An Automated Variance Reduction Method For Global Monte Carlo Neutral Particle Transport Problems
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An Automated Variance Reduction Method For Global Monte Carlo Neutral Particle Transport Problems
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Author : Marc. A. Cooper
language : en
Publisher:
Release Date : 1999
An Automated Variance Reduction Method For Global Monte Carlo Neutral Particle Transport Problems written by Marc. A. Cooper and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
A Variationally Based Variance Reduction Method For Monte Carlo Particle Transport Problems
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Author : Carla Lynn Barrett
language : en
Publisher:
Release Date : 1999
A Variationally Based Variance Reduction Method For Monte Carlo Particle Transport Problems written by Carla Lynn Barrett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Monte Carlo Methods For Particle Transport
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Author : Alireza Haghighat
language : en
Publisher: CRC Press
Release Date : 2020-08-09
Monte Carlo Methods For Particle Transport written by Alireza Haghighat and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-09 with Mathematics categories.
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
Discrete Ordinates Cost Optimization Of Weight Dependent Variance Reduction Techniques For Monte Carlo Neutral Particle Transport
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Author : Clell J. Jr Solomon
language : en
Publisher:
Release Date : 2010
Discrete Ordinates Cost Optimization Of Weight Dependent Variance Reduction Techniques For Monte Carlo Neutral Particle Transport written by Clell J. Jr Solomon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
A method for deterministically calculating the population variances of Monte Carlo particle transport calculations involving weight-dependent variance reduction has been developed. This method solves a set of equations developed by Booth and Cashwell [1979], but extends them to consider the weight-window variance reduction technique. Furthermore, equations that calculate the duration of a single history in an MCNP5 (RSICC version 1.51) calculation have been developed as well. The calculation cost, defined as the inverse figure of merit, of a Monte Carlo calculation can be deterministically minimized from calculations of the expected variance and expected calculation time per history. The method has been applied to one- and two-dimensional multi-group and mixed material problems for optimization of weight-window lower bounds. With the adjoint (importance) function as a basis for optimization, an optimization mesh is superimposed on the geometry. Regions of weight-window lower bounds contained within the same optimization mesh element are optimized together with a scaling parameter. Using this additional optimization mesh restricts the size of the optimization problem, thereby eliminating the need to optimize each individual weight-window lower bound. Application of the optimization method to a one-dimensional problem, designed to replicate the variance reduction iron-window effect, obtains a gain in efficiency by a factor of 2 over standard deterministically generated weight windows. The gain in two dimensional problems varies. For a 2-D block problem and a 2-D two-legged duct problem, the efficiency gain is a factor of about 1.2. The top-hat problem sees an efficiency gain of 1.3, while a 2-D 3-legged duct problem sees an efficiency gain of only 1.05. This work represents the first attempt at deterministic optimization of Monte Carlo calculations with weight-dependent variance reduction. However, the current work is limited in the size of problems that can be run by the amount of computer memory available in computational systems. This limitation results primarily from the added discretization of the Monte Carlo particle weight required to perform the weight-dependent analyses. Alternate discretization methods for the Monte Carlo weight should be a topic of future investigation. Furthermore, the accuracy with which the MCNP5 calculation times can be calculated deterministically merits further study.
Advanced Quadrature Selection For Monte Carlo Variance Reduction
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Author : Kelly Rowland
language : en
Publisher:
Release Date : 2018
Advanced Quadrature Selection For Monte Carlo Variance Reduction written by Kelly Rowland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Neutral particle radiation transport simulations are critical for radiation shielding and deep penetration applications. Arriving at a solution for a given response of interest can be computationally difficult because of the magnitude of particle attenuation often seen in these shielding problems. Hybrid methods, which aim to synergize the individual favorable aspects of deterministic and stochastic solution methods for solving the steady-state neutron transport equation, are commonly used in radiation shielding applications to achieve statistically meaningful results in a reduced amount of computational time and effort. The current state of the art in hybrid calculations is the Consistent Adjoint-Driven Importance Sampling (CADIS) and Forward-Weighted CADIS (FW-CADIS) methods, which generate Monte Carlo variance reduction parameters based on deterministically-calculated scalar flux solutions. For certain types of radiation shielding problems, however, results produced using these methods suffer from unphysical oscillations in scalar flux solutions that are a product of angular discretization. These aberrations are termed “ray effects”. The Lagrange Discrete Ordinates (LDO) equations retain the formal structure of the traditional discrete ordinates formulation of the neutron transport equation and mitigate ray effects at high angular resolution. In this work, the LDO equations have been implemented in the Exnihilo parallel neutral particle radiation transport framework, with the deterministic scalar flux solutions passed to the Automated Variance Reduction Generator (ADVANTG) software and the resultant Monte Carlo variance reduction parameters’ efficacy assessed based on results from MCNP5. Studies were conducted in both the CADIS and FW-CADIS contexts, with the LDO equations’ variance reduction parameters seeing their best performance in the FW-CADIS method, especially for photon transport.
Monte Carlo Particle Transport Methods
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Author : I. Lux
language : en
Publisher: CRC Press
Release Date : 2018-05-04
Monte Carlo Particle Transport Methods written by I. Lux and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Science categories.
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.
Automatic Variance Reduction For Monte Carlo Simulations Via The Local Importance Function Transform
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Author : Scott Allen Turner
language : en
Publisher:
Release Date : 1996
Automatic Variance Reduction For Monte Carlo Simulations Via The Local Importance Function Transform written by Scott Allen Turner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
A Local Exponential Transform Method For Global Variance Reduction In Monte Carlo Transport Problems
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Author :
language : en
Publisher:
Release Date : 1992
A Local Exponential Transform Method For Global Variance Reduction In Monte Carlo Transport Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
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.
Carcino Embryonic Proteins
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Author : International Society for Oncodevelopmental Biology and Medicine
language : en
Publisher:
Release Date : 1979
Carcino Embryonic Proteins written by International Society for Oncodevelopmental Biology and Medicine and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.
A Hybrid Monte Carlo Deterministic Method For Global Binary Stochastic Medium Transport Problems
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Author :
language : en
Publisher:
Release Date : 2010
A Hybrid Monte Carlo Deterministic Method For Global Binary Stochastic Medium Transport Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
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.
