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 Quantum Monte Carlo Methods in Condensed Matter Physics written by Masuo Suzuki and published by World Scientific. This book was released on 1993 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews recent developments of quantum Monte Carlo methods and some remarkable applications to interacting quantum spin systems and strongly correlated electron systems. It contains twenty-two papers by thirty authors. Some of the features are as follows. The first paper gives the foundations of the standard quantum Monte Carlo method, including some recent results on higher-order decompositions of exponential operators and ordered exponentials. The second paper presents a general review of quantum Monte Carlo methods used in the present book. One of the most challenging problems in the field of quantum Monte Carlo techniques, the negative-sign problem, is also discussed and new methods proposed to partially overcome it. In addition, low-dimensional quantum spin systems are studied. Some interesting applications of quantum Monte Carlo methods to fermion systems are also presented to investigate the role of strong correlations and fluctuations of electrons and to clarify the mechanism of high-c superconductivity. Not only thermal properties but also quantum-mechanical ground-state properties have been studied by the projection technique using auxiliary fields. Further, the Haldane gap is confirmed by numerical calculations. Active researchers in the forefront of condensed matter physics as well as young graduate students who want to start learning the quantum Monte Carlo methods will find this book useful.
Download or read book Monte Carlo Methods in Statistical Physics written by Kurt Binder and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the seven years since this volume first appeared. there has been an enormous expansion of the range of problems to which Monte Carlo computer simulation methods have been applied. This fact has already led to the addition of a companion volume ("Applications of the Monte Carlo Method in Statistical Physics", Topics in Current Physics. Vol . 36), edited in 1984, to this book. But the field continues to develop further; rapid progress is being made with respect to the implementation of Monte Carlo algorithms, the construction of special-purpose computers dedicated to exe cute Monte Carlo programs, and new methods to analyze the "data" generated by these programs. Brief descriptions of these and other developments, together with numerous addi tional references, are included in a new chapter , "Recent Trends in Monte Carlo Simulations" , which has been written for this second edition. Typographical correc tions have been made and fuller references given where appropriate, but otherwise the layout and contents of the other chapters are left unchanged. Thus this book, together with its companion volume mentioned above, gives a fairly complete and up to-date review of the field. It is hoped that the reduced price of this paperback edition will make it accessible to a wide range of scientists and students in the fields to which it is relevant: theoretical phYSics and physical chemistry , con densed-matter physics and materials science, computational physics and applied mathematics, etc.
Download or read book Quantum Monte Carlo Approaches for Correlated Systems written by Federico Becca and published by Cambridge University Press. This book was released on 2017-11-30 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to state-of-the-art quantum Monte Carlo techniques for applications in strongly-interacting systems. Including variational wave functions, stochastic samplings, the variational technique, optimisation techniques, real-time dynamics and projection methods and recent developments on the continuum space. An extensive resource for students and researchers.
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 Quantum Monte Carlo Methods in Physics and Chemistry written by M.P. Nightingale and published by Springer Science & Business Media. This book was released on 1998-12-31 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a considerable growth in interest in Monte Carlo methods, and quantum Monte Carlo methods in particlular. Clearly, the ever-increasing computational power available to researchers, has stimulated the development of improved algorithms, and almost all fields in computational physics and chemistry are affected by their applications. Here we just mention some fields that are covered in the lecture notes contained in this volume, viz. electronic structure studies of atoms, molecules and solids, nuclear structure, and low- or zero-temperature studies of strongly-correlated quantum systems, both of the continuum and lattice variety, and cooperative phenomena in classical systems. Although each area of application may have its own peculiarities, requiring specialized solutions, all share the same basic methodology. It was with the intention of bringing together researchers and students from these various areas that the NATO Advanced Study Institute on Quantum Monte Carlo Methods in Physics and Chemistry was held at Cornell University from 12 to 24 July, 1998. This book contains material presented at the Institute in a series of mini courses in quantum Monte Carlo methods. The program consisted of lectures predominantly of a pedagogical nature, and of more specialized seminars. The levels varied from introductory to advanced, and from basic methods to applications; the program was intended for an audience working towards the Ph.D. level and above. Despite the essentially pedagogic nature of the Institute, several of the lectures and seminars contained in this volume present recent developments not previously published.
Download or read book Implementing a Monte Carlo Simulation written by Stuart McCrary and published by . This book was released on 2015 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: This manuscript is program documentation for various Monte Carlo models involving multiple correlated variables, skewed distributions, kurtotic distributions, or combinations of correlation, skew, and kurtosis.
Download or read book Modeling Derivatives in C written by Justin London and published by John Wiley & Sons. This book was released on 2005-01-21 with total page 922 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the definitive and most comprehensive guide to modeling derivatives in C++ today. Providing readers with not only the theory and math behind the models, as well as the fundamental concepts of financial engineering, but also actual robust object-oriented C++ code, this is a practical introduction to the most important derivative models used in practice today, including equity (standard and exotics including barrier, lookback, and Asian) and fixed income (bonds, caps, swaptions, swaps, credit) derivatives. The book provides complete C++ implementations for many of the most important derivatives and interest rate pricing models used on Wall Street including Hull-White, BDT, CIR, HJM, and LIBOR Market Model. London illustrates the practical and efficient implementations of these models in real-world situations and discusses the mathematical underpinnings and derivation of the models in a detailed yet accessible manner illustrated by many examples with numerical data as well as real market data. A companion CD contains quantitative libraries, tools, applications, and resources that will be of value to those doing quantitative programming and analysis in C++. Filled with practical advice and helpful tools, Modeling Derivatives in C++ will help readers succeed in understanding and implementing C++ when modeling all types of derivatives.
Download or read book A Guide to Monte Carlo Simulations in Statistical Physics written by David P. Landau and published by Cambridge University Press. This book was released on 2000-08-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, as well as in related fields, such as polymer science and lattice gauge theory. The authors give a succinct overview of simple sampling methods and develop the importance sampling method. In addition they introduce quantum Monte Carlo methods, aspects of simulations of growth phenomena and other systems far from equilibrium, and the Monte Carlo Renormalization Group approach to critical phenomena. The book includes many applications, examples, and current references, and exercises to help the reader.
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 Quantum Monte Carlo Approaches for Correlated Systems written by Federico Becca and published by Cambridge University Press. This book was released on 2017-11-30 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past several decades, computational approaches to studying strongly-interacting systems have become increasingly varied and sophisticated. This book provides a comprehensive introduction to state-of-the-art quantum Monte Carlo techniques relevant for applications in correlated systems. Providing a clear overview of variational wave functions, and featuring a detailed presentation of stochastic samplings including Markov chains and Langevin dynamics, which are developed into a discussion of Monte Carlo methods. The variational technique is described, from foundations to a detailed description of its algorithms. Further topics discussed include optimisation techniques, real-time dynamics and projection methods, including Green's function, reptation and auxiliary-field Monte Carlo, from basic definitions to advanced algorithms for efficient codes, and the book concludes with recent developments on the continuum space. Quantum Monte Carlo Approaches for Correlated Systems provides an extensive reference for students and researchers working in condensed matter theory or those interested in advanced numerical methods for electronic simulation.
Download or read book A Guide to Monte Carlo Simulations in Statistical Physics written by David Landau and published by Cambridge University Press. This book was released on 2021-07-29 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unique coverage of Monte Carlo methods for both continuum and lattice systems, explaining particularly analysis of phase transitions.
Download or read book Mathematics and Computations Reactor Physics and Environmental Analyses written by and published by . This book was released on 1995 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Guide to Monte Carlo Simulations in Statistical Physics written by David P. Landau and published by Cambridge University Press. This book was released on 2015 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised fourth edition provides an introduction to computer simulations in physics, cutting-edge algorithms, essential techniques, and petascale computing.
Download or read book Monte Carlo Methods written by John Michael Hammersley and published by Taylor & Francis. This book was released on 1964 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1964.
Download or read book The Accuracy Robustness and Relationships Among Correlation Models written by Brent M. Rutherford and published by . This book was released on 1973 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Advances in Quantum Monte Carlo Methods written by W. A. Lester and published by World Scientific. This book was released on 1997 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantum Monte Carlo (QMC) method is gaining interest as a complement to basis set ab initio methods in cases where high accuracy computation of atomic and molecular properties is desired. This volume focuses on recent advances in this area. QMC as used here refers to methods that directly solve the Schrdinger equation, for example, diffusion and Green's function Monte Carlo, as well as variational Monte Carlo. The latter is an approach to computing atomic and molecular properties by the Monte Carlo method that has fundamental similarities to basis set methods with the exception that the limitation to one-particle basis functions to facilitate integral evaluation is avoided. This feature makes possible the consideration of many-body wave functions containing explicitly interparticle distances ? a capability common to all variants of QMC.
