monte Carlo methods in the image quality-patient dose process optimisation, especially in the assessment of imaging conditions not available on standard mammographic units. PMID:15933151
Drag coefficient modeling for grace using Direct Simulation Monte Carlo
NASA Astrophysics Data System (ADS)
Mehta, Piyush M.; McLaughlin, Craig A.; Sutton, Eric K.
2013-12-01
Drag coefficient is a major source of uncertainty in predicting the orbit of a satellite in low Earth orbit (LEO). Computational methods like the Test Particle Monte Carlo (TPMC) and Direct Simulation Monte Carlo (DSMC) are important tools in accurately computing physical drag coefficients. However, the methods are computationally expensive and cannot be employed real time. Therefore, modeling of the physical drag coefficient is required. This work presents a technique of developing parameterized drag coefficients models using the DSMC method. The technique is validated by developing a model for the Gravity Recovery and Climate Experiment (GRACE) satellite. Results show that drag coefficients computed using the developed model for GRACE agree to within 1% with those computed using DSMC.
An Exact Local Hybrid Monte Carlo Algorithm for Gauge Theories
A. D. Kennedy; K. M. Bitar
1993-11-16
We introduce a new Monte Carlo method for pure gauge theories. It is not intended for use with dynamical fermions. It belongs to the class of Local Hybrid Monte Carlo (LHMC) algorithms, which make use of the locality of the action by updating individual sites or links by following a classical mechanics trajectory in fictitious time. We choose to update a one-parameter subgroup of the gauge field on each link of the lattice, and the classical trajectory can be found in closed form in terms of elliptic functions for this case. We show that this gives an overrelaxation algorithm with a tunable parameter which, unlike some previous methods, does not require the numerical integration of the equations of motion.
Quantum Monte Carlo study of the protonated water dimer
Dagrada, Mario; Saitta, Antonino M; Sorella, Sandro; Mauri, Francesco
2013-01-01
We report an extensive theoretical study of the protonated water dimer (Zundel ion) by means of the highly correlated variational Monte Carlo and lattice regularized Monte Carlo approaches. This system represents the simplest model for proton transfer (PT) and a correct description of its properties is essential in order to understand the PT mechanism in more complex acqueous systems. Our Jastrow correlated AGP wave function ensures an accurate treatment of electron correlations. Exploiting the advantages of contracting the primitive basis set over atomic hybrid orbitals, we are able to limit dramatically the number of variational parameters with a systematic control on the numerical precision, crucial in order to simulate larger systems. We investigate energetics and geometrical properties of the Zundel ion as a function of the oxygen-oxygen distance, taken as reaction coordinate. In both cases, our QMC results are found in excellent agreement with coupled cluster CCSD(T) technique, the quantum chemistry "go...
Kinetic Monte Carlo Studies of Hydrogen Abstraction from Graphite
H. M. Cuppen; L. Hornekaer
2008-07-01
We present Monte Carlo simulations on Eley-Rideal abstraction reactions of atomic hydrogen chemisorbed on graphite. The results are obtained via a hybrid approach where energy barriers derived from density functional theory calculations are used as input to Monte Carlo simulations. By comparing with experimental data, we discriminate between contributions from different Eley-Rideal mechanisms. A combination of two different mechanisms yields good quantitative and qualitative agreement between the experimentally derived and the simulated Eley-Rideal abstraction cross sections and surface configurations. These two mechanisms include a direct Eley-Rideal reaction with fast diffusing H atoms and a dimer mediated Eley-Rideal mechanism with increased cross section at low coverage. Such a dimer mediated Eley-Rideal mechanism has not previously been proposed and serves as an alternative explanation to the steering behavior often given as the cause of the coverage dependence observed in Eley-Rideal reaction cross sections.
Computer Monte Carlo simulation in quantitative resource estimation
Root, D.H.; Menzie, W.D.; Scott, W.A.
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 with the historical grades and tonnages of these deposits to produce a probability distribution of the quantities of contained metal. Two examples of the estimation of the number of deposits (step 2) are given. The first example is for mercury deposits in southwestern Alaska and the second is for lode tin deposits in the Seward Peninsula. The flow of the Monte Carlo simulation program is presented with particular attention to the dependencies between grades and tonnages of deposits and between grades of different metals in the same deposit. ?? 1992 Oxford University Press.
Rejection-free Monte Carlo scheme for anisotropic particles.
Sinkovits, Daniel W; Barr, Stephen A; Luijten, Erik
2012-04-14
We extend the geometric cluster algorithm [J. Liu and E. Luijten, Phys. Rev. Lett. 92, 035504 (2004)], a highly efficient, rejection-free Monte Carlo scheme for fluids and colloidal suspensions, to the case of anisotropic particles. This is made possible by adopting hyperspherical boundary conditions. A detailed derivation of the algorithm is presented, along with extensive implementation details as well as benchmark results. We describe how the quaternion notation is particularly suitable for the four-dimensional geometric operations employed in the algorithm. We present results for asymmetric Lennard-Jones dimers and for the Yukawa one-component plasma in hyperspherical geometry. The efficiency gain that can be achieved compared to conventional, Metropolis-type Monte Carlo simulations is investigated for rod-sphere mixtures as a function of rod aspect ratio, rod-sphere diameter ratio, and rod concentration. The effect of curved geometry on physical properties is addressed. PMID:22502505
Monte Carlo Neutrino Transport in Post-Merger Disks
NASA Astrophysics Data System (ADS)
Richers, Sherwood Andrew; Kasen, Daniel; O'Connor, Evan; Fernandez, Rodrigo; Ott, Christian
2015-08-01
The merger of two neutron stars or a neutron star and a black hole are the prime candidate models for short-duration gamma ray bursts and production of r-process elements. Neutrinos can carry away energy and change the ratio of neutrons to protons, in turn affecting the appearance and dynamics of the burst and the types of elements formed from the outflow. We simulate Monte Carlo transport of neutrinos through the accretion disk surrounding the post-merger black hole and/or hypermassive neutron star to explore the influence of neutrinos on the disk composition and temperature profile, and discover faster thermal and composition evolution by a factor of a few when using Monte Carlo as opposed to neutrino leakage. Additionally, we demonstrate smaller (maximum 20%) differences when employing a simplified set of neutrino interactions commonly used in dynamical simulations.
The MCLIB library: Monte Carlo simulation of neutron scattering instruments
Seeger, P.A.
1995-09-01
Monte Carlo is a method to integrate over a large number of variables. Random numbers are used to select a value for each variable, and the integrand is evaluated. The process is repeated a large number of times and the resulting values are averaged. For a neutron transport problem, first select a neutron from the source distribution, and project it through the instrument using either deterministic or probabilistic algorithms to describe its interaction whenever it hits something, and then (if it hits the detector) tally it in a histogram representing where and when it was detected. This is intended to simulate the process of running an actual experiment (but it is much slower). This report describes the philosophy and structure of MCLIB, a Fortran library of Monte Carlo subroutines which has been developed for design of neutron scattering instruments. A pair of programs (LQDGEOM and MC{_}RUN) which use the library are shown as an example.
Using hierarchical octrees in Monte Carlo radiative transfer simulations
Saftly, W; Baes, M; Gordon, K D; Vandewoude, S; Rahimi, A; Stalevski, M
2013-01-01
A crucial aspect of 3D Monte Carlo radiative transfer is the choice of the spatial grid used to partition the dusty medium. We critically investigate the use of octree grids in Monte Carlo dust radiative transfer, with two different octree construction algorithms (regular and barycentric subdivision) and three different octree traversal algorithms (top-down, neighbour list, and the bookkeeping method). In general, regular octree grids need higher levels of subdivision compared to the barycentric grids for a fixed maximum cell mass threshold criterion. The total number of grid cells, however, depends on the geometry of the model. Surprisingly, regular octree grid simulations turn out to be 10 to 20% more efficient in run time than the barycentric grid simulations, even for those cases where the latter contain fewer grid cells than the former. Furthermore, we find that storing neighbour lists for each cell in an octree, ordered according to decreasing overlap area, is worth the additional memory and implementat...
Monte Carlo simulation of xenon filled cylindrical proportional counters
Rachinhas, P.J.B.M.; Dias, T.H.V.T.; Santos, F.P.; Conde, C.A.N. (Univ. of Coimbra (Portugal). Physics Dept.); Stauffer, A.D. (York Univ., Toronto, Ontario (Canada). Physics Dept.)
1994-08-01
Single electron avalanche processes in a xenon filled cylindrical proportional counter have been simulated using a detailed Monte Carlo technique. The avalanche gain A and its average value M, as well as its frequency distribution and spread parameter b have been calculated for xenon at atmospheric pressure, for a 2.55 cm cathode radius and 12.5 and 50 [mu]m anode radii. A discussion is made of the result obtained for M as a function of the anode voltage in terms of prevailing theories. It is found that Monte Carlo calculated M values are markedly lower than those obtained analytically using the first Townsend ionization coefficient calculated under a uniform field. This puts into evidence the relevance of the non-equilibrium nature of avalanche processes.
Fixed-Node Diffusion Monte Carlo of Lithium Systems
Rasch, Kevin
2015-01-01
We study lithium systems over a range of number of atoms, e.g., atomic anion, dimer, metallic cluster, and body-centered cubic crystal by the diffusion Monte Carlo method. The calculations include both core and valence electrons in order to avoid any possible impact by pseudo potentials. The focus of the study is the fixed-node errors, and for that purpose we test several orbital sets in order to provide the most accurate nodal hyper surfaces. We compare our results to other high accuracy calculations wherever available and to experimental results so as to quantify the the fixed-node errors. The results for these Li systems show that fixed-node quantum Monte Carlo achieves remarkably high accuracy total energies and recovers 97-99 % of the correlation energy.
Mesh-based weight window approach for Monte Carlo simulation
Liu, L. [Computalog USA, Fort Worth, TX (United States); Gardner, R.P. [North Carolina State Univ., Raleigh, NC (United States)
1997-12-01
The Monte Carlo method has been increasingly used to solve particle transport problems. Statistical fluctuation from random sampling is the major limiting factor of its application. To obtain the desired precision, variance reduction techniques are indispensable for most practical problems. Among various variance reduction techniques, the weight window method proves to be one of the most general, powerful, and robust. The method is implemented in the current MCNP code. An importance map is estimated during a regular Monte Carlo run, and then the map is used in the subsequent run for splitting and Russian roulette games. The major drawback of this weight window method is lack of user-friendliness. It normally requires that users divide the large geometric cells into smaller ones by introducing additional surfaces to ensure an acceptable spatial resolution of the importance map. In this paper, we present a new weight window approach to overcome this drawback.
Quantum Monte Carlo Calculations of Pt Nanoclusters and (111) Surface
NASA Astrophysics Data System (ADS)
Parker, William; Benali, Anouar; Shulenburger, Luke; Kim, Jeongnim; Romero, Nichols; Greeley, Jeffrey
2014-03-01
Although density functional theory (DFT) has been successfully used to analyze problems in surface catalysis and electrochemistry at a molecular level, there are several important classes of problems where DFT fails spectacularly, predicting incorrect adsorption energies and binding sites. Better understanding these failures and benchmarking methods for correcting them motivates a quantum Monte Carlo (QMC) investigation of platinum nanoclusters and the platinum (111) surface. To evaluate the transferability of our platinum pseudopotential, we first present the fixed-node diffusion Monte Carlo (DMC) equation of state and cohesive energy for fcc platinum. We then show the binding energies of icosahedral nanoclusters with increasing size and the (111) surface energy to lay the groundwork for investigation of adsorption on these catalytically important phases of platinum.
Kinetic Monte Carlo study of nucleation processes on patterned surfaces
NASA Astrophysics Data System (ADS)
Hopp, Stefan Frieder; Heuer, Andreas
2010-11-01
The properties of template-directed nucleation are studied in the transition region where full nucleation control is lost and additional nucleation beyond the prepatterned structure is observed. To get deeper insight into the microscopic mechanisms, Monte Carlo simulations were performed. In this context, the previously used continuous algorithm [F. Kalischewski, J. Zhu, and A. Heuer, Phys. Rev. B 77, 155401, (2008)] was replaced by a discrete one to reduce simulation time and to allow more detailed calculations. The applied method is based on the assumption that the molecules on the surface occupy the sites of a simple fcc lattice. It is shown that a careful mapping of the continuous Monte Carlo technique onto the discrete algorithm leads to a good reproduction of the former results by means of the latter method. Furthermore, the new method facilitates the calculation of the spatial distribution of nuclei on the surface. This provides a detailed comparison with experimental data.
Monte Carlo calculations of molecular-cloud models
NASA Astrophysics Data System (ADS)
Sobolev, A. M.
A model of molecular spectral line formation in interstellar clouds is proposed as an assembly of spherical layers with arbitrary values of density, temperature, and turbulent velocity dispersion. Results of an extended Monte Carlo method for calculating such a model with random density and temperature distributions and an exponential dependence of photon velocity on distance from the cloud center are presented for CO spectral lines. A method for choosing the spatial step is used to solve the radiative transfer equation. The present Monte Carlo method departs from that proposed by Snell and Lauren (1977) in that a central emission source of radius 0.3 pc and temperature 18 K is present, and that the influence of a relic background is considered. Application of the large velocity gradient method proposed by Snell and Lauren for solution of the radiation transfer equation gave incorrect results for a microturbulent velocity dispersion of 3 km/s, and the present method is preferable.
Large-cell Monte Carlo renormalization of irreversible growth processes
NASA Technical Reports Server (NTRS)
Nakanishi, H.; Family, F.
1985-01-01
Monte Carlo sampling is applied to a recently formulated direct-cell renormalization method for irreversible, disorderly growth processes. Large-cell Monte Carlo renormalization is carried out for various nonequilibrium problems based on the formulation dealing with relative probabilities. Specifically, the method is demonstrated by application to the 'true' self-avoiding walk and the Eden model of growing animals for d = 2, 3, and 4 and to the invasion percolation problem for d = 2 and 3. The results are asymptotically in agreement with expectations; however, unexpected complications arise, suggesting the possibility of crossovers, and in any case, demonstrating the danger of using small cells alone, because of the very slow convergence as the cell size b is extrapolated to infinity. The difficulty of applying the present method to the diffusion-limited-aggregation model, is commented on.
Minimising biases in full configuration interaction quantum Monte Carlo.
Vigor, W A; Spencer, J S; Bearpark, M J; Thom, A J W
2015-03-14
We show that Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a Markov chain in its present form. We construct the Markov matrix of FCIQMC for a two determinant system and hence compute the stationary distribution. These solutions are used to quantify the dependence of the population dynamics on the parameters defining the Markov chain. Despite the simplicity of a system with only two determinants, it still reveals a population control bias inherent to the FCIQMC algorithm. We investigate the effect of simulation parameters on the population control bias for the neon atom and suggest simulation setups to, in general, minimise the bias. We show a reweight ing scheme to remove the bias caused by population control commonly used in diffusion Monte Carlo [Umrigar et al., J. Chem. Phys. 99, 2865 (1993)] is effective and recommend its use as a post processing step. PMID:25770522
NASA Astrophysics Data System (ADS)
Müller, Florian; Jenny, Patrick; Daniel, Meyer
2014-05-01
To a large extent, the flow and transport behaviour within a subsurface reservoir is governed by its permeability. Typically, permeability measurements of a subsurface reservoir are affordable at few spatial locations only. Due to this lack of information, permeability fields are preferably described by stochastic models rather than deterministically. A stochastic method is needed to asses the transition of the input uncertainty in permeability through the system of partial differential equations describing flow and transport to the output quantity of interest. Monte Carlo (MC) is an established method for quantifying uncertainty arising in subsurface flow and transport problems. Although robust and easy to implement, MC suffers from slow statistical convergence. To reduce the computational cost of MC, the multilevel Monte Carlo (MLMC) method was introduced. Instead of sampling a random output quantity of interest on the finest affordable grid as in case of MC, MLMC operates on a hierarchy of grids. If parts of the sampling process are successfully delegated to coarser grids where sampling is inexpensive, MLMC can dramatically outperform MC. MLMC has proven to accelerate MC for several applications including integration problems, stochastic ordinary differential equations in finance as well as stochastic elliptic and hyperbolic partial differential equations. In this study, MLMC is combined with a reservoir simulator to assess uncertain two phase (water/oil) flow and transport within a random permeability field. The performance of MLMC is compared to MC for a two-dimensional reservoir with a multi-point Gaussian logarithmic permeability field. It is found that MLMC yields significant speed-ups with respect to MC while providing results of essentially equal accuracy. This finding holds true not only for one specific Gaussian logarithmic permeability model but for a range of correlation lengths and variances.
Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations.
Arampatzis, Georgios; Katsoulakis, Markos A
2014-03-28
In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo (KMC). Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-"coupled"- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g., coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore, the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz-Kalos-Lebowitz algorithm's philosophy, where events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption, and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach. We also provide a complete implementation of the proposed sensitivity analysis algorithms, including various spatial KMC examples, in a supplementary MATLAB source code. PMID:24697425
Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations
Arampatzis, Georgios; Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003 ; Katsoulakis, Markos A.
2014-03-28
In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo (KMC). Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-“coupled”- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g., coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore, the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz–Kalos–Lebowitz algorithm's philosophy, where events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption, and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach. We also provide a complete implementation of the proposed sensitivity analysis algorithms, including various spatial KMC examples, in a supplementary MATLAB source code.
Kinetic Monte Carlo Simulation of Strained Heteroepitaxial Growth with Intermixing
Arvind Baskaran; Jason Devita; Peter Smereka
2009-01-01
An efficient method for the simulation of strained heteroepitaxial growth\\u000awith intermixing using kinetic Monte Carlo is presented. The model used is\\u000abased on a solid-on-solid bond counting formulation in which elastic effects\\u000aare incorporated using a ball and spring model. While idealized, this model\\u000anevertheless captures many aspects of heteroepitaxial growth, including\\u000anucleation, surface diffusion, and long range effects
A Hybrid Monte Carlo Method for Surface Growth Simulations
G. Russo; P. Smereka
2003-01-01
We introduce an algorithm for treating growth on surfaces which combines\\u000aimportant features of continuum methods (such as the level-set method) and\\u000aKinetic Monte Carlo (KMC) simulations. We treat the motion of adatoms in\\u000acontinuum theory, but attach them to islands one atom at a time. The technique\\u000ais borrowed from the Dielectric Breakdown Model. Our method allows us to
Kinetic Monte Carlo simulation of strained heteroepitaxial growth with intermixing
Arvind Baskaran; Jason Devita; Peter Smereka
2010-01-01
An efficient method for the simulation of strained heteroepitaxial growth with intermixing using kinetic Monte Carlo is presented.\\u000a The model used is based on a solid-on-solid bond counting formulation in which elastic effects are incorporated using a ball\\u000a and spring model. While idealized, this model nevertheless captures many aspects of heteroepitaxial growth, including nucleation,\\u000a surface diffusion, and long-range effects due
Validation of the Monte Carlo code MCNP-DSP
T. E. Valentine; J. T. Mihalczo
1997-01-01
Several calculations were performed to validate MCNP-DSP, which is a Monte Carlo code that calculates all the time and frequency analysis parameters associated with the 252Cf-source-driven time and frequency analysis method. The frequency analysis parameters are obtained in two ways: directly by Fourier transforming the detector responses and indirectly by taking the Fourier transform of the autocorrelation and cross-correlation functions.
Applications of Monte Carlo methods to statistical physics
K. Binder
1997-01-01
An introductory review of the Monte Carlo method for the statistical mechanics of condensed matter systems is given. Basic principles (random number generation, simple sampling versus importance sampling, Markov chains and master equations, etc) are explained and some classical applications (self-avoiding walks, percolation, the Ising model) are sketched. The finite-size scaling analysis of both second- and first-order phase transitions is
Some questions of Monte-Carlo modeling on nontrivial bundles
Alexander Yu. Vlasov
2007-06-21
In this work are considered some questions of Monte-Carlo modeling on nontrivial bundles. As a basic example is used problem of generation of straight lines in 3D space, related with modeling of interaction of a solid body with a flux of particles and with some other tasks. Space of lines used in given model is example of nontrivial fiber bundle, that is equivalent with tangent sheaf of a sphere.
Some questions of Monte-Carlo modeling on nontrivial bundles
Vlasov, Alexander Yu
2007-01-01
In this work are considered some questions of Monte-Carlo modeling on nontrivial bundles. As a basic example is used problem of generation of straight lines in 3D space, related with modeling of interaction of a solid body with a flux of particles and with some other tasks. Space of lines used in given model is example of nontrivial fiber bundle, that is equivalent with tangent sheaf of a sphere.
Monte Carlo Methods and Applications for the Nuclear Shell Model
Dean, D.J.; White, J.A.
1998-08-10
The shell-model Monte Carlo (SMMC) technique transforms the traditional nuclear shell-model problem into a path-integral over auxiliary fields. We describe below the method and its applications to four physics issues: calculations of sd-pf-shell nuclei, a discussion of electron-capture rates in pf-shell nuclei, exploration of pairing correlations in unstable nuclei, and level densities in rare earth systems.
Recent advances in the Mercury Monte Carlo particle transport code
Brantley, P. S.; Dawson, S. A.; McKinley, M. S.; O'Brien, M. J.; Stevens, D. E.; Beck, B. R.; Jurgenson, E. D.; Ebbers, C. A.; Hall, J. M.
2013-07-01
We review recent physics and computational science advances in the Mercury Monte Carlo particle transport code under development at Lawrence Livermore National Laboratory. We describe recent efforts to enable a nuclear resonance fluorescence capability in the Mercury photon transport. We also describe recent work to implement a probability of extinction capability into Mercury. We review the results of current parallel scaling and threading efforts that enable the code to run on millions of MPI processes. (authors)
Monte Carlo calculation of patient organ doses from computed tomography.
Oono, Takeshi; Araki, Fujio; Tsuduki, Shoya; Kawasaki, Keiichi
2014-01-01
In this study, we aimed to evaluate quantitatively the patient organ dose from computed tomography (CT) using Monte Carlo calculations. A multidetector CT unit (Aquilion 16, TOSHIBA Medical Systems) was modeled with the GMctdospp (IMPS, Germany) software based on the EGSnrc Monte Carlo code. The X-ray spectrum and the configuration of the bowtie filter for the Monte Carlo modeling were determined from the chamber measurements for the half-value layer (HVL) of aluminum and the dose profile (off-center ratio, OCR) in air. The calculated HVL and OCR were compared with measured values for body irradiation with 120 kVp. The Monte Carlo-calculated patient dose distribution was converted to the absorbed dose measured by a Farmer chamber with a (60)Co calibration factor at the center of a CT water phantom. The patient dose was evaluated from dose-volume histograms for the internal organs in the pelvis. The calculated Al HVL was in agreement within 0.3% with the measured value of 5.2 mm. The calculated dose profile in air matched the measured value within 5% in a range of 15 cm from the central axis. The mean doses for soft tissues were 23.5, 23.8, and 27.9 mGy for the prostate, rectum, and bladder, respectively, under exposure conditions of 120 kVp, 200 mA, a beam pitch of 0.938, and beam collimation of 32 mm. For bones of the femur and pelvis, the mean doses were 56.1 and 63.6 mGy, respectively. The doses for bone increased by up to 2-3 times that of soft tissue, corresponding to the ratio of their mass-energy absorption coefficients. PMID:24293361
Tests for Unit Roots: A Monte Carlo Investigation
G. William Schwert
1989-01-01
Recent work by Said and Dickey (1984, 1985), Phillips (1987), and Phillips and Perron (1988) examines tests for unit roots in the autoregressive part of mixed autoregressive integrated moving average models (tests for stationary). Monte Carlo experiments show that these unit-root tests have different finite-sample distributions from the unit-root tests developed by Fuller (1976) and Dickey and Fuller (1979, 1981)
The CCFM Monte Carlo generator CASCADE 2.2.0
H. Jung; S. Baranov; M. Deak; A. Grebenyuk; F. Hautmann; M. Hentschinski; A. Knutsson; M. Kraemer; K. Kutak; A. Lipatov; N. Zotov
2010-08-01
CASCADE is a full hadron level Monte Carlo event generator for ep, \\gamma p and p\\bar{p} and pp processes, which uses the CCFM evolution equation for the initial state cascade in a backward evolution approach supplemented with off - shell matrix elements for the hard scattering. A detailed program description is given, with emphasis on parameters the user wants to change and variables which completely specify the generated events.
Confining proton beams with longitudinal magnetic fields: Monte Carlo calculations.
Nardi, E; Schulte, R
2000-10-01
The problem of the lateral containment of a 160 MeV proton beam interacting with a medium simulating biological material was studied. The confining action of a longitudinal magnetic field was calculated by means of Monte Carlo simulation, where scattering and motion in the magnetic field were treated simultaneously. Appreciable compression of the beam could only be achieved using fields of the order at least 50 T, much beyond the realm of practical feasibility. PMID:11099205
Monte Carlo simulations of receptor dynamics: Insights into cell signaling
Christopher J. Brinkerhoff; Peter J. Woolf; Jennifer J. Linderman
2004-01-01
Many receptor-level processes involve the diffusion and reaction of receptors with other membrane-localized molecules. Monte Carlo simulation is a powerful technique that allows us to track the motions and discrete reactions of individual receptors, thus simulating receptor dynamics and the early events of signal transduction. In this paper, we discuss simulations of two receptor processes, receptor dimerization and G-protein activation.
Quantum monte carlo simulations for high-Tc superconductors
NASA Astrophysics Data System (ADS)
Muramatsu, A.; Dopf, G.; Wagner, J.; Dieterich, P.; Hanke, W.
Quantum Monte Carlo simulations for a multi-band model of high-Tc superconductors are reviewed with special emphasis on the comparison of different observables with experiments. It is shown that a given parameter set of the three-band Hubbard model leads to a consistent description of normal-state properties as well as pairing correlation functions for the copper-oxide superconductors as a function of doping and temperature.
Monte Carlo approach to nuclei and nuclear matter
Fantoni, Stefano; Gandolfi, Stefano; Illarionov, Alexey Yu.; Schmidt, Kevin E.; Pederiva, Francesco
2008-10-13
We report on the most recent applications of the Auxiliary Field Diffusion Monte Carlo (AFDMC) method. The equation of state (EOS) for pure neutron matter in both normal and BCS phase and the superfluid gap in the low-density regime are computed, using a realistic Hamiltonian containing the Argonne AV8' plus Urbana IX three-nucleon interaction. Preliminary results for the EOS of isospin-asymmetric nuclear matter are also presented.
Regenerative Markov Chain Monte Carlo for any distribution.
Minh, D. (Biosciences Division); (California State Univ.)
2012-01-01
While Markov chain Monte Carlo (MCMC) methods are frequently used for difficult calculations in a wide range of scientific disciplines, they suffer from a serious limitation: their samples are not independent and identically distributed. Consequently, estimates of expectations are biased if the initial value of the chain is not drawn from the target distribution. Regenerative simulation provides an elegant solution to this problem. In this article, we propose a simple regenerative MCMC algorithm to generate variates for any distribution
The hybrid Monte Carlo Algorithm and the chiral transition
Gupta, R.
1987-01-01
In this talk the author describes tests of the Hybrid Monte Carlo Algorithm for QCD done in collaboration with Greg Kilcup and Stephen Sharpe. We find that the acceptance in the glubal Metropolis step for Staggered fermions can be tuned and kept large without having to make the step-size prohibitively small. We present results for the finite temperature transition on 4/sup 4/ and 4 x 6/sup 3/ lattices using this algorithm.
Monte Carlo Localization: Efficient Position Estimation for Mobile Robots
Dieter Fox; Wolfram Burgard; Frank Dellaert; Sebastian Thrun
1999-01-01
This paper presents a new algorithm for mobile robot lo- calization, called Monte Carlo Localization (MCL). MCL is a version of Markov localization, a family of probabilis- tic approaches that have recently been applied with great practical success. However, previous approaches were ei- ther computationally cumbersome (such as grid-based ap- proaches that represent the state space by high-resolution 3D grids),
Monte Carlo simulation of virtual Compton scattering below pion threshold
P. Janssens; L. Van Hoorebeke; H. Fonvieille; N. D'Hose; P. Y. Bertin; I. Bensafa; N. Degrande; M. Distler; R. Di Salvo; L. Doria; J. M. Friedrich; J. Friedrich; Ch. Hyde-Wright; S. Jaminion; S. Kerhoas; G. Laveissiere; D. Lhuillier; D. Marchand; H. Merkel; J. Roche; G. Tamas; M. Vanderhaeghen; R. Van de Vyver; J. Van de Wiele; Th. Walcher
2006-08-31
This paper describes the Monte Carlo simulation developed specifically for the VCS experiments below pion threshold that have been performed at MAMI and JLab. This simulation generates events according to the (Bethe-Heitler + Born) cross section behaviour and takes into account all relevant resolution-deteriorating effects. It determines the `effective' solid angle for the various experimental settings which are used for the precise determination of photon electroproduction absolute cross section.
Monte Carlo Simulation of The Adjoint Coulomb Gas
Omid Saremi
2015-01-29
Monte Carlo simulation results for unitary matrix quantum mechanics, describing two-dimensional Yang-Mills theory coupled to a finite density of non-dynamical quarks (adjoint Coulomb gas), are presented. We characterize the deconfining transition in this model, by measuring the Polyakov Loop Susceptibility and employing finite-size scaling analysis. We provide evidence that the phase transition is first-order. Our results are consistent with the outcome of earlier large-$N$ studies of the model.
Testing trivializing maps in the Hybrid Monte Carlo algorithm
Georg P. Engel; Stefan Schaefer
2011-02-09
We test a recent proposal to use approximate trivializing maps in a field theory to speed up Hybrid Monte Carlo simulations. Simulating the CP^{N-1} model, we find a small improvement with the leading order transformation, which is however compensated by the additional computational overhead. The scaling of the algorithm towards the continuum is not changed. In particular, the effect of the topological modes on the autocorrelation times is studied.
Monte Carlo for top background at the Tevatron
Harel, Amnon
2008-07-01
We review the use of Monte Carlo (MC) 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 (HF), and also comment on the Tevatron experience using matched MC.
Quasi-Monte Carlo estimation in generalized linear mixed models
Jianxin Pan; Robin Thompson
Generalized linear mixed models (GLMMs) are useful for modelling longitudinal and clustered data, but parameter estimation is very challenging because the likelihood may involve high-dimensional integrals that are analytically intractable. Gauss-Hermite quadrature (GHQ) approximation can be applied but is only suitable for low-dimensional random effects. Based on the Quasi-Monte Carlo (QMC) approximation, a heuristic approach is proposed to calculate the
Quasi-Monte Carlo estimation in generalized linear mixed models
Jianxin Pan; Robin Thompson
2007-01-01
Generalized linear mixed models (GLMMs) are useful for modelling longitudinal and clustered data, but parameter estimation is very challenging because the likelihood may involve high-dimensional integrals that are analytically intractable. Gauss–Hermite quadrature (GHQ) approximation can be applied but is only suitable for low-dimensional random effects. Based on the Quasi-Monte Carlo (QMC) approximation, a heuristic approach is proposed to calculate the
Monte Carlo simulation experiments on box-type radon dosimeter
NASA Astrophysics Data System (ADS)
Jamil, Khalid; Kamran, Muhammad; Illahi, Ahsan; Manzoor, Shahid
2014-11-01
Epidemiological studies show that inhalation of radon gas (222Rn) may be carcinogenic especially to mine workers, people living in closed indoor energy conserved environments and underground dwellers. It is, therefore, of paramount importance to measure the 222Rn concentrations (Bq/m3) in indoors environments. For this purpose, box-type passive radon dosimeters employing ion track detector like CR-39 are widely used. Fraction of the number of radon alphas emitted in the volume of the box type dosimeter resulting in latent track formation on CR-39 is the latent track registration efficiency. Latent track registration efficiency is ultimately required to evaluate the radon concentration which consequently determines the effective dose and the radiological hazards. In this research, Monte Carlo simulation experiments were carried out to study the alpha latent track registration efficiency for box type radon dosimeter as a function of dosimeter's dimensions and range of alpha particles in air. Two different self developed Monte Carlo simulation techniques were employed namely: (a) Surface ratio (SURA) method and (b) Ray hitting (RAHI) method. Monte Carlo simulation experiments revealed that there are two types of efficiencies i.e. intrinsic efficiency (?int) and alpha hit efficiency (?hit). The ?int depends upon only on the dimensions of the dosimeter and ?hit depends both upon dimensions of the dosimeter and range of the alpha particles. The total latent track registration efficiency is the product of both intrinsic and hit efficiencies. It has been concluded that if diagonal length of box type dosimeter is kept smaller than the range of alpha particle then hit efficiency is achieved as 100%. Nevertheless the intrinsic efficiency keeps playing its role. The Monte Carlo simulation experimental results have been found helpful to understand the intricate track registration mechanisms in the box type dosimeter. This paper explains that how radon concentration from the experimentally obtained etched track density can be obtained. The program based on RAHI method is also given in this paper.
Monte Carlo Simulations of a Disordered Lattice London Model
Bonabeau, E.; Lederer, P.
1996-12-01
The effects of uncorrelated disorder in three-dimensional type-II superconductors are studied by means of Monte Carlo simulations of the current-voltage characteristics of a disordered lattice London model. Vortex motion observed at any temperature and current in the simulations suggests that there is no finite-{ital T} glass transition in this model because there are finite barriers against vortex motion at any temperature. {copyright} {ital 1996 The American Physical Society.}
Direct Monte Carlo Simulations of Hypersonic Viscous Interactions Including Separation
NASA Technical Reports Server (NTRS)
Moss, James N.; Rault, Didier F. G.; Price, Joseph M.
1993-01-01
Results of calculations obtained using the direct simulation Monte Carlo method for Mach 25 flow over a control surface are presented. The numerical simulations are for a 35-deg compression ramp at a low-density wind-tunnel test condition. Calculations obtained using both two- and three-dimensional solutions are reviewed, and a qualitative comparison is made with the oil flow pictures highlight separation and three-dimensional flow structure.
MCSpearman: Monte Carlo error analyses of Spearman's rank test
NASA Astrophysics Data System (ADS)
Curran, Peter A.
2015-04-01
Spearman’s rank correlation test is commonly used in astronomy to discern whether a set of two variables are correlated or not. Unlike most other quantities quoted in astronomical literature, the Spearman’s rank correlation coefficient is generally quoted with no attempt to estimate the errors on its value. This code implements a number of Monte Carlo based methods to estimate the uncertainty on the Spearman’s rank correlation coefficient.
COMET-PE as an Alternative to Monte Carlo for Photon and Electron Transport
NASA Astrophysics Data System (ADS)
Hayward, Robert M.; Rahnema, Farzad
2014-06-01
Monte Carlo methods are a central component of radiotherapy treatment planning, shielding design, detector modeling, and other applications. Long calculation times, however, can limit the usefulness of these purely stochastic methods. The coarse mesh method for photon and electron transport (COMET-PE) provides an attractive alternative. By combining stochastic pre-computation with a deterministic solver, COMET-PE achieves accuracy comparable to Monte Carlo methods in only a fraction of the time. The method's implementation has been extended to 3D, and in this work, it is validated by comparison to DOSXYZnrc using a photon radiotherapy benchmark. The comparison demonstrates excellent agreement; of the voxels that received more than 10% of the maximum dose, over 97.3% pass a 2% / 2mm acceptance test and over 99.7% pass a 3% / 3mm test. Furthermore, the method is over an order of magnitude faster than DOSXYZnrc and is able to take advantage of both distributed-memory and shared-memory parallel architectures for increased performance.
Variance reduction for Fokker-Planck based particle Monte Carlo schemes
NASA Astrophysics Data System (ADS)
Gorji, M. Hossein; Andric, Nemanja; Jenny, Patrick
2015-08-01
Recently, Fokker-Planck based particle Monte Carlo schemes have been proposed and evaluated for simulations of rarefied gas flows [1-3]. In this paper, the variance reduction for particle Monte Carlo simulations based on the Fokker-Planck model is considered. First, deviational based schemes were derived and reviewed, and it is shown that these deviational methods are not appropriate for practical Fokker-Planck based rarefied gas flow simulations. This is due to the fact that the deviational schemes considered in this study lead either to instabilities in the case of two-weight methods or to large statistical errors if the direct sampling method is applied. Motivated by this conclusion, we developed a novel scheme based on correlated stochastic processes. The main idea here is to synthesize an additional stochastic process with a known solution, which is simultaneously solved together with the main one. By correlating the two processes, the statistical errors can dramatically be reduced; especially for low Mach numbers. To assess the methods, homogeneous relaxation, planar Couette and lid-driven cavity flows were considered. For these test cases, it could be demonstrated that variance reduction based on parallel processes is very robust and effective.
Fast Monte Carlo, slow protein kinetics and perfect loop closure
NASA Astrophysics Data System (ADS)
Wedemeyer, William Joseph
This thesis presents experimental studies of proteins and computational methods which may help in simulations of proteins. The experimental chapters focus on the folding and unfolding of bovine pancreatic ribonuclease A. Methods are developed for tracking the cis-trans isomerization of individual prolines under folding and unfolding conditions, and for identifying critical folding structures by assessing the effects of individual incorrect X-Pro isomers on the conformational folding. The major ?-hairpin region is identified as more critical than the C-terminal hydrophobic core. Site- directed mutagenesis of three nearby tyrosines to phenylalanine indicates that tyrosyl hydrogen bonds are essential to rapid conformational folding. Another experimental chapter presents an analytic solution of the kinetics of competitive binding, which is applied to estimating the association and dissociation rate constants of hirudin and thrombin. An extension of this method is proposed to obtain kinetic rate constants for the conformational folding and unfolding of individual parts of a protein. The analytic solution is found to be roughly one-hundred-fold more efficient than the best numerical integrators. The theoretical chapters present methods potentially useful in protein simulations. The loop closure problem is solved geometrically, allowing the protein to be broken into segments which move quasi-independently. Two bootstrap Monte Carlo methods are developed for sampling functions that are characterized by high anisotropy, e.g. long, narrow valleys. Two chapters are devoted to smoothing methods; the first develops a method for exploiting smoothing to evaluate the energy in order N (not N2) time, while the second examines the limitations of one smoothing method, the Diffusion Equation Method, and suggests improvements to its smoothing transformation and reversing procedure. One chapter develops a highly optimized simulation package for lattice heteropolymers by careful choice of data structures and by treating the Metropolis acceptance criterion itself as a stochastic process. Lastly, a integrated software package, PROSE, is developed to perform molecular simulations. The routines are written in C for high performance, but embedded in scripting languages for convenience. The package is modular and object-oriented to test new algorithms rapidly. A graphical user interface is provided for visualization and to assist non-programmers.
Pattern Recognition for a Flight Dynamics Monte Carlo Simulation
NASA Technical Reports Server (NTRS)
Restrepo, Carolina; Hurtado, John E.
2011-01-01
The design, analysis, and verification and validation of a spacecraft relies heavily on Monte Carlo simulations. Modern computational techniques are able to generate large amounts of Monte Carlo data but flight dynamics engineers lack the time and resources to analyze it all. The growing amounts of data combined with the diminished available time of engineers motivates the need to automate the analysis process. Pattern recognition algorithms are an innovative way of analyzing flight dynamics data efficiently. They can search large data sets for specific patterns and highlight critical variables so analysts can focus their analysis efforts. This work combines a few tractable pattern recognition algorithms with basic flight dynamics concepts to build a practical analysis tool for Monte Carlo simulations. Current results show that this tool can quickly and automatically identify individual design parameters, and most importantly, specific combinations of parameters that should be avoided in order to prevent specific system failures. The current version uses a kernel density estimation algorithm and a sequential feature selection algorithm combined with a k-nearest neighbor classifier to find and rank important design parameters. This provides an increased level of confidence in the analysis and saves a significant amount of time.
Solving the many body pairing problem through Monte Carlo methods
NASA Astrophysics Data System (ADS)
Lingle, Mark; Volya, Alexander
2012-03-01
Nuclear superconductivity is a central part of quantum many-body dynamics. In mesoscopic systems such as atomic nuclei, this phenomenon is influenced by shell effects, mean-field deformation, particle decay, and by other collective and chaotic components of nucleon motion. The ability to find an exact solution to these pairing correlations is of particular importance. In this presentation we develop and investigate the effectiveness of different methods of attacking the nucleon pairing problem in nuclei. In particular, we concentrate on the Monte Carlo approach. We review the configuration space Monte Carlo techniques, the Suzuki-Trotter breakup of the time evolution operator, and treatment of the pairing problem with non-constant matrix elements. The quasi-spin symmetry allows for a mapping of the pairing problem onto a problem of interacting spins which in turn can be solved using a Monte Carlo approach. The algorithms are investigated for convergence to the true ground state of model systems and calculated ground state energies are compared to those found by an exact diagonalization method. The possibility to include other non-pairing interaction components of the Hamiltonian is also investigated.
Improved diffusion coefficients generated from Monte Carlo codes
Herman, B. R.; Forget, B.; Smith, K. [Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Aviles, B. N. [Knolls Atomic Power Laboratory, Bechtel Marine Propulsion Corporation, P.O. Box 1072, Schenectady, NY 12301-1072 (United States)
2013-07-01
Monte Carlo codes are becoming more widely used for reactor analysis. Some of these applications involve the generation of diffusion theory parameters including macroscopic cross sections and diffusion coefficients. Two approximations used to generate diffusion coefficients are assessed using the Monte Carlo code MC21. The first is the method of homogenization; whether to weight either fine-group transport cross sections or fine-group diffusion coefficients when collapsing to few-group diffusion coefficients. The second is a fundamental approximation made to the energy-dependent P1 equations to derive the energy-dependent diffusion equations. Standard Monte Carlo codes usually generate a flux-weighted transport cross section with no correction to the diffusion approximation. Results indicate that this causes noticeable tilting in reconstructed pin powers in simple test lattices with L2 norm error of 3.6%. This error is reduced significantly to 0.27% when weighting fine-group diffusion coefficients by the flux and applying a correction to the diffusion approximation. Noticeable tilting in reconstructed fluxes and pin powers was reduced when applying these corrections. (authors)
Chemical accuracy from quantum Monte Carlo for the benzene dimer.
Azadi, Sam; Cohen, R E
2015-09-14
We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is -2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods. PMID:26374029
Monte Carlo simulation of kinetically slowed down phase separation.
R?ži?ka, Št?pán; Allen, Michael P
2015-06-01
Supercooled colloidal or molecular systems at low densities are known to form liquid, crystalline or glassy drops, which may remain isolated for a long time before they aggregate. This paper analyses the properties of this large time window, and how it can be tackled by computer simulation. We use single-particle and virtual move Monte Carlo simulations of short-range attractive spheres which are undercooled to the temperature region, where the spinodal intersects the attractive glass line. We study two different systems and we report the following kinetic behavior. A low-density system is shown to exhibit universal linear growth regimes under single-particle Monte Carlo correlating the growth rate to the local structure. These regimes are suppressed under collective motion, where droplets aggregate into a single large disordered domain. It is shown that the aggregation can be avoided and linear regimes recovered, if long-range repulsion is added to the short-range attraction. The results provide an insight into the behavior of the virtual move algorithm generating cluster moves according to the local forcefields. We show that different choices of maximum Monte Carlo displacement affect the dynamical trajectories but lead to the same kinetically slowed down or arrested states. PMID:26123773
ALEPH2 - A general purpose Monte Carlo depletion code
Stankovskiy, A.; Van Den Eynde, G.; Baeten, P. [SCK CEN, Boeretang 200, B-2400 Mol (Belgium); Trakas, C.; Demy, P. M.; Villatte, L. [AREVA NP, Tour AREVA, Pl. J. Millier, 92084 Paris La Defense (France)
2012-07-01
The Monte-Carlo burn-up code ALEPH is being developed at SCK-CEN since 2004. A previous version of the code implemented the coupling between the Monte Carlo transport (any version of MCNP or MCNPX) and the ' deterministic' depletion code ORIGEN-2.2 but had important deficiencies in nuclear data treatment and limitations inherent to ORIGEN-2.2. A new version of the code, ALEPH2, has several unique features making it outstanding among other depletion codes. The most important feature is full data consistency between steady-state Monte Carlo and time-dependent depletion calculations. The last generation general-purpose nuclear data libraries (JEFF-3.1.1, ENDF/B-VII and JENDL-4) are fully implemented, including special purpose activation, spontaneous fission, fission product yield and radioactive decay data. The built-in depletion algorithm allows to eliminate the uncertainties associated with obtaining the time-dependent nuclide concentrations. A predictor-corrector mechanism, calculation of nuclear heating, calculation of decay heat, decay neutron sources are available as well. The validation of the code on the results of REBUS experimental program has been performed. The ALEPH2 has shown better agreement with measured data than other depletion codes. (authors)
A Wigner Monte Carlo approach to density functional theory
NASA Astrophysics Data System (ADS)
Sellier, J. M.; Dimov, I.
2014-08-01
In order to simulate quantum N-body systems, stationary and time-dependent density functional theories rely on the capacity of calculating the single-electron wave-functions of a system from which one obtains the total electron density (Kohn-Sham systems). In this paper, we introduce the use of the Wigner Monte Carlo method in ab-initio calculations. This approach allows time-dependent simulations of chemical systems in the presence of reflective and absorbing boundary conditions. It also enables an intuitive comprehension of chemical systems in terms of the Wigner formalism based on the concept of phase-space. Finally, being based on a Monte Carlo method, it scales very well on parallel machines paving the way towards the time-dependent simulation of very complex molecules. A validation is performed by studying the electron distribution of three different systems, a Lithium atom, a Boron atom and a hydrogenic molecule. For the sake of simplicity, we start from initial conditions not too far from equilibrium and show that the systems reach a stationary regime, as expected (despite no restriction is imposed in the choice of the initial conditions). We also show a good agreement with the standard density functional theory for the hydrogenic molecule. These results demonstrate that the combination of the Wigner Monte Carlo method and Kohn-Sham systems provides a reliable computational tool which could, eventually, be applied to more sophisticated problems.
Monte Carlo Fast Dose Calculator for Proton Radiotherapy
NASA Astrophysics Data System (ADS)
Brannan, Travis; Huang, Jessie; Yepes, Pablo
2009-10-01
Monte Carlo methods used in proton radiotherapy are more accurate than commonly used analytical dose calculations, at the cost of being computationally intense. We intend to show the feasibility of the Fast Dose Calculator (FDC), a Monte Carlo track-repeating algorithm based on GEANT4, to perform dose calculations for a clinical proton beam. FDC was developed to retain the accuracy of the Monte Carlo approach while substantially decreasing the calculation time required. FDC uses a database of proton trajectories in water and extrapolates this data in order to calculate the dose in heterogeneous media by scaling the proton range and scattering angles. FDC has been extended to include all of the patient-dependent elements of a passive proton scattering treatment unit: aperture, range compensator, and voxelized patient geometry. Improved database packing provides additional computational efficiency in FDC, which speeds calculation by more than two orders of magnitude. In addition FDC shows no dependence on calculation times with the number of voxels, unlike GEANT4. The dosimetric accuracy of the FDC algorithm was validated by comparing the results with GEANT4.
Using hierarchical octrees in Monte Carlo radiative transfer simulations
NASA Astrophysics Data System (ADS)
Saftly, W.; Camps, P.; Baes, M.; Gordon, K. D.; Vandewoude, S.; Rahimi, A.; Stalevski, M.
2013-06-01
A crucial aspect of 3D Monte Carlo radiative transfer is the choice of the spatial grid used to partition the dusty medium. We critically investigate the use of octree grids in Monte Carlo dust radiative transfer, with two different octree construction algorithms (regular and barycentric subdivision) and three different octree traversal algorithms (top-down, neighbour list, and the bookkeeping method). In general, regular octree grids need higher levels of subdivision compared to the barycentric grids for a fixed maximum cell mass threshold criterion. The total number of grid cells, however, depends on the geometry of the model. Surprisingly, regular octree grid simulations turn out to be 10 to 20% more efficient in run time than the barycentric grid simulations, even for those cases where the latter contain fewer grid cells than the former. Furthermore, we find that storing neighbour lists for each cell in an octree, ordered according to decreasing overlap area, is worth the additional memory and implementation overhead: using neighbour lists can cut down the grid traversal by 20% compared to the traditional top-down method. In conclusion, the combination of a regular node subdivision and the neighbour list method results in the most efficient octree structure for Monte Carlo radiative transfer simulations.
Monte Carlo Methodology Serves Up a Software Success
NASA Technical Reports Server (NTRS)
2003-01-01
Widely used for the modeling of gas flows through the computation of the motion and collisions of representative molecules, the Direct Simulation Monte Carlo method has become the gold standard for producing research and engineering predictions in the field of rarefied gas dynamics. Direct Simulation Monte Carlo was first introduced in the early 1960s by Dr. Graeme Bird, a professor at the University of Sydney, Australia. It has since proved to be a valuable tool to the aerospace and defense industries in providing design and operational support data, as well as flight data analysis. In 2002, NASA brought to the forefront a software product that maintains the same basic physics formulation of Dr. Bird's method, but provides effective modeling of complex, three-dimensional, real vehicle simulations and parallel processing capabilities to handle additional computational requirements, especially in areas where computational fluid dynamics (CFD) is not applicable. NASA's Direct Simulation Monte Carlo Analysis Code (DAC) software package is now considered the Agency s premier high-fidelity simulation tool for predicting vehicle aerodynamics and aerothermodynamic environments in rarified, or low-density, gas flows.
Optimum and efficient sampling for variational quantum Monte Carlo.
Trail, J R; Maezono, Ryo
2010-11-01
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial wave functions, that is to variational quantum Monte Carlo. Almost all previous implementations employ samples distributed as the physical probability density of the trial wave function, and assume the central limit theorem to be valid. In this paper we provide an analysis of random error in estimation and optimization that leads naturally to new sampling strategies with improved computational and statistical properties. A rigorous lower limit to the random error is derived, and an efficient sampling strategy presented that significantly increases computational efficiency. In addition the infinite variance heavy tailed random errors of optimum parameters in conventional methods are replaced with a Normal random error, strengthening the theoretical basis of optimization. The method is applied to a number of first row systems and compared with previously published results. PMID:21054019
Chemical accuracy from quantum Monte Carlo for the benzene dimer
NASA Astrophysics Data System (ADS)
Azadi, Sam; Cohen, R. E.
2015-09-01
We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is -2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.
Comparison of deterministic and Monte Carlo methods in shielding design.
Oliveira, A D; Oliveira, C
2005-01-01
In shielding calculation, deterministic methods have some advantages and also some disadvantages relative to other kind of codes, such as Monte Carlo. The main advantage is the short computer time needed to find solutions while the disadvantages are related to the often-used build-up factor that is extrapolated from high to low energies or with unknown geometrical conditions, which can lead to significant errors in shielding results. The aim of this work is to investigate how good are some deterministic methods to calculating low-energy shielding, using attenuation coefficients and build-up factor corrections. Commercial software MicroShield 5.05 has been used as the deterministic code while MCNP has been used as the Monte Carlo code. Point and cylindrical sources with slab shield have been defined allowing comparison between the capability of both Monte Carlo and deterministic methods in a day-by-day shielding calculation using sensitivity analysis of significant parameters, such as energy and geometrical conditions. PMID:16381723
Monte Carlo study of a Cyberknife stereotactic radiosurgery system
Araki, Fujio [Department of Radiological Technology, Kumamoto University School of Health Sciences, Kumamoto, 862-0976 (Japan)
2006-08-15
This study investigated small-field dosimetry for a Cyberknife stereotactic radiosurgery system using Monte Carlo simulations. The EGSnrc/BEAMnrc Monte Carlo code was used to simulate the Cyberknife treatment head, and the DOSXYZnrc code was implemented to calculate central axis depth-dose curves, off-axis dose profiles, and relative output factors for various circular collimator sizes of 5 to 60 mm. Water-to-air stopping power ratios necessary for clinical reference dosimetry of the Cyberknife system were also evaluated by Monte Carlo simulations. Additionally, a beam quality conversion factor, k{sub Q}, for the Cyberknife system was evaluated for cylindrical ion chambers with different wall material. The accuracy of the simulated beam was validated by agreement within 2% between the Monte Carlo calculated and measured central axis depth-dose curves and off-axis dose profiles. The calculated output factors were compared with those measured by a diode detector and an ion chamber in water. The diode output factors agreed within 1% with the calculated values down to a 10 mm collimator. The output factors with the ion chamber decreased rapidly for collimators below 20 mm. These results were confirmed by the comparison to those from Monte Carlo methods with voxel sizes and materials corresponding to both detectors. It was demonstrated that the discrepancy in the 5 and 7.5 mm collimators for the diode detector is due to the water nonequivalence of the silicon material, and the dose fall-off for the ion chamber is due to its large active volume against collimators below 20 mm. The calculated stopping power ratios of the 60 mm collimator from the Cyberknife system (without a flattening filter) agreed within 0.2% with those of a 10x10 cm{sup 2} field from a conventional linear accelerator with a heavy flattening filter and the incident electron energy, 6 MeV. The difference in the stopping power ratios between 5 and 60 mm collimators was within 0.5% at a 10 cm depth in water. Furthermore, k{sub Q} values for the Cyberknife system were in agreement within 0.3% with those of the conventional 6 MV-linear accelerator for the cylindrical ion chambers with different wall material.
Independent pixel and Monte Carlo estimates of stratocumulus albedo
NASA Technical Reports Server (NTRS)
Cahalan, Robert F.; Ridgway, William; Wiscombe, Warren J.; Gollmer, Steven; HARSHVARDHAN
1994-01-01
Monte Carlo radiative transfer methods are employed here to estimate the plane-parallel albedo bias for marine stratocumulus clouds. This is the bias in estimates of the mesoscale-average albedo, which arises from the assumption that cloud liquid water is uniformly distributed. The authors compare such estimates with those based on a more realistic distribution generated from a fractal model of marine stratocumulus clouds belonging to the class of 'bounded cascade' models. In this model the cloud top and base are fixed, so that all variations in cloud shape are ignored. The model generates random variations in liquid water along a single horizontal direction, forming fractal cloud streets while conserving the total liquid water in the cloud field. The model reproduces the mean, variance, and skewness of the vertically integrated cloud liquid water, as well as its observed wavenumber spectrum, which is approximately a power law. The Monte Carlo method keeps track of the three-dimensional paths solar photons take through the cloud field, using a vectorized implementation of a direct technique. The simplifications in the cloud field studied here allow the computations to be accelerated. The Monte Carlo results are compared to those of the independent pixel approximation, which neglects net horizontal photon transport. Differences between the Monte Carlo and independent pixel estimates of the mesoscale-average albedo are on the order of 1% for conservative scattering, while the plane-parallel bias itself is an order of magnitude larger. As cloud absorption increases, the independent pixel approximation agrees even more closely with the Monte Carlo estimates. This result holds for a wide range of sun angles and aspect ratios. Thus, horizontal photon transport can be safely neglected in estimates of the area-average flux for such cloud models. This result relies on the rapid falloff of the wavenumber spectrum of stratocumulus, which ensures that the smaller-scale variability, where the radiative transfer is more three-dimensional, contributes less to the plane-parallel albedo bias than the larger scales, which are more variable. The lack of significant three-dimensional effects also relies on the assumption of a relatively simple geometry. Even with these assumptions, the independent pixel approximation is accurate only for fluxes averaged over large horizontal areas, many photon mean free paths in diameter, and not for local radiance values, which depend strongly on the interaction between neighboring cloud elements.
Monte Carlo investigation of electron beam relative output factors
NASA Astrophysics Data System (ADS)
Zhang, Geoffrey G.
One of the tasks in commissioning an electron accelerator in cancer clinics is to measure relative output factors (ROFs) versus various parameters such as applicator size (called applicator factors), cutout size (cutout factors) and air-gap size (gap factors) for various electron beam energies and applicator sizes. This kind of measurement takes a lot of time and labour. This thesis shows that Monte Carlo simulation offers an alternative to this task. With BEAM (Med. Phys. 22(1995)503-524), an EGS4 user- code, clinical accelerator electron beams are simulated and ROFs for a Siemens MD2 linear accelerator and a Varian Clinac 2100C accelerator are calculate The study shows that the Monte Carlo method is not only practical in clinics but also powerful in analyzing the related physics. The calculated ROFs agree within 1% with the measurements for most cases and 2% for all cases that have been studied, which is more than acceptable in clinical practice. The details of each component of the dose, such as dose from particles scattered off the photon-jaws and the applicator, the dose from contaminant photon, the dose from direct electrons, etc., are also analyzed. The study also explains quantitatively why the effective SSD (Source to Phantom Surface Distance) is often not the nominal reference SSD. For ROF measurements for small fields using an ion chamber, this study discusses the stopping- power ratio corrections due to changes in the depth of dose maximum as a function of field size and versus various accelerators. Since it handles ROF calculations for arbitrary fields, including square, rectangular, circular and irregular fields, in the same way, Monte Carlo is the simplest method to get ROFs compared to other algorithms. As the first step towards implementing Monte Carlo methods in clinical treatment planning, Monte Carlo calculations for electron beam ROFs can replace measurements in clinical practice. It takes about 6 hours of CPU time on a single Pentium Pro 200MHz computer to simulate an accelerator and additional 2 hours for each ROF.
An automated variance reduction method for global Monte Carlo neutral particle transport problems
NASA Astrophysics Data System (ADS)
Cooper, Marc Andrew
A method to automatically reduce the variance in global neutral particle Monte Carlo problems by using a weight window derived from a deterministic forward solution is presented. This method reduces a global measure of the variance of desired tallies and increases its associated figure of merit. Global deep penetration neutron transport problems present difficulties for analog Monte Carlo. When the scalar flux decreases by many orders of magnitude, so does the number of Monte Carlo particles. This can result in large statistical errors. In conjunction with survival biasing, a weight window is employed which uses splitting and Russian roulette to restrict the symbolic weights of Monte Carlo particles. By establishing a connection between the scalar flux and the weight window, two important concepts are demonstrated. First, such a weight window can be constructed from a deterministic solution of a forward transport problem. Also, the weight window will distribute Monte Carlo particles in such a way to minimize a measure of the global variance. For Implicit Monte Carlo solutions of radiative transfer problems, an inefficient distribution of Monte Carlo particles can result in large statistical errors in front of the Marshak wave and at its leading edge. Again, the global Monte Carlo method is used, which employs a time-dependent weight window derived from a forward deterministic solution. Here, the algorithm is modified to enhance the number of Monte Carlo particles in the wavefront. Simulations show that use of this time-dependent weight window significantly improves the Monte Carlo calculation.
On Filtering the Noise from the Random Parameters in Monte Carlo Rendering
California at Santa Barbara, University of
Carlo (MC) rendering systems can produce beautiful, photo- realistic images by simulating lightOn Filtering the Noise from the Random Parameters in Monte Carlo Rendering PRADEEP SEN and SOHEIL DARABI UNM Advanced Graphics Lab Monte Carlo (MC) rendering systems can produce spectacular images
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FZ2MC: A Tool for Monte Carlo Transport Code Geometry Manipulation
Hackel, B M; Nielsen Jr., D E; Procassini, R J
2009-02-25
The process of creating and validating combinatorial geometry representations of complex systems for use in Monte Carlo transport simulations can be both time consuming and error prone. To simplify this process, a tool has been developed which employs extensions of the Form-Z commercial solid modeling tool. The resultant FZ2MC (Form-Z to Monte Carlo) tool permits users to create, modify and validate Monte Carlo geometry and material composition input data. Plugin modules that export this data to an input file, as well as parse data from existing input files, have been developed for several Monte Carlo codes. The FZ2MC tool is envisioned as a 'universal' tool for the manipulation of Monte Carlo geometry and material data. To this end, collaboration on the development of plug-in modules for additional Monte Carlo codes is desired.
NASA Technical Reports Server (NTRS)
Ponomarev, Artem; Cucinotta, F.
2011-01-01
To create a generalized mechanistic model of DNA damage in human cells that will generate analytical and image data corresponding to experimentally observed DNA damage foci and will help to improve the experimental foci yields by simulating spatial foci patterns and resolving problems with quantitative image analysis. Material and Methods: The analysis of patterns of RIFs (radiation-induced foci) produced by low- and high-LET (linear energy transfer) radiation was conducted by using a Monte Carlo model that combines the heavy ion track structure with characteristics of the human genome on the level of chromosomes. The foci patterns were also simulated in the maximum projection plane for flat nuclei. Some data analysis was done with the help of image segmentation software that identifies individual classes of RIFs and colocolized RIFs, which is of importance to some experimental assays that assign DNA damage a dual phosphorescent signal. Results: The model predicts the spatial and genomic distributions of DNA DSBs (double strand breaks) and associated RIFs in a human cell nucleus for a particular dose of either low- or high-LET radiation. We used the model to do analyses for different irradiation scenarios. In the beam-parallel-to-the-disk-of-a-flattened-nucleus scenario we found that the foci appeared to be merged due to their high density, while, in the perpendicular-beam scenario, the foci appeared as one bright spot per hit. The statistics and spatial distribution of regions of densely arranged foci, termed DNA foci chains, were predicted numerically using this model. Another analysis was done to evaluate the number of ion hits per nucleus, which were visible from streaks of closely located foci. In another analysis, our image segmentaiton software determined foci yields directly from images with single-class or colocolized foci. Conclusions: We showed that DSB clustering needs to be taken into account to determine the true DNA damage foci yield, which helps to determine the DSB yield. Using the model analysis, a researcher can refine the DSB yield per nucleus per particle. We showed that purely geometric artifacts, present in the experimental images, can be analytically resolved with the model, and that the quantization of track hits and DSB yields can be provided to the experimentalists who use enumeration of radiation-induced foci in immunofluorescence experiments using proteins that detect DNA damage. An automated image segmentaiton software can prove useful in a faster and more precise object counting for colocolized foci images.
Coupled Monte Carlo neutronics and thermal hydraulics for power reactors
Bernnat, W.; Buck, M.; Mattes, M. [Institut fuer Kernenergetik und Energiesysteme IKE, Universitaet Stuttgart, Pfaffenwaldring 31, D-70569 Stuttgart (Germany); Zwermann, W.; Pasichnyk, I.; Velkov, K. [Gesellschaft fuer Anlagen- und Reaktorsicherheit GRS MbH, Forschungszentrum, Boltzmannstrase 14, 85748 Garching (Germany)
2012-07-01
The availability of high performance computing resources enables more and more the use of detailed Monte Carlo models even for full core power reactors. The detailed structure of the core can be described by lattices, modeled by so-called repeated structures e.g. in Monte Carlo codes such as MCNP5 or MCNPX. For cores with mainly uniform material compositions, fuel and moderator temperatures, there is no problem in constructing core models. However, when the material composition and the temperatures vary strongly a huge number of different material cells must be described which complicate the input and in many cases exceed code or memory limits. The second problem arises with the preparation of corresponding temperature dependent cross sections and thermal scattering laws. Only if these problems can be solved, a realistic coupling of Monte Carlo neutronics with an appropriate thermal-hydraulics model is possible. In this paper a method for the treatment of detailed material and temperature distributions in MCNP5 is described based on user-specified internal functions which assign distinct elements of the core cells to material specifications (e.g. water density) and temperatures from a thermal-hydraulics code. The core grid itself can be described with a uniform material specification. The temperature dependency of cross sections and thermal neutron scattering laws is taken into account by interpolation, requiring only a limited number of data sets generated for different temperatures. Applications will be shown for the stationary part of the Purdue PWR benchmark using ATHLET for thermal- hydraulics and for a generic Modular High Temperature reactor using THERMIX for thermal- hydraulics. (authors)
Dynamic wedge versus physical wedge: a Monte Carlo study.
Shih, R; Li, X A; Chu, J C
2001-04-01
The purpose of this study is to analyze the characteristics of dynamic wedges (DW) and to compare DW to physical wedges (PW) in terms of their differences in affecting beam spectra, energy fluence, angular distribution, contaminated electrons, and dose distributions. The EGS4/BEAM Monte Carlo codes were used to simulate the exact geometry of a 6 MV beam and to calculate 3-D dose distributions in phantom. The DW was simulated in accordance with the segmented treatment tables (STT). The percentage depth dose curves and beam profiles for PW, DW, and open fields were measured and used to verify the Monte Carlo simulations. The Monte Carlo results were found to agree within 2% with the measurements performed using film and ionizing chambers in a water phantom. The present EGS4 calculation reveals that the effects of a DW on beam spectral and angular distributions, as well as electron contamination, are much less significant than those for a PW. For the 6 MV photon beam, a 45 degrees PW can result in a 30% increase in mean photon energy due to the effect of beam hardening. It can also introduce a 5% dose reduction in the build-up region due to the reduction of contaminated electrons by the PW. Neither this mean-energy increase nor such dose reduction is found for a DW. Compared to a DW, a PW alters the photon-beam spectrum significantly. The dosimetric differences between a DW and a PW are significant and clearly affect the clinical use of these beams. The data presented may be useful for DW commissioning. PMID:11339759
Properties of reactive oxygen species by quantum Monte Carlo
Zen, Andrea [Dipartimento di Fisica, La Sapienza - Università di Roma, Piazzale Aldo Moro 2, 00185 Rome (Italy); Trout, Bernhardt L. [Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, Massachusetts 02139 (United States); Guidoni, Leonardo, E-mail: leonardo.guidoni@univaq.it [Dipartimento di Scienze Fisiche e Chimiche, Università degli studi de L'Aquila, Via Vetoio, 67100 Coppito, L'Aquila (Italy)
2014-07-07
The electronic properties of the oxygen molecule, in its singlet and triplet states, and of many small oxygen-containing radicals and anions have important roles in different fields of chemistry, biology, and atmospheric science. Nevertheless, the electronic structure of such species is a challenge for ab initio computational approaches because of the difficulties to correctly describe the statical and dynamical correlation effects in presence of one or more unpaired electrons. Only the highest-level quantum chemical approaches can yield reliable characterizations of their molecular properties, such as binding energies, equilibrium structures, molecular vibrations, charge distribution, and polarizabilities. In this work we use the variational Monte Carlo (VMC) and the lattice regularized Monte Carlo (LRDMC) methods to investigate the equilibrium geometries and molecular properties of oxygen and oxygen reactive species. Quantum Monte Carlo methods are used in combination with the Jastrow Antisymmetrized Geminal Power (JAGP) wave function ansatz, which has been recently shown to effectively describe the statical and dynamical correlation of different molecular systems. In particular, we have studied the oxygen molecule, the superoxide anion, the nitric oxide radical and anion, the hydroxyl and hydroperoxyl radicals and their corresponding anions, and the hydrotrioxyl radical. Overall, the methodology was able to correctly describe the geometrical and electronic properties of these systems, through compact but fully-optimised basis sets and with a computational cost which scales as N{sup 3} ? N{sup 4}, where N is the number of electrons. This work is therefore opening the way to the accurate study of the energetics and of the reactivity of large and complex oxygen species by first principles.
Quantitative Monte Carlo-based holmium-166 SPECT reconstruction
Elschot, Mattijs; Smits, Maarten L. J.; Nijsen, Johannes F. W.; Lam, Marnix G. E. H.; Zonnenberg, Bernard A.; Bosch, Maurice A. A. J. van den; Jong, Hugo W. A. M. de [Department of Radiology and Nuclear Medicine, University Medical Center Utrecht, Heidelberglaan 100, 3584 CX Utrecht (Netherlands); Viergever, Max A. [Image Sciences Institute, University Medical Center Utrecht, Heidelberglaan 100, 3584 CX Utrecht (Netherlands)] [Image Sciences Institute, University Medical Center Utrecht, Heidelberglaan 100, 3584 CX Utrecht (Netherlands)
2013-11-15
Purpose: Quantitative imaging of the radionuclide distribution is of increasing interest for microsphere radioembolization (RE) of liver malignancies, to aid treatment planning and dosimetry. For this purpose, holmium-166 ({sup 166}Ho) microspheres have been developed, which can be visualized with a gamma camera. The objective of this work is to develop and evaluate a new reconstruction method for quantitative {sup 166}Ho SPECT, including Monte Carlo-based modeling of photon contributions from the full energy spectrum.Methods: A fast Monte Carlo (MC) simulator was developed for simulation of {sup 166}Ho projection images and incorporated in a statistical reconstruction algorithm (SPECT-fMC). Photon scatter and attenuation for all photons sampled from the full {sup 166}Ho energy spectrum were modeled during reconstruction by Monte Carlo simulations. The energy- and distance-dependent collimator-detector response was modeled using precalculated convolution kernels. Phantom experiments were performed to quantitatively evaluate image contrast, image noise, count errors, and activity recovery coefficients (ARCs) of SPECT-fMC in comparison with those of an energy window-based method for correction of down-scattered high-energy photons (SPECT-DSW) and a previously presented hybrid method that combines MC simulation of photopeak scatter with energy window-based estimation of down-scattered high-energy contributions (SPECT-ppMC+DSW). Additionally, the impact of SPECT-fMC on whole-body recovered activities (A{sup est}) and estimated radiation absorbed doses was evaluated using clinical SPECT data of six {sup 166}Ho RE patients.Results: At the same noise level, SPECT-fMC images showed substantially higher contrast than SPECT-DSW and SPECT-ppMC+DSW in spheres ?17 mm in diameter. The count error was reduced from 29% (SPECT-DSW) and 25% (SPECT-ppMC+DSW) to 12% (SPECT-fMC). ARCs in five spherical volumes of 1.96–106.21 ml were improved from 32%–63% (SPECT-DSW) and 50%–80% (SPECT-ppMC+DSW) to 76%–103% (SPECT-fMC). Furthermore, SPECT-fMC recovered whole-body activities were most accurate (A{sup est}= 1.06 × A ? 5.90 MBq, R{sup 2}= 0.97) and SPECT-fMC tumor absorbed doses were significantly higher than with SPECT-DSW (p = 0.031) and SPECT-ppMC+DSW (p = 0.031).Conclusions: The quantitative accuracy of {sup 166}Ho SPECT is improved by Monte Carlo-based modeling of the image degrading factors. Consequently, the proposed reconstruction method enables accurate estimation of the radiation absorbed dose in clinical practice.