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E-grāmata: Monte Carlo Methods for Particle Transport 2nd edition [Taylor & Francis e-book]

  • Formāts: 310 pages, 48 Tables, black and white; 81 Line drawings, black and white; 2 Halftones, black and white; 83 Illustrations, black and white
  • Izdošanas datums: 10-Aug-2020
  • Izdevniecība: CRC Press
  • ISBN-13: 9780429198397
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Monte Carlo Methods for Particle Transport 2nd editionPalielināt
  • Formāts: 310 pages, 48 Tables, black and white; 81 Line drawings, black and white; 2 Halftones, black and white; 83 Illustrations, black and white
  • Izdošanas datums: 10-Aug-2020
  • Izdevniecība: CRC Press
  • ISBN-13: 9780429198397
Citas grāmatas par šo tēmu:
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Rokasgrāmatas mājas lapa: https://www.taylorfrancis.com/books/9780429198397
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 authors research activities
Acknowledgement xvii
About the Author xix
Chapter 1 Introduction
1(6)
1.1 History Of Monte Carlo Simulation
1(3)
1.2 Status Of Monte Carlo Codes
4(1)
1.3 Motivation For Writing This Book
5(1)
1.4 Author's Message To Instructors
6(1)
Chapter 2 Random Variables and Sampling
7(24)
2.1 Introduction
8(1)
2.2 Random Variables
8(4)
2.2.1 Discrete random variable
9(1)
2.2.2 Continuous random variable
10(1)
2.2.3 Notes on pdf and cdf characteristics
11(1)
2.3 Random Numbers
12(1)
2.4 Derivation Of The Fundamental Formulation Of Monte Carlo (Ffmc)
13(2)
2.5 Sampling One-Dimensional Density Functions
15(6)
2.5.1 Analytical inversion
15(1)
2.5.2 Numerical inversion
15(2)
2.5.3 Probability mixing method
17(1)
2.5.4 Rejection technique
18(1)
2.5.5 Numerical evaluation
19(2)
2.5.6 Table lookup
21(1)
2.6 Sampling Multidimensional Density Functions
21(2)
2.7 Example Procedures For Sampling A Few Commonly Used Distributions
23(4)
2.7.1 Normal distribution
24(1)
2.7.2 Watt spectrum
25(1)
2.7.3 Cosine and sine functions sampling
25(2)
2.8 Remarks
27(4)
Chapter 3 Random Number Generator (RNG)
31(24)
3.1 Introduction
31(1)
3.2 Random Number Generation Approaches
32(3)
3.3 Pseudo Random Number Generators (Prngs)
35(8)
3.3.1 Congruential Generators
35(7)
3.3.2 Multiple Recursive Generator
42(1)
3.4 Testing Randomness
43(4)
3.4.1 Χ2 -- Test
44(1)
3.4.1.1 Χ2 -- distribution
44(1)
3.4.1.2 Procedure for the use of Χ2 -- test
45(1)
3.4.2 Frequency test
45(1)
3.4.3 Serial test
46(1)
3.4.4 Gap test
46(1)
3.4.5 Poker test
46(1)
3.4.6 Moment test
46(1)
3.4.7 Serial correlation test
47(1)
3.4.8 Serial test via plotting
47(1)
3.5 Example For Testing A Prng
47(5)
3.5.1 Evaluation of PRNG based on period and average
47(3)
3.5.2 Serial test via plotting
50(2)
3.6 Remarks
52(3)
Chapter 4 Fundamentals of Probability and Statistics
55(42)
4.1 Introduction
56(1)
4.2 Expectation Value
57(5)
4.2.1 Single variable
57(2)
4.2.2 Useful formulation for the expectation operator
59(1)
4.2.3 Multivariate
60(2)
4.3 Sample Expectation Values In Statistics
62(3)
4.3.1 Sample mean
62(1)
4.3.2 Sample variance
63(2)
4.4 Precision And Accuracy Of A Sample Average
65(1)
4.5 Commonly Used Density Functions
65(14)
4.5.1 Uniform density function
65(1)
4.5.2 Binomial density function
66(1)
4.5.2.1 Bernoulli process
66(1)
4.5.2.2 Derivation of the Binomial density function
67(3)
4.5.3 Geometric density function
70(1)
4.5.4 Poisson density function
71(2)
4.5.5 Normal (Gaussian) density function
73(6)
4.6 Limit Theorems And Their Applications
79(6)
4.6.1 Corollary to the de Moivre-Laplace limit theorem
80(3)
4.6.2 Central limite theorem
83(1)
4.6.2.1 Demonstration of the Central Limit Theorem
84(1)
4.7 General Formulation Of The Relative Uncertainty
85(2)
4.7.1 Special case of a Bernoulli random process
87(1)
4.8 Confidence Level For Finite Sampling
87(4)
4.8.1 Student's t-distribution
88(2)
4.8.2 Determination of confidence level and application of the t-distribution
90(1)
4.9 Test Of Normality Of Distribution
91(6)
4.9.1 Test of skewness coefficient
91(1)
4.9.2 Shapiro-Wilk test for normality
91(6)
Chapter 5 Integrals and Associated Variance Reduction Techniques
97(20)
5.1 Introduction
97(1)
5.2 Evaluation Of Integrals
98(1)
5.3 Variance Reduction Techniques For Determination Of Integrals
99(16)
5.3.1 Importance sampling
100(3)
5.3.2 Control variates technique
103(1)
5.3.3 Stratified sampling technique
104(9)
5.3.4 Combined sampling
113(2)
5.4 Remarks
115(2)
Chapter 6 Fixed-Source Monte Carlo Particle Transport
117(20)
6.1 Introduction
117(1)
6.2 Introduction To The Linear Boltzmann Equation
118(2)
6.3 Monte Carlo Method For Simplified Particle Transport
120(8)
6.3.1 Sampling path length
121(2)
6.3.2 Sampling interaction type
123(1)
6.3.2.1 Procedure for N(> 2) interaction type
123(1)
6.3.2.2 Procedure for a discrete random variable with N outcomes of equal probabilities
124(1)
6.3.3 Selection of scattering angle
125(3)
6.4 A 1-D Monte Carlo Algorithm
128(2)
6.5 Perturbation Via Correlated Sampling
130(1)
6.6 How To Examine Statistical Reliability Of Monte Carlo Results
131(1)
6.7 Remarks
132(5)
Chapter 7 Variance reduction techniques for fixed-sourceparticle transport
137(20)
7.1 Introduction
138(1)
7.2 Overview Of Variance Reduction For Fixed-Source Particle Transport
139(1)
7.3 Pdf Biasing With Russian Roulette
140(4)
7.3.1 Implicit capture or survival biasing with Russian roulette
140(1)
7.3.1.1 Russian roulette technique
141(1)
7.3.2 Path-length biasing
141(1)
7.3.3 Exponential transformation biasing
142(1)
7.3.4 Forced collision biasing
143(1)
7.4 Particle Splitting With Russian Roulette
144(3)
7.4.1 Geometric splitting
145(2)
7.4.2 Energy splitting
147(1)
7.4.3 Angular splitting
147(1)
7.5 Weight-Window Technique
147(1)
7.6 Integral Biasing
148(2)
7.6.1 Importance (adjoint) function methodology
148(2)
7.6.2 Source biasing based on the importance sampling
150(1)
7.7 Hybrid Methodologies
150(2)
7.7.1 CADIS methodology
151(1)
7.7.1.1 FW-CADIS technique
152(1)
7.8 Remarks
152(5)
Chapter 8 Scoring/Tallying
157(16)
8.1 Introduction
157(1)
8.2 Major Physical Quantities In Particle Transport
158(1)
8.3 Tallying In A Steady-State System
159(7)
8.3.1 Collision estimator
160(1)
8.3.2 Path-length estimator
161(1)
8.3.3 Surface-crossing estimator
162(1)
8.3.3.1 Estimation of partial and net currents
163(1)
8.3.3.2 Estimation of flux on a surface
163(1)
8.3.4 Analytical estimator
164(2)
8.4 Time-Dependent Tallying
166(2)
8.5 Formulation Of Tallies When Variance Reduction Used
168(1)
8.6 Estimation Of Relative Uncertainty Of Tallies
169(1)
8.7 Uncertainty In A Random Variable Dependent On Other Random Variables
170(1)
8.8 Remarks
171(2)
Chapter 9 Geometry and particle tracking
173(14)
9.1 Introduction
173(1)
9.2 Combinatorial Geometry Approach
174(4)
9.2.1 Definition of a surface
175(2)
9.2.2 Definition of cells
177(1)
9.2.3 Examples for irregular cells
177(1)
9.3 Description Of Boundary Conditions
178(3)
9.4 Particle Tracking
181(2)
9.5 Remarks
183(4)
Chapter 10 Eigenvalue (criticality) Monte Carlo method for particle transport
187(28)
10.1 Introduction
188(1)
10.2 Theory Of Power Iteration For Eigenvalue Problems
189(2)
10.3 Monte Carlo Eigenvalue Calculation
191(9)
10.3.1 Random variables for sampling fission neutrons
192(1)
10.3.1.1 Number of fission neutrons
192(1)
10.3.1.2 Energy of fission neutrons
193(1)
10.3.1.3 Direction of fission neutrons
193(1)
10.3.2 Procedure for Monte Carlo Eigenvalue simulation
194(2)
10.3.2.1 Estimators for sampling fission neutrons
196(2)
10.3.3 A method to combine the estimators
198(2)
10.4 Issues Associated With The Standard Eigenvalue Monte Carlo Simulation Procedure
200(1)
10.5 Diagnostic Tests For Source Convergence
201(3)
10.5.1 Shannon entropy technique
201(1)
10.5.1.1 Concept of Shannon entropy
201(1)
10.5.1.2 Application of the Shannon entropy to the fission neutron source
202(1)
10.5.2 Center of Mass (COM) technique
202(2)
10.6 Standard Eigenvalue Monte Carlo Calculation - Performance, Analysis, Shortcomings
204(7)
10.6.1 A procedure for selection of appropriate eigenvalue parameters
204(1)
10.6.2 Demonstration of the shortcomings of the standard eigenvalue Monte Carlo calculation
204(1)
10.6.2.1 Example problem
205(1)
10.6.2.2 Results and analysis
205(6)
10.7 Remarks
211(4)
Chapter 11 Fission matrix methods for eigenvalue Monte Carlo simulation
215(22)
11.1 Introduction
216(1)
11.2 Derivation Of Formulation Of The Fission-Matrix Methodology
216(5)
11.2.1 Implementation of the FM method - Approach 1
217(2)
11.2.2 Implementation of the FM method - Approach 2
219(1)
11.2.2.1 Issues associated with the FMBMC approach
219(2)
11.3 Application Of The Fm Method - Approach 1
221(13)
11.3.1 Modeling spent fuel facilities
221(1)
11.3.1.1 Problem description
221(1)
11.3.1.2 FM coefficient pre-calculation
222(1)
11.3.1.3 Comparison of RAPID to Serpent - Accuracy and Performance
223(4)
11.3.2 Reactor cores
227(1)
11.3.3 A few innovative techniques for generation or correction of FM coeffiicients
227(1)
11.3.3.1 Geometric similarity
227(1)
11.3.3.2 Boundary correction
228(1)
11.3.3.3 Material discontinuity
229(1)
11.3.4 Simulation of the OECD/NEA benchmark
230(4)
11.4 Development Of Other Fm Matrix Based Formulations
234(1)
11.5 Remarks
234(3)
Chapter 12 "Vector and parallel processing of Monte Carlo particle transport
237(16)
12.1 Introduction
237(1)
12.2 Vector Processing
238(3)
12.2.0.1 Scalar computer
238(1)
12.2.0.2 Vector computer
239(1)
12.2.1 Vector performance
240(1)
12.3 Parallel Processing
241(4)
12.3.1 Parallel performance
242(2)
12.3.1.1 Factors affecting the parallel performance
244(1)
12.4 Vectorization Of The Monte Carlo Particle Transport Methods
245(1)
12.5 Parallelization Of The Monte Carlo Particle Transport Methods
246(1)
12.5.1 Other possible parallel Monte Carlo particle transport algorithms
247(1)
12.6 Development Of A Parallel Algorithm Using Mpi
247(1)
12.7 Remarks
248(5)
APPENDIX A Appendix 1
253(4)
A.1 Integer Operations On A Binary Computer
253(4)
APPENDIX B Appendix 2
257(4)
B.1 Derivation Of A Formulation For The Scattering Direction In A 3-D Domain
257(4)
APPENDIX C Appendix 3
261(2)
C.1 Solid Angle Formulation
261(2)
APPENDIX D Appendix 4
263(4)
D.1 Energy-Dependent Neutron-Nuclear Interactions In Monte Carlo Simulation
263(1)
D.2 Introduction
263(1)
D.3 Elastic Scattering
264(1)
D.4 Inelastic Scattering
265(1)
D.5 Scattering At Thermal Energies
266(1)
APPENDIX E Appendix 5
267(6)
E.1 Shannon Entropy
267(6)
E.1.1 Derivation of the Shannon entropy - Approach 1
267(3)
E.1.2 Derivation of the Shannon entropy - Approach 2
270(3)
Bibliography 273(12)
Index 285
Dr. Alireza Haghighat is professor and Director of Nuclear Engineering Program, Virginia Tech. He is a fellow of the American Nuclear Society. He has made pioneering contributions to the development of accurate and efficient deterministic, stochastic, and hybrid particle transport theory methods and their application to complex problems in nuclear reactors, nuclear security and radiation diagnosis and therapy.
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