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Stochastic Neutron Transport
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Book Synopsis Stochastic Neutron Transport by : Emma Horton
Download or read book Stochastic Neutron Transport written by Emma Horton and published by Springer Nature. This book was released on 2023-12-17 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph highlights the connection between the theory of neutron transport and the theory of non-local branching processes. By detailing this frequently overlooked relationship, the authors provide readers an entry point into several active areas, particularly applications related to general radiation transport. Cutting-edge research published in recent years is collected here for convenient reference. Organized into two parts, the first offers a modern perspective on the relationship between the neutron branching process (NBP) and the neutron transport equation (NTE), as well as some of the core results concerning the growth and spread of mass of the NBP. The second part generalizes some of the theory put forward in the first, offering proofs in a broader context in order to show why NBPs are as malleable as they appear to be. Stochastic Neutron Transport will be a valuable resource for probabilists, and may also be of interest to numerical analysts and engineers in the field of nuclear research.
Book Synopsis Stochastic Analysis of the Neutron Transport Equation by : Emma Horton
Download or read book Stochastic Analysis of the Neutron Transport Equation written by Emma Horton and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Lattice Model Concept of Stochastic Neutron Transport by : Herbert Eugene Hungerford
Download or read book The Lattice Model Concept of Stochastic Neutron Transport written by Herbert Eugene Hungerford and published by . This book was released on 1965 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Stochastic Nonlinear Neutron Transport Equation by : M. Mokhtar-Kharroubi
Download or read book On the Stochastic Nonlinear Neutron Transport Equation written by M. Mokhtar-Kharroubi and published by . This book was released on 1990 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Stochastic Formulation and Interpretation of Neutron Transport Equations by : Chio-min Yang
Download or read book On the Stochastic Formulation and Interpretation of Neutron Transport Equations written by Chio-min Yang and published by . This book was released on with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Topics In Neutron Transport Theory: New Aspects by : Mustapha Mokhtar Kharroubi
Download or read book Mathematical Topics In Neutron Transport Theory: New Aspects written by Mustapha Mokhtar Kharroubi and published by World Scientific. This book was released on 1997-12-18 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some recent mathematical developments about neutron transport equations. Several different topics are dealt with including regularity of velocity averages, spectral analysis of transport operators, inverse problems, nonlinear problems arising in the stochastic theory of neutron chain fissions, compactness properties of perturbed of c0-semigroups in Banach spaces with applications to transport theory, Miyadera perturbations of c0-semigroups in Banach spaces with applications to singular transport equations, a thorough analysis of the leading eigenelements of transport operators and their approximation, scattering theory. Besides the new problems addressed in this book a unification and extension of the classical spectral analysis of neutron transport equations is given.
Book Synopsis Deterministic Methods for Time-dependent Stochastic Neutron Transport by :
Download or read book Deterministic Methods for Time-dependent Stochastic Neutron Transport written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A numerical method is presented for solving the time-dependent survival probability equation in general (lD/2D/3D) geometries using the multi group SNmethod. Although this equation was first formulated by Bell in the early 1960's, it has only been applied to stationary systems (for other than idealized point models) until recently, and detailed descriptions of numerical solution techniques are lacking in the literature. This paper presents such a description and applies it to a dynamic system representative of a figurative criticality accident scenario.
Book Synopsis A Stochastic/deterministic Method for Transient, Three-dimensional Neutron Transport by :
Download or read book A Stochastic/deterministic Method for Transient, Three-dimensional Neutron Transport written by and published by . This book was released on 1992 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Topics in Neutron Transport Theory by : M. Mokhtar-Kharroubi
Download or read book Mathematical Topics in Neutron Transport Theory written by M. Mokhtar-Kharroubi and published by World Scientific. This book was released on 1997 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some recent mathematical developments about neutron transport equations. Several different topics are dealt with including regularity of velocity averages, spectral analysis of transport operators, inverse problems, nonlinear problems arising in the stochastic theory of neutron chain fissions, compactness properties of perturbed of 0-semigroups in Banach spaces with applications to transport theory, Miyadera perturbations of c0-semigroups in Banach spaces with applications to singular transport equations, a thorough analysis of the leading eigenelements of transport operators and their approximation, scattering theory. Besides the new problems addressed in this book a unification and extension of the classical spectral analysis of neutron transport equations is given.
Book Synopsis Development and Implementation of Stochastic Neutron Transport Equations and Development and Analysis of Finite Difference and Galerkin Methods for Approximate Solution to Volterra's Population Equation with Diffusion and Noise by : Wyatt Duncan Sharp
Download or read book Development and Implementation of Stochastic Neutron Transport Equations and Development and Analysis of Finite Difference and Galerkin Methods for Approximate Solution to Volterra's Population Equation with Diffusion and Noise written by Wyatt Duncan Sharp and published by . This book was released on 1999 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Neutron Transport Benchmarks for Binary Stochastic Multiplying Media by : Ian Mack Davis
Download or read book Neutron Transport Benchmarks for Binary Stochastic Multiplying Media written by Ian Mack Davis and published by . This book was released on 2005 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Benchmark calculations are performed for neutron transport in a two material (binary) stochastic multiplying medium. Spatial, angular, and energy dependence are included. The problem considered is based on a fuel assembly of a common pressurized water nuclear reactor. The mean chord length through the assembly is determined and used as the planar geometry system length. According to assumed or calculated material distributions, this system length is populated with alternating fuel and moderator segments of random size. Neutron flux distributions are numerically computed using a discretized form of the Boltzmann transport equation employing diffusion synthetic acceleration. Average quantities (group fluxes and k-eigenvalue) and variances are calculated from an ensemble of realizations of the mixing statistics. The effects of varying two parameters in the fuel, two different boundary conditions, and three different sets of mixing statistics are assessed. A probability distribution function (PDF) of the k-eigenvalue is generated and compared with previous research. Atomic mix solutions are compared with these benchmark ensemble average flux and k-eigenvalue solutions. Mixing statistics with large standard deviations give the most widely varying ensemble solutions of the flux and k-eigenvalue. The shape of the k-eigenvalue PDF qualitatively agrees with previous work. Its overall shape is independent of variations in fuel cross-sections for the problems considered, but its width is impacted by these variations. Statistical distributions with smaller standard deviations alter the shape of this PDF toward a normal distribution. The atomic mix approximation yields large over-predictions of the ensemble average k-eigenvalue and under-predictions of the flux. Qualitatively correct flux shapes are obtained, however. These benchmark calculations indicate that a model which includes higher statistical moments of the mixing statistics is needed for accurate predictions of binary stochastic media k-eigenvalue problems. This is consistent with previous findings.
Book Synopsis Computational Methods of Neutron Transport by : Elmer Eugene Lewis
Download or read book Computational Methods of Neutron Transport written by Elmer Eugene Lewis and published by Wiley-Interscience. This book was released on 1984 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Novel Equivalence Method for High Fidelity Hybrid Stochastic-deterministic Neutron Transport Simulations by : Guillaume Louis Giudicelli
Download or read book A Novel Equivalence Method for High Fidelity Hybrid Stochastic-deterministic Neutron Transport Simulations written by Guillaume Louis Giudicelli and published by . This book was released on 2020 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: With ever increasing available computing resources, the traditional nuclear reactor physics computation schemes, that trade off between spatial, angular and energy resolution to achieve low cost highly-tuned simulations, are being challenged. While existing schemes can reach few-percent accuracy for the current fleet of light water reactors, thanks to a plethora of astute engineering approximations, they cannot provide sufficient accuracy for evolutionary reactor designs with highly heterogeneous geometries. The decades-long process to develop and qualify these simulation tools is also not in phase with the fast-paced development of innovative new reactor designs seeking to address the climate crisis. Enabled by those computing resources, high fidelity Monte Carlo methods can easily tackle challenging geometries, but they lack the computational and algorithmic efficiency of deterministic methods. However, they are increasingly being used for group cross section generation. Downstream highly parallelized 3D deterministic transport can then use those cross sections to compute accurate solutions at the full core scale. This hybrid computation scheme makes the most of both worlds to achieve fast and accurate reactor physics simulations. Among the few remaining approximations are neglecting the angular dependence of group cross sections, which lead to an over-estimation of resonant absorption rates, especially for the lower resonances of 238U. This thesis presents a novel equivalence method based on introducing discontinuities in the track angular fluxes, with a polar dependence of discontinuity factors to preserve the polar dependence of the neutron currents as well as removing the self-shielding error. This new method is systematically benchmarked against the state-of-the-art method, SuPerHomogenization in three different approaches to obtaining equivalence factors: a same-scale iterative approach, a multiscale approach, and a single-step non-iterative approach. Both methods show remarkable agreement with a reference Monte Carlo solution on a wide array of test cases, from 2D pin cells to 3D full core calculations, for the iterative and the multi-scale approaches. The self-shielding error is eliminated, improving significantly the predictive capabilities of the scheme for the distribution of 238U absorption in the core. A single-step non-iterative approach to obtaining equivalence factors is also pursued, and was shown to only be adequate with the novel discontinuity factor-based method. This study is largely enabled by a significant optimization effort of the 3D deterministic neutron transport solver. By leveraging low level parallelism through vectorization of the multi-group neutron transport equation, by increasing the memory locality of the method of characteristics implementation and with a novel inter-domain communication algorithm enabling a near halving of memory requirements, the 3D full core case can now be tackled with only 50 nodes on an industrial sized computing cluster rather than the many thousands of nodes on a TOP20 supercomputer used previously. This thesis presents fully resolved solutions to the steady-state multi-group neutron transport equation for full-core 3D light water reactors, and these solutions are comparable to gold-standard continuous-energy Monte Carlo solutions.
Book Synopsis A Hybrid Stochastic/deterministic Method for Transient, Three-dimensional Neutron Transport by : M. Wesley Waddell
Download or read book A Hybrid Stochastic/deterministic Method for Transient, Three-dimensional Neutron Transport written by M. Wesley Waddell and published by . This book was released on 1993 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Neutron Transport Theory by : J. H. Tait
Download or read book An Introduction to Neutron Transport Theory written by J. H. Tait and published by . This book was released on 1965 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Stochastic Cellular Automata Model for Neutron Transport by : Michael Joseph Gaeta
Download or read book A Stochastic Cellular Automata Model for Neutron Transport written by Michael Joseph Gaeta and published by . This book was released on 1991 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Neutron Diffusion by : S. Chakraverty
Download or read book Neutron Diffusion written by S. Chakraverty and published by CRC Press. This book was released on 2017-04-21 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for a systematic understanding of nuclear diffusion theory along with fuzzy/interval/stochastic uncertainty. This will serve to be a benchmark book for graduate & postgraduate students, teachers, engineers and researchers throughout the globe. In view of the recent developments in nuclear engineering, it is important to study the basic concepts of this field along with the diffusion processes for nuclear reactor design. Also, it is known that uncertainty is a must in every field of engineering and science and, in particular, with regards to nuclear-related problems. As such, one may need to understand the nuclear diffusion principles/theories corresponding with reliable and efficient techniques for the solution of such uncertain problems. Accordingly this book aims to provide a new direction for readers with basic concepts of reactor physics as well as neutron diffusion theory. On the other hand, it also includes uncertainty (in terms of fuzzy, interval, stochastic) and their applications in nuclear diffusion problems in a systematic manner, along with recent developments. The underlying concepts of the presented methods in this book may very well be used/extended to various other engineering disciplines viz. electronics, marine, chemical, mining engineering and other sciences such as physics, chemistry, biotechnology etc. This book then can be widely applied wherever one wants to model their physical problems in terms of non-probabilistic methods viz. fuzzy/stochastic for the true essence of the real problems.
