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 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 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 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 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 Iterative Acceleration Methods for Monte Carlo and Deterministic Criticality Calculations written by Todd James Urbatsch and published by . This book was released on 1995 with total page 354 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 Energy Research Abstracts written by and published by . This book was released on 1985 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Correlations in Monte Carlo Eigenvalue Simulations written by Jilang Miao and published by . This book was released on 2018 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods have mostly been used as a benchmark tool for other transport and diffusion methods in nuclear reactor analysis. One important feature of Monte Carlo calculations is the report of the variance of the estimators as a measure of uncertainty. In the current production codes, the assumption of independence of neutron generations in Monte Carlo eigenvalue simulations leads to the oversimplified estimate of the uncertainty of tallies. The correlation of tallies between neutron generations can make reported uncertainty underestimated by a factor of 8 in assembly size tallies in a typical LWR. This work analyzes the variance/uncertainty convergence rate in Monte Carlo eigenvalue simulations and develops different methods to properly report the variance. To correct the underestimated variance as a post-processing step, a simple correction factor can be calculated from the correlation coefficients estimated from a sufficient number of active generations and fitted to decreasing exponentials. If the variance convergence rate is needed before or during the simulation to optimize the run strategy (number of generations and neutrons per generation), a discrete model can be constructed from the inactive generations that can predict the correlation behavior of the original problem. Since it is not efficient to perform variance correction to all tallies on all problems, a simple correlation indicator is also developed to quickly determine the potential impact of correlations on a given tally in a given problem. This can help decide if more complicated correction analysis or the use of independent simulations should be used to calculate the true variance. Run strategy to reduce correlations is also investigated by introducing the notion of delayed neutrons. A predictive model for the new source update scheme was developed to help identify optimal delayed neutron parameters before implementing in OpenMC. Optimal run strategies in terms of delayed bank size, frequency of delayed bank sampling and true simulation costs are proposed.

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 ERDA Energy Research Abstracts written by and published by . This book was released on 1983 with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Identification and Inference for Econometric Models written by Donald W. K. Andrews and published by Cambridge University Press. This book was released on 2005-06-17 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 collection pushed forward the research frontier in four areas of theoretical econometrics.

Download or read book Transactions of the American Nuclear Society written by American Nuclear Society and published by . This book was released on 2002 with total page 1096 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 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 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.