Stochastic neutron transport : and non-local branching Markov processes / Emma Horton, Andreas E. Kyprianou.
Horton, Emma.; Kyprianou, Andreas E.
2023
QC793.5.N4622 H67 2023
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Title Stochastic neutron transport : and non-local branching Markov processes / Emma Horton, Andreas E. Kyprianou.
Author Horton, Emma.
ISBN 9783031395468 electronic book
3031395468 electronic book
9783031395451
303139545X
DOI https://doi.org/10.1007/978-3-031-39546-8
Published Cham : Birkhäuser, 2023.
Language English
Description 1 online resource (xv, 272 pages) : illustrations (some color).
Item Number 10.1007/978-3-031-39546-8 doi
Call Number QC793.5.N4622 H67 2023
Dewey Decimal Classification 539.7/21301519233
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Added Author Kyprianou, Andreas E.
Series Probability and its applications.
Available in Other Form Stochastic Neutron Transport
Linked Resources Online Access
Record Appears in Online Resources > Ebooks
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Intro
Preface
Acknowledgements
Contents
Part I Stochastic Neutron Transport
1 Classical Neutron Transport Theory
1.1 Basic Neutronics
1.2 Neutron Transport Equation (NTE)
1.3 Flux Versus Neutron Density
1.4 Classical Solutions as an Abstract Cauchy Problem (ACP)
1.5 Principal Eigendecomposition and Criticality
1.6 Remarks on Diffusive Approximations
1.7 Primer to the Stochastic Approach
1.8 Comments
2 Some Background Markov Process Theory
2.1 Markov Processes
2.2 Expectation Semigroups and Evolution Equations

2.3 The Heuristics of Infinitesimal Generators
2.4 Feynman-Kac Heuristics
2.5 Perron-Frobenius-Type Behaviour
2.6 Quasi-Stationarity
2.7 Martingales, Doob h-Transforms, and Conditioning
2.8 Two Instructive Examples of Doob h-Transforms
2.9 Comments
3 Stochastic Representation of the Neutron Transport Equation
3.1 Duality and the Backward NTE
3.2 Advection Transport
3.3 Neutron Random Walk
3.4 Neutron Branching Process
3.5 Mild NTE vs. Backward NTE
3.6 Re-Oriented Mild NTE
3.7 Comments
4 Many-to-One, Perron-Frobenius and Criticality

6.4 Skeletal Decomposition
3223379 -Trees
326C33F -Trees
6.5 Comments
7 Generational Evolution
7.1 keff-Eigenvalue Problem
7.2 Generation Time
7.3 Many-to-One Representation
7.4 Perron-Frobenius Asymptotics
Proof of (A1)
Proof of (A2*)
7.5 Moment Growth
7.6 c-Eigenvalue Problem
7.7 Comments
Part II Non-local Branching Markov Processes
8 A General Family of Branching Markov Processes
8.1 Branching Markov Processes
8.2 Non-linear Semigroup Evolution
8.3 Examples of Branching Markov Processes
8.4 Linear Semigroup Evolution and Many-to-One

8.5 Asmussen-Hering Class, Criticality, and Ergodicity
8.6 Re-oriented Non-linear Semigroup
8.7 Discrete-Time Branching Markov Processes
8.8 Comments
9 Moments
9.1 Evolution Equations for the k-th Moments
9.2 Moment Evolution at Criticality
9.3 Moment Evolution at Non-criticality
9.4 Moments of the Running Occupation at Criticality
9.5 Moments of the Running Occupation at Non-criticality
9.6 Moments for Discrete-Time Branching Markov Processes
9.7 Examples for Specific Branching Processes
9.8 Comments
10 Survival at Criticality
10.1 Yaglom Limit Results for General BMPs

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