Evaluation of gamma ray buildup factor data in water with MCNP4C code
Dariush Sardari; Sassan Saudi; Maryam Tajik
2011-01-01
The exposure buildup factors for gamma and X-ray photons in water are computed using the MCNP4C code. The results are obtained for the energy range 0.04–6MeV and penetration depths up to 10mfp. The results are compared with the published buildup factor data during 1960–2010. Both agreements and discrepancies are observed between our results and the data appearing in the literature.
Monte Carlo method for calculating the radiation skyshine produced by electron accelerators
NASA Astrophysics Data System (ADS)
Kong, Chaocheng; Li, Quanfeng; Chen, Huaibi; Du, Taibin; Cheng, Cheng; Tang, Chuanxiang; Zhu, Li; Zhang, Hui; Pei, Zhigang; Ming, Shenjin
2005-06-01
Using the MCNP4C Monte Carlo code, the X-ray skyshine produced by 9 MeV, 15 MeV and 21 MeV electron linear accelerators were calculated respectively with a new two-step method combined with the split and roulette variance reduction technique. Results of the Monte Carlo simulation, the empirical formulas used for skyshine calculation and the dose measurements were analyzed and compared. In conclusion, the skyshine dose measurements agreed reasonably with the results computed by the Monte Carlo method, but deviated from computational results given by empirical formulas. The effect on skyshine dose caused by different structures of accelerator head is also discussed in this paper.
NASA Astrophysics Data System (ADS)
Zamani, M.; Kasesaz, Y.; Khalafi, H.; Pooya, S. M. Hosseini
Boron Neutron Capture Therapy (BNCT) is used for treatment of many diseases, including brain tumors, in many medical centers. In this method, a target area (e.g., head of patient) is irradiated by some optimized and suitable neutron fields such as research nuclear reactors. Aiming at protection of healthy tissues which are located in the vicinity of irradiated tissue, and based on the ALARA principle, it is required to prevent unnecessary exposure of these vital organs. In this study, by using numerical simulation method (MCNP4C Code), the absorbed dose in target tissue and the equiavalent dose in different sensitive tissues of a patiant treated by BNCT, are calculated. For this purpose, we have used the parameters of MIRD Standard Phantom. Equiavelent dose in 11 sensitive organs, located in the vicinity of target, and total equivalent dose in whole body, have been calculated. The results show that the absorbed dose in tumor and normal tissue of brain equal to 30.35?Gy and 0.19?Gy, respectively. Also, total equivalent dose in 11 sensitive organs, other than tumor and normal tissue of brain, is equal to 14?mGy. The maximum equivalent doses in organs, other than brain and tumor, appear to the tissues of lungs and thyroid and are equal to 7.35?mSv and 3.00?mSv, respectively.
Monte Carlo methods Sequential Monte Carlo
Doucet, Arnaud
Monte Carlo methods Sequential Monte Carlo A. Doucet Carcans Sept. 2011 A. Doucet (MLSS Sept. 2011) Sequential Monte Carlo Sept. 2011 1 / 85 #12;Generic Problem Consider a sequence of probability distributions, Fn = Fn 1 F. A. Doucet (MLSS Sept. 2011) Sequential Monte Carlo Sept. 2011 2 / 85 #12;Generic Problem
Monte Carlo methods Monte Carlo Principle and MCMC
Doucet, Arnaud
Monte Carlo methods Monte Carlo Principle and MCMC A. Doucet Carcans Sept. 2011 A. Doucet (MLSS Sept. 2011) MCMC Sept. 2011 1 / 91 #12;Overview of the Lectures 1 Monte Carlo Principles A. Doucet (MLSS Sept. 2011) MCMC Sept. 2011 2 / 91 #12;Overview of the Lectures 1 Monte Carlo Principles 2 Markov
S. Ulam
1949-01-01
We shall present here the motivation and a general description of a method dealing with a class of problems in mathematical physics. The method is, essentially, a statistical approach to the study of differential equations, or more generally, of integro-differential equations that occur in various branches of the natural sciences.
Shell model Monte Carlo methods
Koonin, S.E. [California Inst. of Tech., Pasadena, CA (United States). W.K. Kellogg Radiation Lab.; Dean, D.J. [Oak Ridge National Lab., TN (United States)
1996-10-01
We review quantum Monte Carlo methods for dealing with large shell model problems. These methods reduce the imaginary-time many-body evolution operator to a coherent superposition of one-body evolutions in fluctuating one-body fields; resultant path integral is evaluated stochastically. We first discuss the motivation, formalism, and implementation of such Shell Model Monte Carlo methods. There then follows a sampler of results and insights obtained from a number of applications. These include the ground state and thermal properties of pf-shell nuclei, thermal behavior of {gamma}-soft nuclei, and calculation of double beta-decay matrix elements. Finally, prospects for further progress in such calculations are discussed. 87 refs.
Monte Carlo Methods for Inference and Learning
Hinton, Geoffrey E.
Monte Carlo Methods for Inference and Learning Guest Lecturer: Ryan Adams CSC 2535 http://www.cs.toronto.edu/~rpa #12;Overview Â·Monte Carlo basics Â·Rejection and Importance sampling Â·Markov chain Monte Carlo Â·Metropolis-Hastings and Gibbs sampling Â·Slice sampling Â·Hamiltonian Monte Carlo #12;Computing Expectations We
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.
On Monte Carlo methods for Bayesian inference
Song S. Qian; Craig A. Stow; Mark E. Borsuky
2003-01-01
Bayesian methods are experiencing increased use for probabilistic ecological modelling. Most Bayesian inference requires the numerical approximation of analytically intractable integrals. Two methods based on Monte Carlo simulation have appeared in the ecological\\/environmental modelling literature. Though they sound similar, the Bayesian Monte Carlo (BMC) and Markov Chain Monte Carlo (MCMC) methods are very different in their efficiency and effectiveness in
Monte Carlo N Particle code - Dose distribution of clinical electron beams in inhomogeneous phantoms
Nedaie, H. A.; Mosleh-Shirazi, M. A.; Allahverdi, M.
2013-01-01
Electron dose distributions calculated using the currently available analytical methods can be associated with large uncertainties. The Monte Carlo method is the most accurate method for dose calculation in electron beams. Most of the clinical electron beam simulation studies have been performed using non- MCNP [Monte Carlo N Particle] codes. Given the differences between Monte Carlo codes, this work aims to evaluate the accuracy of MCNP4C-simulated electron dose distributions in a homogenous phantom and around inhomogeneities. Different types of phantoms ranging in complexity were used; namely, a homogeneous water phantom and phantoms made of polymethyl methacrylate slabs containing different-sized, low- and high-density inserts of heterogeneous materials. Electron beams with 8 and 15 MeV nominal energy generated by an Elekta Synergy linear accelerator were investigated. Measurements were performed for a 10 cm × 10 cm applicator at a source-to-surface distance of 100 cm. Individual parts of the beam-defining system were introduced into the simulation one at a time in order to show their effect on depth doses. In contrast to the first scattering foil, the secondary scattering foil, X and Y jaws and applicator provide up to 5% of the dose. A 2%/2 mm agreement between MCNP and measurements was found in the homogenous phantom, and in the presence of heterogeneities in the range of 1-3%, being generally within 2% of the measurements for both energies in a "complex" phantom. A full-component simulation is necessary in order to obtain a realistic model of the beam. The MCNP4C results agree well with the measured electron dose distributions. PMID:23533162
NASA Astrophysics Data System (ADS)
Pauzi, A. M.
2013-06-01
The neutron transport code, Monte Carlo N-Particle (MCNP) which was wellkown as the gold standard in predicting nuclear reaction was used to model the small nuclear reactor core called "U-batteryTM", which was develop by the University of Manchester and Delft Institute of Technology. The paper introduces on the concept of modeling the small reactor core, a high temperature reactor (HTR) type with small coated TRISO fuel particle in graphite matrix using the MCNPv4C software. The criticality of the core were calculated using the software and analysed by changing key parameters such coolant type, fuel type and enrichment levels, cladding materials, and control rod type. The criticality results from the simulation were validated using the SCALE 5.1 software by [1] M Ding and J L Kloosterman, 2010. The data produced from these analyses would be used as part of the process of proposing initial core layout and a provisional list of materials for newly design reactor core. In the future, the criticality study would be continued with different core configurations and geometries.
Monte Carlo Methods in Statistics Christian Robert
Boyer, Edmond
Monte Carlo Methods in Statistics Christian Robert UniversitÂ´e Paris Dauphine and CREST, INSEE September 2, 2009 Monte Carlo methods are now an essential part of the statistician's toolbox, to the point! We recall in this note some of the advances made in the design of Monte Carlo techniques towards
MONTE CARLO METHOD AND SENSITIVITY ESTIMATIONS
Dufresne, Jean-Louis
MONTE CARLO METHOD AND SENSITIVITY ESTIMATIONS A. de Lataillade a;#3; , S. Blanco b , Y. Clergent b on a formal basis and simple radiative transfer examples are used for illustration. Key words: Monte Carlo submitted to Elsevier Science 18 February 2002 #12; 1 Introduction Monte Carlo methods are commonly used
Applications of Monte Carlo Methods in Calculus.
ERIC Educational Resources Information Center
Gordon, Sheldon P.; Gordon, Florence S.
1990-01-01
Discusses the application of probabilistic ideas, especially Monte Carlo simulation, to calculus. Describes some applications using the Monte Carlo method: Riemann sums; maximizing and minimizing a function; mean value theorems; and testing conjectures. (YP)
Secondproofs Monte Carlo and Quasi-Monte Carlo Methods 2008
L'Ecuyer, Pierre
Pierre L'Ecuyer r Art B. Owen Editors Monte Carlo and Quasi-Monte Carlo Methods 2008 #12;Secondproofs Classification (2000): Primary 11K45, 65-06, 65C05, 65C10; Secondary 11K38, 65D18, 65D30, 65D32, 65R20, 91B28 Universiteit Leuven Luc Devroye, McGill University Henri Faure, CNRS Marseille Paul Glasserman, Columbia
What Monte Carlo methods cannot do
Scott Ferson
1996-01-01
Although extremely flexible and obviously useful for many risk assessment problems, Monte Carlo methods have four significant limitations that risk analysts should keep in mind. (1) Like most methods based on probability theory, Monte Carlo methods are data?intensive. Consequently, they usually cannot produce results unless a considerable body of empirical information has been collected, or unless the analyst is willing
Monte Carlo methods for security pricing
Phelim Boyle; Mark Broadie; Paul Glasserman
1997-01-01
The Monte Carlo approach has proved to be a valuable and flexible computational tool in modern finance. This paper discusses some of the recent applications of the Monte Carlo method to security pricing problems, with emphasis on improvements in efficiency. We first review some variance reduction methods that have proved useful in finance. Then we describe the use of deterministic
Bahreyni Toossi, Mohammad Taghi; Momennezhad, Mehdi; Hashemi, Seyed Mohammad
2012-01-01
Aim Exact knowledge of dosimetric parameters is an essential pre-requisite of an effective treatment in radiotherapy. In order to fulfill this consideration, different techniques have been used, one of which is Monte Carlo simulation. Materials and methods This study used the MCNP-4Cb to simulate electron beams from Neptun 10 PC medical linear accelerator. Output factors for 6, 8 and 10 MeV electrons applied to eleven different conventional fields were both measured and calculated. Results The measurements were carried out by a Wellhofler-Scanditronix dose scanning system. Our findings revealed that output factors acquired by MCNP-4C simulation and the corresponding values obtained by direct measurements are in a very good agreement. Conclusion In general, very good consistency of simulated and measured results is a good proof that the goal of this work has been accomplished. PMID:24377010
Multigrid Monte Carlo method. Conceptual foundations
Jonathan Goodman; Alan D. Sokal
1989-01-01
We present details of a stochastic generalization of the multigrid method, called multigrid Monte Carlo (MGMC), that reduces critical slowing down in Monte Carlo computations of lattice field theories. For Gaussian (free) fields, critical slowing down is completely eliminated. For a phi4 model, numerical experiments show a factor of ~=10 reduction, over a standard heat-bath algorithm, in the CPU time
Monte Carlo Methods in Geophysical Inverse Problems
Malcolm Sambridge; Klaus Mosegaard
2002-01-01
Monte Carlo inversion techniques were first used by Earthscientists more than 30 years ago. Since that time they havebeen applied to a wide range of problems, from the inversion offree oscillation data for whole Earth seismic structure tostudies at the meter-scale lengths encountered in explorationseismology. This paper traces the development and application ofMonte Carlo methods for inverse problems in the
STAN ULAM, JOHN VON NEUMANN, and the MONTE CARLO METHOD
STAN ULAM, JOHN VON NEUMANN, and the MONTE CARLO METHOD by Roger Eckhardt T he Monte Carlo method solitaire. "The first thoughts and attempts I made to practice [the Monte Carlo method] were suggested
Renormalization Group by Monte Carlo Methods
Shang-Keng Ma
1976-01-01
I discuss the basic ideas in applying the Monte Carlo methods to the renormalization-group study of static and dynamic critical phenomena within the framework of a kinetic Ising model. Simple calculations demonstrating these ideas are presented.
Monte Carlo Methods in Reactor Physics
Haghighat, Alireza
2001-06-17
Two approaches exist for particle transport simulation in reactor physics, deterministic and statistical Monte Carlo. The Monte Carlo and deterministic approaches are compared, and their advantages and disadvantages are discussed. Then different issues related to Monte Carlo simulations for solving different types of problems are described, along with methods to resolve some of the issues; these include variance-reduction techniques, automated variance techniques, and parallel computing. Then a few sample examples for real-life problems are presented. In the author's opinion, there are effective variance-reduction techniques and automation tools for the fixed-source simulations. This, however, is not true for the Monte Carlo eigenvalue calculations. The needs in this area are development of methods for determination of a ''good'' starting source and variance-reduction methods for effective sampling of source energies and regions. This is especially important because of emerging new applications including Monte Carlo depletion in general; Generation VI reactor design, which may involve irregular geometries and novel concepts; design and analyses for plutonium disposition; spent-fuel storage; radioactive waste disposal; and criticality safety evaluation of nuclear material handling facilities. The author believe that to make the Monte Carlo methods more effective and reliable, the use of deterministic methods is a must.
MONTE CARLO METHODS IN GEOPHYSICAL INVERSE Malcolm Sambridge
Sambridge, Malcolm
MONTE CARLO METHODS IN GEOPHYSICAL INVERSE PROBLEMS Malcolm Sambridge Research School Earth 27 2000; revised 15 December 2001; accepted 9 September published 5 December Monte Carlo inversion encountered in exploration seismology. traces development application Monte Carlo methods inverse problems
Digital image inpainting using monte carlo method
Jianping Gu; Silong Peng; Xuelin Wang
2004-01-01
Image Inpainting refers to the ill-posed problem of filling in the missing data in digital images by interpolating from the vicinity. It is shown in this paper how inpainting can be performed by means of random simulation of boundary in- tegral, which we call the Monte Carlo method. Our method is computationally less taxing than the classical diffusion methods, and
Monte Carlo methods for fissured porous media: gridless approaches
Paris-Sud XI, UniversitÃ© de
Monte Carlo methods for fissured porous media: gridless approaches Antoine Lejay1, -- Projet OMEGA (INRIA / Institut Â´Elie Cartan, Nancy) Abstract: In this article, we present two Monte Carlo methods) Published in Monte Carlo Methods and Applications. Proc. of the IV IMACS Seminar on Monte Carlo Methods
The Monte Carlo Method and Software Reliability Theory
Pratt, Vaughan
1 The Monte Carlo Method and Software Reliability Theory Brian Korver1 briank@cs.pdx.edu TR 94-1. February 18, 1994 1.0 Abstract The Monte Carlo method of reliability prediction is useful when system for valid, nontrivial input data and an external oracle. 2.0 The Monte Carlo Method The Monte Carlo method
Convergence of Sequential Monte Carlo Methods
Dan Crisan; Arnaud Doucet
2000-01-01
Bayesian estimation problems where the posterior distribution evolves over time through the accumulationof data arise in many applications in statistics and related fields. Recently, a large number of algorithmsand applications based on sequential Monte Carlo methods (also known as particle filtering methods) haveappeared in the literature to solve this class of problems; see (Doucet, de Freitas & Gordon, 2001) for
Sequential Monte Carlo Methods for Dynamic Systems
Jun S. Liu; Rong Chen
1998-01-01
We provide a general framework for using Monte Carlo methods in dynamic systems and discuss its wide applications. Under this framework, several currently available techniques are studied and generalized to accommodate more complex features. All of these methods are partial combinations of three ingredients: importance sampling and resampling, rejection sampling, and Markov chain iterations. We provide guidelines on how they
Monte Carlo method in optical radiometry
A. V. Prokhorov
1998-01-01
State-of-the-art in the application of the Monte Carlo method (MCM) to the computational problems of optical radiometry is discussed. The MCM offers a universal technique for radiation transfer modelling based on the stochastic approach. Developments of the original MCM algorithms and software for calculation of effective emissivities of black bodies, absorption characteristics of cavity radiometers and photometric properties of integrating
THE BEGINNING of the MONTE CARLO METHOD
its new name of the Monte Carlo method. This essay attempts to describe the de- tails that led a preliminary computational model of a thermonuclear reaction for the ENIAC. He felt he could convince different applications.) Our response to von Neumann's suggestion was enthusi- astic, and his heuristic
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.
Dosimetry of gamma chamber blood irradiator using PAGAT gel dosimeter and Monte Carlo simulations.
Mohammadyari, Parvin; Zehtabian, Mehdi; Sina, Sedigheh; Tavasoli, Ali Reza; Faghihi, Reza
2014-01-01
Currently, the use of blood irradiation for inactivating pathogenic microbes in infected blood products and preventing graft-versus-host disease (GVHD) in immune suppressed patients is greater than ever before. In these systems, dose distribution and uniformity are two important concepts that should be checked. In this study, dosimetry of the gamma chamber blood irradiator model Gammacell 3000 Elan was performed by several dosimeter methods including thermoluminescence dosimeters (TLD), PAGAT gel dosimetry, and Monte Carlo simulations using MCNP4C code. The gel dosimeter was put inside a glass phantom and the TL dosimeters were placed on its surface, and the phantom was then irradiated for 5 min and 27 sec. The dose values at each point inside the vials were obtained from the magnetic resonance imaging of the phantom. For Monte Carlo simulations, all components of the irradiator were simulated and the dose values in a fine cubical lattice were calculated using tally F6. This study shows that PAGAT gel dosimetry results are in close agreement with the results of TL dosimetry, Monte Carlo simulations, and the results given by the vendor, and the percentage difference between the different methods is less than 4% at different points inside the phantom. According to the results obtained in this study, PAGAT gel dosimetry is a reliable method for dosimetry of the blood irradiator. The major advantage of this kind of dosimetry is that it is capable of 3D dose calculation. PMID:24423829
A Monte Carlo method for solving unsteady adjoint equations
Wang, Qiqi
A Monte Carlo method for solving unsteady adjoint equations Qiqi Wang a,*, David Gleich a , Amin on this technique and uses a Monte Carlo linear solver. The Monte Carlo solver yields a forward-time algorithm' equation, the Monte Carlo approach is faster for a large class of problems while preserving sufficient
Monte Carlo methods to calculate impact probabilities
NASA Astrophysics Data System (ADS)
Rickman, H.; Wi?niowski, T.; Wajer, P.; Gabryszewski, R.; Valsecchi, G. B.
2014-09-01
Context. Unraveling the events that took place in the solar system during the period known as the late heavy bombardment requires the interpretation of the cratered surfaces of the Moon and terrestrial planets. This, in turn, requires good estimates of the statistical impact probabilities for different source populations of projectiles, a subject that has received relatively little attention, since the works of Öpik (1951, Proc. R. Irish Acad. Sect. A, 54, 165) and Wetherill (1967, J. Geophys. Res., 72, 2429). Aims: We aim to work around the limitations of the Öpik and Wetherill formulae, which are caused by singularities due to zero denominators under special circumstances. Using modern computers, it is possible to make good estimates of impact probabilities by means of Monte Carlo simulations, and in this work, we explore the available options. Methods: We describe three basic methods to derive the average impact probability for a projectile with a given semi-major axis, eccentricity, and inclination with respect to a target planet on an elliptic orbit. One is a numerical averaging of the Wetherill formula; the next is a Monte Carlo super-sizing method using the target's Hill sphere. The third uses extensive minimum orbit intersection distance (MOID) calculations for a Monte Carlo sampling of potentially impacting orbits, along with calculations of the relevant interval for the timing of the encounter allowing collision. Numerical experiments are carried out for an intercomparison of the methods and to scrutinize their behavior near the singularities (zero relative inclination and equal perihelion distances). Results: We find an excellent agreement between all methods in the general case, while there appear large differences in the immediate vicinity of the singularities. With respect to the MOID method, which is the only one that does not involve simplifying assumptions and approximations, the Wetherill averaging impact probability departs by diverging toward infinity, while the Hill sphere method results in a severely underestimated probability. We provide a discussion of the reasons for these differences, and we finally present the results of the MOID method in the form of probability maps for the Earth and Mars on their current orbits. These maps show a relatively flat probability distribution, except for the occurrence of two ridges found at small inclinations and for coinciding projectile/target perihelion distances. Conclusions: Our results verify the standard formulae in the general case, away from the singularities. In fact, severe shortcomings are limited to the immediate vicinity of those extreme orbits. On the other hand, the new Monte Carlo methods can be used without excessive consumption of computer time, and the MOID method avoids the problems associated with the other methods. Appendices are available in electronic form at http://www.aanda.org
A New Highly Convergent Monte Carlo Method for Matrix Computations
Dimov, Ivan
A New Highly Convergent Monte Carlo Method for Matrix Computations I.T. Dimov 1 , V.N. Alexandrov 2 Abstract In this paper a second degree iterative Monte Carlo method for solving Systems of Linear be at least c2 N times less than the number of realizations Nc of the existing Monte Carlo method
Semistochastic Projector Monte Carlo Method F. R. Petruzielo1
Nightingale, Peter
Semistochastic Projector Monte Carlo Method F. R. Petruzielo1 , A. A. Holmes1 , Hitesh J. Changlani. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem, Monte Carlo methods can be used to represent stochas- tically both the vector and multiplication
Introduction to the Diffusion Monte Carlo Method
Ioan Kosztin; Byron Faber; Klaus Schulten
1997-02-20
A self-contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a numerical algorithm is formulated. The algorithm is applied to determine the ground state of the harmonic oscillator, the Morse oscillator, the hydrogen atom, and the electronic ground state of the H2+ ion and of the H2 molecule. A computer program on which the sample calculations are based is available upon request.
The Moment Guided Monte Carlo Method
Pierre Degond; Giacomo Dimarco; Lorenzo Pareschi
2009-08-03
In this work we propose a new approach for the numerical simulation of kinetic equations through Monte Carlo schemes. We introduce a new technique which permits to reduce the variance of particle methods through a matching with a set of suitable macroscopic moment equations. In order to guarantee that the moment equations provide the correct solutions, they are coupled to the kinetic equation through a non equilibrium term. The basic idea, on which the method relies, consists in guiding the particle positions and velocities through moment equations so that the concurrent solution of the moment and kinetic models furnishes the same macroscopic quantities.
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.
MONTE CARLO METHODS IN GEOPHYSICAL INVERSE Malcolm Sambridge
Sambridge, Malcolm
MONTE CARLO METHODS IN GEOPHYSICAL INVERSE PROBLEMS Malcolm Sambridge Research School of Earth 2002. [1] Monte Carlo inversion techniques were first used by Earth scientists more than 30 years ago in exploration seismology. This pa- per traces the development and application of Monte Carlo methods for inverse
MONTE CARLO ANALYSIS: ESTIMATING GPP WITH THE CANOPY CONDUCTANCE METHOD
DeLucia, Evan H.
MONTE CARLO ANALYSIS: ESTIMATING GPP WITH THE CANOPY CONDUCTANCE METHOD 1. Overview A novel method performed a Monte Carlo Analysis to investigate the power of our statistical approach: i.e. what and Assumptions The Monte Carlo Analysis was performed as follows: Â· Natural variation. The only study to date
Monte Carlo Methods: A Computational Pattern for Our Pattern Language
California at Berkeley, University of
Monte Carlo Methods: A Computational Pattern for Our Pattern Language Jike Chong University@eecs.berkeley.edu Kurt Keutzer University of California, Berkeley keutzer@eecs.berkeley.edu ABSTRACT The Monte Carlo for a particular data working set. This paper presents the Monte Carlo Methods software pro- gramming pattern
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.
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.
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.
Quantum Monte Carlo methods for nuclear physics
J. Carlson; S. Gandolfi; F. Pederiva; Steven C. Pieper; R. Schiavilla; K. E. Schmidt; R. B. Wiringa
2014-12-09
Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states and transition moments in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.
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
Monte Carlo methods in an introductory electromagnetic course
M. N. O. Sadiku
1990-01-01
Although the pedagogical value of introducing numerical methods such as finite-element methods, finite-difference methods, and moment methods in an introductory electromagnetics (EM) course has been recognized, no similar attempt has been made to introduce Monte Carlo methods. An attempt is made to fill this gap by presenting Monte Carlo procedures in simple terms that can be presented in an introductory
Hedi Kharrati; Amel Agrebi; Mohamed-Karim Karaoui
2007-01-01
X-ray buildup factors of lead in broad beam geometry for energies from 15 to 150 keV are determined using the general purpose Monte Carlo N-particle radiation transport computer code (MCNP4C). The obtained buildup factors data are fitted to a modified three parameter Archer et al. model for ease in calculating the broad beam transmission with computer at any tube potentials\\/filters
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 methods for TMD analyses
NASA Astrophysics Data System (ADS)
Schnell, Gunar
2015-01-01
Monte Carlo simulations are an indispensable tool in experimental high-energy physics. Indeed, many discoveries rely on realistic modeling of background processes. In the field of transverse-momentum-dependent parton distribution and fragmentation functions there is a clear lack of a reliable Monte Carlo physics generator that can be used in experimental and phenomenological analyses. The need for such Monte Carlo generators, the status of some solutions and prospects are discussed.
Recent Advances in Randomized Quasi-Monte Carlo Methods
Pierre L’Ecuyer; Christiane Lemieux
We survey some of the recent developments on quasi-Monte Carlo (QMC) methods, which, in their basic form, are a deterministic counterpart to the Monte Carlo (MC) method. Our main focus is the applicability of these methods to practical problems that involve the estimation of a high-dimensional integral. We review several QMC constructions and different randomizations that have been proposed to
The Monte Carlo Method. Popular Lectures in Mathematics.
ERIC Educational Resources Information Center
Sobol', I. M.
The Monte Carlo Method is a method of approximately solving mathematical and physical problems by the simulation of random quantities. The principal goal of this booklet is to suggest to specialists in all areas that they will encounter problems which can be solved by the Monte Carlo Method. Part I of the booklet discusses the simulation of random…
4 Monte Carlo Methods in Classical Statistical Physics
Janke, Wolfhard
4 Monte Carlo Methods in Classical Statistical Physics Wolfhard Janke Institut fÂ¨ur Theoretische update algorithms (Metropolis, heat-bath, Glauber). Then methods for the statistical analysis of the thus Carlo Methods in Classical Statistical Physics, Lect. Notes Phys. 739, 79Â140 (2008) DOI 10
TOPICAL REVIEW Monte Carlo methods for phase equilibria of uids
by either Monte Carlo or molecular dynamics methods. Monte Carlo methods are based on generating con over time and length scales that are not directly accessible by molecular dynamics or simple constant techniques are described in detail. The Gibbs ensemble method is based on simulations of two regions coupled
Quasi-Monte Carlo Methods in Numerical Finance
Corwin Joy; Phelim P. Boyle; Ken Seng Tan
1996-01-01
This paper introduces and illustrates a new version of the Monte Carlo method that has attractive properties for the numerical valuation of derivatives. The traditional Monte Carlo method has proven to be a powerful and flexible tool for many types of derivatives calculations. Under the conventional approach pseudo-random numbers are used to evaluate the expression of interest. Unfortunately, the use
Radiative heat transfer with quasi-monte carlo methods
A. Kersch; W. Morokoff; A. Schuster
1994-01-01
Monte Carlo simulation is often used to solve radiative transfer problems wherecomplex physical phenomena and geometries must be handled. Slow convergenceis a well known disadvantage of such methods. In this paper we demonstratethat a significant improvement in computation time can be achieved by usingQuasi-Monte Carlo methods to simulate Rapid Thermal Processing, which is animportant technique for the production of semiconductor
Iterative acceleration methods for Monte Carlo and deterministic criticality calculations
Urbatsch, T.J.
1995-11-01
If you have ever given up on a nuclear criticality calculation and terminated it because it took so long to converge, you might find this thesis of interest. The author develops three methods for improving the fission source convergence in nuclear criticality calculations for physical systems with high dominance ratios for which convergence is slow. The Fission Matrix Acceleration Method and the Fission Diffusion Synthetic Acceleration (FDSA) Method are acceleration methods that speed fission source convergence for both Monte Carlo and deterministic methods. The third method is a hybrid Monte Carlo method that also converges for difficult problems where the unaccelerated Monte Carlo method fails. The author tested the feasibility of all three methods in a test bed consisting of idealized problems. He has successfully accelerated fission source convergence in both deterministic and Monte Carlo criticality calculations. By filtering statistical noise, he has incorporated deterministic attributes into the Monte Carlo calculations in order to speed their source convergence. He has used both the fission matrix and a diffusion approximation to perform unbiased accelerations. The Fission Matrix Acceleration method has been implemented in the production code MCNP and successfully applied to a real problem. When the unaccelerated calculations are unable to converge to the correct solution, they cannot be accelerated in an unbiased fashion. A Hybrid Monte Carlo method weds Monte Carlo and a modified diffusion calculation to overcome these deficiencies. The Hybrid method additionally possesses reduced statistical errors.
Wang, Brian; Kim, Chan-Hyeong; Xua, X George
2004-05-01
Metal-oxide-semiconductor field effect transistor (MOSFET) dosimeters are increasingly utilized in radiation therapy and diagnostic radiology. While it is difficult to characterize the dosimeter responses for monoenergetic sources by experiments, this paper reports a detailed Monte Carlo simulation model of the High-Sensitivity MOSFET dosimeter using Monte Carlo N-Particle (MCNP) 4C. A dose estimator method was used to calculate the dose in the extremely thin sensitive volume. Efforts were made to validate the MCNP model using three experiments: (1) comparison of the simulated dose with the measurement of a Cs-137 source, (2) comparison of the simulated dose with analytical values, and (3) comparison of the simulated energy dependence with theoretical values. Our simulation results show that the MOSFET dosimeter has a maximum response at about 40 keV of photon energy. The energy dependence curve is also found to agree with the predicted value from theory within statistical uncertainties. The angular dependence study shows that the MOSFET dosimeter has a higher response (about 8%) when photons come from the epoxy side, compared with the kapton side for the Cs-137 source. PMID:15191284
Neutron transport calculations using Quasi-Monte Carlo methods
Moskowitz, B.S.
1997-07-01
This paper examines the use of quasirandom sequences of points in place of pseudorandom points in Monte Carlo neutron transport calculations. For two simple demonstration problems, the root mean square error, computed over a set of repeated runs, is found to be significantly less when quasirandom sequences are used ({open_quotes}Quasi-Monte Carlo Method{close_quotes}) than when a standard Monte Carlo calculation is performed using only pseudorandom points.
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.
Sequential Monte Carlo Methods for Statistical Analysis of Tables
Liu, Jun
is a few orders of magnitude more efficient. In particular, compared with Markov chain Monte Carlo (MCMC)-based. Our method compares favorably with other existing Monte Carlo- based algorithms, and sometimes to achieve. KEY WORDS: Conditional inference; Contingency table; Counting problem; Exact test; Sequential
Quantum Monte Carlo Method for Attractive Coulomb Potentials
J. S. Kole; H. De Raedt
2001-02-06
Starting from an exact lower bound on the imaginary-time propagator, we present a Path-Integral Quantum Monte Carlo method that can handle singular attractive potentials. We illustrate the basic ideas of this Quantum Monte Carlo algorithm by simulating the ground state of hydrogen and helium.
Spectral backward Monte Carlo method for surface infrared image simulation
NASA Astrophysics Data System (ADS)
Sun, Haifeng; Xia, Xinlin; Sun, Chuang; Chen, Xue
2014-11-01
The surface infrared radiation is an important part that contributes to the infrared image of the airplane. The Monte Carlo method for the infrared image calculation is suitable for the complex geometry of targets like airplanes. The backward Monte Carlo method is prior to the forward Monte Carlo method for the usually long distance between targets and the detector. Similar to the non-gray absorbing media, the random number relation is developed for the radiation of the spectral surface. In the backward Monte Carlo method, one random number that reverses the wave length (or wave number) may result deferent wave numbers for targets' surface elements on the track of a photon bundle. Through the manipulation of the densities of a photon bundles in arbitrary small intervals near wave numbers, all the wave lengths corresponding to one random number on the targets' surface elements on the track of the photon bundle are kept the same to keep the balance of the energy of the photon bundle. The model developed together with the energy partition model is incorporated into the backward Monte Carlo method to form the spectral backward Monte Carlo method. The developed backward Monte Carlo method is used to calculate the infrared images of a simple configuration with two gray spectral bands, and the efficiency of it is validated by compared the results of it to that of the non-spectral backward Monte Carlo method . Then the validated spectral backward Monte Carlo method is used to simulate the infrared image of the SDM airplane model with spectral surface, and the distribution of received infrared radiation flux of pixels in the detector is analyzed.
Calculating Air Resistance using the Monte Carlo Method
NSDL National Science Digital Library
Students will discover the terminal velocity to mass relationship and use this information to calculate the air resistance constant. They will evaluate the accuracy of their lab using the Monte Carlo method.
An assessment of the MCNP4C weight window
Christopher N. Culbertson; John S. Hendricks
1999-12-01
A new, enhanced weight window generator suite has been developed for MCNP version 4C. The new generator correctly estimates importances in either a user-specified, geometry-independent, orthogonal grid or in MCNP geometric cells. The geometry-independent option alleviates the need to subdivide the MCNP cell geometry for variance reduction purposes. In addition, the new suite corrects several pathologies in the existing MCNP weight window generator. The new generator is applied in a set of five variance reduction problems. The improved generator is compared with the weight window generator applied in MCNP4B. The benefits of the new methodology are highlighted, along with a description of its limitations. The authors also provide recommendations for utilization of the weight window generator.
Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms
Alan D. Sokal
1996-01-01
IntroductionThe goal of these lectures is to give an introduction to current research on MonteCarlo methods in statistical mechanics and quantum field theory, with an emphasis on:1) the conceptual foundations of the method, including the possible dangers andmisuses, and the correct use of statistical error analysis; and2) new Monte Carlo algorithms for problems in critical phenomena and quantumfield theory, aimed
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.
Combinatorial nuclear level density by a Monte Carlo method
N. Cerf
1993-09-14
We present a new combinatorial method for the calculation of the nuclear level density. It is based on a Monte Carlo technique, in order to avoid a direct counting procedure which is generally impracticable for high-A nuclei. The Monte Carlo simulation, making use of the Metropolis sampling scheme, allows a computationally fast estimate of the level density for many fermion systems in large shell model spaces. We emphasize the advantages of this Monte Carlo approach, particularly concerning the prediction of the spin and parity distributions of the excited states, and compare our results with those derived from a traditional combinatorial or a statistical method. Such a Monte Carlo technique seems very promising to determine accurate level densities in a large energy range for nuclear reaction calculations.
Neshasteh-Riz, Ali; Koosha, Fereshteh; Mohsenifar, Afshin; Mahdavi, Seyed Rabee
2012-01-01
Objective: The passage of ionizing radiation in living cells creates clusters of damaged nucleotides in DNA. In this study, DNA strand breaks induced by the beta particle of iodine-131 (I-131), have been determined experimentally and compared to Monte Carlo simulation results as a theoretical method of determining131I damage. Materials and Methods: In this experimental study, in order to create single strand breaks (SSB) and double strand breaks (DSB) in the DNA, glioblastoma (GBM) cells were exposed to 10 mCi I-131, at a dose of 2 Gy. Damage of irradiated cells were evaluated quantitatively by the Fast Micromethod assay. The energy spectrum of electrons released in cells were obtained by the macroscopic Monte Carlo code (MCNP4c) and used as an input of the micro Monte Carlo code (MCDS). The percent of damage induced in cells was analyzed by Mann-Whitney test. Results: A significant reduction (p<0.05) in fluorescence intensity in irradiated cells compared to control cells as determined by the Fast Micromethod assay represented induced SSB and DSB damages in the DNA of irradiated cells. Comparison of experimental and theoretical results showed that the difference between the percentages of SSB per Gy was about 7.4% and DSB was about 1% per Gy. Conclusion: The differences in experimental and theoretical results may be due to the algorithm of applied codes. Since the Fast Micromethod and other experimental techniques do not provide information about the amount of detailed and complex damages of DNA-like base damages, the applied Monte Carlo codes, due to their capability to predict the amount of detailed damages that occur in the DNA of irradiated cells, can be used in in vitro experiments and radiation protection areas. PMID:23626934
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.
American Option Pricing on Reconfigurable Hardware Using Least-Squares Monte Carlo Method
Arslan, Tughrul
American Option Pricing on Reconfigurable Hardware Using Least-Squares Monte Carlo Method Xiang using the simple Monte Carlo method. A number of extended Monte Carlo methods have been published, the Quasi-Monte Carlo method is adopted for stock price paths generation. Our real FPGA hardware
An Asymptotic-Preserving Monte Carlo Method for the Boltzmann Equation$ , Hong Liua,
Jin, Shi
An Asymptotic-Preserving Monte Carlo Method for the Boltzmann Equation$ Wei Rena , Hong Liua, , Shi Carlo method for the Boltzmann equation that is more efficient than the currently available Monte Carlo of this method, and compare it with some other asymptotic-preserving Monte Carlo methods in terms of numerical
Sequential Monte Carlo Methods for Statistical Analysis of Tables
Yuguo CHEN; Susan P. HOLMES; Jun S. LIU
2003-01-01
We describe a sequential importance sampling (SIS) procedure for analyzing two-way zero-one or contingency tables with fixed marginal sums. An essential feature of the new method is that it samples the columns of the table progressively according to certain special distri- butions. Our method produces Monte Carlo samples that are remarkably close to the uniform distribution, enabling one to approximate
On Monte Carlo methods for estimating ratios of normalizing constants
Ming-Hui Chen; Qi-Man Shao
1997-01-01
Recently, estimating ratios of normalizing constants has played an important role in Bayesian computations. Applications of estimating ratios of normalizing constants arise in many aspects of Bayesian statistical inference. In this article, we present an overview and discuss the current Monte Carlo methods for estimating ratios of normalizing constants. Then we propose a new ratio importance sampling method and establish
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.
A Monte Carlo method to compute the exchange coefficient in the double porosity model
Paris-Sud XI, UniversitÃ© de
A Monte Carlo method to compute the exchange coefficient in the double porosity model Fabien: Monte Carlo methods, double porosity model, ran- dom walk on squares, fissured media AMS Classification: 76S05 (65C05 76M35) Published in Monte Carlo Methods Appl.. Proc. of Monte Carlo and probabilistic
A Multi-scale Monte Carlo Method for Electrolytes
Yihao Liang; Zhenli Xu; Xiangjun Xing
2015-04-02
Artifacts arise in the simulations of electrolytes using periodic boundary conditions (PBC). We show the origin of these artifacts are the periodic image charges and the constraint of charge neutrality inside the simulation box, both of which are unphysical from the view point of real systems. To cure these problems, we introduce a multi-scale Monte Carlo method, where ions inside a spherical cavity are simulated explicitly, whilst ions outside are treated implicitly using continuum theory. Using the method of Debye charging, we explicitly derive the effective interactions between ions inside the cavity, arising due to the fluctuations of ions outside. We find that these effective interactions consist of two types: 1) a constant cavity potential due to the asymmetry of the electrolyte, and 2) a reaction potential that depends on the positions of all ions inside. Combining the Grand Canonical Monte Carlo (GCMC) with a recently developed fast algorithm based of image charge method, we perform a multi-scale Monte Carlo simulation of symmetric electrolytes, and compare it with other simulation methods, including PBC+GCMC method, as well as large scale Monte Carlo simulation. We demonstrate that our multi-scale MC method is capable of capturing the correct physics of a large system using a small scale simulation.
Daures, J; Gouriou, J; Bordy, J M
2011-03-01
This work has been performed within the frame of the European Union ORAMED project (Optimisation of RAdiation protection for MEDical staff). The main goal of the project is to improve standards of protection for medical staff for procedures resulting in potentially high exposures and to develop methodologies for better assessing and for reducing, exposures to medical staff. The Work Package WP2 is involved in the development of practical eye-lens dosimetry in interventional radiology. This study is complementary of the part of the ENEA report concerning the calculations with the MCNP-4C code of the conversion factors related to the operational quantity H(p)(3). In this study, a set of energy- and angular-dependent conversion coefficients (H(p)(3)/K(a)), in the newly proposed square cylindrical phantom made of ICRU tissue, have been calculated with the Monte-Carlo code PENELOPE and MCNP5. The H(p)(3) values have been determined in terms of absorbed dose, according to the definition of this quantity, and also with the kerma approximation as formerly reported in ICRU reports. At a low-photon energy (up to 1 MeV), the two results obtained with the two methods are consistent. Nevertheless, large differences are showed at a higher energy. This is mainly due to the lack of electronic equilibrium, especially for small angle incidences. The values of the conversion coefficients obtained with the MCNP-4C code published by ENEA quite agree with the kerma approximation calculations obtained with PENELOPE. We also performed the same calculations with the code MCNP5 with two types of tallies: F6 for kerma approximation and *F8 for estimating the absorbed dose that is, as known, due to secondary electrons. PENELOPE and MCNP5 results agree for the kerma approximation and for the absorbed dose calculation of H(p)(3) and prove that, for photon energies larger than 1 MeV, the transport of the secondary electrons has to be taken into account. PMID:21242167
A Quantum Monte Carlo Method at Fixed Energy
Edward Farhi; Jeffrey Goldstone; David Gosset; Harvey B. Meyer
2009-12-21
In this paper we explore new ways to study the zero temperature limit of quantum statistical mechanics using Quantum Monte Carlo simulations. We develop a Quantum Monte Carlo method in which one fixes the ground state energy as a parameter. The Hamiltonians we consider are of the form $H=H_{0}+\\lambda V$ with ground state energy E. For fixed $H_{0}$ and V, one can view E as a function of $\\lambda$ whereas we view $\\lambda$ as a function of E. We fix E and define a path integral Quantum Monte Carlo method in which a path makes no reference to the times (discrete or continuous) at which transitions occur between states. For fixed E we can determine $\\lambda(E)$ and other ground state properties of H.
A Monte Carlo method for high dimensional integration
Yosihiko Ogata
1989-01-01
Summary A new method for the numerical integration of very high dimensional functions is introduced and implemented based on the Metropolis' Monte Carlo algorithm. The logarithm of the high dimensional integral is reduced to a 1-dimensional integration of a certain statistical function with respect to a scale parameter over the range of the unit interval. The improvement in accuracy is
Calculation of canopy bidirectional reflectance using the Monte Carlo method
J. K. ROSS; A. L. MARSHAK
1988-01-01
For a calculation of the plant canopy bidirectional reflectance distribution function (BRDF) the Monte Carlo method is used. The plant architecture is given by a rather universal mathematical model which allows to consider such structural parameters as canopy density and height, the number of leaves per plant, distance between leaves, dimensions and orientations of leaves and stems, etc., and their
Systolic Matrix Inversion Using a Monte Carlo Method
Graham M. Megson; V. N. Aleksandrov; I. T. Dimov
1994-01-01
A systolic array for inverting an n × n matrix using a Monte Carlo method is proposed. The basic array computes a single row of the inverse in 3n + N + T steps ( including input and output time) and O( nNT) cells where N is the number of chains and T is the length of each chain in
A direct simulation Monte-Carlo method for cluster coagulation
Kurt Liffman
1992-01-01
The study presents a method for analyzing cluster coagulation which relies on a Monte Carlo analysis of individual particles as they interact and form clusters from a homogeneous, monodisperse medium. Four case studies are shown, three of which compare the results of the code to the known analytic solutions of the Smoluchowski equation, and the fourth considers the cluster size
On the Gap-Tooth direct simulation Monte Carlo method
Armour, Jessica D
2012-01-01
This thesis develops and evaluates Gap-tooth DSMC (GT-DSMC), a direct Monte Carlo simulation procedure for dilute gases combined with the Gap-tooth method of Gear, Li, and Kevrekidis. The latter was proposed as a means of ...
Multicanonical multigrid Monte Carlo method and effective autocorellation time
W. Janke; T. Sauer
1993-12-09
We report tests of the recently proposed multicanonical multigrid Monte Carlo method for the two-dimensional $\\Phi^4$ field theory. Defining an effective autocorrelation time we obtain real time improvement factors of about one order of magnitude compared with standard multicanonical simulations.
Structure From Motion Using Sequential Monte Carlo Methods
Gang Qian; Rama Chellappa
2001-01-01
In this papel; the structure from motion (SfM) problem is addressed using sequential Monte Carlo methods. A new Sfn algorithm based on random sampling is derived to esti- mate the posterior distributions of camera motion and scene structure for the perspective projection camera model. Ex- perimental results show that challenging issues in solving the structure from motion problem including errors
Efficient Evaluation of System Reliability by Monte Carlo Method
Hiromitsu Kumamoto; Kazuo Tanaka; Koichi Inoue
1977-01-01
This paper presents a new Monte Carlo method to estimate the reliability of a large complex system represented by a reliability block diagram or by a fault tree. Two binary functions are introduced; one dominates the system structure function and the other is dominated by the structure function. These functions can be constructed easily by using part of path sets
Monte Carlo method for magnetic impurities in metals
NASA Technical Reports Server (NTRS)
Hirsch, J. E.; Fye, R. M.
1986-01-01
The paper discusses a Monte Carlo algorithm to study properties of dilute magnetic alloys; the method can treat a small number of magnetic impurities interacting wiith the conduction electrons in a metal. Results for the susceptibility of a single Anderson impurity in the symmetric case show the expected universal behavior at low temperatures. Some results for two Anderson impurities are also discussed.
Markov chain Monte Carlo method and its application
Stephen P. Brooks
1998-01-01
Summary. The Markov chain Monte Carlo (MCMC) method, as a computer-intensive statistical tool, has enjoyed an enormous upsurge in interest over the last few years. This paper provides a simple, comprehensive and tutorial review of some of the most common areas of research in this field. We begin by discussing how MCMC algorithms can be constructed from standard building- blocks
RADIATIVE HEAT TRANSFER WITH QUASI-MONTE CARLO METHODS
. The radiative heat exchange in such a reactor is a function of the geometry of the problem, the spectralRADIATIVE HEAT TRANSFER WITH QUASI-MONTE CARLO METHODS A. Kersch1 W. Moroko2 A. Schuster1 1Siemens wafers, as well as many other industrial processes. Several factors are considered including surface ab
RADIATIVE HEAT TRANSFER WITH QUASIMONTE CARLO METHODS \\Lambda
, corresponding to an area of 8.64 cm 2 . The radiative heat exchange in such a reactor is a functionRADIATIVE HEAT TRANSFER WITH QUASIÂMONTE CARLO METHODS \\Lambda A. Kersch 1 W. Morokoff 2 A of semiconductor wafers, as well as many other industrial processes. Several factors are considered including
Kinetic Monte Carlo method for simulating reactions in solutions.
Zhang, X-Q; Jansen, A P J
2010-10-01
We present an off-lattice kinetic Monte Carlo method, which is useful to simulate reactions in solutions. We derive the method from first-principles. We assume that diffusion leads to a Gaussian distribution for the position of the particles. This allows us to deal with the diffusion analytically, and we only need to simulate the reactive processes. The rate constants of these reactions can be computed before a simulation is started, and need not be computed on-the-fly as in other off-lattice kinetic Monte Carlo methods. We show how solvent molecules can be removed from the simulations, which minimizes the number of particles that have to be simulated explicitly. We present the relation with the customary macroscopic rate equations, and compare the results of these equations and our method on a variation of the Lotka model. PMID:21230409
An Implicit Monte Carlo Method for Rarefied Gas Dynamics I: The Space Homogeneous Case.
Pareschi, Lorenzo
An Implicit Monte Carlo Method for Rarefied Gas Dynamics I: The Space Homogeneous Case. Lorenzo a hybrid Monte Carlo method that is robust in the fluid dynamic limit. This method is based on an analytic of the new method. Key Words: Boltzmann equation, MonteÂCarlo methods, fluid dyanmic limit, imÂ plicit time
Mammography X-Ray Spectra Simulated with Monte Carlo
NASA Astrophysics Data System (ADS)
Vega-Carrillo, H. R.; González, J. Ramírez; Manzanares-Acuña, E.; Hernández-Dávila, V. M.; Villasana, R. Hernández; Mercado, G. A.
2008-08-01
Monte Carlo calculations have been carried out to obtain the x-ray spectra of various target-filter combinations for a mammography unit. Mammography is widely used to diagnose breast cancer. Further to Mo target with Mo filter combination, Rh/Rh, Mo/Rh, Mo/Al, Rh/Al, and W/Rh are also utilized. In this work Monte Carlo calculations, using MCNP 4C code, were carried out to estimate the x-ray spectra produced when a beam of 28 keV electrons did collide with Mo, Rh and W targets. Resulting x-ray spectra show characteristic x-rays and continuous bremsstrahlung. Spectra were also calculated including filters.
Uncertainties in external dosimetry: analytical vs. Monte Carlo method.
Behrens, R
2010-03-01
Over the years, the International Commission on Radiological Protection (ICRP) and other organisations have formulated recommendations regarding uncertainty in occupational dosimetry. The most practical and widely accepted recommendations are the trumpet curves. To check whether routine dosemeters comply with them, a Technical Report on uncertainties issued by the International Electrotechnical Commission (IEC) can be used. In this report, the analytical method is applied to assess the uncertainty of a dosemeter fulfilling an IEC standard. On the other hand, the Monte Carlo method can be used to assess the uncertainty. In this work, a direct comparison of the analytical and the Monte Carlo methods is performed using the same input data. It turns out that the analytical method generally overestimates the uncertainty by about 10-30 %. Therefore, the results often do not comply with the recommendations of the ICRP regarding uncertainty. The results of the more realistic uncertainty evaluation using the Monte Carlo method usually comply with the recommendations of the ICRP. This is confirmed by results seen in regular tests in Germany. PMID:19942627
Parallel Monte Carlo Synthetic Acceleration methods for discrete transport problems
NASA Astrophysics Data System (ADS)
Slattery, Stuart R.
This work researches and develops Monte Carlo Synthetic Acceleration (MCSA) methods as a new class of solution techniques for discrete neutron transport and fluid flow problems. Monte Carlo Synthetic Acceleration methods use a traditional Monte Carlo process to approximate the solution to the discrete problem as a means of accelerating traditional fixed-point methods. To apply these methods to neutronics and fluid flow and determine the feasibility of these methods on modern hardware, three complementary research and development exercises are performed. First, solutions to the SPN discretization of the linear Boltzmann neutron transport equation are obtained using MCSA with a difficult criticality calculation for a light water reactor fuel assembly used as the driving problem. To enable MCSA as a solution technique a group of modern preconditioning strategies are researched. MCSA when compared to conventional Krylov methods demonstrated improved iterative performance over GMRES by converging in fewer iterations when using the same preconditioning. Second, solutions to the compressible Navier-Stokes equations were obtained by developing the Forward-Automated Newton-MCSA (FANM) method for nonlinear systems based on Newton's method. Three difficult fluid benchmark problems in both convective and driven flow regimes were used to drive the research and development of the method. For 8 out of 12 benchmark cases, it was found that FANM had better iterative performance than the Newton-Krylov method by converging the nonlinear residual in fewer linear solver iterations with the same preconditioning. Third, a new domain decomposed algorithm to parallelize MCSA aimed at leveraging leadership-class computing facilities was developed by utilizing parallel strategies from the radiation transport community. The new algorithm utilizes the Multiple-Set Overlapping-Domain strategy in an attempt to reduce parallel overhead and add a natural element of replication to the algorithm. It was found that for the current implementation of MCSA, both weak and strong scaling improved on that observed for production implementations of Krylov methods.
Bayesian Phylogenetic Inference Using DNA Sequences: A Markov Chain Monte Carlo Method
Yang, Ziheng
Bayesian Phylogenetic Inference Using DNA Sequences: A Markov Chain Monte Carlo Method Ziheng Yang. A Markov Chain Monte Carlo method is used to generate the set of trees with the highest posterior Carlo method avoids the requirement of our earlier method for calculating MAP trees to sum over all
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.
Numerical study of reflectance imaging using a parallel Monte Carlo method
Numerical study of reflectance imaging using a parallel Monte Carlo method Cheng Chen and Jun Q. Lu scattering in biological tissues of turbid nature. We present a parallel Monte Carlo method for accurate
Goddard III, William A.
Monte Carlo Method Derek A. Debe, Matt J. Carlson, Jiro Sadanobu, S. I. Chan,§ and W. A. Goddard III. The foundation of this hierarchy is the Restrained Generic Protein (RGP) Direct Monte Carlo method. The RGP
Blind Data Detection in the Presence of PLL Phase Noise by Sequential Monte Carlo Method
Noels, Nele
Blind Data Detection in the Presence of PLL Phase Noise by Sequential Monte Carlo Method Erdal Abstract-- In this paper, based on a sequential Monte Carlo method, a computationally efficient algorithm
On improving the least squares Monte Carlo option valuation method
Nelson Areal; Artur Rodrigues; Manuel R. Armada
2008-01-01
This paper studies various possible approaches to improving the least squares Monte Carlo option valuation method. We test\\u000a different regression algorithms and suggest a variation to estimating the option continuation value, which can reduce the\\u000a execution time of the algorithm by one third. We test the choice of varying polynomial families with different number of basis\\u000a functions. We compare several
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
Mathematical foundations of the Markov chain Monte Carlo method
Mark Jerrum
1998-01-01
7.2 was jointly undertaken with Vivek Gore, andis published here for the first time.I also thank an anonymous referee for carefully reading and providinghelpful comments on a draft of this chapter.1. IntroductionThe classical Monte Carlo method is an approach to estimating quantitiesthat are hard to compute exactly. The quantity z of interest is expressed as theexpectation z = ExpZ of
Structure from Motion Using Sequential Monte Carlo Methods
Gang Qian; Rama Chellappa
2004-01-01
In this paper, the structure from motion (SfM) problem is addressed using sequential Monte Carlo methods. A new SfM algorithm based on random sampling is derived to estimate the posterior distributions of camera motion and scene structure for the perspective projection camera model. Experimental results show that challenging issues in solving the SfM problem, due to erroneous feature tracking, feature
Statistical error of reactor calculations by the Monte Carlo method
Kalugin, M. A.; Oleynik, D. S.; Sukhino-Khomenko, E. A., E-mail: sukhino-khomenko@adis.vver.kiae.ru [Russian Research Centre Kurchatov Institute (Russian Federation)
2011-12-15
Algorithms for calculating the statistical error with allowance for intergenerational correlations are described. The algorithms are constructed on the basis of statistical analysis of the results of computations by the Monte Carlo method. As a result, simple rules for choosing the parameters of the computational techniques, such as the number of simulated generations necessary for attaining the required accuracy and the number of first skipped generations, are elaborated.
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.
On adaptive resampling strategies for sequential Monte Carlo methods
Del Moral, Pierre; Jasra, Ajay; 10.3150/10-BEJ335
2012-01-01
Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the convergence analysis of a class of SMC methods where the times at which resampling occurs are computed online using criteria such as the effective sample size. This is a popular approach amongst practitioners but there are very few convergence results available for these methods. By combining semigroup techniques with an original coupling argument, we obtain functional central limit theorems and uniform exponential concentration estimates for these algorithms.
Novel extrapolation method in the Monte Carlo shell model
Shimizu, Noritaka; Abe, Takashi [Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033 (Japan); Utsuno, Yutaka [Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195 (Japan); Mizusaki, Takahiro [Institute of Natural Sciences, Senshu University, Tokyo, 101-8425 (Japan); Otsuka, Takaharu [Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033 (Japan); Center for Nuclear Study, University of Tokyo, Hongo Tokyo 113-0033 (Japan); National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan (United States); Honma, Michio [Center for Mathematical Sciences, Aizu University, Ikki-machi, Aizu-Wakamatsu, Fukushima 965-8580 (Japan)
2010-12-15
We propose an extrapolation method utilizing energy variance in the Monte Carlo shell model to estimate the energy eigenvalue and observables accurately. We derive a formula for the energy variance with deformed Slater determinants, which enables us to calculate the energy variance efficiently. The feasibility of the method is demonstrated for the full pf-shell calculation of {sup 56}Ni, and the applicability of the method to a system beyond the current limit of exact diagonalization is shown for the pf+g{sub 9/2}-shell calculation of {sup 64}Ge.
Semistochastic Projector Monte Carlo Method F. R. Petruzielo,1,* A. A. Holmes,1,
Nightingale, Peter
Semistochastic Projector Monte Carlo Method F. R. Petruzielo,1,* A. A. Holmes,1, Hitesh J. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem, for sufficiently large N, this is no longer feasible, Monte Carlo methods can be used to represent stochastically
A Quasi-Monte Carlo Method for Integration with Improved Convergence
Karaivanova, Aneta
A Quasi-Monte Carlo Method for Integration with Improved Convergence Aneta Karaivanova, Ivan Dimov anet@copern.bas.bg, ivdimov@bas.bg, sofia@copern.bas.bg Abstract. Quasi-Monte Carlo methods are based of random numbers with a more uniformly distributed de- terministic sequence. Quasi-Monte Carlo methods
Article type: Opinion Article Why the Monte Carlo Method is so important
Kroese, Dirk P.
Article type: Opinion Article Why the Monte Carlo Method is so important today Article ID Dirk P of Queensland Zdravko I. Botev The University of New South Wales Keywords Monte Carlo method, simulation, MCMC an essential ingredient in many quantitative investigations. Why is the Monte Carlo method (MCM) so important
Bayesian Training of Backpropagation Networks by the Hybrid Monte Carlo Method
Neal, Radford M.
Bayesian Training of Backpropagation Networks by the Hybrid Monte Carlo Method Radford M. Neal of backpropagation neural networks can feasibly be performed by the ``Hybrid Monte Carlo'' method. This approach by a Gaussian. In this work, the Hybrid Monte Carlo method is implemented in conjunction with simulated
A Parallel Quasi-Monte Carlo Method for Computing Extremal Eigenvalues
Mascagni, Michael
A Parallel Quasi-Monte Carlo Method for Computing Extremal Eigenvalues Michael Mascagni1 and Aneta The convergence of Monte Carlo methods for numerical integration can often be improved by replacing pseudorandom). In this paper the convergence of a Monte Carlo method for evaluating the extremal eigenvalues of a given matrix
A Monte Carlo Method for Obtaining the Null Distribution of Functionindexed Logrank Statistics
Kosorok, Michael R.
A Monte Carlo Method for Obtaining the Null Distribution of Functionindexed Logrank Statistics a Monte Carlo method for accurately obtaining pvalues for the functionindexed statistics described in Kosorok and Lin (1998), Sections 1 through 3, and Kosorok (1998), Section 4. 2. THE MONTE CARLO METHOD Let
A Bayesian Approach to Multiscale Inverse Problems Using Sequential Monte Carlo Method
Zabaras, Nicholas J.
A Bayesian Approach to Multiscale Inverse Problems Using Sequential Monte Carlo Method Nicholas-modal, sequential Monte Carlo method is employed. Materials Process Design and Control Laboratory Cornell University are of high dimension and multi-modal, sequential Monte Carlo method is employed. Materials Process Design
Reich, Sebastian
A guided sequential Monte Carlo method for the assimilation of data into stochastic dynamical functions. While sequential Monte Carlo methods have emerged as a methodology for tackling as- similation alternatives to sequential Monte Carlo methods since they also work for high dimensional problems. Typical
Monte Carlo Method for Calculating the Electrostatic Energy of a Molecule
Mascagni, Michael
Monte Carlo Method for Calculating the Electrostatic Energy of a Molecule Michael Mascagni1 ,2 describing Monte Carlo methods for solving boundary value problems for the heat, Laplace and other diffusion's function first passage Monte Carlo method is the natural extension of WOS. The simulation
A new optimal Monte Carlo method for calculating integrals of smooth functions #
Dimov, Ivan
A new optimal Monte Carlo method for calculating integrals of smooth functions # Emanouil I. Atanassov 1 , Ivan T. Dimov 1 , Abstract An optimal Monte Carlo method for numerical integration of multi#ciency of the algorithms are also given. Keywords: Monte Carlo method, optimal quadrature formula, rate of convergence. ASM
A Quasi-Monte Carlo Method for Elliptic Boundary Value Problems Michael Mascagni
Mascagni, Michael
A Quasi-Monte Carlo Method for Elliptic Boundary Value Problems Michael Mascagni Aneta Karaivanova Yaohang Li Abstract In this paper we present and analyze a quasi-Monte Carlo method for solving elliptic estimate the accuracy and the computational complexity of the quasi-Monte Carlo method. Finally, results
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.
A path integral Monte Carlo method for Rényi entanglement entropies
C. M. Herdman; Stephen Inglis; P. -N. Roy; R. G. Melko; A. Del Maestro
2014-08-04
We introduce a quantum Monte Carlo algorithm to measure the R\\'enyi entanglement entropies in systems of interacting bosons in the continuum. This approach is based on a path integral ground state method that can be applied to interacting itinerant bosons in any spatial dimension with direct relevance to experimental systems of quantum fluids. We demonstrate how it may be used to compute spatial mode entanglement, particle partitioned entanglement, and the entanglement of particles, providing insights into quantum correlations generated by fluctuations, indistinguishability and interactions. We present proof-of-principle calculations, and benchmark against an exactly soluble model of interacting bosons in one spatial dimension. As this algorithm retains the fundamental polynomial scaling of quantum Monte Carlo when applied to sign-problem-free models, future applications should allow for the study of entanglement entropy in large scale many-body systems of interacting bosons.
Density of States Monte Carlo Method for Simulation of Fluids
Qiliang Yan; Roland Faller; Juan J. de Pablo
2002-01-25
A Monte Carlo method based on a density-of-states sampling is proposed for study of arbitrary statistical mechanical ensembles in a continuum. A random walk in the two-dimensional space of particle number and energy is used to estimate the density of states of the system; this density of states is continuously updated as the random walk visits individual states. The validity and usefulness of the method are demonstrated by applying it to the simulation of a Lennard-Jones fluid. Results for its thermodynamic properties, including the vapor-liquid phase coexistence curve, are shown to be in good agreement with high-accuracy literature data.
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.
Monte Carlo N-particle simulation of neutron-based sterilisation of anthrax contamination
Liu, B; Xu, J; Liu, T; Ouyang, X
2012-01-01
Objective To simulate the neutron-based sterilisation of anthrax contamination by Monte Carlo N-particle (MCNP) 4C code. Methods Neutrons are elementary particles that have no charge. They are 20 times more effective than electrons or ?-rays in killing anthrax spores on surfaces and inside closed containers. Neutrons emitted from a 252Cf neutron source are in the 100 keV to 2 MeV energy range. A 2.5 MeV D–D neutron generator can create neutrons at up to 1013 n s?1 with current technology. All these enable an effective and low-cost method of killing anthrax spores. Results There is no effect on neutron energy deposition on the anthrax sample when using a reflector that is thicker than its saturation thickness. Among all three reflecting materials tested in the MCNP simulation, paraffin is the best because it has the thinnest saturation thickness and is easy to machine. The MCNP radiation dose and fluence simulation calculation also showed that the MCNP-simulated neutron fluence that is needed to kill the anthrax spores agrees with previous analytical estimations very well. Conclusion The MCNP simulation indicates that a 10 min neutron irradiation from a 0.5 g 252Cf neutron source or a 1 min neutron irradiation from a 2.5 MeV D–D neutron generator may kill all anthrax spores in a sample. This is a promising result because a 2.5 MeV D–D neutron generator output >1013 n s?1 should be attainable in the near future. This indicates that we could use a D–D neutron generator to sterilise anthrax contamination within several seconds. PMID:22573293
Monte Carlo Radiation-Hydrodynamics With Implicit Methods
NASA Astrophysics Data System (ADS)
Roth, Nathaniel; Kasen, Daniel
2015-03-01
We explore the application of Monte Carlo transport methods to solving coupled radiation-hydrodynamics (RHD) problems. We use a time-dependent, frequency-dependent, three-dimensional radiation transport code that is special relativistic and includes some detailed microphysical interactions such as resonant line scattering. We couple the transport code to two different one-dimensional (non-relativistic) hydrodynamics solvers: a spherical Lagrangian scheme and a Eulerian Godunov solver. The gas-radiation energy coupling is treated implicitly, allowing us to take hydrodynamical time-steps that are much longer than the radiative cooling time. We validate the code and assess its performance using a suite of radiation hydrodynamical test problems, including ones in the radiation energy dominated regime. We also develop techniques that reduce the noise of the Monte Carlo estimated radiation force by using the spatial divergence of the radiation pressure tensor. The results suggest that Monte Carlo techniques hold promise for simulating the multi-dimensional RHD of astrophysical systems.
A simple eigenfunction convergence acceleration method for Monte Carlo
Booth, Thomas E [Los Alamos National Laboratory
2010-11-18
Monte Carlo transport codes typically use a power iteration method to obtain the fundamental eigenfunction. The standard convergence rate for the power iteration method is the ratio of the first two eigenvalues, that is, k{sub 2}/k{sub 1}. Modifications to the power method have accelerated the convergence by explicitly calculating the subdominant eigenfunctions as well as the fundamental. Calculating the subdominant eigenfunctions requires using particles of negative and positive weights and appropriately canceling the negative and positive weight particles. Incorporating both negative weights and a {+-} weight cancellation requires a significant change to current transport codes. This paper presents an alternative convergence acceleration method that does not require modifying the transport codes to deal with the problems associated with tracking and cancelling particles of {+-} weights. Instead, only positive weights are used in the acceleration method.
Comparison of vectorization methods used in a Monte Carlo code
Nakagawa, M.; Mori, T.; Sasaki, M. (Japan Atomic Energy Research Inst., Tokai Establishment Tokai-mura, Ibaraki-ken 319-11 (JP))
1991-01-01
This paper examines vectorization methods used in Monte Carlo codes for particle transport calculations. Event and zone selection methods developed from conventional all-zone and one-zone algorithms have been implemented in a general-purpose vectorized code, GMVP. Moreover, a vectorization procedure to treat multiple-lattice geometry has been developed using these methods. Use of lattice geometry can reduce the computation cost for a typical pressurized water reactor fuel subassembly calculation, especially when the zone selection method is used. Sample calculations for external and fission source problems are used to compare the performances of both methods with the results of conventional scalar codes. Though the speedup resulting from vectorization depends on the problem solved, a factor of 7 to 10 is obtained for practical problems on the FACOM VP-100 computer compared with the conventional scalar code, MORSE-CG.
Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference
Nicolas Chopin
2004-01-01
The term “sequential Monte Carlo methods” or, equivalently, “particle filters,” refers to a general class of iterative algorithms that performs Monte Carlo approximations of a given sequence of distributions of interest (?_{t<\\/sub>). We establish in this paper a central limit theorem for the Monte Carlo estimates produced by these computational methods. This result holds under minimal assumptions on the distributions}
Limit theorems for weighted samples with applications to sequential Monte Carlo methods
Randal Douc; Eric Moulines
2008-01-01
In the last decade, sequential Monte Carlo methods (SMC) emerged as a key tool in computational statistics [see, e.g., Sequential Monte Carlo Methods in Practice (2001) Springer, New York, Monte Carlo Strategies in Scientific Computing (2001) Springer, New York, Complex Stochastic Systems (2001) 109–173]. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to
Monte Carlo Methods for Pricing and Hedging American Options in High Dimension
Caramellino, Lucia
Monte Carlo Methods for Pricing and Hedging American Options in High Dimension Lucia Caramellino1.zanette@uniud.it Summary. We numerically compare some recent Monte Carlo algorithms devoted to the pricing and hedging with respect to other Monte Carlo methods in terms of computing time. Here, we propose to suitably combine
Monte Carlo Methods for Exact & Efficient Solution of the Generalized Optimality Equations
Monte Carlo Methods for Exact & Efficient Solution of the Generalized Optimality Equations Pedro A to the complexity of planning. In this paper, we introduce Monte Carlo methods to solve the generalized optimality of Monte Carlo proposals. In particular, it is seen that the number of proposals is essentially independent
Monte Carlo Methods for Computation and Optimization (048715) Winter 2013/4
Shimkin, Nahum
Monte Carlo Methods for Computation and Optimization (048715) Winter 2013/4 Lecture Notes Nahum Shimkin i #12;PREFACE These lecture notes are intended for a first, graduate-level, course on Monte-Carlo, Simulation and the Monte Carlo Method, Wiley, 2008. (2) S. Asmussen and P. Glynn, Stochastic Simulation
Monte-Carlo valorisation of American options: facts and new algorithms to improve existing methods
Boyer, Edmond
Monte-Carlo valorisation of American options: facts and new algorithms to improve existing methods is to discuss efficient algorithms for the pricing of American options by two recently proposed Monte-Carlo type the quantization approach, are performed. Key words: American Options, Monte Carlo methods. 1. Introduction
Monte Carlo methods designed for parallel computation Sheldon B. Opps and Jeremy Scho eld
Schofield, Jeremy
Monte Carlo methods designed for parallel computation Sheldon B. Opps and Jeremy Scho#12;eld of these methods is that individual Monte Carlo chains, which are run on a separate nodes, are coupled together- rate calculation, for example to improve the statistics of a Monte Carlo simulation, one inherent bene
Condensed history Monte Carlo methods for photon transport problems
Bhan, Katherine; Spanier, Jerome
2007-01-01
We study methods for accelerating Monte Carlo simulations that retain most of the accuracy of conventional Monte Carlo algorithms. These methods – called Condensed History (CH) methods – have been very successfully used to model the transport of ionizing radiation in turbid systems. Our primary objective is to determine whether or not such methods might apply equally well to the transport of photons in biological tissue. In an attempt to unify the derivations, we invoke results obtained first by Lewis, Goudsmit and Saunderson and later improved by Larsen and Tolar. We outline how two of the most promising of the CH models – one based on satisfying certain similarity relations and the second making use of a scattering phase function that permits only discrete directional changes – can be developed using these approaches. The main idea is to exploit the connection between the space-angle moments of the radiance and the angular moments of the scattering phase function. We compare the results obtained when the two CH models studied are used to simulate an idealized tissue transport problem. The numerical results support our findings based on the theoretical derivations and suggest that CH models should play a useful role in modeling light-tissue interactions. PMID:18548128
Analysis of real-time networks with monte carlo methods
NASA Astrophysics Data System (ADS)
Mauclair, C.; Durrieu, G.
2013-12-01
Communication networks in embedded systems are ever more large and complex. A better understanding of the dynamics of these networks is necessary to use them at best and lower costs. Todays tools are able to compute upper bounds of end-to-end delays that a packet being sent through the network could suffer. However, in the case of asynchronous networks, those worst end-to-end delay (WEED) cases are rarely observed in practice or through simulations due to the scarce situations that lead to worst case scenarios. A novel approach based on Monte Carlo methods is suggested to study the effects of the asynchrony on the performances.
Application of Monte Carlo methods in tomotherapy and radiation biophysics
NASA Astrophysics Data System (ADS)
Hsiao, Ya-Yun
Helical tomotherapy is an attractive treatment for cancer therapy because highly conformal dose distributions can be achieved while the on-board megavoltage CT provides simultaneous images for accurate patient positioning. The convolution/superposition (C/S) dose calculation methods typically used for Tomotherapy treatment planning may overestimate skin (superficial) doses by 3-13%. Although more accurate than C/S methods, Monte Carlo (MC) simulations are too slow for routine clinical treatment planning. However, the computational requirements of MC can be reduced by developing a source model for the parts of the accelerator that do not change from patient to patient. This source model then becomes the starting point for additional simulations of the penetration of radiation through patient. In the first section of this dissertation, a source model for a helical tomotherapy is constructed by condensing information from MC simulations into series of analytical formulas. The MC calculated percentage depth dose and beam profiles computed using the source model agree within 2% of measurements for a wide range of field sizes, which suggests that the proposed source model provides an adequate representation of the tomotherapy head for dose calculations. Monte Carlo methods are a versatile technique for simulating many physical, chemical and biological processes. In the second major of this thesis, a new methodology is developed to simulate of the induction of DNA damage by low-energy photons. First, the PENELOPE Monte Carlo radiation transport code is used to estimate the spectrum of initial electrons produced by photons. The initial spectrum of electrons are then combined with DNA damage yields for monoenergetic electrons from the fast Monte Carlo damage simulation (MCDS) developed earlier by Semenenko and Stewart (Purdue University). Single- and double-strand break yields predicted by the proposed methodology are in good agreement (1%) with the results of published experimental and theoretical studies for 60Co gamma-rays and low-energy x-rays. The reported studies provide new information about the potential biological consequences of diagnostic x-rays and selected gamma-emitting radioisotopes used in brachytherapy for the treatment of cancer. The proposed methodology is computationally efficient and may also be useful in proton therapy, space applications or internal dosimetry.
ITER Neutronics Modeling Using Hybrid Monte Carlo/Deterministic and CAD-Based Monte Carlo Methods
Ibrahim, A. [University of Wisconsin; Mosher, Scott W [ORNL; Evans, Thomas M [ORNL; Peplow, Douglas E. [ORNL; Sawan, M. [University of Wisconsin; Wilson, P. [University of Wisconsin; Wagner, John C [ORNL; Heltemes, Thad [University of Wisconsin, Madison
2011-01-01
The immense size and complex geometry of the ITER experimental fusion reactor require the development of special techniques that can accurately and efficiently perform neutronics simulations with minimal human effort. This paper shows the effect of the hybrid Monte Carlo (MC)/deterministic techniques - Consistent Adjoint Driven Importance Sampling (CADIS) and Forward-Weighted CADIS (FW-CADIS) - in enhancing the efficiency of the neutronics modeling of ITER and demonstrates the applicability of coupling these methods with computer-aided-design-based MC. Three quantities were calculated in this analysis: the total nuclear heating in the inboard leg of the toroidal field coils (TFCs), the prompt dose outside the biological shield, and the total neutron and gamma fluxes over a mesh tally covering the entire reactor. The use of FW-CADIS in estimating the nuclear heating in the inboard TFCs resulted in a factor of ~ 275 increase in the MC figure of merit (FOM) compared with analog MC and a factor of ~ 9 compared with the traditional methods of variance reduction. By providing a factor of ~ 21 000 increase in the MC FOM, the radiation dose calculation showed how the CADIS method can be effectively used in the simulation of problems that are practically impossible using analog MC. The total flux calculation demonstrated the ability of FW-CADIS to simultaneously enhance the MC statistical precision throughout the entire ITER geometry. Collectively, these calculations demonstrate the ability of the hybrid techniques to accurately model very challenging shielding problems in reasonable execution times.
Monte Carlo method for determining earthquake recurrence parameters from short paleoseismic paleoseismic series. From repeated Monte Carlo draws, it becomes possible to quantitatively estimate most to an overestimate of the hazard should they be used in probability calculations. Therefore a Monte Carlo approach
Monte Carlo methods for short polypeptides Jeremy Schofield a) and Mark A. Ratner
Schofield, Jeremy
Monte Carlo methods for short polypeptides Jeremy Schofield a) and Mark A. Ratner Department! Nonphysical sampling Monte Carlo techniques that enable average structural properties of short in vacuo polypeptide chains to be calculated accurately are discussed. Updating algorithms developed for Monte Carlo
Heavy deformed nuclei in the shell model Monte Carlo method
Y. Alhassid; L. Fang; H. Nakada
2007-10-09
We extend the shell model Monte Carlo approach to heavy deformed nuclei using a new proton-neutron formalism. The low excitation energies of such nuclei necessitate calculations at low temperatures for which a stabilization method is implemented in the canonical ensemble. We apply the method to study a well deformed rare-earth nucleus, 162Dy. The single-particle model space includes the 50-82 shell plus 1f_{7/2} orbital for protons and the 82-126 shell plus 0h_{11/2}, 1g_{9/2} orbitals for neutrons. We show that the spherical shell model reproduces well the rotational character of 162Dy within this model space. We also calculate the level density of 162Dy and find it to be in excellent agreement with the experimental level density, which we extract from several experiments.
A monte carlo method for generating side chain structural ensembles.
Bhowmick, Asmit; Head-Gordon, Teresa
2015-01-01
We report a Monte Carlo side chain entropy (MC-SCE) method that uses a physical energy function inclusive of long-range electrostatics and hydrophobic potential of mean force, coupled with both backbone variations and a backbone dependent side chain rotamer library, to describe protein conformational ensembles. Using the MC-SCE method in conjunction with backbone variability, we can reliably determine the side chain rotamer populations derived from both room temperature and cryogenically cooled X-ray crystallographic structures for CypA and H-Ras and NMR J-coupling constants for CypA, Eglin-C, and the DHFR product binary complexes E:THF and E:FOL. Furthermore, we obtain near perfect discrimination between a protein's native state ensemble and ensembles of misfolded structures for 55 different proteins, thereby generating far more competitive side chain packings for all of these proteins and their misfolded states. PMID:25482539
NASA Astrophysics Data System (ADS)
Vargas Verdesoto, M. X.; Álvarez Romero, J. T.
2003-09-01
To characterize an ionization chamber BEV-CC01 as a standard of absorbed dose to water Dw at SSDL-Mexico, the approach developed by the BIPM for 60Co gamma radiation, [1] has been chosen. This requires the estimation of a factor kp, which stems from the perturbation introduced by the presence of the ionization chamber in the water phantom, and due to finite size of the cavity. This factor is the product of four terms: ?w,c, (?en/?)w,c, (1 + ?'.?)w,c and kcav. Two independent determinations are accomplished using a combination of the Monte Carlo code MCNP4C in ITS mode [2,3] and analytic methods: one kp?=1.1626 ± uc=: 0.90% for the chamber axis parallel to the beam axis; and another kp =1.1079± uc=0.89% for the chamber axis perpendicular to the beam axis. The variance reduction techniques: splitting-Russian roulette, source biasing and forced photon collisions are employed in the simulations to improve the calculation efficiency. The energy fluence for the 60Co housing-source Picker C/9 is obtained by realistic Monte Carlo (MC) simulation, it is verified by comparison of MC calculated and measured beam output air kerma factors, and percent depth dose curves in water, PDD. This spectrum is considered as input energy for a point source (74% is from primary photons and the rest 26% is from scattered radiation) in the determination of the kp factors. Details of the calculations are given together with the theoretical basis of the ionometric standard employed.
Parallel Performance Optimization of the Direct Simulation Monte Carlo Method
NASA Astrophysics Data System (ADS)
Gao, Da; Zhang, Chonglin; Schwartzentruber, Thomas
2009-11-01
Although the direct simulation Monte Carlo (DSMC) particle method is more computationally intensive compared to continuum methods, it is accurate for conditions ranging from continuum to free-molecular, accurate in highly non-equilibrium flow regions, and holds potential for incorporating advanced molecular-based models for gas-phase and gas-surface interactions. As available computer resources continue their rapid growth, the DSMC method is continually being applied to increasingly complex flow problems. Although processor clock speed continues to increase, a trend of increasing multi-core-per-node parallel architectures is emerging. To effectively utilize such current and future parallel computing systems, a combined shared/distributed memory parallel implementation (using both Open Multi-Processing (OpenMP) and Message Passing Interface (MPI)) of the DSMC method is under development. The parallel implementation of a new state-of-the-art 3D DSMC code employing an embedded 3-level Cartesian mesh will be outlined. The presentation will focus on performance optimization strategies for DSMC, which includes, but is not limited to, modified algorithm designs, practical code-tuning techniques, and parallel performance optimization. Specifically, key issues important to the DSMC shared memory (OpenMP) parallel performance are identified as (1) granularity (2) load balancing (3) locality and (4) synchronization. Challenges and solutions associated with these issues as they pertain to the DSMC method will be discussed.
Particle acceleration at shocks - A Monte Carlo method
NASA Technical Reports Server (NTRS)
Kirk, J. G.; Schneider, P.
1987-01-01
A Monte Carlo method is presented for the problem of acceleration of test particles at relativistic shocks. The particles are assumed to diffuse in pitch angle as a result of scattering off magnetic irregularities frozen into the fluid. Several tests are performed using the analytic results available for both relativistic and nonrelativistic shock speeds. The acceleration at relativistic shocks under the influence of radiation losses is investigated, including the effects of a momentum dependence in the diffusion coefficient. The results demonstrate the usefulness of the technique in those situations in which the diffusion approximation cannot be employed, such as when relativistic bulk motion is considered, when particles are permitted to escape at the boundaries, and when the effects of the finite length of the particle mean free path are important.
Kasesaz, Y; Khalafi, H; Rahmani, F
2013-12-01
Optimization of the Beam Shaping Assembly (BSA) has been performed using the MCNP4C Monte Carlo code to shape the 2.45 MeV neutrons that are produced in the D-D neutron generator. Optimal design of the BSA has been chosen by considering in-air figures of merit (FOM) which consists of 70 cm Fluental as a moderator, 30 cm Pb as a reflector, 2mm (6)Li as a thermal neutron filter and 2mm Pb as a gamma filter. The neutron beam can be evaluated by in-phantom parameters, from which therapeutic gain can be derived. Direct evaluation of both set of FOMs (in-air and in-phantom) is very time consuming. In this paper a Response Matrix (RM) method has been suggested to reduce the computing time. This method is based on considering the neutron spectrum at the beam exit and calculating contribution of various dose components in phantom to calculate the Response Matrix. Results show good agreement between direct calculation and the RM method. PMID:23954283
Computation of electron diode characteristics by monte carlo method including effect of collisions.
NASA Technical Reports Server (NTRS)
Goldstein, C. M.
1964-01-01
Consistent field Monte Carlo method calculation for collision effect on electron-ion diode characteristics and for hard sphere electron- neutral collision effect for monoenergetic- thermionic emission
A Constrained Path Monte Carlo Method for Fermion Ground States
Shiwei Zhang; J. Carlson; J. E. Gubernatis
1996-07-09
We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected from an initial wave function by a branching random walk in an over-complete basis of Slater determinants. By constraining the determinants according to a trial wave function $|\\psi_T\\rangle$, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if $|\\psi_T\\rangle$ is exact. We illustrate the method by describing in detail its implementation for the two-dimensional one-band Hubbard model. We show results for lattice sizes up to $16\\times 16$ and for various electron fillings and interaction strengths. Besides highly accurate estimates of the ground-state energy, we find that the method also yields reliable estimates of other ground-state observables, such as superconducting pairing correlation functions. We conclude by discussing possible extensions of the algorithm.
Monte Carlo methods for signal processing: a review in the statistical signal processing context
A. Doucet; Xiaodong Wang
2005-01-01
In this article, MCMC (Markov chain Monte Carlo methods) and SMC (sequential Monte Carlo methods) are introduced to sample and\\/or maximize high-dimensional probability distributions. These methods enable to perform likelihood or Bayesian inference for complex non-Gaussian signal processing problems.
A wave-function Monte Carlo method for simulating conditional master equations
Kurt Jacobs
2010-01-21
Wave-function Monte Carlo methods are an important tool for simulating quantum systems, but the standard method cannot be used to simulate decoherence in continuously measured systems. Here we present a new Monte Carlo method for such systems. This was used to perform the simulations of a continuously measured nano-resonator in [Phys. Rev. Lett. 102, 057208 (2009)].
Monte Carlo methods for light propagation in biological tissues Laura Vinckenbosch1
Boyer, Edmond
, there have been a large development of this kind of therapy for cancers follow- ing the discovery solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods Carlo method based on the Metropolis-Hastings algorithm. The resulting estimating methods
New sequential Monte Carlo methods for nonlinear dynamic systems
Dong Guo; Xiaodong Wang; Rong Chen
2005-01-01
In this paper we present several new sequential Monte Carlo (SMC) algorithms for online estimation (filtering) of nonlinear dynamic systems. SMC has been shown to be a powerful tool for dealing with complex dynamic systems. It sequentially generates Monte Carlo samples from a proposal distribution, adjusted by a set of importance weight with respect to a target distribution, to facilitate
Sequential Monte Carlo Methods to Train Neural Network Models
João F. G. De Freitas; Mahesan Niranjan; Andrew H. Gee; Arnaud Doucet
2000-01-01
We discuss a novel strategy for training neural networks using sequential Monte Carlo algorithms and propose a new hybrid gradient descent\\/sampling importance resampling algorithm (HySIR). In terms of computational time and accuracy, the hybrid SIR is a clear improvement over conventional sequential Monte Carlo techniques. The new algorithm may be viewed as a global optimization strategy that allows us to
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.
The simulation of the recharging method of active medical implant based on Monte Carlo method
NASA Astrophysics Data System (ADS)
Kong, Xianyue; Song, Yong; Hao, Qun; Cao, Jie; Zhang, Xiaoyu; Dai, Pantao; Li, Wansong
2014-11-01
The recharging of Active Medical Implant (AMI) is an important issue for its future application. In this paper, a method for recharging active medical implant using wearable incoherent light source has been proposed. Firstly, the models of the recharging method are developed. Secondly, the recharging processes of the proposed method have been simulated by using Monte Carlo (MC) method. Finally, some important conclusions have been reached. The results indicate that the proposed method will help to result in a convenient, safe and low-cost recharging method of AMI, which will promote the application of this kind of implantable device.
LISA data analysis using Markov chain Monte Carlo methods
Cornish, Neil J.; Crowder, Jeff [Department of Physics, Montana State University, Bozeman, Montana 59717 (United States)
2005-08-15
The Laser Interferometer Space Antenna (LISA) is expected to simultaneously detect many thousands of low-frequency gravitational wave signals. This presents a data analysis challenge that is very different to the one encountered in ground based gravitational wave astronomy. LISA data analysis requires the identification of individual signals from a data stream containing an unknown number of overlapping signals. Because of the signal overlaps, a global fit to all the signals has to be performed in order to avoid biasing the solution. However, performing such a global fit requires the exploration of an enormous parameter space with a dimension upwards of 50 000. Markov Chain Monte Carlo (MCMC) methods offer a very promising solution to the LISA data analysis problem. MCMC algorithms are able to efficiently explore large parameter spaces, simultaneously providing parameter estimates, error analysis, and even model selection. Here we present the first application of MCMC methods to simulated LISA data and demonstrate the great potential of the MCMC approach. Our implementation uses a generalized F-statistic to evaluate the likelihoods, and simulated annealing to speed convergence of the Markov chains. As a final step we supercool the chains to extract maximum likelihood estimates, and estimates of the Bayes factors for competing models. We find that the MCMC approach is able to correctly identify the number of signals present, extract the source parameters, and return error estimates consistent with Fisher information matrix predictions.
MONTE CARLO METHODS FOR THE VALUATION OF MULTIPLE-EXERCISE OPTIONS
N. Meinshausen; B. M. Hambly
2004-01-01
We discuss Monte Carlo methods for valuing options with multiple-exercise features in discrete time. By extending the recently developed duality ideas for American option pricing, we show how to obtain estimates on the prices of such options using Monte Carlo techniques. We prove convergence of our approach and estimate the error. The methods are applied to options in the energy
Kinetic Monte Carlo method for dislocation migration in the presence of solute Chaitanya S. Deo
Cai, Wei
Kinetic Monte Carlo method for dislocation migration in the presence of solute Chaitanya S. Deo, California 94550, USA (Received 21 April 2004; published 6 January 2005) We present a kinetic Monte Carlo method for simulating dislocation motion in alloys within the framework of the kink model. The model
Ciprian Apostol
2009-01-01
Monte Carlo simulation is used with predilection when multidimensional problems are discussed (eg, the outcome depends on more variables or risk factors). The method was invented by American scientists in 1940 when it was used to simulate the trajectory of a neutron in uranium or plutonium. Monte Carlo method, the real is replaced by an artificial process. To obtain accurate
Author's personal copy Monte Carlo methods for design and analysis of radiation detectors
Shultis, J. Kenneth
Author's personal copy Monte Carlo methods for design and analysis of radiation detectors William L Radiation detectors Inverse problems Detector design a b s t r a c t An overview of Monte Carlo as a practical method for designing and analyzing radiation detectors is provided. The emphasis is on detectors
ACOUSTIC NODE CALIBRATION USING HELICOPTER SOUNDS AND MONT E CARLO MARKOV CHAIN METHODS
Cevher, Volkan
ACOUSTIC NODE CALIBRATION USING HELICOPTER SOUNDS AND MONT Â´E CARLO MARKOV CHAIN METHODS Volkan.mcclella}@ece.gatech.edu ABSTRACT A MontÂ´e-Carlo method is used to calibrate a randomly placed sen- sor node using helicopter sounds. The calibration is based on using the GPS information from the helicopter and the estimated DOA's at the node
Quantum Monte Carlo methods and lithium cluster properties. [Atomic clusters
Owen, R.K.
1990-12-01
Properties of small lithium clusters with sizes ranging from n = 1 to 5 atoms were investigated using quantum Monte Carlo (QMC) methods. Cluster geometries were found from complete active space self consistent field (CASSCF) calculations. A detailed development of the QMC method leading to the variational QMC (V-QMC) and diffusion QMC (D-QMC) methods is shown. The many-body aspect of electron correlation is introduced into the QMC importance sampling electron-electron correlation functions by using density dependent parameters, and are shown to increase the amount of correlation energy obtained in V-QMC calculations. A detailed analysis of D-QMC time-step bias is made and is found to be at least linear with respect to the time-step. The D-QMC calculations determined the lithium cluster ionization potentials to be 0.1982(14) (0.1981), 0.1895(9) (0.1874(4)), 0.1530(34) (0.1599(73)), 0.1664(37) (0.1724(110)), 0.1613(43) (0.1675(110)) Hartrees for lithium clusters n = 1 through 5, respectively; in good agreement with experimental results shown in the brackets. Also, the binding energies per atom was computed to be 0.0177(8) (0.0203(12)), 0.0188(10) (0.0220(21)), 0.0247(8) (0.0310(12)), 0.0253(8) (0.0351(8)) Hartrees for lithium clusters n = 2 through 5, respectively. The lithium cluster one-electron density is shown to have charge concentrations corresponding to nonnuclear attractors. The overall shape of the electronic charge density also bears a remarkable similarity with the anisotropic harmonic oscillator model shape for the given number of valence electrons.
Quantum Monte Carlo methods and lithium cluster properties
Owen, R.K.
1990-12-01
Properties of small lithium clusters with sizes ranging from n = 1 to 5 atoms were investigated using quantum Monte Carlo (QMC) methods. Cluster geometries were found from complete active space self consistent field (CASSCF) calculations. A detailed development of the QMC method leading to the variational QMC (V-QMC) and diffusion QMC (D-QMC) methods is shown. The many-body aspect of electron correlation is introduced into the QMC importance sampling electron-electron correlation functions by using density dependent parameters, and are shown to increase the amount of correlation energy obtained in V-QMC calculations. A detailed analysis of D-QMC time-step bias is made and is found to be at least linear with respect to the time-step. The D-QMC calculations determined the lithium cluster ionization potentials to be 0.1982(14) [0.1981], 0.1895(9) [0.1874(4)], 0.1530(34) [0.1599(73)], 0.1664(37) [0.1724(110)], 0.1613(43) [0.1675(110)] Hartrees for lithium clusters n = 1 through 5, respectively; in good agreement with experimental results shown in the brackets. Also, the binding energies per atom was computed to be 0.0177(8) [0.0203(12)], 0.0188(10) [0.0220(21)], 0.0247(8) [0.0310(12)], 0.0253(8) [0.0351(8)] Hartrees for lithium clusters n = 2 through 5, respectively. The lithium cluster one-electron density is shown to have charge concentrations corresponding to nonnuclear attractors. The overall shape of the electronic charge density also bears a remarkable similarity with the anisotropic harmonic oscillator model shape for the given number of valence electrons.
MODELING LEACHING OF VIRUSES BY THE MONTE CARLO METHOD
A predictive screening model was developed for fate and transport of viruses in the unsaturated zone. A database of input parameters allowed Monte Carlo analysis with the model. The resulting kernel densities of predicted attenuation during percolation indicated very ...
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 ...
Jiang, Xu; Deng, Yong; Luo, Zhaoyang; Wang, Kan; Lian, Lichao; Yang, Xiaoquan; Meglinski, Igor; Luo, Qingming
2014-12-29
The path-history-based fluorescence Monte Carlo method used for fluorescence tomography imaging reconstruction has attracted increasing attention. In this paper, we first validate the standard fluorescence Monte Carlo (sfMC) method by experimenting with a cylindrical phantom. Then, we describe a path-history-based decoupled fluorescence Monte Carlo (dfMC) method, analyze different perturbation fluorescence Monte Carlo (pfMC) methods, and compare the calculation accuracy and computational efficiency of the dfMC and pfMC methods using the sfMC method as a reference. The results show that the dfMC method is more accurate and efficient than the pfMC method in heterogeneous medium. PMID:25607163
The Monte Carlo Method: A Fresh Approach to Teaching Probabilistic Concepts.
ERIC Educational Resources Information Center
Travers, Kenneth J.; Gray, Kenneth G.
1981-01-01
Some activities designed around the Monte Carlo method of solving probability problems are described. The instructional applications of this method involve physical models or simple BASIC computer programs. (MP)
Franke, B. C. [Sandia National Laboratories, Albuquerque, NM 87185 (United States); Prinja, A. K. [Department of Chemical and Nuclear Engineering, University of New Mexico, Albuquerque, NM 87131 (United States)
2013-07-01
The stochastic Galerkin method (SGM) is an intrusive technique for propagating data uncertainty in physical models. The method reduces the random model to a system of coupled deterministic equations for the moments of stochastic spectral expansions of result quantities. We investigate solving these equations using the Monte Carlo technique. We compare the efficiency with brute-force Monte Carlo evaluation of uncertainty, the non-intrusive stochastic collocation method (SCM), and an intrusive Monte Carlo implementation of the stochastic collocation method. We also describe the stability limitations of our SGM implementation. (authors)
Bayesian Training of Backpropagation Networks by the Hybrid Monte Carlo Method
Radford Neal
1993-01-01
. It is shown that Bayesian training of backpropagation neural networks can feasiblybe performed by the "Hybrid Monte Carlo" method. This approach allows the true predictivedistribution for a test case given a set of training cases to be approximated arbitrarily closely,in contrast to previous approaches which approximate the posterior weight distribution by aGaussian. In this work, the Hybrid Monte Carlo
A Configurational Bias Monte Carlo Method for Linear and Cyclic Peptides
Michael W. Deem; Joel Bader
1997-09-30
In this manuscript, we describe a new configurational bias Monte Carlo technique for the simulation of peptides. We focus on the biologically relevant cases of linear and cyclic peptides. Our approach leads to an efficient, Boltzmann-weighted sampling of the torsional degrees of freedom in these biological molecules, a feat not possible with previous Monte Carlo and molecular dynamics methods.
Widom, Michael
PHYSICAL REVIEW E 84, 061912 (2011) Kinetic Monte Carlo method applied to nucleic acid hairpin December 2011) Kinetic Monte Carlo on coarse-grained systems, such as nucleic acid secondary structure states. Secondary structure models of nucleic acids, which record the pairings of complementary
Calculation of Nonlinear Thermoelectric Coefficients of InAs1xSbx Using Monte Carlo Method
Calculation of Nonlinear Thermoelectric Coefficients of InAs1ÀxSbx Using Monte Carlo Method RAMIN in the relaxation-time approximation ceases to apply. The Monte Carlo method, on the other hand, proves
Faeder, Jim
Kinetic Monte Carlo method for rule-based modeling of biochemical networks Jin Yang,1,* Michael I June 2008; published 10 September 2008 We present a kinetic Monte Carlo method for simulating chemical
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
A Residual Monte Carlo Method for Spatially Discrete, Angularly Continuous Radiation Transport
Wollaeger, Ryan T. [Los Alamos National Laboratory; Densmore, Jeffery D. [Los Alamos National Laboratory
2012-06-19
Residual Monte Carlo provides exponential convergence of statistical error with respect to the number of particle histories. In the past, residual Monte Carlo has been applied to a variety of angularly discrete radiation-transport problems. Here, we apply residual Monte Carlo to spatially discrete, angularly continuous transport. By maintaining angular continuity, our method avoids the deficiencies of angular discretizations, such as ray effects. For planar geometry and step differencing, we use the corresponding integral transport equation to calculate an angularly independent residual from the scalar flux in each stage of residual Monte Carlo. We then demonstrate that the resulting residual Monte Carlo method does indeed converge exponentially to within machine precision of the exact step differenced solution.
Smoothness and dimension reduction in Quasi-Monte Carlo methods
B. Moskowitz; R. E. Caflisch
1996-01-01
Monte Carlo integration using quasirandom sequences has theoretical error bounds of size O (N?1 logdN) in dimension d, as opposed to the error of size O (N?12) for random or pseudorandom sequences. In practice, however, this improved performance for quasirandom sequences is often not observed. The degradation of performance is due to discontinuity or lack of smoothness in the integrand
Some Continuous Monte Carlo Methods for the Dirichlet Problem
Mervin E. Muller
1956-01-01
Monte Carlo techniques are introduced, using stochastic models which are Markov processes. This material includes the $N$-dimensional Spherical, General Spherical, and General Dirichlet Domain processes. These processes are proved to converge with probability 1, and thus to yield direct statistical estimates of the solution to the $N$-dimensional Dirichlet problem. The results are obtained without requiring any further restrictions on the
Dynamic Conditional Independence Models And Markov Chain Monte Carlo Methods
Carlo Berzuini; Nicola G. Best; Walter R. Gilks; Cristiana Larizza
1997-01-01
In dynamic statistical modeling situations, observations arise sequentially, causingthe model to expand by progressive incorporation of new data items and new unknownparameters. For example, in clinical monitoring, new patient-specific parameters areintroduced with each new patient. Markov chain Monte Carlo (MCMC) might be usedfor posterior inference, but would need to be redone at each expansion stage. Thus suchmethods are often too
arXiv:cond-mat/0304686v130Apr2003 1 Multilevel Monte Carlo method for simulations of fluids
arXiv:cond-mat/0304686v130Apr2003 1 Multilevel Monte Carlo method for simulations of fluids Achi of Science, Rehovot 76100, Israel Monte Carlo methods play important part in modern statistical physics Monte Carlo method described here. The basic approach is to describe the system at increasingly coarser
Sailhac, Pascal
Inversion of surface nuclear magnetic resonance data by an adapted Monte Carlo method applied not yet been any attempt to explore model space. We propose that an adaptation of the Monte Carlo method is better than using the classical Monte Carlo method. We first use a synthetic model and then apply
Faller, Roland
Density-of-states Monte Carlo method for simulation of fluids Qiliang Yan, Roland Faller, and Juan, Wisconsin 53706 Received 6 November 2001; accepted 30 January 2002 A Monte Carlo method based on a density-consistent way. We refer to this approach as the density-of-states DOS Monte Carlo method. For simulations
Li, Yaohang
Monte Carlo Methods and Appl., Vol. 11, No. 1, pp. 39 Â 55 (2005) c VSP 2005 Grid-based Quasi-Monte -- In this paper, we extend the techniques used in Grid-based Monte Carlo appli- cations to Grid-based quasi-Monte in quasirandom sequences prevents us from applying many of our Grid-based Monte Carlo techniques to Grid- based
A Monte Carlo method for the PDF equations of turbulent flow
Pope, S. B.
1980-01-01
A Monte Carlo method is presented which simulates the transport equations of joint probability density functions (pdf's) in turbulent flows. (Finite-difference solutions of the equations are impracticable, mainly because ...
Synthesis of hourly rainfall by a Monte Carlo method using a sixth-order Markov chain
Dale, Walter Marvin
1968-01-01
SYNTHESIS OF HOURLY RAINFALL BY A MONTE CARLO METHOD USING A SIXTH-. ORDER MARKOV CHAIN A Thesis By WALTER M. DALE MAJOR, USAF Submitted to the Graduate College of the Texas AFM University in partial fulfillment of the requirements...
Investigation into the properties and application of the Diffusion Monte Carlo method
Orieka, Ogheneovie (Ogheneovie O.)
2014-01-01
This paper shall be a discussion of the properties of the Diffusion Monte Carlo (DMC) method and its applications. The discussion shall cover the basic theory behind the algorithm and the class of problems it is designed ...
Monte Carlo Methods for Integration A Project for Math 489/889
Dunbar, Steve
Monte Carlo Methods for Integration A Project for Math 489/889 Steven R. Dunbar November 2010.575829304 Using the confidence interval to estimate the required number of trials We desire with probability
NASA Technical Reports Server (NTRS)
Firstenberg, H.
1971-01-01
The statistics are considered of the Monte Carlo method relative to the interpretation of the NUGAM2 and NUGAM3 computer code results. A numerical experiment using the NUGAM2 code is presented and the results are statistically interpreted.
Improvements and applications of the Uniform Fission Site method in Monte Carlo
Hunter, Jessica Lynn
2014-01-01
Monte Carlo methods for reactor analysis have been in development with the eventual goal of full-core analysis. To attain results with reasonable uncertainties, large computational resources are needed. Variance reduction ...
Computational methods for efficient nuclear data management in Monte Carlo neutron simulations
Walsh, Jonathan A. (Jonathan Alan)
2014-01-01
This thesis presents the development and analysis of computational methods for efficiently accessing and utilizing nuclear data in Monte Carlo neutron transport code simulations. Using the OpenMC code, profiling studies ...
Efficient, Automated Monte Carlo Methods for Radiation Transport
Kong, Rong; Ambrose, Martin; Spanier, Jerome
2012-01-01
Monte Carlo simulations provide an indispensible model for solving radiative transport problems, but their slow convergence inhibits their use as an everyday computational tool. In this paper, we present two new ideas for accelerating the convergence of Monte Carlo algorithms based upon an efficient algorithm that couples simulations of forward and adjoint transport equations. Forward random walks are first processed in stages, each using a fixed sample size, and information from stage k is used to alter the sampling and weighting procedure in stage k + 1. This produces rapid geometric convergence and accounts for dramatic gains in the efficiency of the forward computation. In case still greater accuracy is required in the forward solution, information from an adjoint simulation can be added to extend the geometric learning of the forward solution. The resulting new approach should find widespread use when fast, accurate simulations of the transport equation are needed. PMID:23226872
Liu, Chang
2009-05-15
CONTINUOUS RESERVOIR SIMULATION MODEL UPDATING AND FORECASTING USING A MARKOV CHAIN MONTE CARLO METHOD A Thesis by Chang Liu Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment... MONTE CARLO METHOD A Thesis by Chang Liu Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Approved by...
Monte Carlo Method with Heuristic Adjustment for Irregularly Shaped Food Product Volume Measurement
Siswantoro, Joko; Idrus, Bahari
2014-01-01
Volume measurement plays an important role in the production and processing of food products. Various methods have been proposed to measure the volume of food products with irregular shapes based on 3D reconstruction. However, 3D reconstruction comes with a high-priced computational cost. Furthermore, some of the volume measurement methods based on 3D reconstruction have a low accuracy. Another method for measuring volume of objects uses Monte Carlo method. Monte Carlo method performs volume measurements using random points. Monte Carlo method only requires information regarding whether random points fall inside or outside an object and does not require a 3D reconstruction. This paper proposes volume measurement using a computer vision system for irregularly shaped food products without 3D reconstruction based on Monte Carlo method with heuristic adjustment. Five images of food product were captured using five cameras and processed to produce binary images. Monte Carlo integration with heuristic adjustment was performed to measure the volume based on the information extracted from binary images. The experimental results show that the proposed method provided high accuracy and precision compared to the water displacement method. In addition, the proposed method is more accurate and faster than the space carving method. PMID:24892069
Hunter, David
Batch means standard errors for MCMC Batch means is one method used to compute Monte Carlo standard errors. There is a vast literature on sophisticated methods for computing Monte Carlo standard errors Carlo standard error is ^ N . How do we pick b (and hence a) ? b (batch size) should be large enough so
Hunter, David
Batch means standard errors for MCMC Batch means is one method used to compute Monte Carlo standard errors. There is a vast literature on sophisticated methods for computing Monte Carlo standard errors of the Monte Carlo standard error is ^ N . How do we pick b (and hence a) ? The batch size b should be large
Carlo Jacoboni; Lino Reggiani
1983-01-01
This review presents in a comprehensive and tutorial form the basic principles of the Monte Carlo method, as applied to the solution of transport problems in semiconductors. Sufficient details of a typical Monte Carlo simulation have been given to allow the interested reader to create his own Monte Carlo program, and the method has been briefly compared with alternative theoretical
Comparison of Monte Carlo methods for fluorescence molecular tomography—computational efficiency
Chen, Jin; Intes, Xavier
2011-01-01
Purpose: The Monte Carlo method is an accurate model for time-resolved quantitative fluorescence tomography. However, this method suffers from low computational efficiency due to the large number of photons required for reliable statistics. This paper presents a comparison study on the computational efficiency of three Monte Carlo-based methods for time-domain fluorescence molecular tomography. Methods: The methods investigated to generate time-gated Jacobians were the perturbation Monte Carlo (pMC) method, the adjoint Monte Carlo (aMC) method and the mid-way Monte Carlo (mMC) method. The effects of the different parameters that affect the computation time and statistics reliability were evaluated. Also, the methods were applied to a set of experimental data for tomographic application. Results:In silico results establish that, the investigated parameters affect the computational time for the three methods differently (linearly, quadratically, or not significantly). Moreover, the noise level of the Jacobian varies when these parameters change. The experimental results in preclinical settings demonstrates the feasibility of using both aMC and pMC methods for time-resolved whole body studies in small animals within a few hours. Conclusions: Among the three Monte Carlo methods, the mMC method is a computationally prohibitive technique that is not well suited for time-domain fluorescence tomography applications. The pMC method is advantageous over the aMC method when the early gates are employed and large number of detectors is present. Alternatively, the aMC method is the method of choice when a small number of source-detector pairs are used. PMID:21992393
APR1400 LBLOCA uncertainty quantification by Monte Carlo method and comparison with Wilks' formula
Hwang, M.; Bae, S.; Chung, B. D. [Korea Atomic Energy Research Inst., 150 Dukjin-dong, Yuseong-gu, Daejeon (Korea, Republic of)
2012-07-01
An analysis of the uncertainty quantification for the PWR LBLOCA by the Monte Carlo calculation has been performed and compared with the tolerance level determined by Wilks' formula. The uncertainty range and distribution of each input parameter associated with the LBLOCA accident were determined by the PIRT results from the BEMUSE project. The Monte-Carlo method shows that the 95. percentile PCT value can be obtained reliably with a 95% confidence level using the Wilks' formula. The extra margin by the Wilks' formula over the true 95. percentile PCT by the Monte-Carlo method was rather large. Even using the 3 rd order formula, the calculated value using the Wilks' formula is nearly 100 K over the true value. It is shown that, with the ever increasing computational capability, the Monte-Carlo method is accessible for the nuclear power plant safety analysis within a realistic time frame. (authors)
NASA Astrophysics Data System (ADS)
Slattery, Stuart R.; Evans, Thomas M.; Wilson, Paul P. H.
2014-06-01
We present a multiple-set overlapping-domain decomposed strategy for parallelizing the Monte Carlo Synthetic Acceleration method. Monte Carlo Synthetic Acceleration methods use the Neumann-Ulam class of Monte Carlo solvers for linear systems to accelerate a fixed-point iteration sequence. Effective parallel algorithms for these methods require the parallelization of the underlying Neumann-Ulam solvers. To do this in a domain decomposed environment, we borrow strategies traditionally implemented in Monte Carlo particle transport to parallelize the problem. The parallel Neumann-Ulam and multiple-set overlapping-domain decomposition algorithms are presented along with parallel scaling data for the resulting implementation using the Titan Cray XK7 machine at Oak Ridge National Laboratory.
Philip D. O’Neill
2002-01-01
Recent Bayesian methods for the analysis of infectious disease outbreak data using stochastic epidemic models are reviewed. These methods rely on Markov chain Monte Carlo methods. Both temporal and non-temporal data are considered. The methods are illustrated with a number of examples featuring different models and datasets.
Advanced computational methods for nodal diffusion, Monte Carlo, and S(sub N) problems
NASA Astrophysics Data System (ADS)
Martin, W. R.
1993-01-01
This document describes progress on five efforts for improving effectiveness of computational methods for particle diffusion and transport problems in nuclear engineering: (1) Multigrid methods for obtaining rapidly converging solutions of nodal diffusion problems. An alternative line relaxation scheme is being implemented into a nodal diffusion code. Simplified P2 has been implemented into this code. (2) Local Exponential Transform method for variance reduction in Monte Carlo neutron transport calculations. This work yielded predictions for both 1-D and 2-D x-y geometry better than conventional Monte Carlo with splitting and Russian Roulette. (3) Asymptotic Diffusion Synthetic Acceleration methods for obtaining accurate, rapidly converging solutions of multidimensional SN problems. New transport differencing schemes have been obtained that allow solution by the conjugate gradient method, and the convergence of this approach is rapid. (4) Quasidiffusion (QD) methods for obtaining accurate, rapidly converging solutions of multidimensional SN Problems on irregular spatial grids. A symmetrized QD method has been developed in a form that results in a system of two self-adjoint equations that are readily discretized and efficiently solved. (5) Response history method for speeding up the Monte Carlo calculation of electron transport problems. This method was implemented into the MCNP Monte Carlo code. In addition, we have developed and implemented a parallel time-dependent Monte Carlo code on two massively parallel processors.
Advanced computational methods for nodal diffusion, Monte Carlo, and S[sub N] problems
Martin, W.R.
1993-01-01
This document describes progress on five efforts for improving effectiveness of computational methods for particle diffusion and transport problems in nuclear engineering: (1) Multigrid methods for obtaining rapidly converging solutions of nodal diffusion problems. A alternative line relaxation scheme is being implemented into a nodal diffusion code. Simplified P2 has been implemented into this code. (2) Local Exponential Transform method for variance reduction in Monte Carlo neutron transport calculations. This work yielded predictions for both 1-D and 2-D x-y geometry better than conventional Monte Carlo with splitting and Russian Roulette. (3) Asymptotic Diffusion Synthetic Acceleration methods for obtaining accurate, rapidly converging solutions of multidimensional SN problems. New transport differencing schemes have been obtained that allow solution by the conjugate gradient method, and the convergence of this approach is rapid. (4) Quasidiffusion (QD) methods for obtaining accurate, rapidly converging solutions of multidimensional SN Problems on irregular spatial grids. A symmetrized QD method has been developed in a form that results in a system of two self-adjoint equations that are readily discretized and efficiently solved. (5) Response history method for speeding up the Monte Carlo calculation of electron transport problems. This method was implemented into the MCNP Monte Carlo code. In addition, we have developed and implemented a parallel time-dependent Monte Carlo code on two massively parallel processors.
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.
A NEW MONTE CARLO METHOD FOR TIME-DEPENDENT NEUTRINO RADIATION TRANSPORT
Abdikamalov, Ernazar; Ott, Christian D.; O'Connor, Evan [TAPIR, California Institute of Technology, MC 350-17, 1200 E California Blvd., Pasadena, CA 91125 (United States); Burrows, Adam; Dolence, Joshua C. [Department of Astrophysical Sciences, Princeton University, Peyton Hall, Ivy Lane, Princeton, NJ 08544 (United States); Loeffler, Frank; Schnetter, Erik, E-mail: abdik@tapir.caltech.edu [Center for Computation and Technology, Louisiana State University, 216 Johnston Hall, Baton Rouge, LA 70803 (United States)
2012-08-20
Monte Carlo approaches to radiation transport have several attractive properties such as simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are relatively easy to extend to multiple spatial dimensions, which makes them potentially interesting in modeling complex multi-dimensional astrophysical phenomena such as core-collapse supernovae. The aim of this paper is to explore Monte Carlo methods for modeling neutrino transport in core-collapse supernovae. We generalize the Implicit Monte Carlo photon transport scheme of Fleck and Cummings and gray discrete-diffusion scheme of Densmore et al. to energy-, time-, and velocity-dependent neutrino transport. Using our 1D spherically-symmetric implementation, we show that, similar to the photon transport case, the implicit scheme enables significantly larger timesteps compared with explicit time discretization, without sacrificing accuracy, while the discrete-diffusion method leads to significant speed-ups at high optical depth. Our results suggest that a combination of spectral, velocity-dependent, Implicit Monte Carlo and discrete-diffusion Monte Carlo methods represents a robust approach for use in neutrino transport calculations in core-collapse supernovae. Our velocity-dependent scheme can easily be adapted to photon transport.
Densmore, Jeffery D., E-mail: jdd@lanl.gov [Computational Physics and Methods Group, Los Alamos National Laboratory, P.O. Box 1663, MS D409, Los Alamos, NM 87545 (United States); Thompson, Kelly G., E-mail: kgt@lanl.gov [Computational Physics and Methods Group, Los Alamos National Laboratory, P.O. Box 1663, MS D409, Los Alamos, NM 87545 (United States); Urbatsch, Todd J., E-mail: tmonster@lanl.gov [Computational Physics and Methods Group, Los Alamos National Laboratory, P.O. Box 1663, MS D409, Los Alamos, NM 87545 (United States)
2012-08-15
Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations in optically thick media. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Each discrete step replaces many smaller Monte Carlo steps, thus improving the efficiency of the simulation. In this paper, we present an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold, as optical thickness is typically a decreasing function of frequency. Above this threshold we employ standard Monte Carlo, which results in a hybrid transport-diffusion scheme. With a set of frequency-dependent test problems, we confirm the accuracy and increased efficiency of our new DDMC method.
A cavity-biased (T, V, mu) Monte Carlo method for the computer simulation of fluids
Mihaly Mezei
1980-01-01
A modified sampling technique is proposed for use in Monte Carlo calculations in the grand canonical ensemble. The new method, called the cavity-biased (T, V, mu) Monte Carlo procedure, attempts insertions of new particles into existing cavities in the system instead of at randomly selected points. Calculations on supercritical Lennard-Jones fluid showed an 8-fold increase in the efficiency of the
Time-step limits for a Monte Carlo Compton-scattering method
Densmore, Jeffery D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Lowrie, Robert B [Los Alamos National Laboratory
2009-01-01
We perform a stability analysis of a Monte Carlo method for simulating the Compton scattering of photons by free electron in high energy density applications and develop time-step limits that avoid unstable and oscillatory solutions. Implementing this Monte Carlo technique in multi physics problems typically requires evaluating the material temperature at its beginning-of-time-step value, which can lead to this undesirable behavior. With a set of numerical examples, we demonstrate the efficacy of our time-step limits.
Simulation by Monte Carlo of the X ray Transport in PIN Type a-Si:H Radiation Detectors
NASA Astrophysics Data System (ADS)
Shtejer, K.; Leyva, A.; Cruz, C.; Moreira, L.
2004-09-01
Low energy X rays usually employed in mammography, were transported in hydrogenated amorphous silicon PIN diodes using MCNP-4C system code based on Monte Carlo simulation. The deposited energy distribution in these devices, useful as radiation detectors in medical imaging applications, was evaluated for 7-50 ?m thick intrinsic layers. The energy spectrum in different depths of the intrinsic layer shows a lineal increase of the deposited energy, and near the metal electrodes this increase is significantly higher by an order of magnitude. The influence of the material and geometry of the top electrode on the energy deposited inside the intrinsic layer, as well as the effect of the addition of the passivation layer are analysed in the text.
A Monte Carlo Synthetic-Acceleration Method for Solving the Thermal Radiation Diffusion Equation
Evans, Thomas M [ORNL] [ORNL; Mosher, Scott W [ORNL] [ORNL; Slattery, Stuart [University of Wisconsin, Madison] [University of Wisconsin, Madison
2014-01-01
We present a novel synthetic-acceleration based Monte Carlo method for solving the equilibrium thermal radiation diusion equation in three dimensions. The algorithm performance is compared against traditional solution techniques using a Marshak benchmark problem and a more complex multiple material problem. Our results show that not only can our Monte Carlo method be an eective solver for sparse matrix systems, but also that it performs competitively with deterministic methods including preconditioned Conjugate Gradient while producing numerically identical results. We also discuss various aspects of preconditioning the method and its general applicability to broader classes of problems.
A Monte Carlo synthetic-acceleration method for solving the thermal radiation diffusion equation
Evans, Thomas M., E-mail: evanstm@ornl.gov [Oak Ridge National Laboratory, 1 Bethel Valley Rd., Oak Ridge, TN 37831 (United States); Mosher, Scott W., E-mail: moshersw@ornl.gov [Oak Ridge National Laboratory, 1 Bethel Valley Rd., Oak Ridge, TN 37831 (United States); Slattery, Stuart R., E-mail: sslattery@wisc.edu [University of Wisconsin–Madison, 1500 Engineering Dr., Madison, WI 53716 (United States); Hamilton, Steven P., E-mail: hamiltonsp@ornl.gov [Oak Ridge National Laboratory, 1 Bethel Valley Rd., Oak Ridge, TN 37831 (United States)
2014-02-01
We present a novel synthetic-acceleration-based Monte Carlo method for solving the equilibrium thermal radiation diffusion equation in three spatial dimensions. The algorithm performance is compared against traditional solution techniques using a Marshak benchmark problem and a more complex multiple material problem. Our results show that our Monte Carlo method is an effective solver for sparse matrix systems. For solutions converged to the same tolerance, it performs competitively with deterministic methods including preconditioned conjugate gradient and GMRES. We also discuss various aspects of preconditioning the method and its general applicability to broader classes of problems.
M. J. Goldsworthy; M. N. Macrossan; M. M. Abdel-jawad
2007-01-01
The direct simulation Monte Carlo (DSMC) method is used to simulate the flow of rarefied gases. In the macroscopic chemistry method (MCM) for DSMC, chemical reaction rates calculated from local macroscopic flow properties are enforced in each cell. Unlike the standard total collision energy (TCE) chemistry model for DSMC, the new method is not restricted to an Arrhenius form of
Green Function Monte Carlo Method for Excited States of Quantum System
Taksu Cheon
1996-12-13
A novel scheme to solve the quantum eigenvalue problem through the imaginary-time Green function Monte Carlo method is presented. This method is applicable to the excited states as well as to the ground state of a generic system. We demonstrate the validity of the method with the numerical examples on three simple systems including a discretized sine-Gordon model.
The S/sub N//Monte Carlo response matrix hybrid method
Filippone, W.L.; Alcouffe, R.E.
1987-01-01
A hybrid method has been developed to iteratively couple S/sub N/ and Monte Carlo regions of the same problem. This technique avoids many of the restrictions and limitations of previous attempts to do the coupling and results in a general and relatively efficient method. We demonstrate the method with some simple examples.
Implementation of unsteady sampling procedures for the parallel direct simulation Monte Carlo method
H. M. Cave; K.-C. Tseng; J.-S. Wu; M. C. Jermy; J.-C. Huang; S. P. Krumdieck
2008-01-01
An unsteady sampling routine for a general parallel direct simulation Monte Carlo method called PDSC is introduced, allowing the simulation of time-dependent flow problems in the near continuum range. A post-processing procedure called DSMC rapid ensemble averaging method (DREAM) is developed to improve the statistical scatter in the results while minimising both memory and simulation time. This method builds an
NASA Astrophysics Data System (ADS)
Russo, G.; Pareschi, L.; Trazzi, S.; Shevyrin, A.; Bondar, Ye.; Ivanov, M.
2005-05-01
Recently a new class of schemes, called Time Relaxed Monte Carlo (TRMC) has been introduced for the numerical solution of the Boltzmann equation of gas dynamics. The motivation is to propose a systematic framework to derive Monte Carlo methods effective near the fluid dynamic regime. Before the methods can be accepted as alternative tools to other methods, they have to show that they are able to reproduce results obtainable by well established reliable methods. In this paper a detailed comparison is performed between TRMC methods and the Majorant Frequency Scheme in the case of the space-homogeneous Boltzmann equation. In particular, the effect of finite number of particles is considered.
Layer-specific illumination optimization by Monte Carlo method
NASA Astrophysics Data System (ADS)
Kim, Ho-Chul; Nam, Dong-Seok; Hwang, Chan; Kang, Young S.; Woo, Sang-Gyun; Cho, Han-Ku; Han, Woo-Sung
2003-06-01
Layer specific illumination has merits of enhancement of resolution, widening DOF and image fitness. For dense patterns like DRAM cell, layer specific illumination is a major candidate to drive low k1 lithography. To find out the best illumination for a specific pattern, diffracted image of the pattern and the ratio of captured first order to 0th order diffracted beam should be considered. By spectrum analysis, the best illumination is obtained for simple patterns like dense lines, brick wall, and dense contacts. In this paper, the procedure of obtaining the best illumination for specific patterns is presented. Comparing general illuminations such as annular, the resultant illumination is proved to have wider DOF and enhancement of resolution. The best illumination can also be found by Monte Carlo simulation. For simple one-dimensional case, its validity is proved. From the exposure results, wide DOF and enhancement of resolution is confirmed.
Monte Carlo Methods to Model Radiation Interactions and Induced Damage
NASA Astrophysics Data System (ADS)
Muñoz, Antonio; Fuss, Martina C.; Cortés-Giraldo, M. A.; Incerti, Sébastien; Ivanchenko, Vladimir; Ivanchenko, Anton; Quesada, J. M.; Salvat, Francesc; Champion, Christophe; Gómez-Tejedor, Gustavo García
This review is devoted to the analysis of some Monte Carlo (MC) simulation programmes which have been developed to describe radiation interaction with biologically relevant materials. Current versions of the MC codes Geant4 (GEometry ANd Tracking 4), PENELOPE (PENetration and Energy Loss of Positrons and Electrons), EPOTRAN (Electron and POsitron TRANsport), and LEPTS (Low-Energy Particle Track Simulation) are described. Mean features of each model, as the type of radiation to consider, the energy range covered by primary and secondary particles, the type of interactions included in the simulation and the considered target geometries are discussed. Special emphasis lies on recent developments that, together with (still emerging) new databases that include adequate data for biologically relevant materials, bring us continuously closer to a realistic, physically meaningful description of radiation damage in biological tissues.
Monte Carlo Collision method for low temperature plasma simulation
NASA Astrophysics Data System (ADS)
Taccogna, Francesco; Taccogna
2015-01-01
This work shows the basic foundation of the particle-based representation of low temperature plasma description. In particular, the Monte Carlo Collision (MCC) recipe has been described for the case of electron-atom and ion-atom collisions. The model has been applied to the problem of plasma plume expansion from an electric Hall-effect type thruster. The presence of low energy secondary electrons from electron-atom ionization on the electron energy distribution function (EEDF) have been identified in the first 3 mm from the exit plane where, due to the azimuthal heating the ionization continues to play an important role. In addition, low energy charge-exchange ions from ion-atom electron transfer collisions are evident in the ion energy distribution functions (IEDF) 1 m from the exit plane.
Clock Quantum Monte Carlo: an imaginary-time method for real-time quantum dynamics
Jarrod R. McClean; Alán Aspuru-Guzik
2014-10-07
In quantum information theory, there is an explicit mapping between general unitary dynamics and Hermitian ground state eigenvalue problems known as the Feynman-Kitaev Clock. A prominent family of methods for the study of quantum ground states are quantum Monte Carlo methods, and recently the full configuration interaction quantum Monte Carlo (FCIQMC) method has demonstrated great promise for practical systems. We combine the Feynman-Kitaev Clock with FCIQMC to formulate a new technique for the study of quantum dynamics problems. Numerical examples using quantum circuits are provided as well as a technique to further mitigate the sign problem through time-dependent basis rotations. Moreover, this method allows one to combine the parallelism of Monte Carlo techniques with the locality of time to yield an effective parallel-in-time simulation technique.
Clock quantum Monte Carlo technique: An imaginary-time method for real-time quantum dynamics
NASA Astrophysics Data System (ADS)
McClean, Jarrod R.; Aspuru-Guzik, Alán
2015-01-01
In quantum information theory, there is an explicit mapping between general unitary dynamics and Hermitian ground-state eigenvalue problems known as the Feynman-Kitaev clock Hamiltonian. A prominent family of methods for the study of quantum ground states is quantum Monte Carlo methods, and recently the full configuration interaction quantum Monte Carlo (FCIQMC) method has demonstrated great promise for practical systems. We combine the Feynman-Kitaev clock Hamiltonian with FCIQMC to formulate a technique for the study of quantum dynamics problems. Numerical examples using quantum circuits are provided as well as a technique to further mitigate the sign problem through time-dependent basis rotations. Moreover, this method allows one to combine the parallelism of Monte Carlo techniques with the locality of time to yield an effective parallel-in-time simulation technique.
Tackling the Fermionic Sign Problem in the Auxiliary-Field Monte Carlo Method
G. Stoitcheva; W. E. Ormand; D. Neuhauser; D. J. Dean
2007-08-22
We explore a novel and straightforward solution to the sign problem that has plagued the Auxiliary-field Monte Carlo (AFMC) method applied to many-body systems for more than a decade. We present a solution to the sign problem that has plagued the Auxiliary-field Monte Carlo (AFMC) method for more than a decade and report a breakthrough where excellent agreement between AFMC and exact CI calculations for fully realistic nuclear applications is achieved. This result offers the capability, unmatched by other methods, to achieve exact solutions for large-scale quantum many-body systems.
Matching NLO QCD with parton shower in Monte Carlo scheme - the KrkNLO method
Jadach, S; Sapeta, S; Siodmok, A; Skrzypek, M
2015-01-01
A new method of including the complete NLO QCD corrections to hard processes in the LO parton-shower Monte Carlo (PSMC) is presented. This method, called KrkNLO, requires the use of parton distribution functions in a dedicated Monte Carlo factorization scheme, which is also discussed in this paper. In the future, it may simplify introduction of the NNLO corrections to hard processes and the NLO corrections to PSMC. Details of the method and numerical examples of its practical implementation, as well as comparisons with other calculations, such as MCFM, MC@NLO, POWHEG, for single $Z/\\gamma^*$-boson production at the LHC, are presented.
Perfetti, Christopher M [ORNL] [ORNL; Martin, William R [University of Michigan] [University of Michigan; Rearden, Bradley T [ORNL] [ORNL; Williams, Mark L [ORNL] [ORNL
2012-01-01
Three methods for calculating continuous-energy eigenvalue sensitivity coefficients were developed and implemented into the SHIFT Monte Carlo code within the Scale code package. The methods were used for several simple test problems and were evaluated in terms of speed, accuracy, efficiency, and memory requirements. A promising new method for calculating eigenvalue sensitivity coefficients, known as the CLUTCH method, was developed and produced accurate sensitivity coefficients with figures of merit that were several orders of magnitude larger than those from existing methods.
NASA Astrophysics Data System (ADS)
Lin, Lin; Zhang, Mei
2015-02-01
The scaling Monte Carlo method and Gaussian model are applied to simulate the transportation of light beam with arbitrary waist radius. Much of the time, Monte Carlo simulation is performed for pencil or cone beam where the initial status of the photon is identical. In practical application, incident light is always focused on the sample to form approximate Gauss distribution on the surface. With alteration of focus position in the sample, the initial status of the photon will not be identical any more. Using the hyperboloid method, the initial reflect angle and coordinates are generated statistically according to the size of Gaussian waist and focus depth. Scaling calculation is performed with baseline data from standard Monte Carlo simulation. The scaling method incorporated with the Gaussian model was tested, and proved effective over a range of scattering coefficients from 20% to 180% relative to the value used in baseline simulation. In most cases, percentage error was less than 10%. The increasing of focus depth will result in larger error of scaled radial reflectance in the region close to the optical axis. In addition to evaluating accuracy of scaling the Monte Carlo method, this study has given implications for inverse Monte Carlo with arbitrary parameters of optical system.
A Monte Carlo Method Used for the Identification of the Muscle Spindle
Rigas, Alexandros
21 A Monte Carlo Method Used for the Identification of the Muscle Spindle Vassiliki K. Kotti the behavior of the muscle spindle by using a logistic regression model. The system receives input from, the recovery and the summation functions. The most favorable method of estimating the parameters of the muscle
Numerical simulations of acoustics problems using the direct simulation Monte Carlo method
Amanda Danforth Hanford
2008-01-01
In the current study, real gas effects in the propagation of sound waves are simulated using the direct simulation Monte Carlo method for a wide range of systems. This particle method allows for treatment of acoustic phenomena for a wide range of Knudsen numbers, defined as the ratio of molecular mean free path to wavelength. Continuum models such as the
On the use of low discrepancy sequences in Monte Carlo methods
Bruno Tuffin
1996-01-01
Quasi-random (or low discrepancy) sequences are sequences for which the convergence to the uniform distribution on occurs rapidly. Such sequences are used in quasi-Monte Carlo methods for which the convergence speed, with respect to the first terms of the sequence, is in , where is the mathematical dimension of the problem considered. The disadvan- tage of these methods is that
Perturbation Monte Carlo methods to solve inverse photon migration problems in heterogeneous tissues
Carole K. Hayakawa; Jerome Spanier; Frédéric Bevilacqua; Andrew K. Dunn; Joon S. You; Bruce J. Tromberg; Vasan Venugopalan
2001-01-01
We introduce a novel and efficient method to provide solutions to inverse photon migration problems in hetero- geneous turbid media. The method extracts derivative information from a single Monte Carlo simulation to permit the rapid determination of rates of change in the detected photon signal with respect to perturbations in background tissue optical properties. We then feed this derivative information
Kerry Gallagher; Malcolm Sambridge; Guy Drijkoningen
1991-01-01
In providing a method for solving non-linear optimization problems Monte Carlo techniques avoid the need for linearization but, in practice, are often prohibitive because of the large number of models that must be considered. A new class of methods known as Genetic Algorithms have recently been devised in the field of Artificial Intelligence. We outline the basic concept of genetic
Comparison of the Monte Carlo adjoint-weighted and differential operator perturbation methods
Kiedrowski, Brian C [Los Alamos National Laboratory; Brown, Forrest B [Los Alamos National Laboratory
2010-01-01
Two perturbation theory methodologies are implemented for k-eigenvalue calculations in the continuous-energy Monte Carlo code, MCNP6. A comparison of the accuracy of these techniques, the differential operator and adjoint-weighted methods, is performed numerically and analytically. Typically, the adjoint-weighted method shows better performance over a larger range; however, there are exceptions.
The Factorization Method for Monte Carlo Simulations of Systems With a Complex Action
J. Ambjorn; K. N. Anagnostopoulos; J. Nishimura; J. J. M. Verbaarschot
2003-09-15
We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. In some cases, like in the IKKT matrix model, a finite size scaling extrapolation can provide results for systems whose size would make it prohibitive to simulate directly.
On the Application of Markov Chain Monte Carlo Methods to Genetic Analyses on Complex Pedigrees
N. A. Sheehan
2000-01-01
Summary Markov chain Monte Carlo methods are frequently used in the analyses of genetic data on pedigrees for the estimation of probabilities and likelihoods which cannot be calculated by existing exact methods. In the case of discrete data, the underlying Markov chain may be reducible and care must be taken to ensure that reliable estimates are obtained. Potential reducibility thus
On sequential Monte Carlo sampling methods for Bayesian filtering
ARNAUD DOUCET; SIMON GODSILL; CHRISTOPHE ANDRIEU
2000-01-01
In this article, we present an overview of methods for sequential simulation from posterior distribu- tions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and non-Gaussian. A general importance sampling framework is devel- oped that unifies many of the methods which have been proposed over the last few decades in
Bahreyni Toossi, Mohammad Taghi; Ghorbani, Mahdi; Mowlavi, Ali Asghar; Meigooni, Ali Soleimani
2012-01-01
Background Dosimetric characteristics of a high dose rate (HDR) GZP6 Co-60 brachytherapy source have been evaluated following American Association of Physicists in MedicineTask Group 43U1 (AAPM TG-43U1) recommendations for their clinical applications. Materials and methods MCNP-4C and MCNPX Monte Carlo codes were utilized to calculate dose rate constant, two dimensional (2D) dose distribution, radial dose function and 2D anisotropy function of the source. These parameters of this source are compared with the available data for Ralstron 60Co and microSelectron192Ir sources. Besides, a superimposition method was developed to extend the obtained results for the GZP6 source No. 3 to other GZP6 sources. Results The simulated value for dose rate constant for GZP6 source was 1.104±0.03 cGyh-1U-1. The graphical and tabulated radial dose function and 2D anisotropy function of this source are presented here. The results of these investigations show that the dosimetric parameters of GZP6 source are comparable to those for the Ralstron source. While dose rate constant for the two 60Co sources are similar to that for the microSelectron192Ir source, there are differences between radial dose function and anisotropy functions. Radial dose function of the 192Ir source is less steep than both 60Co source models. In addition, the 60Co sources are showing more isotropic dose distribution than the 192Ir source. Conclusions The superimposition method is applicable to produce dose distributions for other source arrangements from the dose distribution of a single source. The calculated dosimetric quantities of this new source can be introduced as input data to the GZP6 treatment planning system (TPS) and to validate the performance of the TPS. PMID:23077455
Lei Wang; Matthias Troyer
2014-07-10
We present a new algorithm for calculating the Renyi entanglement entropy of interacting fermions using the continuous-time quantum Monte Carlo method. The algorithm only samples interaction correction of the entanglement entropy, which by design ensures efficient calculation of weakly interacting systems. Combined with Monte Carlo reweighting, the algorithm also performs well for systems with strong interactions. We demonstrate the potential of this method by studying the quantum entanglement signatures of the charge-density-wave transition of interacting fermions on a square lattice.
Multistage Monte Carlo Method for Solving Influence Diagrams Using Local Computation
Charnes, John M.; Shenoy, Prakash P.
2004-03-01
,whicharein?uencediagramswithoutdeci- sion and value nodes). However, when the num- ber of variables is large, the combined state space of all variables is exponentially large, and the sam- plesizerequiredforpreciseestimatesistoolargeto 405 Charnes and Shenoy: Multistage Monte Carlo Method...=lbraceoriDrbraceoriandDomlparenoriSLchi S rparenori=lbraceoriDcommaoriOcommaoriSrbraceori. Figure1 In?uence Diagram Representation of the OWSR Problem at theGraphicalLevel T R D O S SR ? 1 ? 2 ? 3 Charnes and Shenoy: Multistage Monte Carlo Method for Solving In?uence Diagrams ManagementScience50...
Advantages of Analytical Transformations in Monte Carlo Methods for Radiation Transport
McKinley, M S; Brooks III, E D; Daffin, F
2004-12-13
Monte Carlo methods for radiation transport typically attempt to solve an integral by directly sampling analog or weighted particles, which are treated as physical entities. Improvements to the methods involve better sampling, probability games or physical intuition about the problem. We show that significant improvements can be achieved by recasting the equations with an analytical transform to solve for new, non-physical entities or fields. This paper looks at one such transform, the difference formulation for thermal photon transport, showing a significant advantage for Monte Carlo solution of the equations for time dependent transport. Other related areas are discussed that may also realize significant benefits from similar analytical transformations.
Improved methods of handling massive tallies in reactor Monte Carlo Code RMC
She, D.; Wang, K.; Sun, J.; Qiu, Y. [Department of Engineering Physics, Tsinghua University, Beijing 100084 (China)
2013-07-01
Monte Carlo simulations containing a large number of tallies generally suffer severe performance penalties due to a significant amount of run time spent in searching for and scoring individual tally bins. This paper describes the improved methods of handling large numbers of tallies, which have been implemented in the RMC Monte Carlo code. The calculation results demonstrate that the proposed methods can considerably improve the tally performance when massive tallies are treated. In the calculated case with 6 million of tally regions, only 10% of run time is increased in each active cycle against each inactive cycle. (authors)
High-order path-integral Monte Carlo methods for solving quantum dot problems
NASA Astrophysics Data System (ADS)
Chin, Siu A.
2015-03-01
The conventional second-order path-integral Monte Carlo method is plagued with the sign problem in solving many-fermion systems. This is due to the large number of antisymmetric free-fermion propagators that are needed to extract the ground state wave function at large imaginary time. In this work we show that optimized fourth-order path-integral Monte Carlo methods, which use no more than five free-fermion propagators, can yield accurate quantum dot energies for up to 20 polarized electrons with the use of the Hamiltonian energy estimator.
NASA Astrophysics Data System (ADS)
Schnabel, Stefan; Janke, Wolfhard; Bachmann, Michael
2011-06-01
The investigation of freezing transitions of single polymers is computationally demanding, since surface effects dominate the nucleation process. In recent studies we have systematically shown that the freezing properties of flexible, elastic polymers depend on the precise chain length. Performing multicanonical Monte Carlo simulations, we faced several computational challenges in connection with liquid-solid and solid-solid transitions. For this reason, we developed novel methods and update strategies to overcome the arising problems. We introduce novel Monte Carlo moves and two extensions to the multicanonical method.
A Hamiltonian Monte Carlo method for Bayesian Inference of Supermassive Black Hole Binaries
Edward K. Porter; Jérôme Carré
2013-11-29
We investigate the use of a Hamiltonian Monte Carlo to map out the posterior density function for supermassive black hole binaries. While previous Markov Chain Monte Carlo (MCMC) methods, such as Metropolis-Hastings MCMC, have been successfully employed for a number of different gravitational wave sources, these methods are essentially random walk algorithms. The Hamiltonian Monte Carlo treats the inverse likelihood surface as a "gravitational potential" and by introducing canonical positions and momenta, dynamically evolves the Markov chain by solving Hamilton's equations of motion. We present an implementation of the Hamiltonian Markov Chain that is faster, and more efficient by a factor of approximately the dimension of the parameter space, than the standard MCMC.
A Hamiltonian Monte Carlo method for Bayesian Inference of Supermassive Black Hole Binaries
Porter, Edward K
2013-01-01
We investigate the use of a Hamiltonian Monte Carlo to map out the posterior density function for supermassive black hole binaries. While previous Markov Chain Monte Carlo (MCMC) methods, such as Metropolis-Hastings MCMC, have been successfully employed for a number of different gravitational wave sources, these methods are essentially random walk algorithms. The Hamiltonian Monte Carlo treats the inverse likelihood surface as a "gravitational potential" and by introducing canonical positions and momenta, dynamically evolves the Markov chain by solving Hamilton's equations of motion. We present an implementation of the Hamiltonian Markov Chain that is faster, and more efficient by a factor of approximately the dimension of the parameter space, than the standard MCMC.
A new method to assess the statistical convergence of monte carlo solutions
Forster, R.A.
1991-01-01
Accurate Monte Carlo confidence intervals (CIs), which are formed with an estimated mean and an estimated standard deviation, can only be created when the number of particle histories N becomes large enough so that the central limit theorem can be applied. The Monte Carlo user has a limited number of marginal methods to assess the fulfillment of this condition, such as statistical error reduction proportional to 1/{radical}N with error magnitude guidelines and third and fourth moment estimators. A new method is presented here to assess the statistical convergence of Monte Carlo solutions by analyzing the shape of the empirical probability density function (PDF) of history scores. Related work in this area includes the derivation of analytic score distributions for a two-state Monte Carlo problem. Score distribution histograms have been generated to determine when a small number of histories accounts for a large fraction of the result. This summary describes initial studies of empirical Monte Carlo history score PDFs created from score histograms of particle transport simulations. 7 refs., 1 fig.
A Monte Carlo method for an objective Bayesian procedure
Yosihiko Ogata
1990-01-01
This paper describes a method for an objective selection of the optimal prior distribution, or for adjusting its hyper-parameter, among the competing priors for a variety of Bayesian models. In order to implement this method, the integration of very high dimensional functions is required to get the normalizing constants of the posterior and even of the prior distribution. The logarithm
A multi-group Monte Carlo core analysis method and its application in SCWR design
Zhang, P.; Wang, K.; Yu, G. [Dept. of Engineering Physics, Tsinghua Univ., Beijing, 100084 (China)
2012-07-01
Complex geometry and spectrum have been the characteristics of many newly developed nuclear energy systems, so the suitability and precision of the traditional deterministic codes are doubtable while being applied to simulate these systems. On the contrary, the Monte Carlo method has the inherent advantages of dealing with complex geometry and spectrum. The main disadvantage of Monte Carlo method is that it takes long time to get reliable results, so the efficiency is too low for the ordinary core designs. A new Monte Carlo core analysis scheme is developed, aimed to increase the calculation efficiency. It is finished in two steps: Firstly, the assembly level simulation is performed by continuous energy Monte Carlo method, which is suitable for any geometry and spectrum configuration, and the assembly multi-group constants are tallied at the same time; Secondly, the core level calculation is performed by multi-group Monte Carlo method, using the assembly group constants generated in the first step. Compared with the heterogeneous Monte Carlo calculations of the whole core, this two-step scheme is more efficient, and the precision is acceptable for the preliminary analysis of novel nuclear systems. Using this core analysis scheme, a SCWR core was designed based on a new SCWR assembly design. The core output is about 1,100 MWe, and a cycle length of about 550 EFPDs can be achieved with 3-batch refueling pattern. The average and maximum discharge burn-up are about 53.5 and 60.9 MWD/kgU respectively. (authors)
CrÃ©pey, StÃ©phane
Introduction Semi-linear PDEs Non-linear Monte-Carlo algorithms New method: Marked branching PDEs Non-linear Monte-Carlo algorithms New method: Marked branching diffusions CVA Multi-type M Outline 1 Introduction 2 Semi-linear PDEs 3 Non-linear Monte-Carlo algorithms 4 New method: Marked branching
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.
Kiyoshi SAKURAI; Toshihiro YAMAMOTO
In thexed source problem such as a neutron deep penetration calculation with the Monte Carlo method, the applica- tion of the variance reduction method is most important for a highgure of merit (FOM) and the most reliable calcula- tion. But, MCNP calculation inputs written in published literature are not to be best solution. The most concerned items are setting method
Stabilizing Canonical-Ensemble Calculations in the Auxiliary-Field Monte Carlo Method
C. N. Gilbreth; Y. Alhassid
2014-02-14
Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the auxiliary-field Monte Carlo (AFMC) method, low-temperature or large-model-space calculations require numerically stabilized matrix multiplication. When adapting methods used in the grand-canonical ensemble to the canonical ensemble of fixed particle number, the numerical stabilization increases the number of required floating-point operations for computing observables by a factor of the size of the single-particle model space, and thus can greatly limit the systems that can be studied. We describe an improved method for stabilizing canonical-ensemble calculations in AFMC that exhibits better scaling, and present numerical tests that demonstrate the accuracy and improved performance of the method.
Investigating the Limits of Monte Carlo Tree Search Methods in Computer Go
MÃ¼ller, Martin
and Research Questions about MCTS for Computer Go The main components influencing the strength of current GoInvestigating the Limits of Monte Carlo Tree Search Methods in Computer Go Shih-Chieh Huang1 progress in Com- puter Go. Still, program performance is uneven - most current Go pro- grams are much
Charged-particle thermonuclear reaction rates: I. Monte Carlo method and statistical distributions
Richard Longland; Christian Iliadis; Art Champagne; Joe Newton; Claudio Ugalde; Alain Coc; Ryan Fitzgerald
2010-01-01
A method based on Monte Carlo techniques is presented for evaluating thermonuclear reaction rates. We begin by reviewing commonly applied procedures and point out that reaction rates that have been reported up to now in the literature have no rigorous statistical meaning. Subsequently, we associate each nuclear physics quantity entering in the calculation of reaction rates with a specific probability
Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods
Philip D. ONeill; David J. Balding; Niels G. Becker; Mervi Eerola; Denis Mollison
2000-01-01
This paper exploresthe use of Markov chain Monte Carlo (MCMC) methods for the analysis ofinfectious disease data, with the hope that they will permit analyses to be madeunder more realistic assumptions. Two important kinds of data sets are considered,containing temporal and non-temporal information respectively, from outbreaks ofmeasles and influenza. Stochastic epidemic models are used to describe the processesthat generate the
ERIC Educational Resources Information Center
Kim, Jee-Seon; Bolt, Daniel M.
2007-01-01
The purpose of this ITEMS module is to provide an introduction to Markov chain Monte Carlo (MCMC) estimation for item response models. A brief description of Bayesian inference is followed by an overview of the various facets of MCMC algorithms, including discussion of prior specification, sampling procedures, and methods for evaluating chain…
Multiple target tracking using Sequential Monte Carlo Methods and statistical data association
Oliver Frank; J uan Nieto; Jose Guivant; Steve Scheding
2003-01-01
This paper presents two approaches for the problem of multiple target tracking (MTT) and specifically people tracking. Both filters are based on sequential Monte Carlo methods (SMCM) and joint probability data association (JPDA). The filters have been implemented and tested on real data from a laser measurement system. Experiments show that both approaches are able to track multiple moving persons.
Multilevel Markov Chain Monte Carlo Method for High-Contrast Single-Phase Flow Problems
NASA Astrophysics Data System (ADS)
Efendiev, Yalchin; Jin, Bangti; Michael, Presho; Tan, Xiaosi
2015-01-01
In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems. It is based on the generalized multiscale finite element method (GMsFEM) and multilevel Monte Carlo (MLMC) methods. The former provides a hierarchy of approximations of different resolution, whereas the latter gives an efficient way to estimate quantities of interest using samples on different levels. The number of basis functions in the online GMsFEM stage can be varied to determine the solution resolution and the computational cost, and to efficiently generate samples at different levels. In particular, it is cheap to generate samples on coarse grids but with low resolution, and it is expensive to generate samples on fine grids with high accuracy. By suitably choosing the number of samples at different levels, one can leverage the expensive computation in larger fine-grid spaces toward smaller coarse-grid spaces, while retaining the accuracy of the final Monte Carlo estimate. Further, we describe a multilevel Markov chain Monte Carlo method, which sequentially screens the proposal with different levels of approximations and reduces the number of evaluations required on fine grids, while combining the samples at different levels to arrive at an accurate estimate. The framework seamlessly integrates the multiscale features of the GMsFEM with the multilevel feature of the MLMC methods following the work in \\cite{ketelson2013}, and our numerical experiments illustrate its efficiency and accuracy in comparison with standard Monte Carlo estimates.
Quasi-Monte Carlo Methods in Computer Graphics: The Global Illumination Problem
Alexander Keller
1995-01-01
The main part of the global illumination problem of computer graphics is given by a Fredholm integral equation of the second kind, describing the light distribution in a closed environment. Calculating photorealistic images from that equation requires its kernel to be very complex and discontinuous. Due to this complexity Monte Carlo methods are an interesting tool for estimating a solution.
The Monte Carlo Method and the Evaluation of Retrieval System Performance.
ERIC Educational Resources Information Center
Burgin, Robert
1999-01-01
Introduces the Monte Carlo method which is shown to represent an attractive alternative to the hypergeometric model for identifying the levels at which random retrieval performance is exceeded in retrieval test collections and for overcoming some of the limitations of the hypergeometric model. Practical matters to consider when employing the Monte…
ERIC Educational Resources Information Center
Dumenci, Levent; Windle, Michael
2001-01-01
Used Monte Carlo methods to evaluate the adequacy of cluster analysis to recover group membership based on simulated latent growth curve (LCG) models. Cluster analysis failed to recover growth subtypes adequately when the difference between growth curves was shape only. Discusses circumstances under which it was more successful. (SLD)
A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation
Wolfgang Wagner
1992-01-01
Bird's direct simulation Monte Carlo method for the Boltzmann equation is considered. The limit (as the number of particles tends to infinity) of the random empirical measures associated with the Bird algorithm is shown to be a deterministic measure-valued function satisfying an equation close (in a certain sense) to the Boltzmann equation. A Markov jump process is introduced, which is
A Comparison of Four Monte Carlo Methods for Estimating the Probability of s-t Connectedness
George S. Fishman
1986-01-01
This paper describes and compares the performance of four alternative Monte Carlo sampling plans for estimating the probability that two nodes, s and t, are connected in an undirected network whose arcs fail randomly and independently. Models of this type are commonly used when computing the reliability of a system of randomly failing components. The first method, dagger sampling, relies
Jody Hey; Rasmus Nielsen
2007-01-01
In 1988, Felsenstein described a framework for assessing the likelihood of a genetic data set in which all of the possible genealogical histories of the data are considered, each in proportion to their probability. Although not analytically solvable, several approaches, including Markov chain Monte Carlo methods, have been developed to find approximate solutions. Here, we describe an approach in which
Simulations for gas flows in microgeometries using the direct simulation Monte Carlo method
Moran Wang; Zhixin Li
2004-01-01
Micro gas flows are often encountered in MEMS devices and classical CFD could not accurately predict the flow and thermal behavior due to the high Knudsen number. Therefore, the gas flow in microgeometries was investigated using the direct simulation Monte Carlo (DSMC) method. New treatments for boundary conditions are verified by simulations of micro-Poiseuille flow, compared with the previous boundary
Scalar and Parallel Optimized Implementation of the Direct Simulation Monte Carlo Method
Stefan Dietrich; Iain D. Boyd
1996-01-01
This paper describes a new concept for the implementation of the direct simulation Monte Carlo (DSMC) method. It uses a localized data structure based on a computational cell to achieve high performance, especially on workstation processors, which can also be used in parallel. Since the data structure makes it possible to freely assign any cell to any processor, a domain
Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling
A. Jasra; C. C. Holmes; D. A. Stephens
2005-01-01
In the past ten years there has been a dramatic increase of interest in the Bayesian analysis of finite mixture models. This is primarily because of the emergence of Markov chain Monte Carlo (MCMC) methods. While MCMC provides a convenient way to draw inference from complicated statistical models, there are many, perhaps underappreciated, problems associated with the MCMC analysis of
A Monte Carlo Method for the PDF Equations of Turbulent Reactive Flow
S. B. POPE
1981-01-01
—A Monte Carlo method is presented which simulates the transport equations of joint probability density functions (pdf's) in turbulent flows. (Finite-difference solutions of the equations are impracticable, mainly because of the large dimensionality of the pdf's). Attention is focused on an equation for the joint pdf of chemical and thermodynamic properties in turbulent reactive flows. It is shown that the
Lee, Anthony; Yau, Christopher; Giles, Michael B.; Doucet, Arnaud; Holmes, Christopher C.
2011-01-01
We present a case-study on the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods. Graphics cards, containing multiple Graphics Processing Units (GPUs), are self-contained parallel computational devices that can be housed in conventional desktop and laptop computers and can be thought of as prototypes of the next generation of many-core processors. For certain classes of population-based Monte Carlo algorithms they offer massively parallel simulation, with the added advantage over conventional distributed multi-core processors that they are cheap, easily accessible, easy to maintain, easy to code, dedicated local devices with low power consumption. On a canonical set of stochastic simulation examples including population-based Markov chain Monte Carlo methods and Sequential Monte Carlo methods, we nd speedups from 35 to 500 fold over conventional single-threaded computer code. Our findings suggest that GPUs have the potential to facilitate the growth of statistical modelling into complex data rich domains through the availability of cheap and accessible many-core computation. We believe the speedup we observe should motivate wider use of parallelizable simulation methods and greater methodological attention to their design. PMID:22003276
Schofield, Jeremy
An efficient Monte Carlo method for calculating ab initio transition state theory reaction rates in liquid environments are still inferred from isotope and solvent medium effects on the reaction rate.6 the calculation of kinetic iso- tope effects and reaction rates in solution are associated with the fact
Monte Carlo Methods for Uncertainty Quantification Mathematical Institute, University of Oxford
Giles, Mike
modelling large eddy simulation direct Navier-Stokes simple geometries (e.g. a wing) complex geometries (Oxford) Monte Carlo methods May 3031, 2013 3 / 41 #12;PDEs with Uncertainty The big move now is towards Engineering wants to move to "robust design" taking into account the effects of uncertainty. Other areas want
Quantum Monte Carlo Methods for First Principles Simulation of Liquid Water
ERIC Educational Resources Information Center
Gergely, John Robert
2009-01-01
Obtaining an accurate microscopic description of water structure and dynamics is of great interest to molecular biology researchers and in the physics and quantum chemistry simulation communities. This dissertation describes efforts to apply quantum Monte Carlo methods to this problem with the goal of making progress toward a fully "ab initio"…
Bayesian Phylogenetic Inference Using DNA Sequences: A Markov Chain Monte Carlo Method
Ziheng Yang; Bruce Rannala
An improved Bayesian method is presented for estimating phylogenetic trees using DNA sequence data. The birth- death process with species sampling is used to specify the prior distribution of phylogenies and ancestral speciation times, and the posterior probabilities of phylogenies are used to estimate the maximum posterior probability (MAP) tree. Monte Carlo integration is used to integrate over the ancestral
Electrical conductivity of high-pressure liquid hydrogen by quantum Monte Carlo methods.
Lin, Fei; Morales, Miguel A; Delaney, Kris T; Pierleoni, Carlo; Martin, Richard M; Ceperley, D M
2009-12-18
We compute the electrical conductivity for liquid hydrogen at high pressure using Monte Carlo techniques. The method uses coupled electron-ion Monte Carlo simulations to generate configurations of liquid hydrogen. For each configuration, correlated sampling of electrons is performed in order to calculate a set of lowest many-body eigenstates and current-current correlation functions of the system, which are summed over in the many-body Kubo formula to give ac electrical conductivity. The extrapolated dc conductivity at 3000 K for several densities shows a liquid semiconductor to liquid-metal transition at high pressure. Our results are in good agreement with shock-wave data. PMID:20366267
Monte Carlo Sampling-Based Methods for Stochastic Optimization
2014-01-22
as a classical expectation but in a different form, such as a value-at-risk or ... care, finance, transportation, revenue management, and many others. ...... sampling methods is closely related to the issues of assessment of solution ...... criteria for stochastic dual dynamic programming: a case study in long-term hydrothermal.
Wenner, Michael T.; Haghighat, Alireza; Gardner, Shane
2001-06-17
A methodology to use the solution of a deterministic multigroup S{sub n} transport code as the source distribution for a Monte Carlo criticality calculation is discussed. This methodology is referred to as the S{sub n} Source Initialization method. The effectiveness of this methodology is measured by simulating a loosely coupled benchmark, where standard Monte Carlo codes have shown a bias. The Monte Carlo N-Particle transport code MCNP and PENTRAN (three-dimensional parallel, multigroup, S{sub n}) transport code system were used. The PENTRAN code solution is used as a starting source distribution in the MCNP code, thereby decreasing the necessary active cycle length. The methodology was verified on the basis of a sample benchmark problem of a lattice of 5x5x1 highly enriched uranium metal spheres surrounded by air.
Reducing uncertainty in site characterization using Bayes Monte Carlo methods
Sohn, Michael D.; Small, Mitchell J.; Pantazidou, Marina
2004-04-28
A Bayesian uncertainty analysis approach is developed as a tool for assessing and reducing uncertainty in ground-water flow and chemical transport predictions. The method is illustrated for a site contaminated with chlorinated hydrocarbons. Uncertainty in source characterization, in chemical transport parameters, and in the assumed hydrogeologic structure was evaluated using engineering judgment and updated using observed field data. The updating approach using observed hydraulic head data was able to differentiate between reasonable and unreasonable hydraulic conductivity fields but could not differentiate between alternative conceptual models for the geological structure of the subsurface at the site. Updating using observed chemical concentration data reduced the uncertainty in most parameters and reduced uncertainty in alternative conceptual models describing the geological structure at the site, source locations, and the chemicals released at these sources. Thirty-year transport projections for no-action and source containment scenarios demonstrate a typical application of the methods.
Applications of Malliavin calculus to Monte Carlo methods in finance
Eric Fournié; Jean-Michel Lasry; Jérôme Lebuchoux; Pierre-Louis Lions; Nizar Touzi
1999-01-01
. This paper presents an original probabilistic method for the numerical computations of Greeks (i.e. price sensitivities)\\u000a in finance. Our approach is based on the {\\\\it integration-by-parts} formula, which lies at the core of the theory of variational\\u000a stochastic calculus, as developed in the Malliavin calculus. The Greeks formulae, both with respect to initial conditions\\u000a and for smooth perturbations of
A Hamiltonian Monte-Carlo method for Bayesian inference of supermassive black hole binaries
NASA Astrophysics Data System (ADS)
Porter, Edward K.; Carré, Jérôme
2014-07-01
We investigate the use of a Hamiltonian Monte-Carlo to map out the posterior density function for supermassive black hole binaries. While previous Markov Chain Monte-Carlo (MCMC) methods, such as Metropolis-Hastings MCMC, have been successfully employed for a number of different gravitational wave sources, these methods are essentially random walk algorithms. The Hamiltonian Monte-Carlo treats the inverse likelihood surface as a ‘gravitational potential’ and by introducing canonical positions and momenta, dynamically evolves the Markov chain by solving Hamilton's equations of motion. This method is not as widely used as other MCMC algorithms due to the necessity of calculating gradients of the log-likelihood, which for most applications results in a bottleneck that makes the algorithm computationally prohibitive. We circumvent this problem by using accepted initial phase-space trajectory points to analytically fit for each of the individual gradients. Eliminating the waveform generation needed for the numerical derivatives reduces the total number of required templates for a {{10}^{6}} iteration chain from \\sim {{10}^{9}} to \\sim {{10}^{6}}. The result is in an implementation of the Hamiltonian Monte-Carlo that is faster, and more efficient by a factor of approximately the dimension of the parameter space, than a Hessian MCMC.
NASA Astrophysics Data System (ADS)
Kim, Minho; Lee, Hyounggun; Kim, Hyosim; Park, Hongmin; Lee, Wonho; Park, Sungho
2014-03-01
This study evaluated the Monte Carlo method for determining the dose calculation in fluoroscopy by using a realistic human phantom. The dose was calculated by using Monte Carlo N-particle extended (MCNPX) in simulations and was measured by using Korean Typical Man-2 (KTMAN-2) phantom in the experiments. MCNPX is a widely-used simulation tool based on the Monte-Carlo method and uses random sampling. KTMAN-2 is a virtual phantom written in MCNPX language and is based on the typical Korean man. This study was divided into two parts: simulations and experiments. In the former, the spectrum generation program (SRS-78) was used to obtain the output energy spectrum for fluoroscopy; then, each dose to the target organ was calculated using KTMAN-2 with MCNPX. In the latter part, the output of the fluoroscope was calibrated first and TLDs (Thermoluminescent dosimeter) were inserted in the ART (Alderson Radiation Therapy) phantom at the same places as in the simulation. Thus, the phantom was exposed to radiation, and the simulated and the experimental doses were compared. In order to change the simulation unit to the dose unit, we set the normalization factor (NF) for unit conversion. Comparing the simulated with the experimental results, we found most of the values to be similar, which proved the effectiveness of the Monte Carlo method in fluoroscopic dose evaluation. The equipment used in this study included a TLD, a TLD reader, an ART phantom, an ionization chamber and a fluoroscope.
A Monte Carlo implementation of the predictor-corrector Quasi-Static method
Hackemack, M. W.; Ragusa, J. C. [Department of Nuclear Engineering, Texas A and M University, 337 Zachry Engineering Building, College Station, TX 77843 (United States); Griesheimer, D. P.; Pounders, J. M. [Bettis Atomic Laboratory, Bechtel Marine Propulsion Corporation, P.O. Box 79, West Mifflin, PA 15122 (United States)
2013-07-01
The Quasi-Static method (QS) is a useful tool for solving reactor transients since it allows for larger time steps when updating neutron distributions. Because of the beneficial attributes of Monte Carlo (MC) methods (exact geometries and continuous energy treatment), it is desirable to develop a MC implementation for the QS method. In this work, the latest version of the QS method known as the Predictor-Corrector Quasi-Static method is implemented. Experiments utilizing two energy-groups provide results that show good agreement with analytical and reference solutions. The method as presented can easily be implemented in any continuous energy, arbitrary geometry, MC code. (authors)
Chung, Kiwhan
1996-01-01
While the use of Monte Carlo method has been prevalent in nuclear engineering, it has yet to fully blossom in the study of solute transport in porous media. By using an etched-glass micromodel, an attempt is made to apply Monte Carlo method...
Monte-Carlo methods make Dempster-Shafer formalism feasible
NASA Technical Reports Server (NTRS)
Kreinovich, Vladik YA.; Bernat, Andrew; Borrett, Walter; Mariscal, Yvonne; Villa, Elsa
1991-01-01
One of the main obstacles to the applications of Dempster-Shafer formalism is its computational complexity. If we combine m different pieces of knowledge, then in general case we have to perform up to 2(sup m) computational steps, which for large m is infeasible. For several important cases algorithms with smaller running time were proposed. We prove, however, that if we want to compute the belief bel(Q) in any given query Q, then exponential time is inevitable. It is still inevitable, if we want to compute bel(Q) with given precision epsilon. This restriction corresponds to the natural idea that since initial masses are known only approximately, there is no sense in trying to compute bel(Q) precisely. A further idea is that there is always some doubt in the whole knowledge, so there is always a probability p(sub o) that the expert's knowledge is wrong. In view of that it is sufficient to have an algorithm that gives a correct answer a probability greater than 1-p(sub o). If we use the original Dempster's combination rule, this possibility diminishes the running time, but still leaves the problem infeasible in the general case. We show that for the alternative combination rules proposed by Smets and Yager feasible methods exist. We also show how these methods can be parallelized, and what parallelization model fits this problem best.
Solution of deterministic–stochastic epidemic models by dynamical Monte Carlo method
O. E Aièllo; V. J Haas; M. A. A daSilva; A Caliri
2000-01-01
This work is concerned with dynamical Monte Carlo (MC) method and its application to models originally formulated in a continuous-deterministic approach. Specifically, a susceptible–infected–removed–susceptible (SIRS) model is used in order to analyze aspects of the dynamical MC algorithm and achieve its applications in epidemic contexts. We first examine two known approaches to the dynamical interpretation of the MC method and
NASA Astrophysics Data System (ADS)
Zhang, Xiaofeng
2012-03-01
Image formation in fluorescence diffuse optical tomography is critically dependent on construction of the Jacobian matrix. For clinical and preclinical applications, because of the highly heterogeneous characteristics of the medium, Monte Carlo methods are frequently adopted to construct the Jacobian. Conventional adjoint Monte Carlo method typically compute the Jacobian by multiplying the photon density fields radiated from the source at the excitation wavelength and from the detector at the emission wavelength. Nonetheless, this approach assumes that the source and the detector in Green's function are reciprocal, which is invalid in general. This assumption is particularly questionable in small animal imaging, where the mean free path length of photons is typically only one order of magnitude smaller than the representative dimension of the medium. We propose a new method that does not rely on the reciprocity of the source and the detector by tracing photon propagation entirely from the source to the detector. This method relies on the perturbation Monte Carlo theory to account for the differences in optical properties of the medium at the excitation and the emission wavelengths. Compared to the adjoint methods, the proposed method is more valid in reflecting the physical process of photon transport in diffusive media and is more efficient in constructing the Jacobian matrix for densely sampled configurations.
A Monte Carlo method using octree structure in photon and electron transport
Ogawa, K.; Maeda, S. [Hosei Univ., Tokyo (Japan)] [Hosei Univ., Tokyo (Japan)
1995-12-01
Most of the early Monte Carlo calculations in medical physics were used to calculate absorbed dose distributions, and detector responses and efficiencies. Recently, data acquisition in Single Photon Emission CT (SPECT) has been simulated by a Monte Carlo method to evaluate scatter photons generated in a human body and a collimator. Monte Carlo simulations in SPECT data acquisition are generally based on the transport of photons only because the photons being simulated are low energy, and therefore the bremsstrahlung productions by the electrons generated are negligible. Since the transport calculation of photons without electrons is much simpler than that with electrons, it is possible to accomplish the high-speed simulation in a simple object with one medium. Here, object description is important in performing the photon and/or electron transport using a Monte Carlo method efficiently. The authors propose a new description method using an octree representation of an object. Thus even if the boundaries of each medium are represented accurately, high-speed calculation of photon transport can be accomplished because the number of voxels is much fewer than that of the voxel-based approach which represents an object by a union of the voxels of the same size. This Monte Carlo code using the octree representation of an object first establishes the simulation geometry by reading octree string, which is produced by forming an octree structure from a set of serial sections for the object before the simulation; then it transports photons in the geometry. Using the code, if the user just prepares a set of serial sections for the object in which he or she wants to simulate photon trajectories, he or she can perform the simulation automatically using the suboptimal geometry simplified by the octree representation without forming the optimal geometry by handwriting.
A New Monte Carlo Method and Its Implications for Generalized Cluster Algorithms
C. H. Mak; Arun K. Sharma
2007-04-12
We describe a novel switching algorithm based on a ``reverse'' Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of cluster-type Monte Carlo methods, and the generalization makes it possible to derive cluster algorithms for systems with both discrete and continuous degrees of freedom. The roughening transition in the sine-Gordon model has been studied with this method, and high-accuracy simulations for system sizes up to $1024^2$ were carried out to examine the logarithmic divergence of the surface roughness above the transition temperature, revealing clear evidence for universal scaling of the Kosterlitz-Thouless type.
A Bayesian approach to multiscale inverse problems using the sequential Monte Carlo method
NASA Astrophysics Data System (ADS)
Wan, Jiang; Zabaras, Nicholas
2011-10-01
A new Bayesian computational approach is developed to estimate spatially varying parameters. The sparse grid collocation method is adopted to parameterize the spatial field. Based on a hierarchically structured sparse grid, a multiscale representation of the spatial field is constructed. An adaptive refinement strategy is then used for computing the spatially varying parameter. A sequential Monte Carlo (SMC) sampler is used to explore the posterior distributions defined on multiple scales. The SMC sampling is directly parallelizable and is superior to conventional Markov chain Monte Carlo methods for multi-modal target distributions. The samples obtained at coarser levels of resolution are used to provide prior information for the estimation at finer levels. This Bayesian computational approach is rather general and applicable to various spatially varying parameter estimation problems. The method is demonstrated with the estimation of permeability in flows through porous media.
Application de la methode des sous-groupes au calcul Monte-Carlo multigroupe
NASA Astrophysics Data System (ADS)
Martin, Nicolas
This thesis is dedicated to the development of a Monte Carlo neutron transport solver based on the subgroup (or multiband) method. In this formalism, cross sections for resonant isotopes are represented in the form of probability tables on the whole energy spectrum. This study is intended in order to test and validate this approach in lattice physics and criticality-safety applications. The probability table method seems promising since it introduces an alternative computational way between the legacy continuous-energy representation and the multigroup method. In the first case, the amount of data invoked in continuous-energy Monte Carlo calculations can be very important and tend to slow down the overall computational time. In addition, this model preserves the quality of the physical laws present in the ENDF format. Due to its cheap computational cost, the multigroup Monte Carlo way is usually at the basis of production codes in criticality-safety studies. However, the use of a multigroup representation of the cross sections implies a preliminary calculation to take into account self-shielding effects for resonant isotopes. This is generally performed by deterministic lattice codes relying on the collision probability method. Using cross-section probability tables on the whole energy range permits to directly take into account self-shielding effects and can be employed in both lattice physics and criticality-safety calculations. Several aspects have been thoroughly studied: (1) The consistent computation of probability tables with a energy grid comprising only 295 or 361 groups. The CALENDF moment approach conducted to probability tables suitable for a Monte Carlo code. (2) The combination of the probability table sampling for the energy variable with the delta-tracking rejection technique for the space variable, and its impact on the overall efficiency of the proposed Monte Carlo algorithm. (3) The derivation of a model for taking into account anisotropic effects of the scattering reaction consistent with the subgroup method. In this study, we generalize the Discrete Angle Technique, already proposed for homogeneous, multigroup cross sections, to isotopic cross sections on the form of probability tables. In this technique, the angular density is discretized into probability tables. Similarly to the cross-section case, a moment approach is used to compute the probability tables for the scattering cosine. (4) The introduction of a leakage model based on the B1 fundamental mode approximation. Unlike deterministic lattice packages, most Monte Carlo-based lattice physics codes do not include leakage models. However the generation of homogenized and condensed group constants (cross sections, diffusion coefficients) require the critical flux. This project has involved the development of a program into the DRAGON framework, written in Fortran 2003 and wrapped with a driver in C, the GANLIB 5. Choosing Fortran 2003 has permitted the use of some modern features, such as the definition of objects and methods, data encapsulation and polymorphism. The validation of the proposed code has been performed by comparison with other numerical methods: (1) The continuous-energy Monte Carlo method of the SERPENT code. (2) The Collision Probability (CP) method and the discrete ordinates (SN) method of the DRAGON lattice code. (3) The multigroup Monte Carlo code MORET, coupled with the DRAGON code. Benchmarks used in this work are representative of some industrial configurations encountered in reactor and criticality-safety calculations: (1)Pressurized Water Reactors (PWR) cells and assemblies. (2) Canada-Deuterium Uranium Reactors (CANDU-6) clusters. (3) Critical experiments from the ICSBEP handbook (International Criticality Safety Benchmark Evaluation Program).
Time-step limits for a Monte Carlo Compton-scattering method
Densmore, Jeffery D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Lowrie, Robert B [Los Alamos National Laboratory
2008-01-01
Compton scattering is an important aspect of radiative transfer in high energy density applications. In this process, the frequency and direction of a photon are altered by colliding with a free electron. The change in frequency of a scattered photon results in an energy exchange between the photon and target electron and energy coupling between radiation and matter. Canfield, Howard, and Liang have presented a Monte Carlo method for simulating Compton scattering that models the photon-electron collision kinematics exactly. However, implementing their technique in multiphysics problems that include the effects of radiation-matter energy coupling typically requires evaluating the material temperature at its beginning-of-time-step value. This explicit evaluation can lead to unstable and oscillatory solutions. In this paper, we perform a stability analysis of this Monte Carlo method and present time-step limits that avoid instabilities and nonphysical oscillations by considering a spatially independent, purely scattering radiative-transfer problem. Examining a simplified problem is justified because it isolates the effects of Compton scattering, and existing Monte Carlo techniques can robustly model other physics (such as absorption, emission, sources, and photon streaming). Our analysis begins by simplifying the equations that are solved via Monte Carlo within each time step using the Fokker-Planck approximation. Next, we linearize these approximate equations about an equilibrium solution such that the resulting linearized equations describe perturbations about this equilibrium. We then solve these linearized equations over a time step and determine the corresponding eigenvalues, quantities that can predict the behavior of solutions generated by a Monte Carlo simulation as a function of time-step size and other physical parameters. With these results, we develop our time-step limits. This approach is similar to our recent investigation of time discretizations for the Compton-scattering Fokker-Planck equation.
Isospin-projected nuclear level densities by the shell model Monte Carlo method
H. Nakada; Y. Alhassid
2008-09-24
We have developed an efficient isospin projection method in the shell model Monte Carlo approach for isospin-conserving Hamiltonians. For isoscalar observables this projection method has the advantage of being exact sample by sample. The isospin projection method allows us to take into account the proper isospin dependence of the nuclear interaction, thus avoiding a sign problem that such an interaction introduces in unprojected calculations. We apply our method in the calculation of the isospin dependence of level densities in the complete $pf+g_{9/2}$ shell. We find that isospin-dependent corrections to the total level density are particularly important for $N \\sim Z$ nuclei.
Comparison of Monte Carlo methods for criticality benchmarks: Pointwise compared to multigroup
Choi, J.S.; Alesso, P.H.; Pearson, J.S. (Lawrence Livermore National Lab., CA (USA))
1989-01-01
Transport codes use multigroup cross sections where neutrons are divided into broad energy groups, and the monoenergetic equation is solved for each group with a group-averaged cross section. Monte Carlo codes differ in that they allow the use of the most basic pointwise cross-section data directly in a calculation. Most of the first Monte Carlo codes were not able to utilize this feature, however, because of the memory limitations of early computers and the lack of pointwise cross-section data. Consequently, codes written in 1970s, such as KENO-IV and MORSE-C, were adapted to use multigroup cross-section sets similar to those used in the S{sub n} transport codes. With advances in computer memory capacities and the availability of pointwise cross-section sets, new Monte Carlo codes employing pointwise cross-section libraries, such as the Los Alamos National Laboratory code MCNP and the Lawrence Livermore National Laboratory (LLNL) code COG were developed for criticality, as well as radiation transport calculations. To compare pointwise and multigroup Monte Carlo methods for criticality benchmark calculations, this paper presents and evaluated the results from the KENO-IV, MORSE-C, MCNP, and COG codes. The critical experiments selected for benchmarking include LLNL fast metal systems and low-enriched uranium moderated and reflected systems.
Monte Carlo method for photon heating using temperature-dependent optical properties.
Slade, Adam Broadbent; Aguilar, Guillermo
2015-02-01
The Monte Carlo method for photon transport is often used to predict the volumetric heating that an optical source will induce inside a tissue or material. This method relies on constant (with respect to temperature) optical properties, specifically the coefficients of scattering and absorption. In reality, optical coefficients are typically temperature-dependent, leading to error in simulation results. The purpose of this study is to develop a method that can incorporate variable properties and accurately simulate systems where the temperature will greatly vary, such as in the case of laser-thawing of frozen tissues. A numerical simulation was developed that utilizes the Monte Carlo method for photon transport to simulate the thermal response of a system that allows temperature-dependent optical and thermal properties. This was done by combining traditional Monte Carlo photon transport with a heat transfer simulation to provide a feedback loop that selects local properties based on current temperatures, for each moment in time. Additionally, photon steps are segmented to accurately obtain path lengths within a homogenous (but not isothermal) material. Validation of the simulation was done using comparisons to established Monte Carlo simulations using constant properties, and a comparison to the Beer-Lambert law for temperature-variable properties. The simulation is able to accurately predict the thermal response of a system whose properties can vary with temperature. The difference in results between variable-property and constant property methods for the representative system of laser-heated silicon can become larger than 100K. This simulation will return more accurate results of optical irradiation absorption in a material which undergoes a large change in temperature. This increased accuracy in simulated results leads to better thermal predictions in living tissues and can provide enhanced planning and improved experimental and procedural outcomes. PMID:25488656
Numerical simulations of acoustics problems using the direct simulation Monte Carlo method
NASA Astrophysics Data System (ADS)
Hanford, Amanda Danforth
In the current study, real gas effects in the propagation of sound waves are simulated using the direct simulation Monte Carlo method for a wide range of systems. This particle method allows for treatment of acoustic phenomena for a wide range of Knudsen numbers, defined as the ratio of molecular mean free path to wavelength. Continuum models such as the Euler and Navier-Stokes equations break down for flows greater than a Knudsen number of approximately 0.05. Continuum models also suffer from the inability to simultaneously model nonequilibrium conditions, diatomic or polyatomic molecules, nonlinearity and relaxation effects and are limited in their range of validity. Therefore, direct simulation Monte Carlo is capable of directly simulating acoustic waves with a level of detail not possible with continuum approaches. The basis of direct simulation Monte Carlo lies within kinetic theory where representative particles are followed as they move and collide with other particles. A parallel, object-oriented DSMC solver was developed for this problem. Despite excellent parallel efficiency, computation time is considerable. Monatomic gases, gases with internal energy, planetary environments, and amplitude effects spanning a large range of Knudsen number have all been modeled with the same method and compared to existing theory. With the direct simulation method, significant deviations from continuum predictions are observed for high Knudsen number flows.
GPU-accelerated Monte Carlo simulation of particle coagulation based on the inverse method
NASA Astrophysics Data System (ADS)
Wei, J.; Kruis, F. E.
2013-09-01
Simulating particle coagulation using Monte Carlo methods is in general a challenging computational task due to its numerical complexity and the computing cost. Currently, the lowest computing costs are obtained when applying a graphic processing unit (GPU) originally developed for speeding up graphic processing in the consumer market. In this article we present an implementation of accelerating a Monte Carlo method based on the Inverse scheme for simulating particle coagulation on the GPU. The abundant data parallelism embedded within the Monte Carlo method is explained as it will allow an efficient parallelization of the MC code on the GPU. Furthermore, the computation accuracy of the MC on GPU was validated with a benchmark, a CPU-based discrete-sectional method. To evaluate the performance gains by using the GPU, the computing time on the GPU against its sequential counterpart on the CPU were compared. The measured speedups show that the GPU can accelerate the execution of the MC code by a factor 10-100, depending on the chosen particle number of simulation particles. The algorithm shows a linear dependence of computing time with the number of simulation particles, which is a remarkable result in view of the n2 dependence of the coagulation.
Y. Alhassid; S. Liu; H. Nakada
1999-10-14
We introduce a particle-number reprojection method in the shell model Monte Carlo that enables the calculation of observables for a series of nuclei using a Monte Carlo sampling for a single nucleus. The method is used to calculate nuclear level densities in the complete $(pf+g_{9/2})$-shell using a good-sign Hamiltonian. Level densities of odd-A and odd-odd nuclei are reliably extracted despite an additional sign problem. Both the mass and the $T_z$ dependence of the experimental level densities are well described without any adjustable parameters. The single-particle level density parameter is found to vary smoothly with mass. The odd-even staggering observed in the calculated backshift parameter follows the experimental data more closely than do empirical formulae.
Mesh-based Monte Carlo method in time-domain widefield fluorescence molecular tomography
Chen, Jin; Fang, Qianqian; Intes, Xavier
2012-01-01
Abstract. We evaluated the potential of mesh-based Monte Carlo (MC) method for widefield time-gated fluorescence molecular tomography, aiming to improve accuracy in both shape discretization and photon transport modeling in preclinical settings. An optimized software platform was developed utilizing multithreading and distributed parallel computing to achieve efficient calculation. We validated the proposed algorithm and software by both simulations and in vivo studies. The results establish that the optimized mesh-based Monte Carlo (mMC) method is a computationally efficient solution for optical tomography studies in terms of both calculation time and memory utilization. The open source code, as part of a new release of mMC, is publicly available at http://mcx.sourceforge.net/mmc/. PMID:23224008
Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
Wang, Lei; Corboz, Philippe; Troyer, Matthias
2015-01-01
We present the ground state extension of the efficient quantum Monte Carlo algorithm for lattice fermions of arXiv:1411.0683. Based on continuous-time expansion of imaginary-time projection operator, the algorithm is free of systematic error and scales \\emph{linearly} with projection time and interaction strength. Compared to the conventional quantum Monte Carlo methods for lattice fermions, this approach has greater flexibility and is easier to combine with powerful machinery such as histogram reweighting and extended ensemble simulation techniques. We discuss the implementation of the continuous-time projection in detail using the spinless $t-V$ model as an example and compare the numerical results with exact diagonalization, density-matrix-renormalization-group and infinite projected entangled-pair states calculations. Finally we use the method to study the fermionic quantum critical point of spinless fermions on a honeycomb lattice and confirm previous results concerning its critical exponents.
Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
Lei Wang; Mauro Iazzi; Philippe Corboz; Matthias Troyer
2015-01-05
We present the ground state extension of the efficient quantum Monte Carlo algorithm for lattice fermions of arXiv:1411.0683. Based on continuous-time expansion of imaginary-time projection operator, the algorithm is free of systematic error and scales \\emph{linearly} with projection time and interaction strength. Compared to the conventional quantum Monte Carlo methods for lattice fermions, this approach has greater flexibility and is easier to combine with powerful machinery such as histogram reweighting and extended ensemble simulation techniques. We discuss the implementation of the continuous-time projection in detail using the spinless $t-V$ model as an example and compare the numerical results with exact diagonalization, density-matrix-renormalization-group and infinite projected entangled-pair states calculations. Finally we use the method to study the fermionic quantum critical point of spinless fermions on a honeycomb lattice and confirm previous results concerning its critical exponents.
Implicit Monte Carlo methods and non-equilibrium Marshak wave radiative transport
Lynch, J.E.
1985-01-01
Two enhancements to the Fleck implicit Monte Carlo method for radiative transport are described, for use in transparent and opaque media respectively. The first introduces a spectral mean cross section, which applies to pseudoscattering in transparent regions with a high frequency incident spectrum. The second provides a simple Monte Carlo random walk method for opaque regions, without the need for a supplementary diffusion equation formulation. A time-dependent transport Marshak wave problem of radiative transfer, in which a non-equilibrium condition exists between the radiation and material energy fields, is then solved. These results are compared to published benchmark solutions and to new discrete ordinate S-N results, for both spatially integrated radiation-material energies versus time and to new spatially dependent temperature profiles. Multigroup opacities, which are independent of both temperature and frequency, are used in addition to a material specific heat which is proportional to the cube of the temperature. 7 refs., 4 figs.
Lisal, Martin
equilibria by the reaction ensemble Monte Carlo method: a review C. Heath Turnera *, John K. Brennanb-ideal conditions is the reaction ensemble Monte Carlo method (RxMC). RxMC has been applied to reactions confined
Baker, R.S. [Los Alamos National Lab., NM (United States); Larsen, E.W. [Michigan Univ., Ann Arbor, MI (United States). Dept. of Nuclear Engineering
1992-08-01
Numerous variance reduction techniques, such as splitting/Russian roulette, weight windows, and the exponential transform exist for improving the efficiency of Monte Carlo transport calculations. Typically, however, these methods, while reducing the variance in the problem area of interest tend to increase the variance in other, presumably less important, regions. As such, these methods tend to be not as effective in Monte Carlo calculations which require the minimization of the variance everywhere. Recently, ``Local`` Exponential Transform (LET) methods have been developed as a means of approximating the zero-variance solution. A numerical solution to the adjoint diffusion equation is used, along with an exponential representation of the adjoint flux in each cell, to determine ``local`` biasing parameters. These parameters are then used to bias the forward Monte Carlo transport calculation in a manner similar to the conventional exponential transform, but such that the transform parameters are now local in space and energy, not global. Results have shown that the Local Exponential Transform often offers a significant improvement over conventional geometry splitting/Russian roulette with weight windows. Since the biasing parameters for the Local Exponential Transform were determined from a low-order solution to the adjoint transport problem, the LET has been applied in problems where it was desirable to minimize the variance in a detector region. The purpose of this paper is to show that by basing the LET method upon a low-order solution to the forward transport problem, one can instead obtain biasing parameters which will minimize the maximum variance in a Monte Carlo transport calculation.
Baker, R.S. (Los Alamos National Lab., NM (United States)); Larsen, E.W. (Michigan Univ., Ann Arbor, MI (United States). Dept. of Nuclear Engineering)
1992-01-01
Numerous variance reduction techniques, such as splitting/Russian roulette, weight windows, and the exponential transform exist for improving the efficiency of Monte Carlo transport calculations. Typically, however, these methods, while reducing the variance in the problem area of interest tend to increase the variance in other, presumably less important, regions. As such, these methods tend to be not as effective in Monte Carlo calculations which require the minimization of the variance everywhere. Recently, Local'' Exponential Transform (LET) methods have been developed as a means of approximating the zero-variance solution. A numerical solution to the adjoint diffusion equation is used, along with an exponential representation of the adjoint flux in each cell, to determine local'' biasing parameters. These parameters are then used to bias the forward Monte Carlo transport calculation in a manner similar to the conventional exponential transform, but such that the transform parameters are now local in space and energy, not global. Results have shown that the Local Exponential Transform often offers a significant improvement over conventional geometry splitting/Russian roulette with weight windows. Since the biasing parameters for the Local Exponential Transform were determined from a low-order solution to the adjoint transport problem, the LET has been applied in problems where it was desirable to minimize the variance in a detector region. The purpose of this paper is to show that by basing the LET method upon a low-order solution to the forward transport problem, one can instead obtain biasing parameters which will minimize the maximum variance in a Monte Carlo transport calculation.
G. Wlazlowski; P. Magierski
2008-12-04
We discuss the Auxiliary Field Quantum Monte Carlo (AFQMC) method applied to dilute neutron matter at finite temperatures. We formulate the discrete Hubbard-Stratonovich transformation for the interaction with finite effective range which is free from the sign problem. The AFQMC results are compared with those obtained from exact diagonalization for a toy model. Preliminary calculations of energy and chemical potential as a function of temperature are presented.
Null-collision technique in the direct-simulation Monte Carlo method
Katsuhisa Koura
1986-01-01
The null-collision concept is introduced into the direct-simulation Monte Carlo method in the rarefied gas dynamics. The null-collision technique overcomes the principle fault in the time-counter technique and the difficulties in the collision-frequency technique. The computation time required for the null-collision technique is comparable to that for the time-counter technique. Therefore, it is concluded that the null-collision technique is superior
Applications of Malliavin calculus to Monte-Carlo methods in finance. II
Eric Fournié; Jean-Michel Lasry; Jérôme Lebuchoux; Pierre-Louis Lions
2001-01-01
. This paper is the sequel of Part I [1], where we showed how to use the so-called Malliavin calculus in order to devise efficient\\u000a Monte-Carlo (numerical) methods for Finance. First, we return to the formulas developed in [1] concerning the “greeks” used\\u000a in European options, and we answer to the question of optimal weight functional in the sense of
Calculation of the Effective Emissivities of Specular-Diffuse Cavities by the Monte Carlo Method
V. I. Sapritsky; A. V. Prokhorov
1992-01-01
An algorithm of the Monte Carlo method is described which allows evaluation of the effective emissivities of isothermal and nonisothermal specular-diffuse black-body cavities for use in radiometry, photometry and optical pyrometry. The calculation provides estimates of normal spectral effective emissivity for black-body cavities, formed by cone surfaces and a cylinder. It does this for an isothermal cavity and for a
Direct simulation Monte Carlo method for gas cluster ion beam technology
Z. Insepov; I. Yamada
2003-01-01
A direct simulation Monte Carlo method has been developed and applied for the simulation of a supersonic Ar gas expansion through a converging–diverging nozzle, with the stagnation pressures of P0=0.1–10 atm, at various temperatures. A body-fitted coordinate system has been developed that allows modeling nozzles of arbitrary shape. A wide selection of nozzle sizes, apex angles, with diffuse and specular
A Monte Carlo method for quantum spins using boson world lines
E. Loh
1986-01-01
A new Monte Carlo method is described for quantum (s= 1\\/2) spins which maps the spin model onto a model of hard-core bosons. The Hamiltonian is then broken up into kinetic and\\u000a potential parts and the Trotter formula used to simulate the Bose system. The power of this mapping comes from the fact that,\\u000a by letting the system evolve through
Application of the vector Monte-Carlo method in polarisation optical coherence tomography
Churmakov, D Yu [Cranfield Health, Cranfield University, Silsoe (United Kingdom); Kuz'min, V L [Saint Petersburg Institute of Commerce and Economics (Russian Federation); Meglinskii, I V [Department of Physics, N G Chernyshevskii Saratov State University, Saratov (Russian Federation)
2006-11-30
The vector Monte-Carlo method is developed and applied to polarisation optical coherence tomography. The basic principles of simulation of the propagation of polarised electromagnetic radiation with a small coherence length are considered under conditions of multiple scattering. The results of numerical simulations for Rayleigh scattering well agree with the Milne solution generalised to the case of an electromagnetic field and with theoretical calculations in the diffusion approximation. (special issue devoted to multiple radiation scattering in random media)
Inverse Monte Carlo method in a multilayered tissue model for diffuse reflectance spectroscopy.
Fredriksson, Ingemar; Larsson, Marcus; Strömberg, Tomas
2012-04-01
Model based data analysis of diffuse reflectance spectroscopy data enables the estimation of optical and structural tissue parameters. The aim of this study was to present an inverse Monte Carlo method based on spectra from two source-detector distances (0.4 and 1.2 mm), using a multilayered tissue model. The tissue model variables include geometrical properties, light scattering properties, tissue chromophores such as melanin and hemoglobin, oxygen saturation and average vessel diameter. The method utilizes a small set of presimulated Monte Carlo data for combinations of different levels of epidermal thickness and tissue scattering. The path length distributions in the different layers are stored and the effect of the other parameters is added in the post-processing. The accuracy of the method was evaluated using Monte Carlo simulations of tissue-like models containing discrete blood vessels, evaluating blood tissue fraction and oxygenation. It was also compared to a homogeneous model. The multilayer model performed better than the homogeneous model and all tissue parameters significantly improved spectral fitting. Recorded in vivo spectra were fitted well at both distances, which we previously found was not possible with a homogeneous model. No absolute intensity calibration is needed and the algorithm is fast enough for real-time processing. PMID:22559695
Lattice-switching Monte Carlo method for crystals of flexible molecules
NASA Astrophysics Data System (ADS)
Bridgwater, Sally; Quigley, David
2014-12-01
We discuss implementation of the lattice-switching Monte Carlo method (LSMC) as a binary sampling between two synchronized Markov chains exploring separated minima in the potential energy landscape. When expressed in this fashion, the generalization to more complex crystals is straightforward. We extend the LSMC method to a flexible model of linear alkanes, incorporating bond length and angle constraints. Within this model, we accurately locate a transition between two polymorphs of n -butane with increasing density, and suggest this as a benchmark problem for other free-energy methods.
Lattice-switching Monte Carlo method for crystals of flexible molecules.
Bridgwater, Sally; Quigley, David
2014-12-01
We discuss implementation of the lattice-switching Monte Carlo method (LSMC) as a binary sampling between two synchronized Markov chains exploring separated minima in the potential energy landscape. When expressed in this fashion, the generalization to more complex crystals is straightforward. We extend the LSMC method to a flexible model of linear alkanes, incorporating bond length and angle constraints. Within this model, we accurately locate a transition between two polymorphs of n-butane with increasing density, and suggest this as a benchmark problem for other free-energy methods. PMID:25615228
Exact solutions of the QCD evolution equations using Monte Carlo method
S. Jadach; M. Skrzypek
2004-01-15
We present the exact and precise (~0.1%) numerical solution of the QCD evolution equations for the parton distributions in a wide range of $Q$ and $x$ using Monte Carlo (MC) method, which relies on the so-called Markovian algorithm. We point out certain advantages of such a method with respect to the existing non-MC methods. We also formulate a challenge of constructing non-Markovian MC algorithm for the evolution equations for the initial state QCD radiation with tagging the type and $x$ of the exiting parton. This seems to be within the reach of the presently available computer CPUs and the sophistication of the MC techniques.
A modification of the Monte Carlo method for simulation of radiative transfer in molecular clouds
Maxim A. Voronkov
2000-08-30
We propose a method of simulation that is based on the averaging of formal solutions of the transfer equation by taking the integral by the Monte Carlo method. This method is used to compute two models, which correspond to the limiting cases of hot gas and cold background radiation and of hot background radiation and cold gas, for E-methanol emission from a compact homogeneous spherical region. We analyse model level populations by using rotational diagrams in the limiting cases mentioned above. Model optical depths of the lines with frequencies below 300 GHz up to J=11 inclusive are given.
Level Densities of Heavy Nuclei by the Shell Model Monte Carlo Method
Y. Alhassid; C. Özen; H. Nakada
2013-05-24
The microscopic calculation of nuclear level densities in the presence of correlations is a difficult many-body problem. The shell model Monte Carlo method provides a powerful technique to carry out such calculations using the framework of the configuration-interaction shell model in spaces that are many orders of magnitude larger than spaces that can be treated by conventional methods. We present recent applications of the method to the calculation of level densities and their collective enhancement factors in heavy nuclei. The calculated level densities are in close agreement with experimental data.
NASA Astrophysics Data System (ADS)
Zhong, Zhaopeng; Talamo, Alberto; Gohar, Yousry
2013-07-01
The effective delayed neutron fraction ? plays an important role in kinetics and static analysis of the reactor physics experiments. It is used as reactivity unit referred to as "dollar". Usually, it is obtained by computer simulation due to the difficulty in measuring it experimentally. In 1965, Keepin proposed a method, widely used in the literature, for the calculation of the effective delayed neutron fraction ?. This method requires calculation of the adjoint neutron flux as a weighting function of the phase space inner products and is easy to implement by deterministic codes. With Monte Carlo codes, the solution of the adjoint neutron transport equation is much more difficult because of the continuous-energy treatment of nuclear data. Consequently, alternative methods, which do not require the explicit calculation of the adjoint neutron flux, have been proposed. In 1997, Bretscher introduced the k-ratio method for calculating the effective delayed neutron fraction; this method is based on calculating the multiplication factor of a nuclear reactor core with and without the contribution of delayed neutrons. The multiplication factor set by the delayed neutrons (the delayed multiplication factor) is obtained as the difference between the total and the prompt multiplication factors. Using Monte Carlo calculation Bretscher evaluated the ? as the ratio between the delayed and total multiplication factors (therefore the method is often referred to as the k-ratio method). In the present work, the k-ratio method is applied by Monte Carlo (MCNPX) and deterministic (PARTISN) codes. In the latter case, the ENDF/B nuclear data library of the fuel isotopes (235U and 238U) has been processed by the NJOY code with and without the delayed neutron data to prepare multi-group WIMSD neutron libraries for the lattice physics code DRAGON, which was used to generate the PARTISN macroscopic cross sections. In recent years Meulekamp and van der Marck in 2006 and Nauchi and Kameyama in 2005 proposed new methods for the effective delayed neutron fraction calculation with only one Monte Carlo computer simulation, compared with the k-ratio method which require two criticality calculations. In this paper, the Meulekamp/Marck and Nauchi/Kameyama methods are applied for the first time by the MCNPX computer code and the results obtained by all different methods are compared.
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.
Quasi-Monte Carlo methods for lattice systems: A first look
NASA Astrophysics Data System (ADS)
Jansen, K.; Leovey, H.; Ammon, A.; Griewank, A.; Müller-Preussker, M.
2014-03-01
We investigate the applicability of quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Markov chain Monte Carlo simulation behaves like N, where N is the number of observations. By means of quasi-Monte Carlo methods it is possible to improve this behavior for certain problems to N-1, or even further if the problems are regular enough. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling. Catalogue identifier: AERJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERJ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence version 3 No. of lines in distributed program, including test data, etc.: 67759 No. of bytes in distributed program, including test data, etc.: 2165365 Distribution format: tar.gz Programming language: C and C++. Computer: PC. Operating system: Tested on GNU/Linux, should be portable to other operating systems with minimal efforts. Has the code been vectorized or parallelized?: No RAM: The memory usage directly scales with the number of samples and dimensions: Bytes used = “number of samples” × “number of dimensions” × 8 Bytes (double precision). Classification: 4.13, 11.5, 23. External routines: FFTW 3 library (http://www.fftw.org) Nature of problem: Certain physical models formulated as a quantum field theory through the Feynman path integral, such as quantum chromodynamics, require a non-perturbative treatment of the path integral. The only known approach that achieves this is the lattice regularization. In this formulation the path integral is discretized to a finite, but very high dimensional integral. So far only Monte Carlo, and especially Markov chain-Monte Carlo methods like the Metropolis or the hybrid Monte Carlo algorithm have been used to calculate approximate solutions of the path integral. These algorithms often lead to the undesired effect of autocorrelation in the samples of observables and suffer in any case from the slow asymptotic error behavior proportional to N, if N is the number of samples. Solution method: This program applies the quasi-Monte Carlo approach and the reweighting technique (respectively the weighted uniform sampling method) to generate uncorrelated samples of observables of the anharmonic oscillator with an improved asymptotic error behavior. Unusual features: The application of the quasi-Monte Carlo approach is quite revolutionary in the field of lattice field theories. Running time: The running time depends directly on the number of samples N and dimensions d. On modern computers a run with up to N=216=65536 (including 9 replica runs) and d=100 should not take much longer than one minute.
A general method for spatially coarse-graining Metropolis Monte Carlo simulations onto a lattice
NASA Astrophysics Data System (ADS)
Liu, Xiao; Seider, Warren D.; Sinno, Talid
2013-03-01
A recently introduced method for coarse-graining standard continuous Metropolis Monte Carlo simulations of atomic or molecular fluids onto a rigid lattice of variable scale [X. Liu, W. D. Seider, and T. Sinno, Phys. Rev. E 86, 026708 (2012)], 10.1103/PhysRevE.86.026708 is further analyzed and extended. The coarse-grained Metropolis Monte Carlo technique is demonstrated to be highly consistent with the underlying full-resolution problem using a series of detailed comparisons, including vapor-liquid equilibrium phase envelopes and spatial density distributions for the Lennard-Jones argon and simple point charge water models. In addition, the principal computational bottleneck associated with computing a coarse-grained interaction function for evolving particle positions on the discretized domain is addressed by the introduction of new closure approximations. In particular, it is shown that the coarse-grained potential, which is generally a function of temperature and coarse-graining level, can be computed at multiple temperatures and scales using a single set of free energy calculations. The computational performance of the method relative to standard Monte Carlo simulation is also discussed.
Visual improvement for bad handwriting based on Monte-Carlo method
NASA Astrophysics Data System (ADS)
Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua
2014-03-01
A visual improvement algorithm based on Monte Carlo simulation is proposed in this paper, in order to enhance visual effects for bad handwriting. The whole improvement process is to use well designed typeface so as to optimize bad handwriting image. In this process, a series of linear operators for image transformation are defined for transforming typeface image to approach handwriting image. And specific parameters of linear operators are estimated by Monte Carlo method. Visual improvement experiments illustrate that the proposed algorithm can effectively enhance visual effect for handwriting image as well as maintain the original handwriting features, such as tilt, stroke order and drawing direction etc. The proposed visual improvement algorithm, in this paper, has a huge potential to be applied in tablet computer and Mobile Internet, in order to improve user experience on handwriting.
Beyond the Born-Oppenheimer approximation with quantum Monte Carlo methods
NASA Astrophysics Data System (ADS)
Tubman, Norm M.; Kylänpää, Ilkka; Hammes-Schiffer, Sharon; Ceperley, David M.
2014-10-01
In this work we develop tools that enable the study of nonadiabatic 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.
Hey, Jody; Nielsen, Rasmus
2007-01-01
In 1988, Felsenstein described a framework for assessing the likelihood of a genetic data set in which all of the possible genealogical histories of the data are considered, each in proportion to their probability. Although not analytically solvable, several approaches, including Markov chain Monte Carlo methods, have been developed to find approximate solutions. Here, we describe an approach in which Markov chain Monte Carlo simulations are used to integrate over the space of genealogies, whereas other parameters are integrated out analytically. The result is an approximation to the full joint posterior density of the model parameters. For many purposes, this function can be treated as a likelihood, thereby permitting likelihood-based analyses, including likelihood ratio tests of nested models. Several examples, including an application to the divergence of chimpanzee subspecies, are provided. PMID:17301231
Solution of the radiative transfer theory problems by the Monte Carlo method
NASA Technical Reports Server (NTRS)
Marchuk, G. I.; Mikhailov, G. A.
1974-01-01
The Monte Carlo method is used for two types of problems. First, there are interpretation problems of optical observations from meteorological satellites in the short wave part of the spectrum. The sphericity of the atmosphere, the propagation function, and light polarization are considered. Second, problems dealt with the theory of spreading narrow light beams. Direct simulation of light scattering and the mathematical form of medium radiation model representation are discussed, and general integral transfer equations are calculated. The dependent tests method, derivative estimates, and solution to the inverse problem are also considered.
NASA Astrophysics Data System (ADS)
Sharma, Anupam; Long, Lyle N.
2004-10-01
A particle approach using the Direct Simulation Monte Carlo (DSMC) method is used to solve the problem of blast impact with structures. A novel approach to model the solid boundary condition for particle methods is presented. The solver is validated against an analytical solution of the Riemann shocktube problem and against experiments on interaction of a planar shock with a square cavity. Blast impact simulations are performed for two model shapes, a box and an I-shaped beam, assuming that the solid body does not deform. The solver uses domain decomposition technique to run in parallel. The parallel performance of the solver on two Beowulf clusters is also presented.
Temperature-extrapolation method for Implicit Monte Carlo - Radiation hydrodynamics calculations
McClarren, R. G. [Department of Nuclear Engineering, Texas A and M University, 3133 TAMU, College Station, TX 77802 (United States); Urbatsch, T. J. [XTD-5: Air Force Systems, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 77845 (United States)
2013-07-01
We present a method for implementing temperature extrapolation in Implicit Monte Carlo solutions to radiation hydrodynamics problems. The method is based on a BDF-2 type integration to estimate a change in material temperature over a time step. We present results for radiation only problems in an infinite medium and for a 2-D Cartesian hohlraum problem. Additionally, radiation hydrodynamics simulations are presented for an RZ hohlraum problem and a related 3D problem. Our results indicate that improvements in noise and general behavior are possible. We present considerations for future investigations and implementations. (authors)
NASA Astrophysics Data System (ADS)
Hohenadler, Martin; von der Linden, Wolfgang
In this chapter, we shall mainly review different versions of a recently developed quantum Monte Carlo (QMC) method applicable to Holstein-type models with one, two or many electrons. The appealing advantages of QMC over other numerical methods include the accessibility of rather large systems, the exact treatment of bosonic degrees of freedom (i.e., no truncation is necessary), and the possibility to consider finite temperatures to study phase transitions. The important new aspect here is the use of canonically transformed Hamiltonians, which permits the introduction of exact sampling for the phonon degrees of freedom, enabling us to carry out accurate simulations in practically all interesting parameter regimes.
Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants
NASA Astrophysics Data System (ADS)
Zhang, Shiwei; Krakauer, Henry
2003-04-01
We develop a quantum Monte Carlo method for many fermions using random walks in the space of Slater determinants. An approximate approach is formulated with a trial wave function |?T> to control the phase problem. Using a plane-wave basis and nonlocal pseudopotentials, we apply the method to Be, Si, and P atoms and dimers, and to bulk Si supercells. Single-determinant wave functions from density functional theory calculations were used as |?T> with no additional optimization. The calculated binding energies of dimers and cohesive energy of bulk Si are in excellent agreement with experiments and are comparable to the best existing theoretical results.
Extrapolation method in the Monte Carlo Shell Model and its applications
Shimizu, Noritaka; Abe, Takashi [Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033 (Japan); Utsuno, Yutaka [Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195 (Japan); Mizusaki, Takahiro [Institute of Natural Sciences, Senshu University, Tokyo, 101-8425 (Japan); Otsuka, Takaharu [Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033 (Japan); Center for Nuclear Study, University of Tokyo, Hongo, Tokyo 113-0033 (Japan); National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan (United States); Honma, Michio [Center for Mathematical Sciences, Aizu University, Aizu-Wakamatsu, Fukushima 965-8580 (Japan)
2011-05-06
We demonstrate how the energy-variance extrapolation method works using the sequence of the approximated wave functions obtained by the Monte Carlo Shell Model (MCSM), taking {sup 56}Ni with pf-shell as an example. The extrapolation method is shown to work well even in the case that the MCSM shows slow convergence, such as {sup 72}Ge with f5pg9-shell. The structure of {sup 72}Se is also studied including the discussion of the shape-coexistence phenomenon.
Dynamical properties from quantum Monte Carlo by the Maximum Entropy Method
Silver, R.N.; Sivia, D.S.; Gubernatis, J.E.
1989-01-01
An outstanding problem in the simulation of condensed matter phenomena is how to obtain dynamical information. We consider the numerical analytic continuation of imaginary time Quantum Monte Carlo data to obtain real frequency spectral functions. We suggest an image reconstruction approach which has been widely applied to data analysis in experimental research, the Maximum Entropy Method (MaxEnt). We report encouraging preliminary results for the Fano-Anderson model of an impurity state in a continuum. The incorporation of additional prior information, such as sum rules and asymptotic behavior, can be expected to significantly improve results. We also compare MaxEnt to alternative methods. 17 refs., 4 figs.
A high order method for orbital conjunctions analysis: Monte Carlo collision probability computation
NASA Astrophysics Data System (ADS)
Morselli, Alessandro; Armellin, Roberto; Di Lizia, Pierluigi; Bernelli Zazzera, Franco
2015-01-01
Three methods for the computation of the probability of collision between two space objects are presented. These methods are based on the high order Taylor expansion of the time of closest approach (TCA) and distance of closest approach (DCA) of the two orbiting objects with respect to their initial conditions. The identification of close approaches is first addressed using the nominal objects states. When a close approach is identified, the dependence of the TCA and DCA on the uncertainties in the initial states is efficiently computed with differential algebra (DA) techniques. In the first method the collision probability is estimated via fast DA-based Monte Carlo simulation, in which, for each pair of virtual objects, the DCA is obtained via the fast evaluation of its Taylor expansion. The second and the third methods are the DA version of Line Sampling and Subset Simulation algorithms, respectively. These are introduced to further improve the efficiency and accuracy of Monte Carlo collision probability computation, in particular for cases of very low collision probabilities. The performances of the methods are assessed on orbital conjunctions occurring in different orbital regimes and dynamical models. The probabilities obtained and the associated computational times are compared against standard (i.e. not DA-based) version of the algorithms and analytical methods. The dependence of the collision probability on the initial orbital state covariance is investigated as well.
NASA Astrophysics Data System (ADS)
Jacoboni, Carlo; Reggiani, Lino
1983-07-01
This review presents in a comprehensive and tutorial form the basic principles of the Monte Carlo method, as applied to the solution of transport problems in semiconductors. Sufficient details of a typical Monte Carlo simulation have been given to allow the interested reader to create his own Monte Carlo program, and the method has been briefly compared with alternative theoretical techniques. Applications have been limited to the case of covalent semiconductors. Particular attention has been paid to the evaluation of the integrated scattering probabilities, for which final expressions are given in a form suitable for their direct use. A collection of results obtained with Monte Carlo simulations is presented, with the aim of showing the power of the method in obtaining physical insights into the processes under investigation. Special technical aspects of the method and updated microscopic models have been treated in some appendixes.
Cheng, Xiuzhen "Susan"
A Monte Carlo Method for Mobile Target Counting Dengyuan Wu, Xiuzhen Cheng, Dechang Chen, Wei Cheng, Biao Chen, Wei Zhao Department of Computer Science, The George Washington University, Washington, DC
A method based on Monte Carlo simulation for the determination of the G(E) function.
Chen, Wei; Feng, Tiancheng; Liu, Jun; Su, Chuanying; Tian, Yanjie
2015-02-01
The G(E) function method is a spectrometric method for the exposure dose estimation; this paper describes a method based on Monte Carlo method to determine the G(E) function of a 4? × 4? × 16? NaI(Tl) detector. Simulated spectrums of various monoenergetic gamma rays in the region of 40 -3200 keV and the corresponding deposited energy in an air ball in the energy region of full-energy peak were obtained using Monte Carlo N-particle Transport Code. Absorbed dose rate in air was obtained according to the deposited energy and divided by counts of corresponding full-energy peak to get the G(E) function value at energy E in spectra. Curve-fitting software 1st0pt was used to determine coefficients of the G(E) function. Experimental results show that the calculated dose rates using the G(E) function determined by the authors' method are accordant well with those values obtained by ionisation chamber, with a maximum deviation of 6.31 %. PMID:24795395
Phase-free quantum Monte Carlo method: random walks using general basis sets
NASA Astrophysics Data System (ADS)
Krakauer, Henry; Zhang, Shiwei
2003-08-01
Fermion quantum Monte Carlo (QMC) methods that work in a general basis space may be more effective for some problems than the traditional diffusion QMC method. Projection of the ground state energy is achieved by random walks in the space of Slater determinants whose one-particle orbitals are expressed in terms of the chosen basis set. A complication is that the determinants will in general acquire complex phases. This a consequence of ground state Monte Carlo projection using the Hubbard-Stratonovich transformation of the two-body interaction. To control the resulting "sign" decay, we describe a method we have recently introduced for the propagation of phaseless determinants. The approximation relies on importance sampling with a trial wave function. The approximation has features in common with diffusion MC fixed node and lattice-model constrained path methods. Using a planewave basis and non-local pseudopotentials, we apply the method to Si atom, dimer, and 2, 16, 54 atom (216 electrons) bulk supercells. Single Slater determinant wave functions from density functional theory calculations were used as |?T> with no additional optimization. The calculated binding energy of Si2 and cohesive energy of bulk Si are in excellent agreement with experiments and are comparable to the best existing theoretical results.
A new time quantifiable Monte Carlo method in simulating magnetization reversal process
X. Z. Cheng; M. B. A. Jalil; H. K. Lee; Y. Okabe
2005-04-14
We propose a new time quantifiable Monte Carlo (MC) method to simulate the thermally induced magnetization reversal for an isolated single domain particle system. The MC method involves the determination of density of states, and the use of Master equation for time evolution. We derive an analytical factor to convert MC steps into real time intervals. Unlike a previous time quantified MC method, our method is readily scalable to arbitrarily long time scales, and can be repeated for different temperatures with minimal computational effort. Based on the conversion factor, we are able to make a direct comparison between the results obtained from MC and Langevin dynamics methods, and find excellent agreement between them. An analytical formula for the magnetization reversal time is also derived, which agrees very well with both numerical Langevin and time-quantified MC results, over a large temperature range and for parallel and oblique easy axis orientations.
Michiel R. Hogerheijde; Floris F. S. van der Tak
2000-08-10
We present a numerical method and computer code to calculate the radiative transfer and excitation of molecular lines. Formulating the Monte Carlo method from the viewpoint of cells rather than photons allows us to separate local and external contributions to the radiation field. This separation is critical to accurate and fast performance at high optical depths (tau>100). The random nature of the Monte Carlo method serves to verify the independence of the solution to the angular, spatial, and frequency sampling of the radiation field. These features allow use of our method in a wide variety of astrophysical problems without specific adaptations: in any axially symmetric source model and for all atoms or molecules for which collisional rate coefficients are available. Continuum emission and absorption by dust is explicitly taken into account but scattering is neglected. We illustrate these features in calculations of (i) the HCO+ J=1-0 and 3-2 emission from a flattened protostellar envelope with infall and rotation, (ii) the CO, HCO+, CN and HCN emission from a protoplanetary disk and (iii) HCN emission from a high-mass young stellar object, where infrared pumping is important. The program can be used for optical depths up to 1000-10,000, depending on source model. We expect this program to be an important tool in analysing data from present and future infrared and (sub) millimetre telescopes.
Parsons, Tom
2008-01-01
Paleoearthquake observations often lack enough events at a given site to directly define a probability density function (PDF) for earthquake recurrence. Sites with fewer than 10-15 intervals do not provide enough information to reliably determine the shape of the PDF using standard maximum-likelihood techniques [e.g., Ellsworth et al., 1999]. In this paper I present a method that attempts to fit wide ranges of distribution parameters to short paleoseismic series. From repeated Monte Carlo draws, it becomes possible to quantitatively estimate most likely recurrence PDF parameters, and a ranked distribution of parameters is returned that can be used to assess uncertainties in hazard calculations. In tests on short synthetic earthquake series, the method gives results that cluster around the mean of the input distribution, whereas maximum likelihood methods return the sample means [e.g., NIST/SEMATECH, 2006]. For short series (fewer than 10 intervals), sample means tend to reflect the median of an asymmetric recurrence distribution, possibly leading to an overestimate of the hazard should they be used in probability calculations. Therefore a Monte Carlo approach may be useful for assessing recurrence from limited paleoearthquake records. Further, the degree of functional dependence among parameters like mean recurrence interval and coefficient of variation can be established. The method is described for use with time-independent and time-dependent PDF?s, and results from 19 paleoseismic sequences on strike-slip faults throughout the state of California are given.
Parsons, T.
2008-01-01
Paleoearthquake observations often lack enough events at a given site to directly define a probability density function (PDF) for earthquake recurrence. Sites with fewer than 10-15 intervals do not provide enough information to reliably determine the shape of the PDF using standard maximum-likelihood techniques (e.g., Ellsworth et al., 1999). In this paper I present a method that attempts to fit wide ranges of distribution parameters to short paleoseismic series. From repeated Monte Carlo draws, it becomes possible to quantitatively estimate most likely recurrence PDF parameters, and a ranked distribution of parameters is returned that can be used to assess uncertainties in hazard calculations. In tests on short synthetic earthquake series, the method gives results that cluster around the mean of the input distribution, whereas maximum likelihood methods return the sample means (e.g., NIST/SEMATECH, 2006). For short series (fewer than 10 intervals), sample means tend to reflect the median of an asymmetric recurrence distribution, possibly leading to an overestimate of the hazard should they be used in probability calculations. Therefore a Monte Carlo approach may be useful for assessing recurrence from limited paleoearthquake records. Further, the degree of functional dependence among parameters like mean recurrence interval and coefficient of variation can be established. The method is described for use with time-independent and time-dependent PDFs, and results from 19 paleoseismic sequences on strike-slip faults throughout the state of California are given.
Fast Monte Carlo Electron-Photon Transport Method and Application in Accurate Radiotherapy
NASA Astrophysics Data System (ADS)
Hao, Lijuan; Sun, Guangyao; Zheng, Huaqing; Song, Jing; Chen, Zhenping; Li, Gui
2014-06-01
Monte Carlo (MC) method is the most accurate computational method for dose calculation, but its wide application on clinical accurate radiotherapy is hindered due to its poor speed of converging and long computation time. In the MC dose calculation research, the main task is to speed up computation while high precision is maintained. The purpose of this paper is to enhance the calculation speed of MC method for electron-photon transport with high precision and ultimately to reduce the accurate radiotherapy dose calculation time based on normal computer to the level of several hours, which meets the requirement of clinical dose verification. Based on the existing Super Monte Carlo Simulation Program (SuperMC), developed by FDS Team, a fast MC method for electron-photon coupled transport was presented with focus on two aspects: firstly, through simplifying and optimizing the physical model of the electron-photon transport, the calculation speed was increased with slightly reduction of calculation accuracy; secondly, using a variety of MC calculation acceleration methods, for example, taking use of obtained information in previous calculations to avoid repeat simulation of particles with identical history; applying proper variance reduction techniques to accelerate MC method convergence rate, etc. The fast MC method was tested by a lot of simple physical models and clinical cases included nasopharyngeal carcinoma, peripheral lung tumor, cervical carcinoma, etc. The result shows that the fast MC method for electron-photon transport was fast enough to meet the requirement of clinical accurate radiotherapy dose verification. Later, the method will be applied to the Accurate/Advanced Radiation Therapy System ARTS as a MC dose verification module.
Kinetic Monte Carlo Method for Rule-based Modeling of Biochemical Networks
Yang, Jin; Monine, Michael I.; Faeder, James R.; Hlavacek, William S.
2009-01-01
We present a kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes. A rule identifies the molecular components involved in a transformation, how these components change, conditions that affect whether a transformation occurs, and a rate law. The computational cost of the method, unlike conventional simulation approaches, is independent of the number of possible reactions, which need not be specified in advance or explicitly generated in a simulation. To demonstrate the method, we apply it to study the kinetics of multivalent ligand-receptor interactions. We expect the method will be useful for studying cellular signaling systems and other physical systems involving aggregation phenomena. PMID:18851068
Y. Alhassid; M. Bonett-Matiz; S. Liu; A. Mukherjee; H. Nakada
2014-01-01
The shell model Monte Carlo (SMMC) method enables calculations in model spaces that are many orders of magnitude larger than those that can be treated by conventional methods, and is particularly suitable for the calculation of level densities in the presence of correlations. We review recent advances and applications of SMMC for the microscopic calculation of level densities. Recent developments include (i) a method to calculate accurately the ground-state energy of an odd-mass nucleus, circumventing a sign problem that originates in the projection on an odd number of particles, and (ii) a method to calculate directly level densities, which, unlike state densities, do not include the spin degeneracy of the levels. We calculated the level densities of a family of nickel isotopes $^{59-64}$Ni and of a heavy deformed rare-earth nucleus $^{162}$Dy and found them to be in close agreement with various experimental data sets.
Hunter, J. L. [Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., 24-107, Cambridge, MA 02139 (United States); Sutton, T. M. [Knolls Atomic Power Laboratory, Bechtel Marine Propulsion Corporation, P. O. Box 1072, Schenectady, NY 12301-1072 (United States)
2013-07-01
In Monte Carlo iterated-fission-source calculations relative uncertainties on local tallies tend to be larger in lower-power regions and smaller in higher-power regions. Reducing the largest uncertainties to an acceptable level simply by running a larger number of neutron histories is often prohibitively expensive. The uniform fission site method has been developed to yield a more spatially-uniform distribution of relative uncertainties. This is accomplished by biasing the density of fission neutron source sites while not biasing the solution. The method is integrated into the source iteration process, and does not require any auxiliary forward or adjoint calculations. For a given amount of computational effort, the use of the method results in a reduction of the largest uncertainties relative to the standard algorithm. Two variants of the method have been implemented and tested. Both have been shown to be effective. (authors)
A steady-state convergence detection method for Monte Carlo simulation
NASA Astrophysics Data System (ADS)
Karchani, Abolfazl; Ejtehadi, Omid; Myong, Rho Shin
2014-12-01
In the direct simulation Monte Carlo (DSMC), exclusion of microscopic data sampled in the unsteady phase can accelerate the convergence and lead to more accurate results in the steady state problem. In this study, a new method for detection of the steady state onset, called Probabilistic Automatic Reset Sampling (PARS), is introduced. The new method can detect the steady state automatically and reset sample after satisfying the reset criteria based on statistics. The method is simple and does not need any user-specified inputs. The simulation results show that the proposed strategy can work well even in condition with constant number of particles inside the domain which was the main drawback of the previous methods.
A Monte Carlo method for chemical potential determination in single and multiple occupancy crystals
Nigel B. Wilding; Peter Sollich
2012-09-14
We describe a Monte Carlo scheme which, in a single simulation, yields a measurement of the chemical potential of a crystalline solid. Within the isobaric ensemble, this immediately provides an estimate of the system free energy, with statistical uncertainties that are determined precisely and transparently. An extension to multiple occupancy ("cluster") solids permits the direct determination of the cluster chemical potential and hence the equilibrium conditions. We apply the method to a model exhibiting cluster crystalline phases, where we find evidence for an infinite cascade of critical points terminating coexistence between crystals of differing site occupancies.
Application of the direct simulation Monte Carlo method to the full shuttle geometry
NASA Technical Reports Server (NTRS)
Bird, G. A.
1990-01-01
A new set of programs has been developed for the application of the direct simulation Monte Carlo (or DSMC) method to rarefied gas flows with complex three-dimensional boundaries. The programs are efficient in terms of the computational load and also in terms of the effort required to set up particular cases. This efficiency is illustrated through computations of the flow about the Shuttle Orbiter. The general flow features are illustrated for altitudes from 170 to 100 km. Also, the computed lift-drag ratio during re-entry is compared with flight measurements.
Three-dimensional hypersonic rarefied flow calculations using direct simulation Monte Carlo method
NASA Technical Reports Server (NTRS)
Celenligil, M. Cevdet; Moss, James N.
1993-01-01
A summary of three-dimensional simulations on the hypersonic rarefied flows in an effort to understand the highly nonequilibrium flows about space vehicles entering the Earth's atmosphere for a realistic estimation of the aerothermal loads is presented. Calculations are performed using the direct simulation Monte Carlo method with a five-species reacting gas model, which accounts for rotational and vibrational internal energies. Results are obtained for the external flows about various bodies in the transitional flow regime. For the cases considered, convective heating, flowfield structure and overall aerodynamic coefficients are presented and comparisons are made with the available experimental data. The agreement between the calculated and measured results are very good.
A numerical study of rays in random media. [Monte Carlo method simulation
NASA Technical Reports Server (NTRS)
Youakim, M. Y.; Liu, C. H.; Yeh, K. C.
1973-01-01
Statistics of electromagnetic rays in a random medium are studied numerically by the Monte Carlo method. Two dimensional random surfaces with prescribed correlation functions are used to simulate the random media. Rays are then traced in these sample media. Statistics of the ray properties such as the ray positions and directions are computed. Histograms showing the distributions of the ray positions and directions at different points along the ray path as well as at given points in space are given. The numerical experiment is repeated for different cases corresponding to weakly and strongly random media with isotropic and anisotropic irregularities. Results are compared with those derived from theoretical investigations whenever possible.
CCMR: Method Development of Dynamic Mass Diffusion Monte Carlo using Lennard-Jones Clusters
NSDL National Science Digital Library
Craig, Helen A.
2007-08-29
The Lennard-Jones clusters, clusters of inert particles have a long history of being studied. Many algorithms have been proposed and used with a varying level of success from "basin hopping" [1] to “greedy search” [2]. Despite these achievements, the Lennard-Jones potential continues to be a widely studied model. Not only is it a good test case for new particle structure algorithms, but it is still an interesting model that we can yet learn from. In this project we proposed to study these cluster using a method never before attempted: dynamic mass diffusion Monte Carlo.
Refinement of overlapping local/global iteration method based on Monte Carlo/p-CMFD calculations
Jo, Y.; Yun, S.; Cho, N. Z. [Korea Advanced Institute of Science and Technology - KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701 (Korea, Republic of)
2013-07-01
In this paper, the overlapping local/global (OLG) iteration method based on Monte Carlo/p-CMFD calculations is refined in two aspects. One is the consistent use of estimators to generate homogenized scattering cross sections. Another is that the incident or exiting angular interval is divided into multi-angular bins to modulate albedo boundary conditions for local problems. Numerical tests show that, compared to the one angle bin case in a previous study, the four angle bin case shows significantly improved results. (authors)
A Bayesian Monte Carlo Markov Chain Method for the Analysis of GPS Position Time Series
NASA Astrophysics Data System (ADS)
Olivares, German; Teferle, Norman
2013-04-01
Position time series from continuous GPS are an essential tool in many areas of the geosciences and are, for example, used to quantify long-term movements due to processes such as plate tectonics or glacial isostatic adjustment. It is now widely established that the stochastic properties of the time series do not follow a random behavior and this affects parameter estimates and associated uncertainties. Consequently, a comprehensive knowledge of the stochastic character of the position time series is crucial in order to obtain realistic error bounds and for this a number of methods have already been applied successfully. We present a new Bayesian Monte Carlo Markov Chain (MCMC) method to simultaneously estimate the model and the stochastic parameters of the noise in GPS position time series. This method provides a sample of the likelihood function and thereby, using Monte Carlo integration, all parameters and their uncertainties are estimated simultaneously. One advantage of the MCMC method is that the computational time increases linearly with the number of parameters, hence being very suitable for dealing with a high number of parameters. A second advantage is that the properties of the estimator used in this method do not depend on the stationarity of the time series. At least on a theoretical level, no other estimator has been shown to have this feature. Furthermore, the MCMC method provides a means to detect multi-modality of the parameter estimates. We present an evaluation of the new MCMC method through comparison with widely used optimization and empirical methods for the analysis of GPS position time series.
Configuration-interaction Monte Carlo method and its application to the trapped unitary Fermi gas
Abhishek Mukherjee; Y. Alhassid
2013-04-05
We develop a quantum Monte Carlo method to estimate the ground-state energy of a fermionic many-particle system in the configuration-interaction shell model approach. The fermionic sign problem is circumvented by using a guiding wave function in Fock space. The method provides an upper bound on the ground-state energy whose tightness depends on the choice of the guiding wave function. We argue that the antisymmetric geminal product class of wave functions is a good choice for guiding wave functions. We demonstrate our method for the trapped two-species fermionic cold atom system in the unitary regime of infinite scattering length using the particle-number projected Hartree-Fock-Bogoliubov wave function as the guiding wave function. We estimate the ground-state energy and energy-staggering pairing gap as a function of the number of particles. Our results compare favorably with exact numerical diagonalization results and with previous coordinate-space Monte Carlo calculations.
A new Monte Carlo method for dynamical evolution of non-spherical stellar systems
Vasiliev, Eugene
2014-01-01
We have developed a novel Monte Carlo method for simulating the dynamical evolution of stellar systems in arbitrary geometry. The orbits of stars are followed in a smooth potential represented by a basis-set expansion and perturbed after each timestep using local velocity diffusion coefficients from the standard two-body relaxation theory. The potential and diffusion coefficients are updated after an interval of time that is a small fraction of the relaxation time, but may be longer than the dynamical time. Thus our approach is a bridge between the Spitzer's formulation of the Monte Carlo method and the temporally smoothed self-consistent field method. The primary advantages are the ability to follow the secular evolution of shape of the stellar system, and the possibility of scaling the amount of two-body relaxation to the necessary value, unrelated to the actual number of particles in the simulation. Possible future applications of this approach in galaxy dynamics include the problem of consumption of stars...
A new Monte Carlo method for dynamical evolution of non-spherical stellar systems
NASA Astrophysics Data System (ADS)
Vasiliev, Eugene
2015-01-01
We have developed a novel Monte Carlo method for simulating the dynamical evolution of stellar systems in arbitrary geometry. The orbits of stars are followed in a smooth potential represented by a basis-set expansion and perturbed after each timestep using local velocity diffusion coefficients from the standard two-body relaxation theory. The potential and diffusion coefficients are updated after an interval of time that is a small fraction of the relaxation time, but may be longer than the dynamical time. Thus, our approach is a bridge between the Spitzer's formulation of the Monte Carlo method and the temporally smoothed self-consistent field method. The primary advantages are the ability to follow the secular evolution of shape of the stellar system, and the possibility of scaling the amount of two-body relaxation to the necessary value, unrelated to the actual number of particles in the simulation. Possible future applications of this approach in galaxy dynamics include the problem of consumption of stars by a massive black hole in a non-spherical galactic nucleus, evolution of binary supermassive black holes, and the influence of chaos on the shape of galaxies, while for globular clusters it may be used for studying the influence of rotation.
Configuration-interaction Monte Carlo method and its application to the trapped unitary Fermi gas
NASA Astrophysics Data System (ADS)
Mukherjee, Abhishek; Alhassid, Y.
2013-11-01
We develop a quantum Monte Carlo method to estimate the ground-state energy of a fermionic many-particle system in the configuration-interaction shell model approach. The fermionic sign problem is circumvented by using a guiding wave function in Fock space. The method provides an upper bound on the ground-state energy whose tightness depends on the choice of the guiding wave function. We argue that the antisymmetric geminal product class of wave functions is a good choice for guiding wave functions. We demonstrate our method for the trapped two-species fermionic cold atom system in the unitary regime of infinite scattering length using the particle-number projected Hartree-Fock-Bogoliubov wave function as the guiding wave function. We estimate the ground-state energy and energy-staggering pairing gap as a function of the number of particles. We compare our results with exact numerical diagonalization results and with previous fixed-node coordinate-space Monte Carlo calculations.
Self-optimizing Monte Carlo method for nuclear well logging simulation
NASA Astrophysics Data System (ADS)
Liu, Lianyan
1997-09-01
In order to increase the efficiency of Monte Carlo simulation for nuclear well logging problems, a new method has been developed for variance reduction. With this method, an importance map is generated in the regular Monte Carlo calculation as a by-product, and the importance map is later used to conduct the splitting and Russian roulette for particle population control. By adopting a spatial mesh system, which is independent of physical geometrical configuration, the method allows superior user-friendliness. This new method is incorporated into the general purpose Monte Carlo code MCNP4A through a patch file. Two nuclear well logging problems, a neutron porosity tool and a gamma-ray lithology density tool are used to test the performance of this new method. The calculations are sped up over analog simulation by 120 and 2600 times, for the neutron porosity tool and for the gamma-ray lithology density log, respectively. The new method enjoys better performance by a factor of 4~6 times than that of MCNP's cell-based weight window, as per the converged figure-of-merits. An indirect comparison indicates that the new method also outperforms the AVATAR process for gamma-ray density tool problems. Even though it takes quite some time to generate a reasonable importance map from an analog run, a good initial map can create significant CPU time savings. This makes the method especially suitable for nuclear well logging problems, since one or several reference importance maps are usually available for a given tool. Study shows that the spatial mesh sizes should be chosen according to the mean-free-path. The overhead of the importance map generator is 6% and 14% for neutron and gamma-ray cases. The learning ability towards a correct importance map is also demonstrated. Although false-learning may happen, physical judgement can help diagnose with contributon maps. Calibration and analysis are performed for the neutron tool and the gamma-ray tool. Due to the fact that a very good initial importance map is always available after the first point has been calculated, high computing efficiency is maintained. The availability of contributon maps provides an easy way of understanding the logging measurement and analyzing for the depth of investigation.
The applicability of certain Monte Carlo methods to the analysis of interacting polymers
Krapp, D.M. Jr. [Univ. of California, Berkeley, CA (United States)
1998-05-01
The authors consider polymers, modeled as self-avoiding walks with interactions on a hexagonal lattice, and examine the applicability of certain Monte Carlo methods for estimating their mean properties at equilibrium. Specifically, the authors use the pivoting algorithm of Madras and Sokal and Metroplis rejection to locate the phase transition, which is known to occur at {beta}{sub crit} {approx} 0.99, and to recalculate the known value of the critical exponent {nu} {approx} 0.58 of the system for {beta} = {beta}{sub crit}. Although the pivoting-Metropolis algorithm works well for short walks (N < 300), for larger N the Metropolis criterion combined with the self-avoidance constraint lead to an unacceptably small acceptance fraction. In addition, the algorithm becomes effectively non-ergodic, getting trapped in valleys whose centers are local energy minima in phase space, leading to convergence towards different values of {nu}. The authors use a variety of tools, e.g. entropy estimation and histograms, to improve the results for large N, but they are only of limited effectiveness. Their estimate of {beta}{sub crit} using smaller values of N is 1.01 {+-} 0.01, and the estimate for {nu} at this value of {beta} is 0.59 {+-} 0.005. They conclude that even a seemingly simple system and a Monte Carlo algorithm which satisfies, in principle, ergodicity and detailed balance conditions, can in practice fail to sample phase space accurately and thus not allow accurate estimations of thermal averages. This should serve as a warning to people who use Monte Carlo methods in complicated polymer folding calculations. The structure of the phase space combined with the algorithm itself can lead to surprising behavior, and simply increasing the number of samples in the calculation does not necessarily lead to more accurate results.
Finite-Temperature Constrained Path Monte Carlo Method for Fermion Systems
NASA Astrophysics Data System (ADS)
Zhang, Shiwei
1998-03-01
We present a new quantum Monte Carlo method to study finite-temperature properties of many-fermion systems. The method relies on the usual field-theory formalism(R. Blankenbecler, D. J. Scalapino, and R. L. Sugar, Phys. Rev. D 24), 2278 (1981). with Hubbard-Stratonovich (HS) transformation. It enables simulations of the grand canonical ensemble. An approach is formulated to constrain paths in the auxiliary HS field space according to a trial imaginary-time propagator. This approximation removes the exponential decay of signal-to-noise ratio (or ``sign'') characteristic of the fermion sign problem. Similar to its ground-state counterpart(Shiwei Zhang, J. Carlson, and J. E. Gubernatis, Phys. Rev. Lett. 74), 3652 (1995); Phys. Rev. B, 55, 7464 (1997)., the method can yield accurate results with simple choices of the trial propagator and becomes exact if the latter is exact. We show illustrative results for the two-dimensional Hubbard model.
Auxiliary-field quantum Monte Carlo method for strongly paired fermions
Carlson, J.; Gandolfi, Stefano [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Schmidt, Kevin E. [Department of Physics, Arizona State University, Tempe, Arizona 85287 (United States); Zhang, Shiwei [Department of Physics, College of William and Mary, Williamsburg, Virginia 23187 (United States)
2011-12-15
We solve the zero-temperature unitary Fermi gas problem by incorporating a BCS importance function into the auxiliary-field quantum Monte Carlo method. We demonstrate that this method does not suffer from a sign problem and that it increases the efficiency of standard techniques by many orders of magnitude for strongly paired fermions. We calculate the ground-state energies exactly for unpolarized systems with up to 66 particles on lattices of up to 27{sup 3} sites, obtaining an accurate result for the universal parameter {xi}. We also obtain results for interactions with different effective ranges and find that the energy is consistent with a universal linear dependence on the product of the Fermi momentum and the effective range. This method will have many applications in superfluid cold atom systems and in both electronic and nuclear structures where pairing is important.
Investigation of a New Monte Carlo Method for the Transitional Gas Flow
Luo, X.; Day, Chr. [Karlsruhe Institute of Technology(KIT), Institute for Technical Physics, 76021, Karlsruhe (Germany)
2011-05-20
The Direct Simulation Monte Carlo method (DSMC) is well developed for rarefied gas flow in transition flow regime when 0.01
Monte Carlo Monte Carlo at Work by Gary D. Doolen and John Hendricks E very second nearly 10,000,000,000 "random" numbers are being generated on computers around the world for Monte Carlo solutions to problems hundreds of full-time careers invested in the fine art of generating Monte Carlo solutions--a livelihood
Kinetics of electron-positron pair plasmas using an adaptive Monte Carlo method
Ravi P. Pilla; Jacob Shaham
1997-02-21
A new algorithm for implementing the adaptive Monte Carlo method is given. It is used to solve the relativistic Boltzmann equations that describe the time evolution of a nonequilibrium electron-positron pair plasma containing high-energy photons and pairs. The collision kernels for the photons as well as pairs are constructed for Compton scattering, pair annihilation and creation, bremsstrahlung, and Bhabha & Moller scattering. For a homogeneous and isotropic plasma, analytical equilibrium solutions are obtained in terms of the initial conditions. For two non-equilibrium models, the time evolution of the photon and pair spectra is determined using the new method. The asymptotic numerical solutions are found to be in a good agreement with the analytical equilibrium states. Astrophysical applications of this scheme are discussed.
Analysis of vibrational-translational energy transfer using the direct simulation Monte Carlo method
NASA Technical Reports Server (NTRS)
Boyd, Iain D.
1991-01-01
A new model is proposed for energy transfer between the vibrational and translational modes for use in the direct simulation Monte Carlo method (DSMC). The model modifies the Landau-Teller theory for a harmonic oscillator and the rate transition is related to an experimental correlation for the vibrational relaxation time. Assessment of the model is made with respect to three different computations: relaxation in a heat bath, a one-dimensional shock wave, and hypersonic flow over a two-dimensional wedge. These studies verify that the model achieves detailed balance, and excellent agreement with experimental data is obtained in the shock wave calculation. The wedge flow computation reveals that the usual phenomenological method for simulating vibrational nonequilibrium in the DSMC technique predicts much higher vibrational temperatures in the wake region.
DSMC calculations for the double ellipse. [direct simulation Monte Carlo method
NASA Technical Reports Server (NTRS)
Moss, James N.; Price, Joseph M.; Celenligil, M. Cevdet
1990-01-01
The direct simulation Monte Carlo (DSMC) method involves the simultaneous computation of the trajectories of thousands of simulated molecules in simulated physical space. Rarefied flow about the double ellipse for test case 6.4.1 has been calculated with the DSMC method of Bird. The gas is assumed to be nonreacting nitrogen flowing at a 30 degree incidence with respect to the body axis, and for the surface boundary conditions, the wall is assumed to be diffuse with full thermal accommodation and at a constant wall temperature of 620 K. A parametric study is presented that considers the effect of variations of computational domain, gas model, cell size, and freestream density on surface quantities.
Monte Carlo method for polarized radiative transfer in gradient-index media
Zhao, J M; Liu, L H
2014-01-01
Light transfer in gradient-index media generally follows curved ray trajectories, which will cause light beam to converge or diverge during transfer and induce the rotation of polarization ellipse even when the medium is transparent. Furthermore, the combined process of scattering and transfer along curved ray path makes the problem more complex. In this paper, a Monte Carlo method is presented to simulate polarized radiative transfer in gradient-index media that only support planar ray trajectories. The ray equation is solved to the second order to address the effect induced by curved ray trajectories. Three types of test cases are presented to verify the performance of the method, which include transparent medium, Mie scattering medium with assumed gradient index distribution, and Rayleigh scattering with realistic atmosphere refractive index profile. It is demonstrated that the atmospheric refraction has significant effect for long distance polarized light transfer.
Umadevi, V; Suresh, S; Raghavan, S V
2009-01-01
Breast thermography is one of the scanning techniques used for breast cancer detection. Looking at breast thermal image it is difficult to interpret parameters or tumor such as depth, size and location which are useful for diagnosis and treatment of breast cancer. In our previous work (ITBIC) we proposed a framework for estimation of tumor size using clever algorithms and the radiative heat transfer model. In this paper, we expand it to incorporate the more realistic Pennes bio-heat transfer model and Markov Chain Monte Carlo (MCMC) method, and analyze it's performance in terms of computational speed, accuracy, robustness against noisy inputs, ability to make use of prior information and ability to estimate multiple parameters simultaneously. We discuss the influence of various parameters used in its implementation. We apply this method on clinical data and extract reliable results for the first time using breast thermography. PMID:20198744
The Linked Neighbour List (LNL) method for fast off-lattice Monte Carlo simulations of fluids
NASA Astrophysics Data System (ADS)
Mazzeo, M. D.; Ricci, M.; Zannoni, C.
2010-03-01
We present a new algorithm, called linked neighbour list (LNL), useful to substantially speed up off-lattice Monte Carlo simulations of fluids by avoiding the computation of the molecular energy before every attempted move. We introduce a few variants of the LNL method targeted to minimise memory footprint or augment memory coherence and cache utilisation. Additionally, we present a few algorithms which drastically accelerate neighbour finding. We test our methods on the simulation of a dense off-lattice Gay-Berne fluid subjected to periodic boundary conditions observing a speedup factor of about 2.5 with respect to a well-coded implementation based on a conventional link-cell. We provide several implementation details of the different key data structures and algorithms used in this work.
Electron-Phonon Scattering in Planar MOSFETs: NEGF and Monte Carlo Methods
Himadri S. Pal; Dmitri E. Nikonov; Raseong Kim; Mark S. Lundstrom
2012-09-21
A formalism for incorporating electron-phonon scattering into the nonequilibrium Green's function (NEGF) framework that is applicable to planar MOSFETs is presented. Restructuring the NEGF equations in terms of approximate summation of transverse momentum modes leads to a rigorous and efficient method of solution. This helps to drastically reduce the computational complexity, allowing treatment of both quantum mechanics and dissipative electron-phonon scattering processes for device sizes from nanometers to microns. The formalism is systematically benchmarked against Monte Carlo solutions of the classical Boltzmann transport for model potential profiles. Results show a remarkably close agreement between the two methods for variety of channel lengths and bias conditions, both for elastic and inelastic scattering processes.
Hybrid Monte Carlo/Deterministic Methods for Accelerating Active Interrogation Modeling
Peplow, Douglas E. [ORNL; Miller, Thomas Martin [ORNL; Patton, Bruce W [ORNL; Wagner, John C [ORNL
2013-01-01
The potential for smuggling special nuclear material (SNM) into the United States is a major concern to homeland security, so federal agencies are investigating a variety of preventive measures, including detection and interdiction of SNM during transport. One approach for SNM detection, called active interrogation, uses a radiation source, such as a beam of neutrons or photons, to scan cargo containers and detect the products of induced fissions. In realistic cargo transport scenarios, the process of inducing and detecting fissions in SNM is difficult due to the presence of various and potentially thick materials between the radiation source and the SNM, and the practical limitations on radiation source strength and detection capabilities. Therefore, computer simulations are being used, along with experimental measurements, in efforts to design effective active interrogation detection systems. The computer simulations mostly consist of simulating radiation transport from the source to the detector region(s). Although the Monte Carlo method is predominantly used for these simulations, difficulties persist related to calculating statistically meaningful detector responses in practical computing times, thereby limiting their usefulness for design and evaluation of practical active interrogation systems. In previous work, the benefits of hybrid methods that use the results of approximate deterministic transport calculations to accelerate high-fidelity Monte Carlo simulations have been demonstrated for source-detector type problems. In this work, the hybrid methods are applied and evaluated for three example active interrogation problems. Additionally, a new approach is presented that uses multiple goal-based importance functions depending on a particle s relevance to the ultimate goal of the simulation. Results from the examples demonstrate that the application of hybrid methods to active interrogation problems dramatically increases their calculational efficiency.
Rational Monte Carlo method for flood frequency analysis in urban catchments
NASA Astrophysics Data System (ADS)
Brodie, Ian M.
2013-04-01
SummaryThe January 2011 flash flood at Toowoomba, Australia was substantially larger than other high ranking observed floods. Flood frequency analysis (FFA) is often performed with limited hydrological data so the occurrence of an exceptional flood provides valuable data. Peak 1 h rainfall intensities during the storm varied from <10 to >1000 year ARI across the catchment. Average recurrence interval (ARI) estimates of the resulting streamflow peak discharge were 220 year ARI for a General Extreme Value distribution fitted to the Annual Series and 450 year ARI based on a log-Pearson 3 distribution. An independent method referred to as the Rational Monte Carlo method (RMC) was developed in order to provide an independent check of the ARI estimate. The RMC method is a simple derived distribution approach where the Rational equation links observed rainfall intensity at a reference pluviograph to the peak flood discharge. The RMC 2011 flood ARI estimate was 475-515 years, comparable with the log-Pearson 3 method. Although the proposed method has limitations, the RMC approach shows promise as an alternative and independent FFA method for urban catchments. For all methods, the ARI estimates were sensitive to whether the January 2011 peak discharge was included in the analysis. Overall, the study highlights the inherent difficulty in extrapolating ARI estimates beyond the range of the available historical record.
Applications of the Monte Carlo method in nuclear physics using the GEANT4 toolkit
NASA Astrophysics Data System (ADS)
Moralles, Maurício; Guimarães, Carla C.; Bonifácio, Daniel A. B.; Okuno, Emico; Murata, Hélio M.; Bottaro, Márcio; Menezes, Mário O.; Guimarães, Valdir
2009-06-01
The capabilities of the personal computers allow the application of Monte Carlo methods to simulate very complex problems that involve the transport of particles through matter. Among the several codes commonly employed in nuclear physics problems, the GEANT4 has received great attention in the last years, mainly due to its flexibility and possibility to be improved by the users. Differently from other Monte Carlo codes, GEANT4 is a toolkit written in object oriented language (C++) that includes the mathematical engine of several physical processes, which are suitable to be employed in the transport of practically all types of particles and heavy ions. GEANT4 has also several tools to define materials, geometry, sources of radiation, beams of particles, electromagnetic fields, and graphical visualization of the experimental setup. After a brief description of the GEANT4 toolkit, this presentation reports investigations carried out by our group that involve simulations in the areas of dosimetry, nuclear instrumentation and medical physics. The physical processes available for photons, electrons, positrons and heavy ions were used in these simulations.
Bianchini, G.; Burgio, N.; Carta, M. [ENEA C.R. CASACCIA, via Anguillarese, 301, 00123 S. Maria di Galeria Roma (Italy); Peluso, V. [ENEA C.R. BOLOGNA, Via Martiri di Monte Sole, 4, 40129 Bologna (Italy); Fabrizio, V.; Ricci, L. [Univ. of Rome La Sapienza, C/o ENEA C.R. CASACCIA, via Anguillarese, 301, 00123 S. Maria di Galeria Roma (Italy)
2012-07-01
The GUINEVERE experiment (Generation of Uninterrupted Intense Neutrons at the lead Venus Reactor) is an experimental program in support of the ADS technology presently carried out at SCK-CEN in Mol (Belgium). In the experiment a modified lay-out of the original thermal VENUS critical facility is coupled to an accelerator, built by the French body CNRS in Grenoble, working in both continuous and pulsed mode and delivering 14 MeV neutrons by bombardment of deuterons on a tritium-target. The modified lay-out of the facility consists of a fast subcritical core made of 30% U-235 enriched metallic Uranium in a lead matrix. Several off-line and on-line reactivity measurement techniques will be investigated during the experimental campaign. This report is focused on the simulation by deterministic (ERANOS French code) and Monte Carlo (MCNPX US code) calculations of three reactivity measurement techniques, Slope ({alpha}-fitting), Area-ratio and Source-jerk, applied to a GUINEVERE subcritical configuration (namely SC1). The inferred reactivity, in dollar units, by the Area-ratio method shows an overall agreement between the two deterministic and Monte Carlo computational approaches, whereas the MCNPX Source-jerk results are affected by large uncertainties and allow only partial conclusions about the comparison. Finally, no particular spatial dependence of the results is observed in the case of the GUINEVERE SC1 subcritical configuration. (authors)
Monte Carlo Method for a Quantum Measurement Process by a Single-Electron Transistor
Hsi-Sheng Goan
2004-06-15
We derive the quantum trajectory or stochastic (conditional) master equation for a single superconducting Cooper-pair box (SCB) charge qubit measured by a single-electron transistor (SET) detector. This stochastic master equation describes the random evolution of the measured SCB qubit density matrix which both conditions and is conditioned on a particular realization of the measured electron tunneling events through the SET junctions. Hence it can be regarded as a Monte Carlo method that allows us to simulate the continuous quantum measurement process. We show that the master equation for the "partially" reduced density matrix [Y. Makhlin et.al., Phys. Rev. Lett. 85, 4578 (2000)] can be obtained when a "partial" average is taken on the stochastic master equation over the fine grained measurement records of the tunneling events in the SET. Finally, we present some Monte Carlo simulation results for the SCB/SET measurement process. We also analyze the probability distribution P(m,t) of finding m electrons that have tunneled into the drain of the SET in time t to demonstrate the connection between the quantum trajectory approach and the "partially" reduced density matrix approach.
Radiation Transport for Explosive Outflows: A Multigroup Hybrid Monte Carlo Method
NASA Astrophysics Data System (ADS)
Wollaeger, Ryan T.; van Rossum, Daniel R.; Graziani, Carlo; Couch, Sean M.; Jordan, George C., IV; Lamb, Donald Q.; Moses, Gregory A.
2013-12-01
We explore Implicit Monte Carlo (IMC) and discrete diffusion Monte Carlo (DDMC) for radiation transport in high-velocity outflows with structured opacity. The IMC method is a stochastic computational technique for nonlinear radiation transport. IMC is partially implicit in time and may suffer in efficiency when tracking MC particles through optically thick materials. DDMC accelerates IMC in diffusive domains. Abdikamalov extended IMC and DDMC to multigroup, velocity-dependent transport with the intent of modeling neutrino dynamics in core-collapse supernovae. Densmore has also formulated a multifrequency extension to the originally gray DDMC method. We rigorously formulate IMC and DDMC over a high-velocity Lagrangian grid for possible application to photon transport in the post-explosion phase of Type Ia supernovae. This formulation includes an analysis that yields an additional factor in the standard IMC-to-DDMC spatial interface condition. To our knowledge the new boundary condition is distinct from others presented in prior DDMC literature. The method is suitable for a variety of opacity distributions and may be applied to semi-relativistic radiation transport in simple fluids and geometries. Additionally, we test the code, called SuperNu, using an analytic solution having static material, as well as with a manufactured solution for moving material with structured opacities. Finally, we demonstrate with a simple source and 10 group logarithmic wavelength grid that IMC-DDMC performs better than pure IMC in terms of accuracy and speed when there are large disparities between the magnitudes of opacities in adjacent groups. We also present and test our implementation of the new boundary condition.
A modular method to handle multiple time-dependent quantities in Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Shin, J.; Perl, J.; Schümann, J.; Paganetti, H.; Faddegon, B. A.
2012-06-01
A general method for handling time-dependent quantities in Monte Carlo simulations was developed to make such simulations more accessible to the medical community for a wide range of applications in radiotherapy, including fluence and dose calculation. To describe time-dependent changes in the most general way, we developed a grammar of functions that we call ‘Time Features’. When a simulation quantity, such as the position of a geometrical object, an angle, a magnetic field, a current, etc, takes its value from a Time Feature, that quantity varies over time. The operation of time-dependent simulation was separated into distinct parts: the Sequence samples time values either sequentially at equal increments or randomly from a uniform distribution (allowing quantities to vary continuously in time), and then each time-dependent quantity is calculated according to its Time Feature. Due to this modular structure, time-dependent simulations, even in the presence of multiple time-dependent quantities, can be efficiently performed in a single simulation with any given time resolution. This approach has been implemented in TOPAS (TOol for PArticle Simulation), designed to make Monte Carlo simulations with Geant4 more accessible to both clinical and research physicists. To demonstrate the method, three clinical situations were simulated: a variable water column used to verify constancy of the Bragg peak of the Crocker Lab eye treatment facility of the University of California, the double-scattering treatment mode of the passive beam scattering system at Massachusetts General Hospital (MGH), where a spinning range modulator wheel accompanied by beam current modulation produces a spread-out Bragg peak, and the scanning mode at MGH, where time-dependent pulse shape, energy distribution and magnetic fields control Bragg peak positions. Results confirm the clinical applicability of the method.
Geir Evensen
1994-01-01
A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in
A First-Passage Kinetic Monte Carlo method for reaction–drift–diffusion processes
Mauro, Ava J., E-mail: avamauro@bu.edu [Department of Mathematics and Statistics, Boston University, 111 Cummington Mall, Boston, MA 02215 (United States); Sigurdsson, Jon Karl; Shrake, Justin [Department of Mathematics, University of California, Santa Barbara (United States)] [Department of Mathematics, University of California, Santa Barbara (United States); Atzberger, Paul J., E-mail: atzberg@math.ucsb.edu [6712 South Hall, Department of Mathematics, University of California, Santa Barbara, CA 93106 (United States); Isaacson, Samuel A., E-mail: isaacson@math.bu.edu [Department of Mathematics and Statistics, Boston University, 111 Cummington Mall, Boston, MA 02215 (United States)
2014-02-15
Stochastic reaction–diffusion models are now a popular tool for studying physical systems in which both the explicit diffusion of molecules and noise in the chemical reaction process play important roles. The Smoluchowski diffusion-limited reaction model (SDLR) is one of several that have been used to study biological systems. Exact realizations of the underlying stochastic processes described by the SDLR model can be generated by the recently proposed First-Passage Kinetic Monte Carlo (FPKMC) method. This exactness relies on sampling analytical solutions to one and two-body diffusion equations in simplified protective domains. In this work we extend the FPKMC to allow for drift arising from fixed, background potentials. As the corresponding Fokker–Planck equations that describe the motion of each molecule can no longer be solved analytically, we develop a hybrid method that discretizes the protective domains. The discretization is chosen so that the drift–diffusion of each molecule within its protective domain is approximated by a continuous-time random walk on a lattice. New lattices are defined dynamically as the protective domains are updated, hence we will refer to our method as Dynamic Lattice FPKMC or DL-FPKMC. We focus primarily on the one-dimensional case in this manuscript, and demonstrate the numerical convergence and accuracy of our method in this case for both smooth and discontinuous potentials. We also present applications of our method, which illustrate the impact of drift on reaction kinetics.
NASA Astrophysics Data System (ADS)
Yoo, Hongki; Kang, Dong-Kyun; Lee, SeungWoo; Lee, Junhee; Gweon, Dae-Gab
2004-07-01
The errors can cause the serious loss of the performance of a precision machine system. In this paper, we propose the method of allocating the alignment tolerances of the components and apply this method to Confocal Scanning Microscopy (CSM) to get the optimal tolerances. CSM uses confocal aperture, which blocks the out-of-focus information. Thus, it provides images with superior resolution and has unique property of optical sectioning. Recently, due to these properties, it has been widely used for measurement in biological field, medical science, material science and semiconductor industry. In general, tight tolerances are required to maintain the performance of a system, but a high cost of manufacturing and assembling is required to preserve the tight tolerances. The purpose of allocating the optimal tolerances is minimizing the cost while keeping the performance of the system. In the optimal problem, we set the performance requirements as constraints and maximized the tolerances. The Monte Carlo Method, a statistical simulation method, is used in tolerance analysis. Alignment tolerances of optical components of the confocal scanning microscopy are optimized, to minimize the cost and to maintain the observation performance of the microscopy. We can also apply this method to the other precision machine system.
A First-Passage Kinetic Monte Carlo method for reaction-drift-diffusion processes
NASA Astrophysics Data System (ADS)
Mauro, Ava J.; Sigurdsson, Jon Karl; Shrake, Justin; Atzberger, Paul J.; Isaacson, Samuel A.
2014-02-01
Stochastic reaction-diffusion models are now a popular tool for studying physical systems in which both the explicit diffusion of molecules and noise in the chemical reaction process play important roles. The Smoluchowski diffusion-limited reaction model (SDLR) is one of several that have been used to study biological systems. Exact realizations of the underlying stochastic processes described by the SDLR model can be generated by the recently proposed First-Passage Kinetic Monte Carlo (FPKMC) method. This exactness relies on sampling analytical solutions to one and two-body diffusion equations in simplified protective domains. In this work we extend the FPKMC to allow for drift arising from fixed, background potentials. As the corresponding Fokker-Planck equations that describe the motion of each molecule can no longer be solved analytically, we develop a hybrid method that discretizes the protective domains. The discretization is chosen so that the drift-diffusion of each molecule within its protective domain is approximated by a continuous-time random walk on a lattice. New lattices are defined dynamically as the protective domains are updated, hence we will refer to our method as Dynamic Lattice FPKMC or DL-FPKMC. We focus primarily on the one-dimensional case in this manuscript, and demonstrate the numerical convergence and accuracy of our method in this case for both smooth and discontinuous potentials. We also present applications of our method, which illustrate the impact of drift on reaction kinetics.
An Efficient Monte Carlo Method for Modeling Radiative Transfer in Protoplanetary Disks
NASA Technical Reports Server (NTRS)
Kim, Stacy
2011-01-01
Monte Carlo methods have been shown to be effective and versatile in modeling radiative transfer processes to calculate model temperature profiles for protoplanetary disks. Temperatures profiles are important for connecting physical structure to observation and for understanding the conditions for planet formation and migration. However, certain areas of the disk such as the optically thick disk interior are under-sampled, or are of particular interest such as the snow line (where water vapor condenses into ice) and the area surrounding a protoplanet. To improve the sampling, photon packets can be preferentially scattered and reemitted toward the preferred locations at the cost of weighting packet energies to conserve the average energy flux. Here I report on the weighting schemes developed, how they can be applied to various models, and how they affect simulation mechanics and results. We find that improvements in sampling do not always imply similar improvements in temperature accuracies and calculation speeds.
Microscopic Nuclear Level Densities from Fe to Ge by the Shell Model Monte Carlo Method
H. Nakada; Y. Alhassid
1998-09-22
We calculate microscopically total and parity-projected level densities for $\\beta$-stable even-even nuclei between Fe and Ge, using the shell model Monte Carlo methods in the complete $(pf+0g_{9/2})$-shell. A single-particle level density parameter $a$ and backshift parameter $\\Delta$ are extracted by fitting the calculated densities to a backshifted Bethe formula, and their systematics are studied across the region. Shell effects are observed in $\\Delta$ for nuclei with Z=28 or N=28 and in the behavior of $A/a$ as a function of the number of neutrons. We find a significant parity-dependence of the level densities for nuclei with $A \\alt 60$, which diminishes as $A$ increases.
The Auxiliary Field Diffusion Monte Carlo Method for Nuclear Physics and Nuclear Astrophysics
Stefano Gandolfi
2007-12-09
In this thesis, I discuss the use of the Auxiliary Field Diffusion Monte Carlo method to compute the ground state of nuclear Hamiltonians, and I show several applications to interesting problems both in nuclear physics and in nuclear astrophysics. In particular, the AFDMC algorithm is applied to the study of several nuclear systems, finite, and infinite matter. Results about the ground state of nuclei ($^4$He, $^8$He, $^{16}$O and $^{40}$Ca), neutron drops (with 8 and 20 neutrons) and neutron rich-nuclei (isotopes of oxygen and calcium) are discussed, and the equation of state of nuclear and neutron matter are calculated and compared with other many-body calculations. The $^1S_0$ superfluid phase of neutron matter in the low-density regime was also studied.
A Monte Carlo method for variance estimation for estimators based on induced smoothing.
Jin, Zhezhen; Shao, Yongzhao; Ying, Zhiliang
2015-01-01
An important issue in statistical inference for semiparametric models is how to provide reliable and consistent variance estimation. Brown and Wang (2005. Standard errors and covariance matrices for smoothed rank estimators. Biometrika 92: , 732-746) proposed a variance estimation procedure based on an induced smoothing for non-smooth estimating functions. Herein a Monte Carlo version is developed that does not require any explicit form for the estimating function itself, as long as numerical evaluation can be carried out. A general convergence theory is established, showing that any one-step iteration leads to a consistent variance estimator and continuation of the iterations converges at an exponential rate. The method is demonstrated through the Buckley-James estimator and the weighted log-rank estimators for censored linear regression, and rank estimation for multiple event times data. PMID:24812418
Investigation of a V{sub 15} magnetic molecular nanocluster by the Monte Carlo method
Khizriev, K. Sh., E-mail: kamal71@mail.ru [Russian Academy of Sciences, Kh.I. Amirkhanov Institute of Physics, Dagestan Scientific Center (Russian Federation); Dzhamalutdinova, I. S.; Taaev, T. A. [Dagestan State University (Russian Federation)
2013-06-15
Exchange interactions in a V{sub 15} magnetic molecular nanocluster are considered, and the process of magnetization reversal for various values of the set of exchange constants is analyzed by the Monte Carlo method. It is shown that the best agreement between the field dependence of susceptibility and experimental results is observed for the following set of exchange interaction constants in a V{sub 15} magnetic molecular nanocluster: J = 500 K, J Prime = 150 K, J Double-Prime = 225 K, J{sub 1} = 50 K, and J{sub 2} = 50 K. It is observed for the first time that, in a strong magnetic field, for each of the three transitions from low-spin to high-spin states, the heat capacity exhibits two closely spaced maxima.
A spectral analysis of the domain decomposed Monte Carlo method for linear systems
Slattery, S. R.; Wilson, P. P. H. [Engineering Physics Department, University of Wisconsin - Madison, 1500 Engineering Dr., Madison, WI 53706 (United States); Evans, T. M. [Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37830 (United States)
2013-07-01
The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)
NASA Astrophysics Data System (ADS)
Wu, Jong-Shinn; Lee, Fred; Wong, Shwin-Chung
Two numerical procedures in the Direct Simulation Monte Carlo(DSMC) method, applying particle flux conservation at inflow/outflow pressure boundaries, have been developed to treat the two most important boundary conditions encountered in micromechanical devices involving gaseous flows. The first one is for both specified pressures at inlet and exit; while the second one is for specified mass flow rate and exit pressure. Both numerical procedures have been tested on short and long microchannels in the slip and transitional regimes. Excellent agreement has been found between the current results and the previous reported numerical results as well as the experimental data for the first type of boundary conditions. Finally, the developed numerical procedures have been applied to backward-facing micro-step gaseous flows to demonstrate its general applicability in more complicated flows.
On choosing effective elasticity tensors using a Monte-Carlo method
NASA Astrophysics Data System (ADS)
Danek, Tomasz; Slawinski, Michael A.
2014-03-01
A generally anisotropic elasticity tensor can be related to its closest counterparts in various symmetry classes. We refer to these counterparts as effective tensors in these classes. In finding effective tensors, we do not assume a priori orientations of their symmetry planes and axes. Knowledge of orientations of Hookean solids allows us to infer properties of materials represented by these solids. Obtaining orientations and parameter values of effective tensors is a highly nonlinear process involving finding absolute minima for orthogonal projections under all three-dimensional rotations. Given the standard deviations of the components of a generally anisotropic tensor, we examine the influence of measurement errors on the properties of effective tensors. We use a global optimization method to generate thousands of realizations of a generally anisotropic tensor, subject to errors. Using this optimization, we perform a Monte Carlo analysis of distances between that tensor and its counterparts in different symmetry classes, as well as of their orientations and elasticity parameters.
Study of temperature drop in microchannel using direct simulation Monte Carlo method
NASA Astrophysics Data System (ADS)
Gavasane, Abhimanyu; Agrawal, Amit; Pradeep, A. M.; Bhandarkar, Upendra
2014-12-01
The Direct Simulation Monte Carlo (DSMC) method has long been used to study subsonic rarefied gas flows in microchannels. A considerable temperature drop across the length is observed in the previous studies. Such simulations are performed for small aspect ratios (length / height) of the order of 10. However, most experimental studies are performed at aspect ratios of 100 or more, where such temperature drops are not observed. The objective of this paper is to study the effect of the aspect ratio as well as the pressure ratio (P_inlet/P_exit) on the temperature drop across microchannels for inlet Kn ranging from 0.05 to 3. It is aimed to find out the aspect ratio and the pressure ratio to have isothermal flow situation. Apart from DSMC simulations, a simple analysis is carried out to calculate the outlet temperature by solving the conservation of mass, momentum and energy. The parameter values required for isothermal conditions are identified.
Kinetic Monte Carlo Method to Model Diffusion Controlled Phase Transformations in the Solid State
NASA Astrophysics Data System (ADS)
Martin, Georges; Soisson, Frédéric
The classical theories of diffusion-controlled transformations in the solid state (precipitate-nucleation, -growth, -coarsening, order-disorder transformation, domain growth) imply several kinetic coefficients: diffusion coefficients (for the solute to cluster into nuclei, or to move from smaller to larger precipitates…), transfer coefficients (for the solute to cross the interface in the case of interface-reaction controlled kinetics) and ordering kinetic coefficients. If we restrict to coherent phase transformations, i.e., transformations, which occur keeping the underlying lattice the same, all such events (diffusion, transfer, ordering) are nothing but jumps of atoms from site to site on the lattice. Recent progresses have made it possible to model, by various techniques, diffusion controlled phase transformations, in the solid state, starting from the jumps of atoms on the lattice. The purpose of the present chapter is to introduce one of the techniques, the Kinetic Monte Carlo method (KMC).
A Monte Carlo Method for Modeling Thermal Damping: Beyond the Brownian-Motion Master Equation
Kurt Jacobs
2009-01-06
The "standard" Brownian motion master equation, used to describe thermal damping, is not completely positive, and does not admit a Monte Carlo method, important in numerical simulations. To eliminate both these problems one must add a term that generates additional position diffusion. He we show that one can obtain a completely positive simple quantum Brownian motion, efficiently solvable, without any extra diffusion. This is achieved by using a stochastic Schroedinger equation (SSE), closely analogous to Langevin's equation, that has no equivalent Markovian master equation. Considering a specific example, we show that this SSE is sensitive to nonlinearities in situations in which the master equation is not, and may therefore be a better model of damping for nonlinear systems.
Electronic correlation effects in a fullerene molecule studied by the variational Monte Carlo method
Krivnov, V.Y. (Institute of Chemical Physics, Russian Academy of Sciences, Kosygina 4, 117 977 Moscow (Russian Federation)); Shamovsky, I.L. (Institute of Chemical Physics, Russian Academy of Sciences, Kosygina 4, 117 977 Moscow (Russian Federation) Chemistry Department, University of West Indies Mona Campus, St. Andrew, Kingston 7 (Jamaica)); Tornau, E.E. (Semiconductor Physics Institute, Gostauto 11, 2600, Vilnius (Lithuania)); Rosengren, A. (Department of Theoretical Physics, Royal Institute of Technology, S-100 44 Stockholm (Sweden))
1994-10-15
Electron-correlation effects in the fullerene molecule and its ions are investigated in the framework of the Hubbard model. The variational Monte Carlo method and the Gutzwiller wave function are used. Most attention is paid to the case of intermediate interactions, but also the strong coupling limit, where the Hubbard model reduces to the antiferromagnetic Heisenberg model, is considered for the fullerene molecule. In this case we obtain a very low variational ground state energy. Futher, we have calculated the main spin correlation functions in the ground state. Only short-range order is found. The pairing energy of two electrons added to a fullerene molecule or to a fullerene ion is also calculated. Contrary to the results obtained by second-order perturbation theory, pair binding is not found.
A Monte Carlo Method for Projecting Uncertainty in 2D Lagrangian Trajectories
NASA Astrophysics Data System (ADS)
Robel, A.; Lozier, S.; Gary, S. F.
2009-12-01
In this study, a novel method is proposed for modeling the propagation of uncertainty due to subgrid-scale processes through a Lagrangian trajectory advected by ocean surface velocities. The primary motivation and application is differentiating between active and passive trajectories for sea turtles as observed through satellite telemetry. A spatiotemporal launch box is centered on the time and place of actual launch and populated with launch points. Synthetic drifters are launched at each of these locations, adding, at each time step along the trajectory, Monte Carlo perturbations in velocity scaled to the natural variability of the velocity field. The resulting trajectory cloud provides a dynamically evolving density field of synthetic drifter locations that represent the projection of subgrid-scale uncertainty out in time. Subsequently, by relaunching synthetic drifters at points along the trajectory, plots are generated in a daisy chain configuration of the “most likely passive pathways” for the drifter.
NASA Technical Reports Server (NTRS)
Haviland, J. K.
1974-01-01
The results are reported of two unrelated studies. The first was an investigation of the formulation of the equations for non-uniform unsteady flows, by perturbation of an irrotational flow to obtain the linear Green's equation. The resulting integral equation was found to contain a kernel which could be expressed as the solution of the adjoint flow equation, a linear equation for small perturbations, but with non-constant coefficients determined by the steady flow conditions. It is believed that the non-uniform flow effects may prove important in transonic flutter, and that in such cases, the use of doublet type solutions of the wave equation would then prove to be erroneous. The second task covered an initial investigation into the use of the Monte Carlo method for solution of acoustical field problems. Computed results are given for a rectangular room problem, and for a problem involving a circular duct with a source located at the closed end.
On Choosing Effective Elasticity Tensors Using a Monte-Carlo Method
NASA Astrophysics Data System (ADS)
Danek, Tomasz; Slawinski, Michael A.
2015-02-01
A generally anisotropic elasticity tensor can be related to its closest counterparts in various symmetry classes. We refer to these counterparts as effective tensors in these classes. In finding effective tensors, we do not assume a priori orientations of their symmetry planes and axes. Knowledge of orientations of Hookean solids allows us to infer properties of materials represented by these solids. Obtaining orientations and parameter values of effective tensors is a highly nonlinear process involving finding absolute minima for orthogonal projections under all three-dimensional rotations. Given the standard deviations of the components of a generally anisotropic tensor, we examine the influence of measurement errors on the properties of effective tensors. We use a global optimization method to generate thousands of realizations of a generally anisotropic tensor, subject to errors. Using this optimization, we perform a Monte Carlo analysis of distances between that tensor and its counterparts in different symmetry classes, as well as of their orientations and elasticity parameters
The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations
NASA Astrophysics Data System (ADS)
Sellier, J. M.; Dimov, I.
2014-09-01
The aim of ab-initio approaches is the simulation of many-body quantum systems from the first principles of quantum mechanics. These methods are traditionally based on the many-body Schrödinger equation which represents an incredible mathematical challenge. In this paper, we introduce the many-body Wigner Monte Carlo method in the context of distinguishable particles and in the absence of spin-dependent effects. Despite these restrictions, the method has several advantages. First of all, the Wigner formalism is intuitive, as it is based on the concept of a quasi-distribution function. Secondly, the Monte Carlo numerical approach allows scalability on parallel machines that is practically unachievable by means of other techniques based on finite difference or finite element methods. Finally, this method allows time-dependent ab-initio simulations of strongly correlated quantum systems. In order to validate our many-body Wigner Monte Carlo method, as a case study we simulate a relatively simple system consisting of two particles in several different situations. We first start from two non-interacting free Gaussian wave packets. We, then, proceed with the inclusion of an external potential barrier, and we conclude by simulating two entangled (i.e. correlated) particles. The results show how, in the case of negligible spin-dependent effects, the many-body Wigner Monte Carlo method provides an efficient and reliable tool to study the time-dependent evolution of quantum systems composed of distinguishable particles.
Wagner, John C [ORNL] [ORNL; Peplow, Douglas E. [ORNL] [ORNL; Mosher, Scott W [ORNL] [ORNL
2014-01-01
This paper presents a new hybrid (Monte Carlo/deterministic) method for increasing the efficiency of Monte Carlo calculations of distributions, such as flux or dose rate distributions (e.g., mesh tallies), as well as responses at multiple localized detectors and spectra. This method, referred to as Forward-Weighted CADIS (FW-CADIS), is an extension of the Consistent Adjoint Driven Importance Sampling (CADIS) method, which has been used for more than a decade to very effectively improve the efficiency of Monte Carlo calculations of localized quantities, e.g., flux, dose, or reaction rate at a specific location. The basis of this method is the development of an importance function that represents the importance of particles to the objective of uniform Monte Carlo particle density in the desired tally regions. Implementation of this method utilizes the results from a forward deterministic calculation to develop a forward-weighted source for a deterministic adjoint calculation. The resulting adjoint function is then used to generate consistent space- and energy-dependent source biasing parameters and weight windows that are used in a forward Monte Carlo calculation to obtain more uniform statistical uncertainties in the desired tally regions. The FW-CADIS method has been implemented and demonstrated within the MAVRIC sequence of SCALE and the ADVANTG/MCNP framework. Application of the method to representative, real-world problems, including calculation of dose rate and energy dependent flux throughout the problem space, dose rates in specific areas, and energy spectra at multiple detectors, is presented and discussed. Results of the FW-CADIS method and other recently developed global variance reduction approaches are also compared, and the FW-CADIS method outperformed the other methods in all cases considered.
ATR WG-MOX Fuel Pellet Burnup Measurement by Monte Carlo - Mass Spectrometric Method
Chang, Gray Sen I
2002-10-01
This paper presents a new method for calculating the burnup of nuclear reactor fuel, the MCWO-MS method, and describes its application to an experiment currently in progress to assess the suitability for use in light-water reactors of Mixed-OXide (MOX) fuel that contains plutonium derived from excess nuclear weapons material. To demonstrate that the available experience base with Reactor-Grade Mixed uranium-plutonium OXide (RGMOX) can be applied to Weapons-Grade (WG)-MOX in light water reactors, and to support potential licensing of MOX fuel made from weapons-grade plutonium and depleted uranium for use in United States reactors, an experiment containing WG-MOX fuel is being irradiated in the Advanced Test Reactor (ATR) at the Idaho National Engineering and Environmental Laboratory. Fuel burnup is an important parameter needed for fuel performance evaluation. For the irradiated MOX fuel’s Post-Irradiation Examination, the 148Nd method is used to measure the burnup. The fission product 148Nd is an ideal burnup indicator, when appropriate correction factors are applied. In the ATR test environment, the spectrum-dependent and burnup-dependent correction factors (see Section 5 for detailed discussion) can be substantial in high fuel burnup. The validated Monte Carlo depletion tool (MCWO) used in this study can provide a burnup-dependent correction factor for the reactor parameters, such as capture-to-fission ratios, isotopic concentrations and compositions, fission power, and spectrum in a straightforward fashion. Furthermore, the correlation curve generated by MCWO can be coupled with the 239Pu/Pu ratio measured by a Mass Spectrometer (in the new MCWO-MS method) to obtain a best-estimate MOX fuel burnup. A Monte Carlo - MCWO method can eliminate the generation of few-group cross sections. The MCWO depletion tool can analyze the detailed spatial and spectral self-shielding effects in UO2, WG-MOX, and reactor-grade mixed oxide (RG-MOX) fuel pins. The MCWO-MS tool only needs the MS-measured 239Pu/Pu ratio, without the measured isotope 148Nd concentration data, to determine the burnup accurately. MCWO-MS not only provided linear heat generation rate, Pu isotopic composition versus burnup, and burnup distributions within the WG-MOX fuel capsules, but also correctly pointed out the inconsistency in the large difference in burnups obtained by the 148Nd method.
Uncertainty Quantification of Prompt Fission Neutron Spectra Using the Unified Monte Carlo Method
NASA Astrophysics Data System (ADS)
Rising, M. E.; Talou, P.; Prinja, A. K.
2014-04-01
In the ENDF/B-VII.1 nuclear data library, the existing covariance evaluations of the prompt fission neutron spectra (PFNS) were computed by combining the available experimental differential data with theoretical model calculations, relying on the use of a first-order linear Bayesan approach, the Kalman filter. This approach assumes that the theoretical model response to changes in input model parameters be linear about the a priori central values. While the Unified Monte Carlo (UMC) method remains a Bayesian approach, like the Kalman filter, this method does not make any assumption about the linearity of the model response or shape of the a posteriori distribution of the parameters. By sampling from a distribution centered about the a priori model parameters, the UMC method computes the moments of the a posteriori parameter distribution. As the number of samples increases, the statistical noise in the computed a posteriori moments decrease and an appropriately converged solution corresponding to the true mean of the a posteriori PDF results. The UMC method has been successfully implemented using both a uniform and Gaussian sampling distribution and has been used for the evaluation of the PFNS and its associated uncertainties. While many of the UMC results are similar to the first-order Kalman filter results, significant differences are shown when experimental data are excluded from the evaluation process. When experimental data are included a few small nonlinearities are present in the high outgoing energy tail of the PFNS.
An energy transfer method for 4D Monte Carlo dose calculation
Siebers, Jeffrey V.; Zhong, Hualiang
2008-01-01
This article presents a new method for four-dimensional Monte Carlo dose calculations which properly addresses dose mapping for deforming anatomy. The method, called the energy transfer method (ETM), separates the particle transport and particle scoring geometries: Particle transport takes place in the typical rectilinear coordinate system of the source image, while energy deposition scoring takes place in a desired reference image via use of deformable image registration. Dose is the energy deposited per unit mass in the reference image. ETM has been implemented into DOSXYZnrc and compared with a conventional dose interpolation method (DIM) on deformable phantoms. For voxels whose contents merge in the deforming phantom, the doses calculated by ETM are exactly the same as an analytical solution, contrasting to the DIM which has an average 1.1% dose discrepancy in the beam direction with a maximum error of 24.9% found in the penumbra of a 6 MV beam. The DIM error observed persists even if voxel subdivision is used. The ETM is computationally efficient and will be useful for 4D dose addition and benchmarking alternative 4D dose addition algorithms. PMID:18841862
Fast perturbation Monte Carlo method for photon migration in heterogeneous turbid media.
Sassaroli, Angelo
2011-06-01
We present a two-step Monte Carlo (MC) method that is used to solve the radiative transfer equation in heterogeneous turbid media. The method exploits the one-to-one correspondence between the seed value of a random number generator and the sequence of random numbers. In the first step, a full MC simulation is run for the initial distribution of the optical properties and the "good" seeds (the ones leading to detected photons) are stored in an array. In the second step, we run a new MC simulation with only the good seeds stored in the first step, i.e., we propagate only detected photons. The effect of a change in the optical properties is calculated in a short time by using two scaling relationships. By this method we can increase the speed of a simulation up to a factor of 1300 in typical situations found in near-IR tissue spectroscopy and diffuse optical tomography, with a minimal requirement for hard disk space. Potential applications of this method for imaging of turbid media and the inverse problem are discussed. PMID:21633460
Low-Density Nozzle Flow by the Direct Simulation Monte Carlo and Continuum Methods
NASA Technical Reports Server (NTRS)
Chung, Chang-Hong; Kim, Sku C.; Stubbs, Robert M.; Dewitt, Kenneth J.
1994-01-01
Two different approaches, the direct simulation Monte Carlo (DSMC) method based on molecular gasdynamics, and a finite-volume approximation of the Navier-Stokes equations, which are based on continuum gasdynamics, are employed in the analysis of a low-density gas flow in a small converging-diverging nozzle. The fluid experiences various kinds of flow regimes including continuum, slip, transition, and free-molecular. Results from the two numerical methods are compared with Rothe's experimental data, in which density and rotational temperature variations along the centerline and at various locations inside a low-density nozzle were measured by the electron-beam fluorescence technique. The continuum approach showed good agreement with the experimental data as far as density is concerned. The results from the DSMC method showed good agreement with the experimental data, both in the density and the rotational temperature. It is also shown that the simulation parameters, such as the gas/surface interaction model, the energy exchange model between rotational and translational modes, and the viscosity-temperature exponent, have substantial effects on the results of the DSMC method.
NASA Astrophysics Data System (ADS)
Ceballos, C.; Baldazzi, G.; Bollini, D.; Cabal Rodríguez, A. E.; Dabrowski, W.; Días García, A.; Gambaccini, M.; Giubellino, P.; Gombia, M.; Grybos, P.; Idzik, M.; Marzari-Chiesa, A.; Montaño, L. M.; Prino, F.; Ramello, L.; Sitta, M.; Swientek, K.; Taibi, A.; Tomassi, E.; Tuffanelli, A.; Wiacek, P.
2003-09-01
We present First results of Monte Carlo simulation by the general purpose MCNP-4C transport code of an experimental facility at Bologna S. Orsola hospital for studying the possible application of a X-Ray detection system based on a silicon strip detector on a dual energy angiography. The quasi-monochromatic X-ray beam with the detector in the edge-on configuration has been used to acquire images of a test object at two different energies (namely 31 and 35 keV) suitable for the K-edge subtraction angiography application. As a test object a Plexiglas step wedge phantom with four cylindrical cavities, having 1 mm diameter was used. The cavities have been drilled and filled, with iodated contrast medium, whose concentration varied from 370 mg/ml to 92 mg/ml. Both the profiles obtained from measurements and the generated images where reproduced by computer simulation on a first approach to use this technique as an evaluation tool for future developments on the experimental setup.
Monte Carlo Assessment of Time Dependent Spectral Indexes for Benchmarking Neutron Transport in Iron
NASA Astrophysics Data System (ADS)
Hawari, Ayman I.; Adams, James M.
2003-06-01
Monte Carlo simulations (MCNP4C2) were performed to assess the ability to benchmark neutron transport calculations in iron using a pulsed-neutron slowing-down experiment. Specifically, calculations were performed to obtain the time dependent neutron energy spectra inside a 1 × 1 × 1 m natural iron moderator that is driven by a 14-MeV pulsed neutron source (simulating a pulsed D-T neutron generator). At various time intervals after the pulse, the energy spectrum was tallied and used to estimate the integral time-dependent reaction rates in 235U, 238U, 237Np, and 239Pu fission detectors that were located inside the moderator. The results show that within 0.05 ?s after the pulse, the average energy of the neutrons drops below 800 keV. Therefore, the threshold detectors (237Np, and 238U) can be useful at early times, while the fissile detectors (235U and 239Pu) can be utilized throughout the experiment. For these detectors, the time dependent reaction rates and spectral indexes (235U/239Pu, 237Np/239Pu, and 238U/239Pu) are developed and discussed.
NASA Astrophysics Data System (ADS)
Takoudis, G.; Xanthos, S.; Clouvas, A.; Potiriadis, C.
2010-02-01
Portal monitoring radiation detectors are commonly used by steel industries in the probing and detection of radioactivity contamination in scrap metal. These portal monitors typically consist of polystyrene or polyvinyltoluene (PVT) plastic scintillating detectors, one or more photomultiplier tubes (PMT), an electronic circuit, a controller that handles data output and manipulation linking the system to a display or a computer with appropriate software and usually, a light guide. Such a portal used by the steel industry was opened and all principal materials were simulated using a Monte Carlo simulation tool (MCNP4C2). Various source-detector configurations were simulated and validated by comparison with corresponding measurements. Subsequently an experiment with a uniform cargo along with two sets of experiments with different scrap loads and radioactive sources ( 137Cs, 152Eu) were performed and simulated. Simulated and measured results suggested that the nature of scrap is crucial when simulating scrap load-detector experiments. Using the same simulating configuration, a series of runs were performed in order to estimate minimum alarm activities for 137Cs, 60Co and 192Ir sources for various simulated scrap densities. The minimum alarm activities as well as the positions in which they were recorded are presented and discussed.
MONTE CARLO EXTENSION OF QUASIMONTE CARLO Art B. Owen
Owen, Art
MONTE CARLO EXTENSION OF QUASIÂMONTE CARLO Art B. Owen Department of Statistics Stanford University Stanford CA 94305, U.S.A. ABSTRACT This paper surveys recent research on using Monte Carlo techniques to improve quasiÂMonte Carlo techÂ niques. Randomized quasiÂMonte Carlo methods proÂ vide a basis for error
Bridging the gap between quantum Monte Carlo and F12-methods
NASA Astrophysics Data System (ADS)
Chinnamsetty, Sambasiva Rao; Luo, Hongjun; Hackbusch, Wolfgang; Flad, Heinz-Jürgen; Uschmajew, André
2012-06-01
Tensor product approximation of pair-correlation functions opens a new route from quantum Monte Carlo (QMC) to explicitly correlated F12 methods. Thereby one benefits from stochastic optimization techniques used in QMC to get optimal pair-correlation functions which typically recover more than 85% of the total correlation energy. Our approach incorporates, in particular, core and core-valence correlation which are poorly described by homogeneous and isotropic ansatz functions usually applied in F12 calculations. We demonstrate the performance of the tensor product approximation by applications to atoms and small molecules. It turns out that the canonical tensor format is especially suitable for the efficient computation of two- and three-electron integrals required by explicitly correlated methods. The algorithm uses a decomposition of three-electron integrals, originally introduced by Boys and Handy and further elaborated by Ten-no in his 3d numerical quadrature scheme, which enables efficient computations in the tensor format. Furthermore, our method includes the adaptive wavelet approximation of tensor components where convergence rates are given in the framework of best N-term approximation theory.
NASA Technical Reports Server (NTRS)
Hueser, J. E.; Brock, F. J.; Melfi, L. T., Jr.; Bird, G. A.
1984-01-01
A new solution procedure has been developed to analyze the flowfield properties in the vicinity of the Inertial Upper Stage/Spacecraft during the 1st stage (SRMI) burn. Continuum methods are used to compute the nozzle flow and the exhaust plume flowfield as far as the boundary where the breakdown of translational equilibrium leaves these methods invalid. The Direct Simulation Monte Carlo (DSMC) method is applied everywhere beyond this breakdown boundary. The flowfield distributions of density, velocity, temperature, relative abundance, surface flux density, and pressure are discussed for each species for 2 sets of boundary conditions: vacuum and freestream. The interaction of the exhaust plume and the freestream with the spacecraft and the 2-stream direct interaction are discussed. The results show that the low density, high velocity, counter flowing free-stream substantially modifies the flowfield properties and the flux density incident on the spacecraft. A freestream bow shock is observed in the data, located forward of the high density region of the exhaust plume into which the freestream gas does not penetrate. The total flux density incident on the spacecraft, integrated over the SRM1 burn interval is estimated to be of the order of 10 to the 22nd per sq m (about 1000 atomic layers).
Statistical Properties of Nuclei by the Shell Model Monte Carlo Method
Y. Alhassid
2006-04-26
We use quantum Monte Carlo methods in the framework of the interacting nuclear shell model to calculate the statistical properties of nuclei at finite temperature and/or excitation energies. With this approach we can carry out realistic calculations in much larger configuration spaces than are possible by conventional methods. A major application of the methods has been the microscopic calculation of nuclear partition functions and level densities, taking into account both correlations and shell effects. Our results for nuclei in the mass region A ~ 50 - 70 are in remarkably good agreement with experimental level densities without any adjustable parameters and are an improvement over empirical formulas. We have recently extended the shell model theory of level statistics to higher temperatures, including continuum effects. We have also constructed simple statistical models to explain the dependence of the microscopically calculated level densities on good quantum numbers such as parity. Thermal signatures of pairing correlations are identified through odd-even effects in the heat capacity.
Density-of-states based Monte Carlo methods for simulation of biological systems
NASA Astrophysics Data System (ADS)
Rathore, Nitin; Knotts, Thomas A.; de Pablo, Juan J.
2004-03-01
We have developed density-of-states [1] based Monte Carlo techniques for simulation of biological molecules. Two such methods are discussed. The first, Configurational Temperature Density of States (CTDOS) [2], relies on computing the density of states of a peptide system from knowledge of its configurational temperature. The reciprocal of this intrinsic temperature, computed from instantaneous configurational information of the system, is integrated to arrive at the density of states. The method shows improved efficiency and accuracy over techniques that are based on histograms of random visits to distinct energy states. The second approach, Expanded Ensemble Density of States (EXEDOS), incorporates elements from both the random walk method and the expanded ensemble formalism. It is used in this work to study mechanical deformation of model peptides. Results are presented in the form of force-extension curves and the corresponding potentials of mean force. The application of this proposed technique is further generalized to other biological systems; results will be presented for ion transport through protein channels, base stacking in nucleic acids and hybridization of DNA strands. [1]. F. Wang and D. P. Landau, Phys. Rev. Lett., 86, 2050 (2001). [2]. N. Rathore, T. A. Knotts IV and J. J. de Pablo, Biophys. J., Dec. (2003).
Bishop, Joseph E. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Strack, O. E. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
2011-10-21
A novel method is presented for assessing the convergence of a sequence of statistical distributions generated by direct Monte Carlo sampling. The primary application is to assess the mesh or grid convergence, and possibly divergence, of stochastic outputs from non-linear continuum systems. Example systems include those from fluid or solid mechanics, particularly those with instabilities and sensitive dependence on initial conditions or system parameters. The convergence assessment is based on demonstrating empirically that a sequence of cumulative distribution functions converges in the Linfty norm. The effect of finite sample sizes is quantified using confidence levels from the Kolmogorov–Smirnov statistic. The statistical method is independent of the underlying distributions. The statistical method is demonstrated using two examples: (1) the logistic map in the chaotic regime, and (2) a fragmenting ductile ring modeled with an explicit-dynamics finite element code. In the fragmenting ring example the convergence of the distribution describing neck spacing is investigated. The initial yield strength is treated as a random field. Two different random fields are considered, one with spatial correlation and the other without. Both cases converged, albeit to different distributions. The case with spatial correlation exhibited a significantly higher convergence rate compared with the one without spatial correlation.
A general Monte Carlo method for mapping multiple quantitative trait loci
Ritsert C. Jansen
1996-01-01
In this paper we address the mapping of multiple quantitative trait loci (QTLs) in line crosses for which the genetic data are highly incomplete. Such complicated situations occur, for instance, when dominant markers are used or when unequally informative markers are used in experiments with outbred populations. We describe a general and flexible Monte Carlo expectation-maximization (Monte Carlo EM) algorithm
NASA Technical Reports Server (NTRS)
Olynick, David P.; Hassan, H. A.; Moss, James N.
1988-01-01
A grid generation and adaptation procedure based on the method of transfinite interpolation is incorporated into the Direct Simulation Monte Carlo Method of Bird. In addition, time is advanced based on a local criterion. The resulting procedure is used to calculate steady flows past wedges and cones. Five chemical species are considered. In general, the modifications result in a reduced computational effort. Moreover, preliminary results suggest that the simulation method is time step dependent if requirements on cell sizes are not met.
Favorite, J.A.
1999-09-01
In previous work, exponential convergence of Monte Carlo solutions using the reduced source method with Legendre expansion has been achieved only in one-dimensional rod and slab geometries. In this paper, the method is applied to three-dimensional (right parallelepiped) problems, with resulting evidence suggesting success. As implemented in this paper, the method approximates an angular integral of the flux with a discrete-ordinates numerical quadrature. It is possible that this approximation introduces an inconsistency that must be addressed.
Kalugin, M. A.; Oleynik, D. S.; Sukhino-Khomenko, E. A., E-mail: sukhino-khomenko@adis.vver.kiae.ru [National Research Centre Kurchatov Institute (Russian Federation)
2012-12-15
The algorithms of estimation of the time series correlation functions in nuclear reactor calculations using the Monte Carlo method are described. Correlation functions are used for the estimation of biases, for calculations of variance taking into account the correlations between neutron generations, and for choosing skipped generations.
Bendele, Travis Henry
2013-02-22
A honeycomb probe was designed to measure the optical properties of biological tissues using single Monte Carlo method. The ongoing project is intended to be a multi-wavelength, real time, and in-vivo technique to detect breast cancer. Preliminary...
Cheng-Chien Liu; J. D. Woods
2004-01-01
The annual variation of ocean-colour signals in the North Atlantic Ocean is successfully simulated by combining the plankton ecosystem model and the optical model. The first model uses the Lagrangian Ensemble method of Woods and Barkmann to simulate the upper-ocean ecosystem, including the vertical profile of chlorophyll concentration. The second model employs the Monte Carlo technique to compute the optical
Straub, John E.
On Monte Carlo and molecular dynamics methods inspired by Tsallis statistics: Methodology a generalized statistical distribution derived from a modification of the GibbsÂShannon entropy proposed of the phase space may result in distinct time averages. Statistical theories of chemical sys- tems are often
Monte Carlo Method for Collision Probability Calculations using 3D Satellite Models
NASA Astrophysics Data System (ADS)
de Vries, W.; Phillion, D.
2010-09-01
We developed an efficient method for calculating the collision probability using a Monte Carlo approach. The method requires knowledge of the full 6x6 covariance matrix information for each of the objects under consideration, and is capable of incorporating not just the positional uncertainty information, but also the velocity component of the uncertainties in its calculation. This ensures a higher level of accuracy and robustness over strictly analytic methods, albeit at the cost of a larger computational load. It is part of the Testbed Environment for Space Situational Awareness (TESSA) development effort at Lawrence Livermore National Laboratory (LLNL). This paper will describe our implementation as well as an overview of the capabilities and expectations for the cases where orbital refinement has reduced the size of the uncertainty ellipsoids to much less than a kilometer. Under this regime a spherical approximation of the collision cross-section is not utilizing the full potential of the available information. The combination of direct or indirect attitude information of the satellites, their detailed 3D mesh models, and the relatively accurate information on the size, shape, and separations of the uncertainty ellipsoids can be used to not only refine the collision calculation, but also allow for detailed assessment of the relative likelihood of various impact scenarios. The distribution of Monte Carlo trajectories that form the collection of collision cases is, provided the uncertainties are small enough, distinctly non uniform across the combined satellite cross-section shape. This can significantly modify the relative collision rates based on surface area alone (for instance, the collision geometry and relative positions of the uncertainties may make a hit on the main body more likely than an impact on the solar panels, even though the latter are larger). In cases where a satellite might survive a collision (e.g., a small piece of debris puncturing a solar panel), we can now augment the probability of collision with the odds of survival given a collision. Furthermore, this information allows us to constrain the possible impact scenarios a-posteriori, reducing the number of computationally costly hydro-code simulations we have to run for our detailed debris modeling capabilities (cf. K. Springer et al. in these proceedings for a report on our Cosmos - Iridium analysis).
Wolfhard Janke; Tilman Sauer
1994-12-17
We discuss the recently proposed multicanonical multigrid Monte Carlo method and apply it to the scalar $\\phi^4$-model on a square lattice. To investigate the performance of the new algorithm at the field-driven first-order phase transitions between the two ordered phases we carefully analyze the autocorrelations of the Monte Carlo process. Compared with standard multicanonical simulations a real-time improvement of about one order of magnitude is established. The interface tension between the two ordered phases is extracted from high-statistics histograms of the magnetization applying histogram reweighting techniques.
H. Nakada; Y. Alhassid
1998-01-21
Total and parity-projected level densities of iron-region nuclei are calculated microscopically by using Monte Carlo methods for the nuclear shell model in the complete $(pf+0g_{9/2})$-shell. The calculated total level density is found to be in good agreement with the experimental level density. The Monte Carlo calculations offer a significant improvement over the thermal Hartree-Fock approximation. Contrary to the Fermi gas model, it is found that the level density has a significant parity-dependence in the neutron resonance region. The systematics of the level density parameters (including shell effects) in the iron region is presented.
Da, B.; Sun, Y.; Ding, Z. J. [Hefei National Laboratory for Physical Sciences at Microscale and Department of Physics, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026, People's Republic of China (China)] [Hefei National Laboratory for Physical Sciences at Microscale and Department of Physics, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026, People's Republic of China (China); Mao, S. F. [School of Nuclear Science and Technology, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026, People's Republic of China (China)] [School of Nuclear Science and Technology, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026, People's Republic of China (China); Zhang, Z. M. [Centre of Physical Experiments, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026, People's Republic of China (China)] [Centre of Physical Experiments, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026, People's Republic of China (China); Jin, H.; Yoshikawa, H.; Tanuma, S. [Advanced Surface Chemical Analysis Group, National Institute for Materials Science, 1-2-1 Sengen Tsukuba, Ibaraki 305-0047 (Japan)] [Advanced Surface Chemical Analysis Group, National Institute for Materials Science, 1-2-1 Sengen Tsukuba, Ibaraki 305-0047 (Japan)
2013-06-07
A reverse Monte Carlo (RMC) method is developed to obtain the energy loss function (ELF) and optical constants from a measured reflection electron energy-loss spectroscopy (REELS) spectrum by an iterative Monte Carlo (MC) simulation procedure. The method combines the simulated annealing method, i.e., a Markov chain Monte Carlo (MCMC) sampling of oscillator parameters, surface and bulk excitation weighting factors, and band gap energy, with a conventional MC simulation of electron interaction with solids, which acts as a single step of MCMC sampling in this RMC method. To examine the reliability of this method, we have verified that the output data of the dielectric function are essentially independent of the initial values of the trial parameters, which is a basic property of a MCMC method. The optical constants derived for SiO{sub 2} in the energy loss range of 8-90 eV are in good agreement with other available data, and relevant bulk ELFs are checked by oscillator strength-sum and perfect-screening-sum rules. Our results show that the dielectric function can be obtained by the RMC method even with a wide range of initial trial parameters. The RMC method is thus a general and effective method for determining the optical properties of solids from REELS measurements.
Quantum Monte Carlo Method for Materials --- Random Walks in Slater Determinant Space
NASA Astrophysics Data System (ADS)
Zhang, S.; Krakauer, H.
2003-12-01
In order to reliably predict materials properties, it is critical to have accurate and robust calculations at the most fundamental level. Often the desired effects of the materials originate from electron interaction and correlation effects, and small errors in treating such effects will result in crucial and qualitative differences in the properties. Density functional approaches, despite its tremendous success in allowing detailed microscopic calculations of a variety of materials, is not always reliable. We have developed a new quantum Monte Carlo (QMC) method [1] for treating electron correlations. Similar to existing QMC methods, it allows calculations of ground-state equilibrium properties in CPU times that scale as a power law with system size. In addition it allows direct incorporation of state-of-the-art techniques (non-local pseudopotentials; high quality basis sets) from the very best mean-field calculations into a true many-body framework. The method projects out the many-body ground state by random walks in the space of Slater determinants. An approximate approach is formulated to control the phase problem with a trial wave function. The method allows the use of any one-particle basis. Using a plane-wave basis and non-local pseudopotentials, we apply the method to Be, Si, P atoms and dimers, and to bulk Si with 2, 16, 54 atom (216 electrons) supercells. Single Slater determinant wave functions from density functional theory calculations were used as the trial wave function with no additional optimization. The calculated dissociation energy of the dimer molecules and the cohesive energy of bulk Si are in excellent agreement with experiment and are comparable to or better than the best existing theoretical results. {[1]} Shiwei Zhang and Henry Krakauer, Phys. Rev. Lett., 90, 136401 (2003).
NASA Astrophysics Data System (ADS)
Farah, J.; Martinetti, F.; Sayah, R.; Lacoste, V.; Donadille, L.; Trompier, F.; Nauraye, C.; De Marzi, L.; Vabre, I.; Delacroix, S.; Hérault, J.; Clairand, I.
2014-06-01
Monte Carlo calculations are increasingly used to assess stray radiation dose to healthy organs of proton therapy patients and estimate the risk of secondary cancer. Among the secondary particles, neutrons are of primary concern due to their high relative biological effectiveness. The validation of Monte Carlo simulations for out-of-field neutron doses remains however a major challenge to the community. Therefore this work focused on developing a global experimental approach to test the reliability of the MCNPX models of two proton therapy installations operating at 75 and 178 MeV for ocular and intracranial tumor treatments, respectively. The method consists of comparing Monte Carlo calculations against experimental measurements of: (a) neutron spectrometry inside the treatment room, (b) neutron ambient dose equivalent at several points within the treatment room, (c) secondary organ-specific neutron doses inside the Rando-Alderson anthropomorphic phantom. Results have proven that Monte Carlo models correctly reproduce secondary neutrons within the two proton therapy treatment rooms. Sensitive differences between experimental measurements and simulations were nonetheless observed especially with the highest beam energy. The study demonstrated the need for improved measurement tools, especially at the high neutron energy range, and more accurate physical models and cross sections within the Monte Carlo code to correctly assess secondary neutron doses in proton therapy applications.
Neutrino transport in type II supernovae: Boltzmann solver vs. Monte Carlo method
Shoichi Yamada; Hans-Thomas Janka; Hideyuki Suzuki
1998-09-02
We have coded a Boltzmann solver based on a finite difference scheme (S_N method) aiming at calculations of neutrino transport in type II supernovae. Close comparison between the Boltzmann solver and a Monte Carlo transport code has been made for realistic atmospheres of post bounce core models under the assumption of a static background. We have also investigated in detail the dependence of the results on the numbers of radial, angular, and energy grid points and the way to discretize the spatial advection term which is used in the Boltzmann solver. A general relativistic calculation has been done for one of the models. We find overall good agreement between the two methods. However, because of a relatively small number of angular grid points (which is inevitable due to limitations of the computation time) the Boltzmann solver tends to underestimate the flux factor and the Eddington factor outside the (mean) ``neutrinosphere'' where the angular distribution of the neutrinos becomes highly anisotropic. This fact suggests that one has to be cautious in applying the Boltzmann solver to a calculation of the neutrino heating in the hot-bubble region because it might tend to overestimate the local energy deposition rate. A comparison shows that this trend is opposite to the results obtained with a multi-group flux-limited diffusion approximation of neutrino transport. The accuracy of the Boltzmann solver can be considerably improved by using a variable angular mesh to increase the angular resolution in the semi-transparent regime.
Bednarz, Bryan; Lu, Hsiao-Ming; Engelsman, Martijn; Paganetti, Harald
2011-01-01
Monte Carlo models of proton therapy treatment heads are being used to improve beam delivery systems and to calculate the radiation field for patient dose calculations. The achievable accuracy of the model depends on the exact knowledge of the treatment head geometry and time structure, the material characteristics, and the underlying physics. This work aimed at studying the uncertainties in treatment head simulations for passive scattering proton therapy. The sensitivities of spread-out Bragg peak (SOBP) dose distributions on material densities, mean ionization potentials, initial proton beam energy spread and spot size were investigated. An improved understanding of the nature of these parameters may help to improve agreement between calculated and measured SOBP dose distributions and to ensure that the range, modulation width, and uniformity are within clinical tolerance levels. Furthermore, we present a method to make small corrections to the uniformity of spread-out Bragg peaks by utilizing the time structure of the beam delivery. In addition, we re-commissioned the models of the two proton treatment heads located at our facility using the aforementioned correction methods presented in this paper. PMID:21478569
Cu-Au Alloys Using Monte Carlo Simulations and the BFS Method for Alloys
NASA Technical Reports Server (NTRS)
Bozzolo, Guillermo; Good, Brian; Ferrante, John
1996-01-01
Semi empirical methods have shown considerable promise in aiding in the calculation of many properties of materials. Materials used in engineering applications have defects that occur for various reasons including processing. In this work we present the first application of the BFS method for alloys to describe some aspects of microstructure due to processing for the Cu-Au system (Cu-Au, CuAu3, and Cu3Au). We use finite temperature Monte Carlo calculations, in order to show the influence of 'heat treatment' in the low-temperature phase of the alloy. Although relatively simple, it has enough features that could be used as a first test of the reliability of the technique. The main questions to be answered in this work relate to the existence of low temperature ordered structures for specific concentrations, for example, the ability to distinguish between rather similar phases for equiatomic alloys (CuAu I and CuAu II, the latter characterized by an antiphase boundary separating two identical phases).
Simulation of Watts Bar Unit 1 Initial Startup Tests with Continuous Energy Monte Carlo Methods
Godfrey, Andrew T [ORNL; Gehin, Jess C [ORNL; Bekar, Kursat B [ORNL; Celik, Cihangir [ORNL
2014-01-01
The Consortium for Advanced Simulation of Light Water Reactors* is developing a collection of methods and software products known as VERA, the Virtual Environment for Reactor Applications. One component of the testing and validation plan for VERA is comparison of neutronics results to a set of continuous energy Monte Carlo solutions for a range of pressurized water reactor geometries using the SCALE component KENO-VI developed by Oak Ridge National Laboratory. Recent improvements in data, methods, and parallelism have enabled KENO, previously utilized predominately as a criticality safety code, to demonstrate excellent capability and performance for reactor physics applications. The highly detailed and rigorous KENO solutions provide a reliable nu-meric reference for VERAneutronics and also demonstrate the most accurate predictions achievable by modeling and simulations tools for comparison to operating plant data. This paper demonstrates the performance of KENO-VI for the Watts Bar Unit 1 Cycle 1 zero power physics tests, including reactor criticality, control rod worths, and isothermal temperature coefficients.
Quantum Monte Carlo method using phase-free random walks with Slater determinants
NASA Astrophysics Data System (ADS)
Zhang, Shiwei; Krakauer, Henry
2003-03-01
Without an exact solution to the sign/phase problem, reducing the reliance on trial wave functions is clearly of key importance to increasing the predictive power of QMC. We have developed a quantum Monte Carlo method [1] using Hubbard-Stratonovich auxiliary fields for many fermions that allows the use of any one-particle basis. It projects out the ground state by random walks in the space of Slater determinants. An approximate approach is formulated to control the phase problem with a trial wave function. For periodic systems the formalism allows arbitrary k-point sampling with complex trial wave functions. Using a plane-wave basis and non-local pseudopotentials, we apply the method to Si atom, dimer, and 2, 16, 54 atom (216 electrons) bulk supercells. Single Slater determinant wave functions from density functional theory calculations were used as the trial wave function with no additional optimization. The calculated dissociation energy of the Si dimer molecule and the cohesive energy of bulk Si are in excellent agreement with experiment and are comparable to the best existing theoretical results. Results for other systems will also be presented. [1] S. Zhang and H. Krakauer, cond-mat/0208340.
Uncertainty quantification through the Monte Carlo method in a cloud computing setting
NASA Astrophysics Data System (ADS)
Cunha, Americo; Nasser, Rafael; Sampaio, Rubens; Lopes, Hélio; Breitman, Karin
2014-05-01
The Monte Carlo (MC) method is the most common technique used for uncertainty quantification, due to its simplicity and good statistical results. However, its computational cost is extremely high, and, in many cases, prohibitive. Fortunately, the MC algorithm is easily parallelizable, which allows its use in simulations where the computation of a single realization is very costly. This work presents a methodology for the parallelization of the MC method, in the context of cloud computing. This strategy is based on the MapReduce paradigm, and allows an efficient distribution of tasks in the cloud. This methodology is illustrated on a problem of structural dynamics that is subject to uncertainties. The results show that the technique is capable of producing good results concerning statistical moments of low order. It is shown that even a simple problem may require many realizations for convergence of histograms, which makes the cloud computing strategy very attractive (due to its high scalability capacity and low-cost). Additionally, the results regarding the time of processing and storage space usage allow one to qualify this new methodology as a solution for simulations that require a number of MC realizations beyond the standard.
Monte Carlo simulation methods for computing the wetting and drying properties of model systems.
Rane, Kaustubh S; Kumar, Vaibhaw; Errington, Jeffrey R
2011-12-21
We introduce general Monte Carlo simulation methods for determining the wetting and drying properties of model systems. We employ an interface-potential-based approach in which the interfacial properties of a system are related to the surface excess free energy of a thin fluid film in contact with a surface. Two versions of this approach are explored: a "spreading" method focused on the growth of a thin liquid film from a surface in a mother vapor and a "drying" method focused on the growth of a thin vapor film from a surface in a mother liquid. The former provides a direct measure of the spreading coefficient while the latter provides an analogous drying coefficient. When coupled with an independent measure of the liquid-vapor surface tension, these coefficients enable one to compute the contact angle. We also show how one can combine information gathered from application of the spreading and drying methods at a common state point to obtain direct measures of the contact angle and liquid-vapor surface tension. The computational strategies introduced here are applied to two model systems. One includes a monatomic Lennard-Jones fluid that interacts with a structureless substrate via a long-ranged substrate potential. The second model contains a monatomic Lennard-Jones fluid that interacts with an atomistically detailed substrate via a short-ranged potential. Expanded ensemble techniques are coupled with the interface potential approach to compile the temperature- and substrate strength-dependence of various interfacial properties for these systems. Overall, we find that the approach pursued here provides an efficient and precise means to calculate the wetting and drying properties of model systems. PMID:22191859
Statistical analysis of chemical transformation kinetics using Markov-Chain Monte Carlo methods.
Görlitz, Linus; Gao, Zhenglei; Schmitt, Walter
2011-05-15
For the risk assessment of chemicals intentionally released into the environment, as, e.g., pesticides, it is indispensable to investigate their environmental fate. Main characteristics in this context are transformation rates and partitioning behavior. In most cases the relevant parameters are not directly measurable but are determined indirectly from experimentally determined concentrations in various environmental compartments. Usually this is done by fitting mathematical models, which are usually nonlinear, to the observed data and such deriving estimates of the parameter values. Statistical analysis is then used to judge the uncertainty of the estimates. Of particular interest in this context is the question whether degradation rates are significantly different from zero. Standard procedure is to use nonlinear least-squares methods to fit the models and to estimate the standard errors of the estimated parameters from Fisher's Information matrix and estimated level of measurement noise. This, however, frequently leads to counterintuitive results as the estimated probability distributions of the parameters based on local linearization of the optimized models are often too wide or at least differ significantly in shape from the real distribution. In this paper we identify the shortcoming of this procedure and propose a statistically valid approach based on Markov-Chain Monte Carlo sampling that is appropriate to determine the real probability distribution of model parameters. The effectiveness of this method is demonstrated on three data sets. Although it is generally applicable to different problems where model parameters are to be inferred, in the present case for simplicity we restrict the discussion to the evaluation of metabolic degradation of chemicals in soil. It is shown that the method is successfully applicable to problems of different complexity. We applied it to kinetic data from compounds with one and five metabolites. Additionally, using simulated data, it is shown that the MCMC method estimates the real probability distributions of parameters well and much better than the standard optimization approach. PMID:21526818
Accuracy of Monte Carlo Criticality Calculations During BR2 Operation
Kalcheva, Silva; Koonen, Edgar; Ponsard, Bernard [SCK-CEN (Belgium)
2005-08-15
The Belgian Material Test Reactor BR2 is a strongly heterogeneous high-flux engineering test reactor at SCK-CEN (Centre d'Etude de l'Energie Nucleaire) in Mol with a thermal power of 60 to 100 MW. It deploys highly enriched uranium, water-cooled concentric plate fuel elements, positioned inside a beryllium reflector with a complex hyperboloid arrangement of test holes. The objective of this paper is to validate the MCNP and ORIGEN-S three-dimensional (3-D) model for reactivity predictions of the entire BR2 core during reactor operation. We employ the Monte Carlo code MCNP-4C to evaluate the effective multiplication factor k{sub eff} and 3-D space-dependent specific power distribution. The one-dimensional code ORIGEN-S is used to calculate the isotopic fuel depletion versus burnup and to prepare a database with depleted fuel compositions. The approach taken is to evaluate the 3-D power distribution at each time step and along with the database to evaluate the 3-D isotopic fuel depletion at the next step and to deduce the corresponding shim rod positions of the reactor operation. The capabilities of both codes are fully exploited without constraints on the number of involved isotope depletion chains or an increase of the computational time. The reactor has a complex operation, with important shutdowns between cycles, and its reactivity is strongly influenced by poisons, mainly {sup 3}He and {sup 6}Li from the beryllium reflector, and the burnable absorbers {sup 149}Sm and {sup 10}B in the fresh UAl{sub x} fuel. The computational predictions for the shim rod positions at various restarts are within 0.5 $ ({beta}{sub eff} = 0.0072)
Summarizing the output of a Monte Carlo method for uncertainty evaluation
NASA Astrophysics Data System (ADS)
Harris, P. M.; Matthews, C. E.; Cox, M. G.; Forbes, A. B.
2014-06-01
The ‘Guide to the Expression of Uncertainty in Measurement’ (GUM) requires that the way a measurement uncertainty is expressed should be transferable. It should be possible to use directly the uncertainty evaluated for one measurement as a component in evaluating the uncertainty for another measurement that depends on the first. Although the method for uncertainty evaluation described in the GUM meets this requirement of transferability, it is less clear how this requirement is to be achieved when GUM Supplement 1 is applied. That Supplement uses a Monte Carlo method to provide a sample composed of many values drawn randomly from the probability distribution for the measurand. Such a sample does not constitute a convenient way of communicating knowledge about the measurand. In this paper consideration is given to obtaining a more compact summary of such a sample that preserves information about the measurand contained in the sample and can be used in a subsequent uncertainty evaluation. In particular, a coverage interval for the measurand that corresponds to a given coverage probability is often required. If the measurand is characterized by a probability distribution that is not close to being Gaussian, sufficient information has to be conveyed to enable such a coverage interval to be computed reliably. A quantile function in the form of an extended lambda distribution can provide adequate approximations in a number of cases. This distribution is defined by a fixed number of adjustable parameters determined, for example, by matching the moments of the distribution to those calculated in terms of the sample of values. In this paper, alternative flexible models for the quantile function and methods for determining a quantile function from a sample of values are proposed for meeting the above needs.
NASA Astrophysics Data System (ADS)
Velazquez, L.; Castro-Palacio, J. C.
2015-03-01
Velazquez and Curilef [J. Stat. Mech. (2010) P02002, 10.1088/1742-5468/2010/02/P02002; J. Stat. Mech. (2010) P04026, 10.1088/1742-5468/2010/04/P04026] have proposed a methodology to extend Monte Carlo algorithms that are based on canonical ensemble. According to our previous study, their proposal allows us to overcome slow sampling problems in systems that undergo any type of temperature-driven phase transition. After a comprehensive review about ideas and connections of this framework, we discuss the application of a reweighting technique to improve the accuracy of microcanonical calculations, specifically, the well-known multihistograms method of Ferrenberg and Swendsen [Phys. Rev. Lett. 63, 1195 (1989), 10.1103/PhysRevLett.63.1195]. As an example of application, we reconsider the study of the four-state Potts model on the square lattice L ×L with periodic boundary conditions. This analysis allows us to detect the existence of a very small latent heat per site qL during the occurrence of temperature-driven phase transition of this model, whose size dependence seems to follow a power law qL(L ) ?(1/L ) z with exponent z ?0 .26 ±0 .02. Discussed is the compatibility of these results with the continuous character of temperature-driven phase transition when L ?+? .
Bayesian Inference for LISA Pathfinder using Markov Chain Monte Carlo Methods
Luigi Ferraioli; Edward K. Porter; Eric Plagnol
2012-11-30
We present a parameter estimation procedure based on a Bayesian framework by applying a Markov Chain Monte Carlo algorithm to the calibration of the dynamical parameters of a space based gravitational wave detector. The method is based on the Metropolis-Hastings algorithm and a two-stage annealing treatment in order to ensure an effective exploration of the parameter space at the beginning of the chain. We compare two versions of the algorithm with an application to a LISA Pathfinder data analysis problem. The two algorithms share the same heating strategy but with one moving in coordinate directions using proposals from a multivariate Gaussian distribution, while the other uses the natural logarithm of some parameters and proposes jumps in the eigen-space of the Fisher Information matrix. The algorithm proposing jumps in the eigen-space of the Fisher Information matrix demonstrates a higher acceptance rate and a slightly better convergence towards the equilibrium parameter distributions in the application to LISA Pathfinder data . For this experiment, we return parameter values that are all within $\\sim1\\sigma$ of the injected values. When we analyse the accuracy of our parameter estimation in terms of the effect they have on the force-per-unit test mass noise estimate, we find that the induced errors are three orders of magnitude less than the expected experimental uncertainty in the power spectral density.
Monte carlo method-based QSAR modeling of penicillins binding to human serum proteins.
Veselinovi?, Jovana B; Toropov, Andrey A; Toropova, Alla P; Nikoli?, Goran M; Veselinovi?, Aleksandar M
2015-01-01
The binding of penicillins to human serum proteins was modeled with optimal descriptors based on the Simplified Molecular Input-Line Entry System (SMILES). The concentrations of protein-bound drug for 87 penicillins expressed as percentage of the total plasma concentration were used as experimental data. The Monte Carlo method was used as a computational tool to build up the quantitative structure-activity relationship (QSAR) model for penicillins binding to plasma proteins. One random data split into training, test and validation set was examined. The calculated QSAR model had the following statistical parameters: r(2) ?=?0.8760, q(2) ?=?0.8665, s?=?8.94 for the training set and r(2) ?=?0.9812, q(2) ?=?0.9753, s?=?7.31 for the test set. For the validation set, the statistical parameters were r(2) ?=?0.727 and s?=?12.52, but after removing the three worst outliers, the statistical parameters improved to r(2) ?=?0.921 and s?=?7.18. SMILES-based molecular fragments (structural indicators) responsible for the increase and decrease of penicillins binding to plasma proteins were identified. The possibility of using these results for the computer-aided design of new penicillins with desired binding properties is presented. PMID:25408278
Development of a software package for solid-angle calculations using the Monte Carlo method
NASA Astrophysics Data System (ADS)
Zhang, Jie; Chen, Xiulian; Zhang, Changsheng; Li, Gang; Xu, Jiayun; Sun, Guangai
2014-02-01
Solid-angle calculations play an important role in the absolute calibration of radioactivity measurement systems and in the determination of the activity of radioactive sources, which are often complicated. In the present paper, a software package is developed to provide a convenient tool for solid-angle calculations in nuclear physics. The proposed software calculates solid angles using the Monte Carlo method, in which a new type of variance reduction technique was integrated. The package, developed under the environment of Microsoft Foundation Classes (MFC) in Microsoft Visual C++, has a graphical user interface, in which, the visualization function is integrated in conjunction with OpenGL. One advantage of the proposed software package is that it can calculate the solid angle subtended by a detector with different geometric shapes (e.g., cylinder, square prism, regular triangular prism or regular hexagonal prism) to a point, circular or cylindrical source without any difficulty. The results obtained from the proposed software package were compared with those obtained from previous studies and calculated using Geant4. It shows that the proposed software package can produce accurate solid-angle values with a greater computation speed than Geant4.
Analysis of probabilistic short run marginal cost using Monte Carlo method
Gutierrez-Alcaraz, G.; Navarrete, N.; Tovar-Hernandez, J.H.; Fuerte-Esquivel, C.R. [Inst. Tecnologico de Morelia, Michoacan (Mexico). Dept. de Ing. Electrica y Electronica; Mota-Palomino, R. [Inst. Politecnico Nacional (Mexico). Escuela Superior de Ingenieria Mecanica y Electrica
1999-11-01
The structure of the Electricity Supply Industry is undergoing dramatic changes to provide new services options. The main aim of this restructuring is allowing generating units the freedom of selling electricity to anybody they wish at a price determined by market forces. Several methodologies have been proposed in order to quantify different costs associated with those new services offered by electrical utilities operating under a deregulated market. The new wave of pricing is heavily influenced by economic principles designed to price products to elastic market segments on the basis of marginal costs. Hence, spot pricing provides the economic structure for many of new services. At the same time, the pricing is influenced by uncertainties associated to the electric system state variables which defined its operating point. In this paper, nodal probabilistic short run marginal costs are calculated, considering as random variables the load, the production cost and availability of generators. The effect of the electrical network is evaluated taking into account linearized models. A thermal economic dispatch is used to simulate each operational condition generated by Monte Carlo method on small fictitious power system in order to assess the effect of the random variables on the energy trading. First, this is carry out by introducing each random variable one by one, and finally considering the random interaction of all of them.
Monte Carlo analysis of thermochromatography as a fast separation method for nuclear forensics
Hall, Howard L [ORNL
2012-01-01
Nuclear forensic science has become increasingly important for global nuclear security, and enhancing the timeliness of forensic analysis has been established as an important objective in the field. New, faster techniques must be developed to meet this objective. Current approaches for the analysis of minor actinides, fission products, and fuel-specific materials require time-consuming chemical separation coupled with measurement through either nuclear counting or mass spectrometry. These very sensitive measurement techniques can be hindered by impurities or incomplete separation in even the most painstaking chemical separations. High-temperature gas-phase separation or thermochromatography has been used in the past for the rapid separations in the study of newly created elements and as a basis for chemical classification of that element. This work examines the potential for rapid separation of gaseous species to be applied in nuclear forensic investigations. Monte Carlo modeling has been used to evaluate the potential utility of the thermochromatographic separation method, albeit this assessment is necessarily limited due to the lack of available experimental data for validation.
IR imaging simulation and analysis for aeroengine exhaust system based on reverse Monte Carlo method
NASA Astrophysics Data System (ADS)
Chen, Shiguo; Chen, Lihai; Mo, Dongla; Shi, Jingcheng
2014-11-01
The IR radiation characteristics of aeroengine are the important basis for IR stealth design and anti-stealth detection of aircraft. With the development of IR imaging sensor technology, the importance of aircraft IR stealth increases. An effort is presented to explore target IR radiation imaging simulation based on Reverse Monte Carlo Method (RMCM), which combined with the commercial CFD software. Flow and IR radiation characteristics of an aeroengine exhaust system are investigated, which developing a full size geometry model based on the actual parameters, using a flow-IR integration structured mesh, obtaining the engine performance parameters as the inlet boundary conditions of mixer section, and constructing a numerical simulation model of engine exhaust system of IR radiation characteristics based on RMCM. With the above models, IR radiation characteristics of aeroengine exhaust system is given, and focuses on the typical detecting band of IR spectral radiance imaging at azimuth 20°. The result shows that: (1) in small azimuth angle, the IR radiation is mainly from the center cone of all hot parts; near the azimuth 15°, mixer has the biggest radiation contribution, while center cone, turbine and flame stabilizer equivalent; (2) the main radiation components and space distribution in different spectrum is different, CO2 at 4.18, 4.33 and 4.45 micron absorption and emission obviously, H2O at 3.0 and 5.0 micron absorption and emission obviously.
Absorbed Dose Calculations Using Mesh-based Human Phantoms And Monte Carlo Methods
NASA Astrophysics Data System (ADS)
Kramer, Richard
2011-08-01
Health risks attributable to the exposure to ionizing radiation are considered to be a function of the absorbed or equivalent dose to radiosensitive organs and tissues. However, as human tissue cannot express itself in terms of equivalent dose, exposure models have to be used to determine the distribution of equivalent dose throughout the human body. An exposure model, be it physical or computational, consists of a representation of the human body, called phantom, plus a method for transporting ionizing radiation through the phantom and measuring or calculating the equivalent dose to organ and tissues of interest. The FASH2 (Female Adult meSH) and the MASH2 (Male Adult meSH) computational phantoms have been developed at the University of Pernambuco in Recife/Brazil based on polygon mesh surfaces using open source software tools and anatomical atlases. Representing standing adults, FASH2 and MASH2 have organ and tissue masses, body height and body mass adjusted to the anatomical data published by the International Commission on Radiological Protection for the reference male and female adult. For the purposes of absorbed dose calculations the phantoms have been coupled to the EGSnrc Monte Carlo code, which can transport photons, electrons and positrons through arbitrary media. This paper reviews the development of the FASH2 and the MASH2 phantoms and presents dosimetric applications for X-ray diagnosis and for prostate brachytherapy.
Improving Bayesian analysis for LISA Pathfinder using an efficient Markov Chain Monte Carlo method
NASA Astrophysics Data System (ADS)
Ferraioli, Luigi; Porter, Edward K.; Armano, Michele; Audley, Heather; Congedo, Giuseppe; Diepholz, Ingo; Gibert, Ferran; Hewitson, Martin; Hueller, Mauro; Karnesis, Nikolaos; Korsakova, Natalia; Nofrarias, Miquel; Plagnol, Eric; Vitale, Stefano
2014-02-01
We present a parameter estimation procedure based on a Bayesian framework by applying a Markov Chain Monte Carlo algorithm to the calibration of the dynamical parameters of the LISA Pathfinder satellite. The method is based on the Metropolis-Hastings algorithm and a two-stage annealing treatment in order to ensure an effective exploration of the parameter space at the beginning of the chain. We compare two versions of the algorithm with an application to a LISA Pathfinder data analysis problem. The two algorithms share the same heating strategy but with one moving in coordinate directions using proposals from a multivariate Gaussian distribution, while the other uses the natural logarithm of some parameters and proposes jumps in the eigen-space of the Fisher Information matrix. The algorithm proposing jumps in the eigen-space of the Fisher Information matrix demonstrates a higher acceptance rate and a slightly better convergence towards the equilibrium parameter distributions in the application to LISA Pathfinder data. For this experiment, we return parameter values that are all within ˜1 ? of the injected values. When we analyse the accuracy of our parameter estimation in terms of the effect they have on the force-per-unit of mass noise, we find that the induced errors are three orders of magnitude less than the expected experimental uncertainty in the power spectral density.
A Monte-Carlo method for interface dosimetry of beta emitters.
Buffa, Francesca M; Verhaegen, Frank; Flux, Glenn D; Dearnaley, David P
2003-06-01
Biologically targeted radiotherapy optimization requires accurate dose estimation, from macroscopic to cellular/subcellular dimensions. In particular, dose perturbations produced at interfaces between dissimilar media could affect therapy outcome. The magnitude of these perturbations depends on a complex set of parameters. This study investigates perturbations on electron dose for materials with atomic numbers (Z) up to 79 (79Au) at their interface with water as a function of Z, energy, distance from interface and geometry. A Monte-Carlo method that produces absorbed dose distributions in a voxel geometry has been developed using EGSnrc transport routines. Heterogeneous media and activity distributions can be input into this code. The backscatter dose factor (BSDF), which quantifies interface dose perturbations, was estimated using this code. The BSDF magnitude ranged from approximately 3% to approximately 50%, depending on source energy and Z. The BSDF decreased with increasing energy and showed a logarithmic dependence on Z. Empirical functions were fit to the results, that could be used to correct dose calculations performed using dose-point-kernels estimated in water, to cases involving different scattering materials. The BSDF was found to be highly dependent on interface geometry and scoring volume; thus it is vital that BSDFs are used only in geometry conditions that are similar to those in which they were originally produced. PMID:12954134
Deterministic flows of order-parameters in stochastic processes of quantum Monte Carlo method
NASA Astrophysics Data System (ADS)
Inoue, Jun-ichi
2010-06-01
In terms of the stochastic process of quantum-mechanical version of Markov chain Monte Carlo method (the MCMC), we analytically derive macroscopically deterministic flow equations of order parameters such as spontaneous magnetization in infinite-range (d(= ?)-dimensional) quantum spin systems. By means of the Trotter decomposition, we consider the transition probability of Glauber-type dynamics of microscopic states for the corresponding (d + 1)-dimensional classical system. Under the static approximation, differential equations with respect to macroscopic order parameters are explicitly obtained from the master equation that describes the microscopic-law. In the steady state, we show that the equations are identical to the saddle point equations for the equilibrium state of the same system. The equation for the dynamical Ising model is recovered in the classical limit. We also check the validity of the static approximation by making use of computer simulations for finite size systems and discuss several possible extensions of our approach to disordered spin systems for statistical-mechanical informatics. Especially, we shall use our procedure to evaluate the decoding process of Bayesian image restoration. With the assistance of the concept of dynamical replica theory (the DRT), we derive the zero-temperature flow equation of image restoration measure showing some 'non-monotonic' behaviour in its time evolution.
Monte Carlo studies of 3d N=6 SCFT via localization method
Masazumi Honda; Masanori Hanada; Yoshinori Honma; Jun Nishimura; Shotaro Shiba; Yutaka Yoshida
2012-11-29
We perform Monte Carlo study of the 3d N=6 superconformal U(N)*U(N) Chern-Simons gauge theory (ABJM theory), which is conjectured to be dual to M-theory or type IIA superstring theory on certain AdS backgrounds. Our approach is based on a localization method, which reduces the problem to the simulation of a simple matrix model. This enables us to circumvent the difficulties in the original theory such as the sign problem and the SUSY breaking on a lattice. The new approach opens up the possibility of probing the quantum aspects of M-theory and testing the AdS_4/CFT_3 duality at the quantum level. Here we calculate the free energy, and confirm the N^{3/2} scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes.
Feasibility of a Monte Carlo-deterministic hybrid method for fast reactor analysis
Heo, W.; Kim, W.; Kim, Y. [Korea Advanced Institute of Science and Technology - KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701 (Korea, Republic of); Yun, S. [Korea Atomic Energy Research Institute - KAERI, 989-111 Daedeok-daero, Yuseong-gu, Daejeon, 305-353 (Korea, Republic of)
2013-07-01
A Monte Carlo and deterministic hybrid method is investigated for the analysis of fast reactors in this paper. Effective multi-group cross sections data are generated using a collision estimator in the MCNP5. A high order Legendre scattering cross section data generation module was added into the MCNP5 code. Both cross section data generated from MCNP5 and TRANSX/TWODANT using the homogeneous core model were compared, and were applied to DIF3D code for fast reactor core analysis of a 300 MWe SFR TRU burner core. For this analysis, 9 groups macroscopic-wise data was used. In this paper, a hybrid calculation MCNP5/DIF3D was used to analyze the core model. The cross section data was generated using MCNP5. The k{sub eff} and core power distribution were calculated using the 54 triangle FDM code DIF3D. A whole core calculation of the heterogeneous core model using the MCNP5 was selected as a reference. In terms of the k{sub eff}, 9-group MCNP5/DIF3D has a discrepancy of -154 pcm from the reference solution, 9-group TRANSX/TWODANT/DIF3D analysis gives -1070 pcm discrepancy. (authors)
A new method for RGB to CIELAB color space transformation based on Markov chain Monte Carlo
NASA Astrophysics Data System (ADS)
Chen, Yajun; Liu, Ding; Liang, Junli
2013-10-01
During printing quality inspection, the inspection of color error is an important content. However, the RGB color space is device-dependent, usually RGB color captured from CCD camera must be transformed into CIELAB color space, which is perceptually uniform and device-independent. To cope with the problem, a Markov chain Monte Carlo (MCMC) based algorithms for the RGB to the CIELAB color space transformation is proposed in this paper. Firstly, the modeling color targets and testing color targets is established, respectively used in modeling and performance testing process. Secondly, we derive a Bayesian model for estimation the coefficients of a polynomial, which can be used to describe the relation between RGB and CIELAB color space. Thirdly, a Markov chain is set up base on Gibbs sampling algorithm (one of the MCMC algorithm) to estimate the coefficients of polynomial. Finally, the color difference of testing color targets is computed for evaluating the performance of the proposed method. The experimental results showed that the nonlinear polynomial regression based on MCMC algorithm is effective, whose performance is similar to the least square approach and can accurately model the RGB to the CIELAB color space conversion and guarantee the color error evaluation for printing quality inspection system.
Spaceborne imaging simulation of ship based on Monte Carlo ray tracing method
NASA Astrophysics Data System (ADS)
Wang, Biao; He, Hong-fei; Lin, Jia-xuan
2014-11-01
To demonstrate image quality and sensor's performance for target detection before the satellite launched, it is necessary to establish an end-to-end model that express the detection probability in terms of atmosphere effects, the sensor, and optical scattering properties of target. It is difficult to develop an accurate 3D radiation transfer model for scene including complex target, especially for large scale scene. It is beneficial to process separately the target and large scale background. Radiance from sea background can be solved exactly with atmospheric-ocean coupling radiation transfer model. However for ship target, it is only but sufficient to using the sample model. In the model the illuminated light is separate into direct sunlight and sky light, and the sensor received radiance is radiance scatted from target and attenuated by atmosphere. High spatial/spectral resolution image simulated with Monte Carlo ray tracing method is used as input for modeling space-borne imagery, which is economic for demonstrating sensor's performance at different conditions and multiple scattering can also be considered. Bidirectional reflectance distribution function (BRDF) is introduced to characterize the light scattering model of the ship sample material.
HRMC_1.1: Hybrid Reverse Monte Carlo method with silicon and carbon potentials
NASA Astrophysics Data System (ADS)
Opletal, G.; Petersen, T. C.; O'Malley, B.; Snook, I. K.; McCulloch, D. G.; Yarovsky, I.
2011-02-01
The Hybrid Reverse Monte Carlo (HRMC) code models the atomic structure of materials via the use of a combination of constraints including experimental diffraction data and an empirical energy potential. This energy constraint is in the form of either the Environment Dependent Interatomic Potential (EDIP) for carbon and silicon and the original and modified Stillinger-Weber potentials applicable to silicon. In this version, an update is made to correct an error in the EDIP carbon energy calculation routine. New version program summaryProgram title: HRMC version 1.1 Catalogue identifier: AEAO_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAO_v1_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 36 991 No. of bytes in distributed program, including test data, etc.: 907 800 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Any computer capable of running executables produced by the g77 Fortran compiler. Operating system: Unix, Windows RAM: Depends on the type of empirical potential use, number of atoms and which constraints are employed. Classification: 7.7 Catalogue identifier of previous version: AEAO_v1_0 Journal reference of previous version: Comput. Phys. Comm. 178 (2008) 777 Does the new version supersede the previous version?: Yes Nature of problem: Atomic modelling using empirical potentials and experimental data. Solution method: Monte Carlo Reasons for new version: An error in a term associated with the calculation of energies using the EDIP carbon potential which results in incorrect energies. Summary of revisions: Fix to correct brackets in the two body part of the EDIP carbon potential routine. Additional comments: The code is not standard FORTRAN 77 but includes some additional features and therefore generates errors when compiled using the Nag95 compiler. It does compile successfully with the GNU g77 compiler ( http://www.gnu.org/software/fortran/fortran.html). Running time: Depends on the type of empirical potential use, number of atoms and which constraints are employed. The test included in the distribution took 37 minutes on a DEC Alpha PC.
S. M. Mesli; M. Habchi; M. Kotbi; H. Xu
2013-03-25
The choice of appropriate interaction models is among the major disadvantages of conventional methods such as molecular dynamics and Monte Carlo simulations. On the other hand, the so-called reverse Monte Carlo (RMC) method, based on experimental data, can be applied without any interatomic and/or intermolecular interactions. The RMC results are accompanied by artificial satellite peaks. To remedy this problem, we use an extension of the RMC algorithm, which introduces an energy penalty term into the acceptance criteria. This method is referred to as the hybrid reverse Monte Carlo (HRMC) method. The idea of this paper is to test the validity of a combined potential model of coulomb and Lennard-Jones in a fluoride glass system BaMnMF_{7} (M=Fe,V) using HRMC method. The results show a good agreement between experimental and calculated characteristics, as well as a meaningful improvement in partial pair distribution functions. We suggest that this model should be used in calculating the structural properties and in describing the average correlations between components of fluoride glass or a similar system. We also suggest that HRMC could be useful as a tool for testing the interaction potential models, as well as for conventional applications.
NASA Astrophysics Data System (ADS)
Harries, Tim J.
2015-04-01
We present a set of new numerical methods that are relevant to calculating radiation pressure terms in hydrodynamics calculations, with a particular focus on massive star formation. The radiation force is determined from a Monte Carlo estimator and enables a complete treatment of the detailed microphysics, including polychromatic radiation and anisotropic scattering, in both the free-streaming and optically thick limits. Since the new method is computationally demanding we have developed two new methods that speed up the algorithm. The first is a photon packet splitting algorithm that enables efficient treatment of the Monte Carlo process in very optically thick regions. The second is a parallelization method that distributes the Monte Carlo workload over many instances of the hydrodynamic domain, resulting in excellent scaling of the radiation step. We also describe the implementation of a sink particle method that enables us to follow the accretion on to, and the growth of, the protostars. We detail the results of extensive testing and benchmarking of the new algorithms.
Capote, Roberto [Nuclear Data Section, International Atomic Energy Agency, P.O. Box 100, Wagramer Strasse 5, A-1400 Vienna (Austria)], E-mail: Roberto.CapoteNoy@iaea.org; Smith, Donald L. [Argonne National Laboratory, 1710 Avenida del Mundo, Coronado, California 92118-3073 (United States)
2008-12-15
The Unified Monte Carlo method (UMC) has been suggested to avoid certain limitations and approximations inherent to the well-known Generalized Least Squares (GLS) method of nuclear data evaluation. This contribution reports on an investigation of the performance of the UMC method in comparison with the GLS method. This is accomplished by applying both methods to simple examples with few input values that were selected to explore various features of the evaluation process that impact upon the quality of an evaluation. Among the issues explored are: i) convergence of UMC results with the number of Monte Carlo histories and the ranges of sampled values; ii) a comparison of Monte Carlo sampling using the Metropolis scheme and a brute force approach; iii) the effects of large data discrepancies; iv) the effects of large data uncertainties; v) the effects of strong or weak model or experimental data correlations; and vi) the impact of ratio data and integral data. Comparisons are also made of the evaluated results for these examples when the input values are first transformed to comparable logarithmic values prior to performing the evaluation. Some general conclusions that are applicable to more realistic evaluation exercises are offered.
Forward treatment planning for modulated electron radiotherapy (MERT) employing Monte Carlo methods
Henzen, D., E-mail: henzen@ams.unibe.ch; Manser, P.; Frei, D.; Volken, W.; Born, E. J.; Lössl, K.; Aebersold, D. M.; Fix, M. K. [Division of Medical Radiation Physics and Department of Radiation Oncology, Inselspital, Bern University Hospital, University of Bern, CH-3010 Berne (Switzerland)] [Division of Medical Radiation Physics and Department of Radiation Oncology, Inselspital, Bern University Hospital, University of Bern, CH-3010 Berne (Switzerland); Neuenschwander, H. [Clinic for Radiation-Oncology, Lindenhofspital Bern, CH-3012 Berne (Switzerland)] [Clinic for Radiation-Oncology, Lindenhofspital Bern, CH-3012 Berne (Switzerland); Stampanoni, M. F. M. [Institute for Biomedical Engineering, ETH Zürich and Paul Scherrer Institut, CH-5234 Villigen (Switzerland)] [Institute for Biomedical Engineering, ETH Zürich and Paul Scherrer Institut, CH-5234 Villigen (Switzerland)
2014-03-15
Purpose: This paper describes the development of a forward planning process for modulated electron radiotherapy (MERT). The approach is based on a previously developed electron beam model used to calculate dose distributions of electron beams shaped by a photon multi leaf collimator (pMLC). Methods: As the electron beam model has already been implemented into the Swiss Monte Carlo Plan environment, the Eclipse treatment planning system (Varian Medical Systems, Palo Alto, CA) can be included in the planning process for MERT. In a first step, CT data are imported into Eclipse and a pMLC shaped electron beam is set up. This initial electron beam is then divided into segments, with the electron energy in each segment chosen according to the distal depth of the planning target volume (PTV) in beam direction. In order to improve the homogeneity of the dose distribution in the PTV, a feathering process (Gaussian edge feathering) is launched, which results in a number of feathered segments. For each of these segments a dose calculation is performed employing the in-house developed electron beam model along with the macro Monte Carlo dose calculation algorithm. Finally, an automated weight optimization of all segments is carried out and the total dose distribution is read back into Eclipse for display and evaluation. One academic and two clinical situations are investigated for possible benefits of MERT treatment compared to standard treatments performed in our clinics and treatment with a bolus electron conformal (BolusECT) method. Results: The MERT treatment plan of the academic case was superior to the standard single segment electron treatment plan in terms of organs at risk (OAR) sparing. Further, a comparison between an unfeathered and a feathered MERT plan showed better PTV coverage and homogeneity for the feathered plan, with V{sub 95%} increased from 90% to 96% and V{sub 107%} decreased from 8% to nearly 0%. For a clinical breast boost irradiation, the MERT plan led to a similar homogeneity in the PTV compared to the standard treatment plan while the mean body dose was lower for the MERT plan. Regarding the second clinical case, a whole breast treatment, MERT resulted in a reduction of the lung volume receiving more than 45% of the prescribed dose when compared to the standard plan. On the other hand, the MERT plan leads to a larger low-dose lung volume and a degraded dose homogeneity in the PTV. For the clinical cases evaluated in this work, treatment plans using the BolusECT technique resulted in a more homogenous PTV and CTV coverage but higher doses to the OARs than the MERT plans. Conclusions: MERT treatments were successfully planned for phantom and clinical cases, applying a newly developed intuitive and efficient forward planning strategy that employs a MC based electron beam model for pMLC shaped electron beams. It is shown that MERT can lead to a dose reduction in OARs compared to other methods. The process of feathering MERT segments results in an improvement of the dose homogeneity in the PTV.
Numerical simulations of blast-impact problems using the direct simulation Monte Carlo method
NASA Astrophysics Data System (ADS)
Sharma, Anupam
There is an increasing need to design protective structures that can withstand or mitigate the impulsive loading due to the impact of a blast or a shock wave. A preliminary step in designing such structures is the prediction of the pressure loading on the structure. This is called the "load definition." This thesis is focused on a numerical approach to predict the load definition on arbitrary geometries for a given strength of the incident blast/shock wave. A particle approach, namely the Direct Simulation Monte Carlo (DSMC) method, is used as the numerical model. A three-dimensional, time-accurate DSMC flow solver is developed as a part of this study. Embedded surfaces, modeled as triangulations, are used to represent arbitrary-shaped structures. Several techniques to improve the computational efficiency of the algorithm of particle-structure interaction are presented. The code is designed using the Object Oriented Programming (OOP) paradigm. Domain decomposition with message passing is used to solve large problems in parallel. The solver is extensively validated against analytical results and against experiments. Two kinds of geometries, a box and an I-shaped beam are investigated for blast impact. These simulations are performed in both two- and three-dimensions. A major portion of the thesis is dedicated to studying the uncoupled fluid dynamics problem where the structure is assumed to remain stationary and intact during the simulation. A coupled, fluid-structure dynamics problem is solved in one spatial dimension using a simple, spring-mass-damper system to model the dynamics of the structure. A parametric study, by varying the mass, spring constant, and the damping coefficient, to study their effect on the loading and the displacement of the structure is also performed. Finally, the parallel performance of the solver is reported for three sample-size problems on two Beowulf clusters.
Geometrically-compatible 3-D Monte Carlo and discrete-ordinates methods
Morel, J.E.; Wareing, T.A.; McGhee, J.M.; Evans, T.M.
1998-12-31
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The purpose of this project was two-fold. The first purpose was to develop a deterministic discrete-ordinates neutral-particle transport scheme for unstructured tetrahedral spatial meshes, and implement it in a computer code. The second purpose was to modify the MCNP Monte Carlo radiation transport code to use adjoint solutions from the tetrahedral-mesh discrete-ordinates code to reduce the statistical variance of Monte Carlo solutions via a weight-window approach. The first task has resulted in a deterministic transport code that is much more efficient for modeling complex 3-D geometries than any previously existing deterministic code. The second task has resulted in a powerful new capability for dramatically reducing the cost of difficult 3-D Monte Carlo calculations.
D'Angola, A.; Tuttafesta, M.; Guadagno, M.; Santangelo, P.; Laricchiuta, A.; Colonna, G.; Capitelli, M. [Scuola di Ingegneria SI, Universita della Basilicata, via dell'Ateneo Lucano, 10 - 85100 Potenza (Italy); Universita di Bari, via Orabona, 4 - 70126 Bari (Italy); Scuola di Ingegneria SI, Universita della Basilicata, via dell'Ateneo Lucano, 10 - 85100 Potenza (Italy); CNR-IMIP Bari, via Amendola 122/D - 70126 Bari (Italy); Universita di Bari, via Orabona, 4 - 70126 Bari (Italy) and CNR-IMIP Bari, via Amendola 122/D - 70126 Bari (Italy)
2012-11-27
Calculations of thermodynamic properties of Helium plasma by using the Reaction Ensemble Monte Carlo method (REMC) are presented. Non ideal effects at high pressure are observed. Calculations, performed by using Exp-6 or multi-potential curves in the case of neutral-charge interactions, show that in the thermodynamic conditions considered no significative differences are observed. Results have been obtained by using a Graphics Processing Unit (GPU)-CUDA C version of REMC.
Williams, M. L.; Gehin, J. C.; Clarno, K. T. [Oak Ridge National Laboratory, Bldg. 5700, P.O. Box 2008, Oak Ridge, TN 37831-6170 (United States)
2006-07-01
The TSUNAMI computational sequences currently in the SCALE 5 code system provide an automated approach to performing sensitivity and uncertainty analysis for eigenvalue responses, using either one-dimensional discrete ordinates or three-dimensional Monte Carlo methods. This capability has recently been expanded to address eigenvalue-difference responses such as reactivity changes. This paper describes the methodology and presents results obtained for an example advanced CANDU reactor design. (authors)
Estimation of gamma- and X-ray photons buildup factor in soft tissue with Monte Carlo method
Dariush Sardari; Ali Abbaspour; Samaneh Baradaran; Farshid Babapour
2009-01-01
Buildup factor of gamma- and X-ray photons in the energy range 0.2–2MeV in water and soft tissue is computed using Monte Carlo method. The results are compared with the existing buildup factor data of pure water. The difference between soft tissue and water buildup factor is studied. Soft tissue is assumed to have a composition as H63C6O28N. The importance of
Lawson, A B
The spatial modelling of small area health data has, for some time, included spatial autocorrelation as a random effect. This effect is non-specific and global and does not address the location of clusters of disease (a specific task). This paper addresses the need for specific and non-specific random effects within spatial epidemiology. In addition, individual frailty is also considered important and a computational algorithm based on reversible jump Markov chain Monte Carlo (RJMCMC) methods is described. PMID:10960859
G. Desrochers; M. Blanchard; S. Sud
1986-01-01
A method for determining the costeffectiveness of wind energy and the economic limitations of penetration into electrical power systems is presented. It is based on a Monte-Carlo approach which simulates the hour-by-hour operation of the power system. The hourly random variations in wind and load are modeled in addition to the operating constraints inherent in conventional generation. The economic assessment
NASA Astrophysics Data System (ADS)
Yesilyurt, Gokhan
Two of the primary challenges associated with the neutronic analysis of the Very High Temperature Reactor (VHTR) are accounting for resonance self-shielding in the particle fuel (contributing to the double heterogeneity) and accounting for temperature feedback due to Doppler broadening. The double heterogeneity challenge is addressed by defining a "double heterogeneity factor" (DHF) that allows conventional light water reactor (LWR) lattice physics codes to analyze VHTR configurations. The challenge of treating Doppler broadening is addressed by a new "on-the-fly" methodology that is applied during the random walk process with negligible impact on computational efficiency. Although this methodology was motivated by the need to treat temperature feedback in a VHTR, it is applicable to any reactor design. The on-the-fly Doppler methodology is based on a combination of Taylor and asymptotic series expansions. The type of series representation was determined by investigating the temperature dependence of U238 resonance cross sections in three regions: near the resonance peaks, mid-resonance, and the resonance wings. The coefficients for these series expansions were determined by regressions over the energy and temperature range of interest. The comparison of the broadened cross sections using this methodology with the NJOY cross sections was excellent. A Monte Carlo code was implemented to apply the combined regression model and used to estimate the additional computing cost which was found to be less than 1%. The DHF accounts for the effect of the particle heterogeneity on resonance absorption in particle fuel. The first level heterogeneity posed by the VHTR fuel particles is a unique characteristic that cannot be accounted for by conventional LWR lattice physics codes. On the other hand, Monte Carlo codes can take into account the detailed geometry of the VHTR including resolution of individual fuel particles without performing any type of resonance approximation. The DHF, basically a self shielding factor, was found to be weakly dependent on space and fuel depletion. The DHF only depends strongly on the packing fraction in a fuel compact. Therefore, it is proposed that DHFs be tabulated as a function of packing fraction to analyze the heterogeneous fuel in VHTR configuration with LWR lattice physics codes.
Use of Monte Carlo methods in environmental risk assessments at the INEL: Applications and issues
Harris, G.; Van Horn, R.
1996-06-01
The EPA is increasingly considering the use of probabilistic risk assessment techniques as an alternative or refinement of the current point estimate of risk. This report provides an overview of the probabilistic technique called Monte Carlo Analysis. Advantages and disadvantages of implementing a Monte Carlo analysis over a point estimate analysis for environmental risk assessment are discussed. The general methodology is provided along with an example of its implementation. A phased approach to risk analysis that allows iterative refinement of the risk estimates is recommended for use at the INEL.
Alrefae, T
2014-12-01
A simple method of efficiency calibration for gamma spectrometry was performed. This method, which focused on measuring the radioactivity of (137)Cs in food samples, was based on Monte Carlo simulations available in the free-of-charge toolkit GEANT4. Experimentally, the efficiency values of a high-purity germanium detector were calculated for three reference materials representing three different food items. These efficiency values were compared with their counterparts produced by a computer code that simulated experimental conditions. Interestingly, the output of the simulation code was in acceptable agreement with the experimental findings, thus validating the proposed method. PMID:24214912
Pauw, Brian R.; Pedersen, Jan Skov; Tardif, Samuel; Takata, Masaki; Iversen, Bo B.
2013-01-01
Monte Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve form-free particle size distributions from small-angle scattering patterns of non-interacting low-concentration scatterers such as particles in solution or precipitates in metals. Improvements are presented to existing MC methods, such as a non-ambiguous convergence criterion, nonlinear scaling of contributions to match their observability in a scattering measurement, and a method for estimating the minimum visibility threshold and uncertainties on the resulting size distributions. PMID:23596341
Evans, J. S.; Chan, S. I.; Goddard, W. A.
1995-01-01
Many interesting proteins possess defined sequence stretches containing negatively charged amino acids. At present, experimental methods (X-ray crystallography, NMR) have failed to provide structural data for many of these sequence domains. We have applied the dihedral probability grid-Monte Carlo (DPG-MC) conformational search algorithm to a series of N- and C-capped polyelectrolyte peptides, (Glu)20, (Asp)20, (PSer)20, and (PSer-Asp)10, that represent polyanionic regions in a number of important proteins, such as parathymosin, calsequestrin, the sodium channel protein, and the acidic biomineralization proteins. The atomic charges were estimated from charge equilibration and the valence and van der Waals parameters are from DREIDING. Solvation of the carboxylate and phosphate groups was treated using sodium counterions for each charged side chain (one Na+ for COO-; two Na for CO(PO3)-2) plus a distance-dependent (shielded) dielectric constant, epsilon = epsilon 0 R, to simulate solvent water. The structures of these polyelectrolyte polypeptides were obtained by the DPG-MC conformational search with epsilon 0 = 10, followed by calculation of solvation energies for the lowest energy conformers using the protein dipole-Langevin dipole method of Warshel. These calculations predict a correlation between amino acid sequence and global folded conformational minima: 1. Poly-L-Glu20, our structural benchmark, exhibited a preference for right-handed alpha-helix (47% helicity), which approximates experimental observations of 55-60% helicity in solution. 2. For Asp- and PSer-containing sequences, all conformers exhibited a low preference for right-handed alpha-helix formation (< or = 10%), but a significant percentage (approximately 20% or greater) of beta-strand and beta-turn dihedrals were found in all three sequence cases: (1) Aspn forms supercoil conformers, with a 2:1:1 ratio of beta-turn:beta-strand:alpha-helix dihedral angles; (2) PSer20 features a nearly 1:1 ratio of beta-turn:beta-sheet dihedral preferences, with very little preference for alpha-helical structure, and possesses short regions of strand and turn combinations that give rise to a collapsed bend or hairpin structure; (3) (PSer-Asp)10 features a 3:2:1 ratio of beta-sheet:beta-turn:alpha-helix and gives rise to a superturn or C-shaped structure. PMID:8535238
A study of the XY model by the Monte Carlo method
NASA Technical Reports Server (NTRS)
Suranyi, Peter; Harten, Paul
1987-01-01
The massively parallel processor is used to perform Monte Carlo simulations for the two dimensional XY model on lattices of sizes up to 128 x 128. A parallel random number generator was constructed, finite size effects were studied, and run times were compared with those on a CRAY X-MP supercomputer.
An Evaluation of a Markov Chain Monte Carlo Method for the Two-Parameter Logistic Model.
ERIC Educational Resources Information Center
Kim, Seock-Ho; Cohen, Allan S.
The accuracy of the Markov Chain Monte Carlo (MCMC) procedure Gibbs sampling was considered for estimation of item parameters of the two-parameter logistic model. Data for the Law School Admission Test (LSAT) Section 6 were analyzed to illustrate the MCMC procedure. In addition, simulated data sets were analyzed using the MCMC, marginal Bayesian…
Madsen, Jonathan R
2013-08-13
for predicting molecule-specific ionization, excitation, and scattering cross sections in the very low energy regime that can be applied in a condensed history Monte Carlo track-structure code. The present methodology begins with the calculation of a solution...
An application of the Monte Carlo method to determine an active volume of a semiconductor detector
NASA Astrophysics Data System (ADS)
Kozma, P.; Bém, P.; Vincour, J.
1980-05-01
A Monte Carlo model of scattering and absorption events of a gamma-ray in a finite detector is presented. For the effect of a finite detector to be included, energy spectra of scattered electrons are calculated using random sampling technique. This makes possible the accurate calculation of an active volume of a given semiconductor detector.
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Mark Jerrum; Alistair Sinclair
1996-01-01
In the area of statistical physics, Monte Carlo algorithms based on Markov chain simulation have been in use for many years. The validity of these algorithms depends cru- cially on the rate of convergence to equilibrium of the Markov chain being simulated. Unfortunately, the classical theory of stochastic processes hardly touches on the sort of non-asymptotic analysis required in this
A Monte Carlo Comparison of Parametric and Nonparametric Polytomous DIF Detection Methods.
ERIC Educational Resources Information Center
Bolt, Daniel M.
2002-01-01
Compared two parametric procedures for detecting differential item functioning (DIF) using the graded response model (GRM), the GRM-likelihood ratio test and the GRM-differential functioning of items and tests, with a nonparametric DIF detection procedure, Poly-SIBTEST. Monte Carlo simulation results show that Poly-SIBTEST showed the least amount…
NASA Astrophysics Data System (ADS)
Rinaldi, G.; Ciarniello, M.; Capaccioni, F.; Fink, U.; Filacchione, G.; Tozzi, G. P.; B??cka, M.
2014-04-01
In this paper we present simulations of the radiance coming from the coma of 67/P Churyumov- Gerasimenko, that are meant to support the scientific investigation of VIRTIS (Visible and Infrared Thermal Imaging Spectrometer) instrument onboard of the Rosetta spacecraft, working in the 0.25-5 ?m spectral range. During the observation plan phase such simulations drive the selection of the integration times and spacecraft's pointing while during the postprocessing phase the same model shall be used to retrieve the physical properties of the coma. Cometary coma spectra are strongly affected by the dynamical processes involving dust and ice grains present in the coma. The solar light illuminates the grains that can scatter, absorb and emit radiation. Radiative transfer in the coma can be modeled by means of Monte Carlo methods. Here we show results from two different routines: SCATRD 06.10 code (Vasilyev et al., 2006) and 3D Monte Carlo code developed by (Ciarniello et al., 2014).
Development of CT scanner models for patient organ dose calculations using Monte Carlo methods
NASA Astrophysics Data System (ADS)
Gu, Jianwei
There is a serious and growing concern about the CT dose delivered by diagnostic CT examinations or image-guided radiation therapy imaging procedures. To better understand and to accurately quantify radiation dose due to CT imaging, Monte Carlo based CT scanner models are needed. This dissertation describes the development, validation, and application of detailed CT scanner models including a GE LightSpeed 16 MDCT scanner and two image guided radiation therapy (IGRT) cone beam CT (CBCT) scanners, kV CBCT and MV CBCT. The modeling process considered the energy spectrum, beam geometry and movement, and bowtie filter (BTF). The methodology of validating the scanner models using reported CTDI values was also developed and implemented. Finally, the organ doses to different patients undergoing CT scan were obtained by integrating the CT scanner models with anatomically-realistic patient phantoms. The tube current modulation (TCM) technique was also investigated for dose reduction. It was found that for RPI-AM, thyroid, kidneys and thymus received largest dose of 13.05, 11.41 and 11.56 mGy/100 mAs from chest scan, abdomen-pelvis scan and CAP scan, respectively using 120 kVp protocols. For RPI-AF, thymus, small intestine and kidneys received largest dose of 10.28, 12.08 and 11.35 mGy/100 mAs from chest scan, abdomen-pelvis scan and CAP scan, respectively using 120 kVp protocols. The dose to the fetus of the 3 month pregnant patient phantom was 0.13 mGy/100 mAs and 0.57 mGy/100 mAs from the chest and kidney scan, respectively. For the chest scan of the 6 month patient phantom and the 9 month patient phantom, the fetal doses were 0.21 mGy/100 mAs and 0.26 mGy/100 mAs, respectively. For MDCT with TCM schemas, the fetal dose can be reduced with 14%-25%. To demonstrate the applicability of the method proposed in this dissertation for modeling the CT scanner, additional MDCT scanner was modeled and validated by using the measured CTDI values. These results demonstrated that the CT scanner models in this dissertation were versatile and accurate tools for estimating dose to different patient phantoms undergoing various CT procedures. The organ doses from kV and MV CBCT were also calculated. This dissertation finally summarizes areas where future research can be performed including MV CBCT further validation and application, dose reporting software and image and dose correlation study.
Nanothermodynamics of large iron clusters by means of a flat histogram Monte Carlo method
Basire, M.; Soudan, J.-M.; Angelié, C., E-mail: christian.angelie@cea.fr [Laboratoire Francis Perrin, CNRS-URA 2453, CEA/DSM/IRAMIS/LIDyL, F-91191 Gif-sur-Yvette Cedex (France)
2014-09-14
The thermodynamics of iron clusters of various sizes, from 76 to 2452 atoms, typical of the catalyst particles used for carbon nanotubes growth, has been explored by a flat histogram Monte Carlo (MC) algorithm (called the ?-mapping), developed by Soudan et al. [J. Chem. Phys. 135, 144109 (2011), Paper I]. This method provides the classical density of states, g{sub p}(E{sub p}) in the configurational space, in terms of the potential energy of the system, with good and well controlled convergence properties, particularly in the melting phase transition zone which is of interest in this work. To describe the system, an iron potential has been implemented, called “corrected EAM” (cEAM), which approximates the MEAM potential of Lee et al. [Phys. Rev. B 64, 184102 (2001)] with an accuracy better than 3 meV/at, and a five times larger computational speed. The main simplification concerns the angular dependence of the potential, with a small impact on accuracy, while the screening coefficients S{sub ij} are exactly computed with a fast algorithm. With this potential, ergodic explorations of the clusters can be performed efficiently in a reasonable computing time, at least in the upper half of the solid zone and above. Problems of ergodicity exist in the lower half of the solid zone but routes to overcome them are discussed. The solid-liquid (melting) phase transition temperature T{sub m} is plotted in terms of the cluster atom number N{sub at}. The standard N{sub at}{sup ?1/3} linear dependence (Pawlow law) is observed for N{sub at} >300, allowing an extrapolation up to the bulk metal at 1940 ±50 K. For N{sub at} <150, a strong divergence is observed compared to the Pawlow law. The melting transition, which begins at the surface, is stated by a Lindemann-Berry index and an atomic density analysis. Several new features are obtained for the thermodynamics of cEAM clusters, compared to the Rydberg pair potential clusters studied in Paper I.
Wade, A. C. J.; Baillie, D.; Blakie, P. B. [Department of Physics, Jack Dodd Centre for Quantum Technology, University of Otago, Dunedin (New Zealand)
2011-08-15
In this paper, we develop a direct simulation Monte Carlo method for simulating highly nonequilibrium dynamics of nondegenerate ultracold gases. We show that our method can simulate the high-energy collision of two thermal clouds in the regime observed in experiments [Thomas et al. Phys. Rev. Lett. 93, 173201 (2004)], which requires the inclusion of beyond s-wave scattering. We also consider the long-time dynamics of this system, demonstrating that this would be a practical experimental scenario for testing the Boltzmann equation and studying rethermalization.
NASA Astrophysics Data System (ADS)
Sadovich, Sergey; Talamo, A.; Burnos, V.; Kiyavitskaya, H.; Fokov, Yu.
2014-06-01
In subcritical systems driven by an external neutron source, the experimental methods based on pulsed neutron source and statistical techniques play an important role for reactivity measurement. Simulation of these methods is very time-consumed procedure. For simulations in Monte-Carlo programs several improvements for neutronic calculations have been made. This paper introduces a new method for simulation PNS and statistical measurements. In this method all events occurred in the detector during simulation are stored in a file using PTRAC feature in the MCNP. After that with a special code (or post-processing) PNS and statistical methods can be simulated. Additionally different shapes of neutron pulses and its lengths as well as dead time of detectors can be included into simulation. The methods described above were tested on subcritical assembly Yalina-Thermal, located in Joint Institute for Power and Nuclear Research SOSNY, Minsk, Belarus. A good agreement between experimental and simulated results was shown.
Stefanakis, N
2014-01-01
In this paper we model by using the Monte Carlo simulation code PENELOPE [1, 2] a Broad Energy Germanium (BEGe) detector and determine its efficiency. The simulated geometry consists of a point source located close to the detector as well as volume sources with cylindrical geometry. A comparison of the simulation is made to experimental results as well as to analytical calculations.
The Metropolis Monte Carlo method with CUDA enabled Graphic Processing Units
Hall, Clifford [Computational Materials Science Center, George Mason University, 4400 University Dr., Fairfax, VA 22030 (United States) [Computational Materials Science Center, George Mason University, 4400 University Dr., Fairfax, VA 22030 (United States); School of Physics, Astronomy, and Computational Sciences, George Mason University, 4400 University Dr., Fairfax, VA 22030 (United States); Ji, Weixiao [Computational Materials Science Center, George Mason University, 4400 University Dr., Fairfax, VA 22030 (United States)] [Computational Materials Science Center, George Mason University, 4400 University Dr., Fairfax, VA 22030 (United States); Blaisten-Barojas, Estela, E-mail: blaisten@gmu.edu [Computational Materials Science Center, George Mason University, 4400 University Dr., Fairfax, VA 22030 (United States) [Computational Materials Science Center, George Mason University, 4400 University Dr., Fairfax, VA 22030 (United States); School of Physics, Astronomy, and Computational Sciences, George Mason University, 4400 University Dr., Fairfax, VA 22030 (United States)
2014-02-01
We present a CPU–GPU system for runtime acceleration of large molecular simulations using GPU computation and memory swaps. The memory architecture of the GPU can be used both as container for simulation data stored on the graphics card and as floating-point code target, providing an effective means for the manipulation of atomistic or molecular data on the GPU. To fully take advantage of this mechanism, efficient GPU realizations of algorithms used to perform atomistic and molecular simulations are essential. Our system implements a versatile molecular engine, including inter-molecule interactions and orientational variables for performing the Metropolis Monte Carlo (MMC) algorithm, which is one type of Markov chain Monte Carlo. By combining memory objects with floating-point code fragments we have implemented an MMC parallel engine that entirely avoids the communication time of molecular data at runtime. Our runtime acceleration system is a forerunner of a new class of CPU–GPU algorithms exploiting memory concepts combined with threading for avoiding bus bandwidth and communication. The testbed molecular system used here is a condensed phase system of oligopyrrole chains. A benchmark shows a size scaling speedup of 60 for systems with 210,000 pyrrole monomers. Our implementation can easily be combined with MPI to connect in parallel several CPU–GPU duets. -- Highlights: •We parallelize the Metropolis Monte Carlo (MMC) algorithm on one CPU—GPU duet. •The Adaptive Tempering Monte Carlo employs MMC and profits from this CPU—GPU implementation. •Our benchmark shows a size scaling-up speedup of 62 for systems with 225,000 particles. •The testbed involves a polymeric system of oligopyrroles in the condensed phase. •The CPU—GPU parallelization includes dipole—dipole and Mie—Jones classic potentials.
Gu, Heng
2010-01-14
A NUMERICAL SIMULATION OF THERMAL AND ELECTRICAL PROPERTIES OF NANO-FIBER NETWORK POLYMER COMPOSITES USING PERCOLATION THEORY AND MONTE CARLO METHOD A Thesis by HENG GU Submitted to the Office of Graduate Studies of Texas A... COMPOSITES USING PERCOLATION THEORY AND MONTE CARLO METHOD A Thesis by HENG GU Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Approved by...
NASA Astrophysics Data System (ADS)
Krzakala, Florent; Rosso, Alberto; Semerjian, Guilhem; Zamponi, Francesco
2008-10-01
The cavity method is a well-established technique for solving classical spin models on sparse random graphs (mean-field models with finite connectivity). Laumann [Phys. Rev. B 78, 134424 (2008)] proposed recently an extension of this method to quantum spin-1/2 models in a transverse field, using a discretized Suzuki-Trotter imaginary-time formalism. Here we show how to take analytically the continuous imaginary-time limit. Our main technical contribution is an explicit procedure to generate the spin trajectories in a path-integral representation of the imaginary-time dynamics. As a side result we also show how this procedure can be used in simple heat bath Monte Carlo simulations of generic quantum spin models. The replica symmetric continuous-time quantum cavity method is formulated for a wide class of models and applied as a simple example on the Bethe lattice ferromagnet in a transverse field. The results of the methods are confronted with various approximation schemes in this particular case. On this system we performed quantum Monte Carlo simulations that confirm the exactness of the cavity method in the thermodynamic limit.
Wang Haifeng [Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853 (United States)], E-mail: hw98@cornell.edu; Popov, Pavel P.; Pope, Stephen B. [Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853 (United States)
2010-03-01
We study a class of methods for the numerical solution of the system of stochastic differential equations (SDEs) that arises in the modeling of turbulent combustion, specifically in the Monte Carlo particle method for the solution of the model equations for the composition probability density function (PDF) and the filtered density function (FDF). This system consists of an SDE for particle position and a random differential equation for particle composition. The numerical methods considered advance the solution in time with (weak) second-order accuracy with respect to the time step size. The four primary contributions of the paper are: (i) establishing that the coefficients in the particle equations can be frozen at the mid-time (while preserving second-order accuracy), (ii) examining the performance of three existing schemes for integrating the SDEs, (iii) developing and evaluating different splitting schemes (which treat particle motion, reaction and mixing on different sub-steps), and (iv) developing the method of manufactured solutions (MMS) to assess the convergence of Monte Carlo particle methods. Tests using MMS confirm the second-order accuracy of the schemes. In general, the use of frozen coefficients reduces the numerical errors. Otherwise no significant differences are observed in the performance of the different SDE schemes and splitting schemes.
A highly heterogeneous 3D PWR core benchmark: deterministic and Monte Carlo method comparison
NASA Astrophysics Data System (ADS)
Jaboulay, J.-C.; Damian, F.; Douce, S.; Lopez, F.; Guenaut, C.; Aggery, A.; Poinot-Salanon, C.
2014-06-01
Physical analyses of the LWR potential performances with regards to the fuel utilization require an important part of the work dedicated to the validation of the deterministic models used for theses analyses. Advances in both codes and computer technology give the opportunity to perform the validation of these models on complex 3D core configurations closed to the physical situations encountered (both steady-state and transient configurations). In this paper, we used the Monte Carlo Transport code TRIPOLI-4®; to describe a whole 3D large-scale and highly-heterogeneous LWR core. The aim of this study is to validate the deterministic CRONOS2 code to Monte Carlo code TRIPOLI-4®; in a relevant PWR core configuration. As a consequence, a 3D pin by pin model with a consistent number of volumes (4.3 millions) and media (around 23,000) is established to precisely characterize the core at equilibrium cycle, namely using a refined burn-up and moderator density maps. The configuration selected for this analysis is a very heterogeneous PWR high conversion core with fissile (MOX fuel) and fertile zones (depleted uranium). Furthermore, a tight pitch lattice is selcted (to increase conversion of 238U in 239Pu) that leads to harder neutron spectrum compared to standard PWR assembly. In these conditions two main subjects will be discussed: the Monte Carlo variance calculation and the assessment of the diffusion operator with two energy groups for the core calculation.
NASA Astrophysics Data System (ADS)
Pereira, Pedro F.; Sherif, Sherif S.
2012-10-01
Numerical simulation of the interaction between light and tissue is important for the design and analysis of many optical imaging modalities. Most current simulations are based on the Transport Theory of light in a dielectric, and only calculate the intensity of light in a volume. These simulations do not provide phase information, which is important for many biomedical imaging systems. We are interested in obtaining the optical field, magnitude and phase, due to the interaction of light with tissue. Therefore, we need to solve the integral equation for scalar scattering in a volume of interest. Since the wavelength of light is in the order of nanometres, simulation of volumes of more than a few millimetres requires intensive computational resources. For large volumes, Monte Carlo methods are a suitable choice because their computational complexity is independent of the mathematical dimension of the problem. Also by a careful selection of the random sampling scheme the number of samples needed can be further reduced. In this paper we present an implementation of a method to solve Fredholm integral equations of the second kind using Reversible Jump Markov chain Monte Carlo (RJMCMC). This method could be used to simulate light in tissue with very large electrical size, meaning tissue whose physical dimensions are much larger than the wavelength of light, by solving the integral equation of scalar scattering over a large domain. We implemented this method based on RJMCMC and present in this paper the results of applying it to solve integral equations of one and two dimensions.
Martin, W.R.
1993-01-01
This document describes progress on five efforts for improving effectiveness of computational methods for particle diffusion and transport problems in nuclear engineering: (1) Multigrid methods for obtaining rapidly converging solutions of nodal diffusion problems. A alternative line relaxation scheme is being implemented into a nodal diffusion code. Simplified P2 has been implemented into this code. (2) Local Exponential Transform method for variance reduction in Monte Carlo neutron transport calculations. This work yielded predictions for both 1-D and 2-D x-y geometry better than conventional Monte Carlo with splitting and Russian Roulette. (3) Asymptotic Diffusion Synthetic Acceleration methods for obtaining accurate, rapidly converging solutions of multidimensional SN problems. New transport differencing schemes have been obtained that allow solution by the conjugate gradient method, and the convergence of this approach is rapid. (4) Quasidiffusion (QD) methods for obtaining accurate, rapidly converging solutions of multidimensional SN Problems on irregular spatial grids. A symmetrized QD method has been developed in a form that results in a system of two self-adjoint equations that are readily discretized and efficiently solved. (5) Response history method for speeding up the Monte Carlo calculation of electron transport problems. This method was implemented into the MCNP Monte Carlo code. In addition, we have developed and implemented a parallel time-dependent Monte Carlo code on two massively parallel processors.
A new Monte Carlo method to study the fluid-solid phase transition of polydisperse hard spheres
Mingcheng Yang; Hongru Ma
2008-07-04
A new Monte Carlo approach is proposed to investigate the fluid-solid phase transition of the polydisperse system. By using the extended ensemble, a reversible path was constructed to link the monodisperse and corresponding polydisperse system. Once the fluid-solid coexistence point of the monodisperse system is known, the fluid-solid coexistence point of the polydisperse system can be obtained from the simulation. The validity of the method is checked by the simulation of the fluid-solid phase transition of a size-polydisperse hard sphere colloid. The results are in agreement with the previous studies.
Y. Alhassid; S. Liu; H. Nakada
2006-07-27
We introduce spin projection methods in the shell model Monte Carlo approach and apply them to calculate the spin distribution of level densities for iron-region nuclei using the complete $(pf+g_{9/2})$-shell. We compare the calculated distributions with the spin-cutoff model and extract an energy-dependent moment of inertia. For even-even nuclei and at low excitation energies, we observe a significant suppression of the moment of inertia and odd-even staggering in the spin dependence of level densities.
Calculation of angular distribution of 662 keV gamma rays by Monte Carlo method in copper medium.
Kahraman, A; Ozmutlu, E N; Gurler, O; Yalcin, S; Kaynak, G; Gundogdu, O
2009-12-01
This paper presents results on the angular distribution of Compton scattering of 662 keV gamma photons in both forward and backward hemispheres in copper medium. The number of scattered events graph has been determined for scattered gamma photons in both the forward and backward hemispheres and theoretical saturation thicknesses have been obtained using these results. Furthermore, response function of a 51 x 51 mm NaI(Tl) detector at 60 degrees angle with incoming photons scattered from a 10mm thick copper layer has been determined using Monte Carlo method. PMID:19487129
NASA Astrophysics Data System (ADS)
Starukhin, P. Yu.; Klinaev, Yu. V.
2011-05-01
We present the results of numerical modeling of passage of ultrashort laser pulses through an inhomogeneous layered medium with moving scatterers, based on solution of the nonsteady-state radiation transport equation by the Monte Carlo method. We consider the effects of Doppler broadening of the backscattered radiation spectrum in biological tissues. We have analyzed the dynamics of propagation of a short laser pulse within a multilayer model of human skin. We have studied the possibilities for tomography of different layers of biological tissue based on analysis of the spectrum of the scattered radiation pulse.
Xu, Feng; Davis, Anthony B; West, Robert A; Esposito, Larry W
2011-01-17
Building on the Markov chain formalism for scalar (intensity only) radiative transfer, this paper formulates the solution to polarized diffuse reflection from and transmission through a vertically inhomogeneous atmosphere. For verification, numerical results are compared to those obtained by the Monte Carlo method, showing deviations less than 1% when 90 streams are used to compute the radiation from two types of atmospheres, pure Rayleigh and Rayleigh plus aerosol, when they are divided into sublayers of optical thicknesses of less than 0.03. PMID:21263634
GPU and Multi-core based Reaction Ensemble Monte Carlo method for non-ideal thermodynamic systems
NASA Astrophysics Data System (ADS)
Tuttafesta, M.; D'Angola, A.; Laricchiuta, A.; Minelli, P.; Capitelli, M.; Colonna, G.
2014-02-01
A Graphics Processing Unit (GPU)-CUDA C and (Multi-core)-OpenMP versions of the Reaction Ensemble Monte Carlo method (REMC) are presented. The REMC algorithm is a powerful tool to investigate the equilibrium behavior of chemically reacting systems in highly non-ideal conditions. Both the GPU and the Multi-core versions of the code are particularly efficient when the total potential energy of the system must be calculated, as in the constant-pressure systems. Results, obtained in the case of Helium plasma at high pressure, show differences between real and ideal cases.
Calculation of images from an anthropomorphic chest phantom using Monte Carlo methods
NASA Astrophysics Data System (ADS)
Ullman, Gustaf; Malusek, Alexandr; Sandborg, Michael; Dance, David R.; Alm Carlsson, Gudrun
2006-03-01
Monte Carlo (MC) computer simulation of chest x-ray imaging systems has hitherto been performed using anthropomorphic phantoms with too large (3 mm) voxel sizes. The aim for this work was to develop and use a Monte Carlo computer program to compute projection x-ray images of a high-resolution anthropomorphic voxel phantom for visual clinical image quality evaluation and dose-optimization. An Alderson anthropomorphic chest phantom was imaged in a CT-scanner and reconstructed with isotropic voxels of 0.7 mm. The phantom was segmented and included in a Monte Carlo computer program using the collision density estimator to derive the energies imparted to the detector per unit area of each pixel by scattered photons. The image due to primary photons was calculated analytically including a pre-calculated detector response function. Attenuation and scatter of x-rays in the phantom, grid and image detector was considered. Imaging conditions (tube voltage, anti-scatter device) were varied and the images compared to a real computed radiography (Fuji FCR 9501) image. Four imaging systems were simulated (two tube voltages 81 kV and 141 kV using either a grid with ratio 10 or a 30 cm air gap). The effect of scattered radiation on the visibility of thoracic vertebrae against the heart and lungs is demonstrated. The simplicity in changing the imaging conditions will allow us not only to produce images of existing imaging systems, but also of hypothetical, future imaging systems. We conclude that the calculated images of the high-resolution voxel phantom are suitable for human detection experiments of low-contrast lesions.
Nuclear Level Density of ${}^{161}$Dy in the Shell Model Monte Carlo Method
Cem Özen; Yoram Alhassid; Hitoshi Nakada
2012-06-27
We extend the shell-model Monte Carlo applications to the rare-earth region to include the odd-even nucleus ${}^{161}$Dy. The projection on an odd number of particles leads to a sign problem at low temperatures making it impractical to extract the ground-state energy in direct calculations. We use level counting data at low energies and neutron resonance data to extract the shell model ground-state energy to good precision. We then calculate the level density of ${}^{161}$Dy and find it in very good agreement with the level density extracted from experimental data.
Prediction of rocket plume radiative heating using backward Monte-Carlo method
NASA Technical Reports Server (NTRS)
Wang, K. C.
1993-01-01
A backward Monte-Carlo plume radiation code has been developed to predict rocket plume radiative heating to the rocket base region. This paper provides a description of this code and provides sample results. The code was used to predict radiative heating to various locations during test firings of 48-inch solid rocket motors at NASA Marshall Space Flight Center. Comparisons with test measurements are provided. Predictions of full scale sea level Redesigned Solid Rocket Motor (RSRM) and Advanced Solid Rocket Motor (ASRM) plume radiative heating to the Space Shuttle external tank (ET) dome center were also made. A comparison with the Development Flight Instrumentation (DFI) measurements is also provided.
Lin, Uei-Tyng; Chu, Chien-Hau
2006-05-01
Monte Carlo method was used to simulate the correction factors for electron loss and scattered photons for two improved cylindrical free-air ionization chambers (FACs) constructed at the Institute of Nuclear Energy Research (INER, Taiwan). The method is based on weighting correction factors for mono-energetic photons with X-ray spectra. The newly obtained correction factors for the medium-energy free-air chamber were compared with the current values, which were based on a least-squares fit to experimental data published in the NBS Handbook 64 [Wyckoff, H.O., Attix, F.H., 1969. Design of free-air ionization chambers. National Bureau Standards Handbook, No. 64. US Government Printing Office, Washington, DC, pp. 1-16; Chen, W.L., Su, S.H., Su, L.L., Hwang, W.S., 1999. Improved free-air ionization chamber for the measurement of X-rays. Metrologia 36, 19-24]. The comparison results showed the agreement between the Monte Carlo method and experimental data is within 0.22%. In addition, mono-energetic correction factors for the low-energy free-air chamber were calculated. Average correction factors were then derived for measured and theoretical X-ray spectra at 30-50 kVp. Although the measured and calculated spectra differ slightly, the resulting differences in the derived correction factors are less than 0.02%. PMID:16427292
NASA Technical Reports Server (NTRS)
Shinn, Judy L.; Wilson, John W.; Nealy, John E.; Cucinotta, Francis A.
1990-01-01
Continuing efforts toward validating the buildup factor method and the BRYNTRN code, which use the deterministic approach in solving radiation transport problems and are the candidate engineering tools in space radiation shielding analyses, are presented. A simplified theory of proton buildup factors assuming no neutron coupling is derived to verify a previously chosen form for parameterizing the dose conversion factor that includes the secondary particle buildup effect. Estimates of dose in tissue made by the two deterministic approaches and the Monte Carlo method are intercompared for cases with various thicknesses of shields and various types of proton spectra. The results are found to be in reasonable agreement but with some overestimation by the buildup factor method when the effect of neutron production in the shield is significant. Future improvement to include neutron coupling in the buildup factor theory is suggested to alleviate this shortcoming. Impressive agreement for individual components of doses, such as those from the secondaries and heavy particle recoils, are obtained between BRYNTRN and Monte Carlo results.
Shinn, J.L.; Wilson, J.W.; Nealy, J.E.; Cucinotta, F.A.
1990-10-01
Continuing efforts toward validating the buildup factor method and the BRYNTRN code, which use the deterministic approach in solving radiation transport problems and are the candidate engineering tools in space radiation shielding analyses, are presented. A simplified theory of proton buildup factors assuming no neutron coupling is derived to verify a previously chosen form for parameterizing the dose conversion factor that includes the secondary particle buildup effect. Estimates of dose in tissue made by the two deterministic approaches and the Monte Carlo method are intercompared for cases with various thicknesses of shields and various types of proton spectra. The results are found to be in reasonable agreement but with some overestimation by the buildup factor method when the effect of neutron production in the shield is significant. Future improvement to include neutron coupling in the buildup factor theory is suggested to alleviate this shortcoming. Impressive agreement for individual components of doses, such as those from the secondaries and heavy particle recoils, are obtained between BRYNTRN and Monte Carlo results.
Brown, F.B.; Sutton, T.M.
1996-02-01
This report is composed of the lecture notes from the first half of a 32-hour graduate-level course on Monte Carlo methods offered at KAPL. These notes, prepared by two of the principle developers of KAPL`s RACER Monte Carlo code, cover the fundamental theory, concepts, and practices for Monte Carlo analysis. In particular, a thorough grounding in the basic fundamentals of Monte Carlo methods is presented, including random number generation, random sampling, the Monte Carlo approach to solving transport problems, computational geometry, collision physics, tallies, and eigenvalue calculations. Furthermore, modern computational algorithms for vector and parallel approaches to Monte Carlo calculations are covered in detail, including fundamental parallel and vector concepts, the event-based algorithm, master/slave schemes, parallel scaling laws, and portability issues.
Gudjonson, Herman; Kats, Mikhail A.; Liu, Kun; Nie, Zhihong; Kumacheva, Eugenia; Capasso, Federico
2014-01-01
Many experimental systems consist of large ensembles of uncoupled or weakly interacting elements operating as a single whole; this is particularly the case for applications in nano-optics and plasmonics, including colloidal solutions, plasmonic or dielectric nanoparticles on a substrate, antenna arrays, and others. In such experiments, measurements of the optical spectra of ensembles will differ from measurements of the independent elements as a result of small variations from element to element (also known as polydispersity) even if these elements are designed to be identical. In particular, sharp spectral features arising from narrow-band resonances will tend to appear broader and can even be washed out completely. Here, we explore this effect of inhomogeneous broadening as it occurs in colloidal nanopolymers comprising self-assembled nanorod chains in solution. Using a technique combining finite-difference time-domain simulations and Monte Carlo sampling, we predict the inhomogeneously broadened optical spectra of these colloidal nanopolymers and observe significant qualitative differences compared with the unbroadened spectra. The approach combining an electromagnetic simulation technique with Monte Carlo sampling is widely applicable for quantifying the effects of inhomogeneous broadening in a variety of physical systems, including those with many degrees of freedom that are otherwise computationally intractable. PMID:24469797
Gudjonson, Herman; Kats, Mikhail A; Liu, Kun; Nie, Zhihong; Kumacheva, Eugenia; Capasso, Federico
2014-02-11
Many experimental systems consist of large ensembles of uncoupled or weakly interacting elements operating as a single whole; this is particularly the case for applications in nano-optics and plasmonics, including colloidal solutions, plasmonic or dielectric nanoparticles on a substrate, antenna arrays, and others. In such experiments, measurements of the optical spectra of ensembles will differ from measurements of the independent elements as a result of small variations from element to element (also known as polydispersity) even if these elements are designed to be identical. In particular, sharp spectral features arising from narrow-band resonances will tend to appear broader and can even be washed out completely. Here, we explore this effect of inhomogeneous broadening as it occurs in colloidal nanopolymers comprising self-assembled nanorod chains in solution. Using a technique combining finite-difference time-domain simulations and Monte Carlo sampling, we predict the inhomogeneously broadened optical spectra of these colloidal nanopolymers and observe significant qualitative differences compared with the unbroadened spectra. The approach combining an electromagnetic simulation technique with Monte Carlo sampling is widely applicable for quantifying the effects of inhomogeneous broadening in a variety of physical systems, including those with many degrees of freedom that are otherwise computationally intractable. PMID:24469797
S. Yalcin; O. Gurler; G. Kaynak; O. Gundogdu
2007-01-01
This paper presents results on the total gamma counting efficiency of a NaI(Tl) detector from point and disk sources. The directions of photons emitted from the source were determined by Monte-Carlo techniques and the photon path lengths in the detector were determined by analytic equations depending on photon directions. This is called the hybrid Monte-Carlo method where analytical expressions are