[PDF] On The Stochastic Nonlinear Neutron Transport Equation eBook

Author : Emma Horton
Publisher : Springer Nature
Page : 278 pages
File Size : 13,90 MB
Release : 2023-12-17
Category : Mathematics
ISBN : 3031395468

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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.

Author : Mustapha Mokhtar Kharroubi
Publisher : World Scientific
Page : 372 pages
File Size : 34,75 MB
Release : 1997-12-18
Category : Science
ISBN : 981449819X

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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.

Author : M. Mokhtar-Kharroubi
Publisher : World Scientific
Page : 372 pages
File Size : 33,31 MB
Release : 1997
Category : Mathematics
ISBN : 9789810228699

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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.

Author : S. Chakraverty
Publisher : CRC Press
Page : 216 pages
File Size : 25,41 MB
Release : 2017-04-21
Category : Mathematics
ISBN : 1351667505

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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.

Author : Jacek Banasiak
Publisher : Springer
Page : 505 pages
File Size : 29,99 MB
Release : 2014-11-07
Category : Mathematics
ISBN : 3319113224

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With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory. Truly unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory. The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering.

Author : Guillaume Louis Giudicelli
Publisher :
Page : 542 pages
File Size : 13,63 MB
Release : 2020
Category :
ISBN :

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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.