Download or read book Biases in Monte Carlo Eigenvalue Calculations written by and published by . This book was released on 1992 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monte Carlo method has been used for many years to analyze the neutronics of nuclear reactors. In fact, as the power of computers has increased the importance of Monte Carlo in neutronics has also increased, until today this method plays a central role in reactor analysis and design. Monte Carlo is used in neutronics for two somewhat different purposes, i.e., (a) to compute the distribution of neutrons in a given medium when the neutron source-density is specified, and (b) to compute the neutron distribution in a self-sustaining chain reaction, in which case the source is determined as the eigenvector of a certain linear operator. In (b), then, the source is not given, but must be computed. In the first case (the ''fixed-source'' case) the Monte Carlo calculation is unbiased. That is to say that, if the calculation is repeated (''replicated'') over and over, with independent random number sequences for each replica, then averages over all replicas will approach the correct neutron distribution as the number of replicas goes to infinity. Unfortunately, the computation is not unbiased in the second case, which we discuss here.
Download or read book Magnitude of Bias in Monte Carlo Eigenvalue Calculations written by and published by . This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Most Monte Carlo eigenvalue calculations are based on power iteration methods, like those used in analytical algorithms. But if N/sub H/, the number of histories in each generation is fixed, then such Monte Carlo calculations will be biased. Various arguments lead to the conclusion that eigenvalue and shape biases are both proportional to 1/N/sub H/, but little more is known about their magnitudes. Numerical experiments on simple matrices suggest that the biases are small, but information more relevant to real reactor calculations is very sparse. In fact to determine the bias in real reactor calculations is quite expensive. It seems worthwhile, therefore, to try to understand the Monte Carlo biases in systems more realistic than arbitrary matrices, but simpler than real reactors. For this reason biases in simple one-group model problems have been computed.
Download or read book Biases in Monte Carlo Eigenvalue Calculations written by Ely M. Gelbard and published by . This book was released on 1992 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book K effective of the World written by and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods have been used to compute k{sub eff} and the fundamental model eigenfunction of critical systems since the 1950s. Despite the sophistication of today's Monte Carlo codes for representing realistic geometry and physics interactions, correct results can be obtained in criticality problems only if users pay attention to source convergence in the Monte Carlo iterations and to running a sufficient number of neutron histories to adequately sample all significant regions of the problem. Recommended best practices for criticality calculations are reviewed and applied to several practical problems for nuclear reactors and criticality safety, including the 'K-effective of the World' problem. Numerical results illustrate the concerns about convergence and bias. The general conclusion is that with today's high-performance computers, improved understanding of the theory, new tools for diagnosing convergence (e.g., Shannon entropy of the fission distribution), and clear practical guidance for performing calculations, practitioners will have a greater degree of confidence than ever of obtaining correct results for Monte Carlo criticality calculations.
Download or read book Monte Carlo Particle Transport Methods written by I. Lux and published by CRC Press. This book was released on 2018-05-04 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this book we try to reach several more-or-less unattainable goals namely: To compromise in a single book all the most important achievements of Monte Carlo calculations for solving neutron and photon transport problems. To present a book which discusses the same topics in the three levels known from the literature and gives us useful information for both beginners and experienced readers. It lists both well-established old techniques and also newest findings.
Download or read book Quantum Monte Carlo Methods written by James Gubernatis and published by Cambridge University Press. This book was released on 2016-06-02 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and researchers interested in quantum Monte Carlo techniques.
Download or read book Bias in Dynamic Monte Carlo Alpha Calculations written by and published by . This book was released on 2015 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 1/N bias in the estimate of the neutron time-constant (commonly denoted as [alpha]) has been seen in dynamic neutronic calculations performed with MCATK. In this paper we show that the bias is most likely caused by taking the logarithm of a stochastic quantity. We also investigate the known bias due to the particle population control method used in MCATK. We conclude that this bias due to the particle population control method is negligible compared to other sources of bias.
Download or read book Development of a Multiple Perturbation Monte Carlo Method for Eigenvalue Problems and Implementation on Parallel Processors written by Amitava Majumdar and published by . This book was released on 1996 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book U Bias in Dynamic Monte Carlo Alpha Calculations written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo Methods in Chemical Physics written by David M. Ferguson and published by John Wiley & Sons. This book was released on 2009-09-09 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Monte Carlo Methods in Chemical Physics: An Introduction to the Monte Carlo Method for Particle Simulations J. Ilja Siepmann Random Number Generators for Parallel Applications Ashok Srinivasan, David M. Ceperley and Michael Mascagni Between Classical and Quantum Monte Carlo Methods: "Variational" QMC Dario Bressanini and Peter J. Reynolds Monte Carlo Eigenvalue Methods in Quantum Mechanics and Statistical Mechanics M. P. Nightingale and C.J. Umrigar Adaptive Path-Integral Monte Carlo Methods for Accurate Computation of Molecular Thermodynamic Properties Robert Q. Topper Monte Carlo Sampling for Classical Trajectory Simulations Gilles H. Peslherbe Haobin Wang and William L. Hase Monte Carlo Approaches to the Protein Folding Problem Jeffrey Skolnick and Andrzej Kolinski Entropy Sampling Monte Carlo for Polypeptides and Proteins Harold A. Scheraga and Minh-Hong Hao Macrostate Dissection of Thermodynamic Monte Carlo Integrals Bruce W. Church, Alex Ulitsky, and David Shalloway Simulated Annealing-Optimal Histogram Methods David M. Ferguson and David G. Garrett Monte Carlo Methods for Polymeric Systems Juan J. de Pablo and Fernando A. Escobedo Thermodynamic-Scaling Methods in Monte Carlo and Their Application to Phase Equilibria John Valleau Semigrand Canonical Monte Carlo Simulation: Integration Along Coexistence Lines David A. Kofke Monte Carlo Methods for Simulating Phase Equilibria of Complex Fluids J. Ilja Siepmann Reactive Canonical Monte Carlo J. Karl Johnson New Monte Carlo Algorithms for Classical Spin Systems G. T. Barkema and M.E.J. Newman
Download or read book VARIANCE ESTIMATION IN DOMAIN DECOMPOSED MONTE CARLO EIGENVALUE CALCULATIONS written by and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The number of tallies performed in a given Monte Carlo calculation is limited in most modern Monte Carlo codes by the amount of memory that can be allocated on a single processor. By using domain decomposition, the calculation is now limited by the total amount of memory available on all processors, allowing for significantly more tallies to be performed. However, decomposing the problem geometry introduces significant issues with the way tally statistics are conventionally calculated. In order to deal with the issue of calculating tally variances in domain decomposed environments for the Shift hybrid Monte Carlo code, this paper presents an alternative approach for reactor scenarios in which an assumption is made that once a particle leaves a domain, it does not reenter the domain. Particles that reenter the domain are instead treated as separate independent histories. This assumption introduces a bias that inevitably leads to under-prediction of the calculated variances for tallies within a few mean free paths of the domain boundaries. However, through the use of different decomposition strategies, primarily overlapping domains, the negative effects of such an assumption can be significantly reduced to within reasonable levels.
Download or read book Diagnosing Undersampling in Monte Carlo Eigenvalue and Flux Tally Estimates written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This study explored the impact of undersampling on the accuracy of tally estimates in Monte Carlo (MC) calculations. Steady-state MC simulations were performed for models of several critical systems with varying degrees of spatial and isotopic complexity, and the impact of undersampling on eigenvalue and fuel pin flux/fission estimates was examined. This study observed biases in MC eigenvalue estimates as large as several percent and biases in fuel pin flux/fission tally estimates that exceeded tens, and in some cases hundreds, of percent. This study also investigated five statistical metrics for predicting the occurrence of undersampling biases in MC simulations. Three of the metrics (the Heidelberger-Welch RHW, the Geweke Z-Score, and the Gelman-Rubin diagnostics) are commonly used for diagnosing the convergence of Markov chains, and two of the methods (the Contributing Particles per Generation and Tally Entropy) are new convergence metrics developed in the course of this study. These metrics were implemented in the KENO MC code within the SCALE code system and were evaluated for their reliability at predicting the onset and magnitude of undersampling biases in MC eigenvalue and flux tally estimates in two of the critical models. Of the five methods investigated, the Heidelberger-Welch RHW, the Gelman-Rubin diagnostics, and Tally Entropy produced test metrics that correlated strongly to the size of the observed undersampling biases, indicating their potential to effectively predict the size and prevalence of undersampling biases in MC simulations.
Download or read book Monte Carlo Methods for Particle Transport written by Alireza Haghighat and published by CRC Press. This book was released on 2020-08-09 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fully updated with the latest developments in the eigenvalue Monte Carlo calculations and automatic variance reduction techniques and containing an entirely new chapter on fission matrix and alternative hybrid techniques. This second edition explores the uses of the Monte Carlo method for real-world applications, explaining its concepts and limitations. Featuring illustrative examples, mathematical derivations, computer algorithms, and homework problems, it is an ideal textbook and practical guide for nuclear engineers and scientists looking into the applications of the Monte Carlo method, in addition to students in physics and engineering, and those engaged in the advancement of the Monte Carlo methods. Describes general and particle-transport-specific automated variance reduction techniques Presents Monte Carlo particle transport eigenvalue issues and methodologies to address these issues Presents detailed derivation of existing and advanced formulations and algorithms with real-world examples from the author’s research activities
Download or read book Under Prediction of Localized Tally Uncertainties in Monte Carlo Eigenvalue Calculations written by and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and simulation using Monte Carlo methods is widely used in nuclear reactor criticality benchmarking applications. However, obtaining good statistics not only takes a large amount of computational time, but it has been shown that localized tally uncertainties may be under-predicted by a factor of five or more in select cases. The primary components of this under-prediction include poor sampling due to improper source convergence and cycle-to-cycle correlations in the fission source. Additional components relate to the flux shape and the size of the tally cells. These issues must be understood and dealt with in order to support the practical use of modern Monte Carlo software packages.
Download or read book A Review of Monte Carlo Criticality Calculations Convergence Bias Statistics written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo Eigenvalue Calculations written by and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
