Monte Carlo Principles and Neutron Transport Problems

by Spanier, Jerome; Gelbard, Ely M.

• ISBN13: 9780486462936
• ISBN10: 0486462935
• Format: Paperback
• Copyright: 2008-02-04
• Publisher: Dover Publications

Summary

This two-part treatment introduces the general principles of the Monte Carlo method within a unified mathematical point of view, applying them to specific problems in neutron transport.

Table of Contents

Preface to the Dover Edition	p. vii
Introduction	p. ix
Fundamentals of Monte Carlo Methods
Introduction	p. 1
Random variables	p. 1
Statistical analysis	p. 11
Sampling distributions and confidence intervals	p. 16
The construction of samples	p. 21
The rejection method	p. 26
Multi-dimensional generalizations	p. 28
Special methods	p. 33
Random number generation	p. 36
Discrete and Continuous Random Walk Processes
Introduction	p. 41
Discrete random walks	p. 42
Solutions of linear systems	p. 47
Solutions of integral equations	p. 55
Basic estimators for integral equations	p. 60
The track length estimator	p. 66
Extensions of the track length estimator	p. 76
Standard Variance Reduction Techniques
Introduction	p. 83
General principles	p. 84
Random walk processes and their associated probabilities	p. 85
The binomial estimator	p. 97
Systematic source sampling	p. 98
The use of expected values	p. 101
Importance sampling	p. 110
Russian roulette and splitting	p. 124
Correlated sampling	p. 129
Antithetic variates	p. 132
Optimum combinations of variables	p. 135
Use of Superposition and Reciprocity In One-Energy Problems
Introduction	p. 139
The superposition method	p. 141
The surface source method	p. 144
Sticking and escape probabilities	p. 151
Superposition as a perturbation method	p. 155
The inclusion of scattering	p. 157
First method re-examined	p. 160
Second method	p. 165
Other applications of superposition	p. 167
Use of the adjoint transport equation	p. 169
Computation of Thermal Neutron Fluxes
Introduction	p. 176
Statement of the thermal problem	p. 176
The Monte Carlo calculation	p. 183
Refinements of the formulation	p. 192
Treatment of small perturbations	p. 198
The Superposition Principle in Resonance Escape Computations
Introduction	p. 203
First method	p. 204
Computation of P*	p. 209
Analysis of model problem	p. 211
Second method	p. 216
Storage-saving techniques	p. 223
Utility of the superposition method	p. 224
Errata	p. 227
Author Index	p. 237
Subject Index	p. 239
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