Verfügbarkeit: Monte Carlo methods for particle transport

Monte Carlo methods for particle transport:

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Bibliographische Detailangaben
1. Verfasser:	Haghighat, Alireza (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Boca Raton ; London ; New York CRC Press 2021
Ausgabe:	Second edition
Schlagworte:	Monte Carlo method.. Particles (Nuclear physics)-Mathematical models.. Radiative transfer
Online-Zugang:	TUM01
Beschreibung:	Description based on publisher supplied metadata and other sources
Beschreibung:	1 Online-Ressource Illustrationen, Diagramme
ISBN:	9780429582202 9780429198397

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MARC


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245	1	0	\|a Monte Carlo methods for particle transport \|c Alireza Haghighat
250			\|a Second edition
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264		4	\|c ©2021
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505	8		\|a Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Acknowledgement -- About the Author -- Chapter 1: Introduction -- 1.1 HISTORY OF MONTE CARLO SIMULATION -- 1.2 STATUS OF MONTE CARLO CODES -- 1.3 MOTIVATION FOR WRITING THIS BOOK -- 1.4 AUTHOR'S MESSAGE TO INSTRUCTORS -- Chapter 2: Random Variables and Sampling -- 2.1 INTRODUCTION -- 2.2 RANDOM VARIABLES -- 2.2.1 Discrete random variable -- 2.2.2 Continuous random variable -- 2.2.3 Notes on pdf and cdf characteristics -- 2.3 RANDOM NUMBERS -- 2.4 DERIVATION OF THE FUNDAMENTAL FORMULATION OF MONTE CARLO (FFMC) -- 2.5 SAMPLING ONE DIMENSIONAL DENSITY FUNCTIONS -- 2.5.1 Analytical inversion -- 2.5.2 Numerical inversion -- 2.5.3 Probability mixing method -- 2.5.4 Rejection technique -- 2.5.5 Numerical evaluation -- 2.5.6 Table lookup -- 2.6 SAMPLING MULTIDIMENSIONAL DENSITY FUNCTIONS -- 2.7 EXAMPLE PROCEDURES FOR SAMPLING A FEW COMMONLY USED DISTRIBUTIONS -- 2.7.1 Normal distribution -- 2.7.2 Watt spectrum -- 2.7.3 Cosine and sine functions sampling -- 2.8 REMARKS -- Chapter 3: Random Number Generator (RNG) -- 3.1 INTRODUCTION -- 3.2 RANDOM NUMBER GENERATION APPROACHES -- 3.3 PSEUDO RANDOM NUMBER GENERATORS (PRNGS) -- 3.3.1 Congruential Generators -- 3.3.2 Multiple Recursive Generator -- 3.4 TESTING RANDOMNESS -- 3.4.1 χ2 − Test -- 3.4.1.1 χ2 − distribution -- 3.4.1.2 Procedure for the use of χ2 − test -- 3.4.2 Frequency test -- 3.4.3 Serial test -- 3.4.4 Gap test -- 3.4.5 Poker test -- 3.4.6 Moment test -- 3.4.7 Serial correlation test -- 3.4.8 Serial test via plotting -- 3.5 EXAMPLE FOR TESTING A PRNG -- 3.5.1 Evaluation of PRNG based on period and average -- 3.5.2 Serial test via plotting -- 3.6 REMARKS -- Chapter 4: Fundamentals of Probability and Statistics -- 4.1 INTRODUCTION -- 4.2 EXPECTATION VALUE -- 4.2.1 Single variable
505	8		\|a 4.2.2 Useful formulation for the expectation operator -- 4.2.3 Multivariable -- 4.3 SAMPLE EXPECTATION VALUES IN STATISTICS -- 4.3.1 Sample mean -- 4.3.2 Sample variance -- 4.4 PRECISION AND ACCURACY OF A SAMPLE AVERAGE -- 4.5 COMMONLY USED DENSITY FUNCTIONS -- 4.5.1 Uniform density function -- 4.5.2 Binomial density function -- 4.5.2.1 Bernoulli process -- 4.5.2.2 Derivation of the Binomial density function -- 4.5.3 Geometric density function -- 4.5.4 Poisson density function -- 4.5.5 Normal ( -- 4.6 LIMIT THEOREMS AND THEIR APPLICATIONS -- 4.6.1 Corollary to the de Moivre-Laplace limit theorem -- 4.6.2 Central limite theorem -- 4.6.2.1 Demonstration of the Central Limit Theorem -- 4.7 GENERAL FORMULATION OF THE RELATIVE UNCERTAINTY -- 4.7.1 Special case of a Bernoulli random process -- 4.8 CONFIDENCE LEVEL FOR FINITE SAMPLING -- 4.8.1 Student's t-distribution -- 4.8.2 Determination of confidence level and application of the t-distribution -- 4.9 TEST OF NORMALITY OF DISTRIBUTION -- 4.9.1 Test of skewness coefficient -- 4.9.2 Shapiro-Wilk test for normality -- Chapter 5: Integrals and Associated Variance Reduction Techniques -- 5.1 INTRODUCTION -- 5.2 EVALUATION OF INTEGRALS -- 5.3 VARIANCE REDUCTION TECHNIQUES FOR DETERMINATION OF INTEGRALS -- 5.3.1 Importance sampling -- 5.3.2 Control variates technique -- 5.3.3 Stratified sampling technique -- 5.3.4 Combined sampling -- 5.4 REMARKS -- Chapter 6: Fixed-Source Monte Carlo Particle Transport -- 6.1 INTRODUCTION -- 6.2 INTRODUCTION TO THE LINEAR BOLTZMANN EQUATION -- 6.3 MONTE CARLO METHOD FOR SIMPLIFIED PARTICLE TRANSPORT -- 6.3.1 Sampling path length -- 6.3.2 Sampling interaction type -- 6.3.2.1 Procedure for N (&gt -- 2) interaction type -- 6.3.2.2 Procedure for a discrete random variable with N outcomes of equal probabilities -- 6.3.3 Selection of scattering angle
505	8		\|a 6.4 A 1-D MONTE CARLO ALGORITHM -- 6.5 PERTURBATION VIA CORRELATED SAMPLING -- 6.6 HOW TO EXAMINE STATISTICAL RELIABILITY OF MONTE CARLO RESULTS -- 6.7 REMARKS -- Chapter 7: Variance reduction techniques for fixed-source particle transport -- 7.1 INTRODUCTION -- 7.2 OVERVIEW OF VARIANCE REDUCTION FOR FIXED SOURCE PARTICLE TRANSPORT -- 7.3 PDF BIASING WITH RUSSIAN ROULETTE -- 7.3.1 Implicit capture or survival biasing with Russian roulette -- 7.3.1.1 Russian roulette technique -- 7.3.2 Path-length biasing -- 7.3.3 Exponential transformation biasing -- 7.3.4 Forced collision biasing -- 7.4 PARTICLE SPLITTING WITH RUSSIAN ROULETTE -- 7.4.1 Geometric splitting -- 7.4.2 Energy splitting -- 7.4.3 Angular splitting -- 7.5 WEIGHT-WINDOW TECHNIQUE -- 7.6 INTEGRAL BIASING -- 7.6.1 Importance (adjoint) function methodology -- 7.6.2 Source biasing based on the importance sampling -- 7.7 HYBRID METHODOLOGIES -- 7.7.1 CADIS methodology -- 7.7.1.1 FW-CADIS technique -- 7.8 REMARKS -- Chapter 8: Scoring/Tallying -- 8.1 INTRODUCTION -- 8.2 MAJOR PHYSICAL QUANTITIES IN PARTICLE TRANSPORT -- 8.3 TALLYING IN A STEADY STATE SYSTEM -- 8.3.1 Collision estimator -- 8.3.2 Path-length estimator -- 8.3.3 Surface-crossing estimator -- 8.3.3.1 Estimation of partial and net currents -- 8.3.3.2 Estimation of flux on a surface -- 8.3.4 Analytical estimator -- 8.4 TIME DEPENDENT TALLYING -- 8.5 FORMULATION OF TALLIES WHEN VARIANCE REDUCTION USED -- 8.6 ESTIMATION OF RELATIVE UNCERTAINTY OF TALLIES -- 8.7 UNCERTAINTY IN A RANDOM VARIABLE DEPENDENT ON OTHER RANDOM VARIABLES -- 8.8 REMARKS -- Chapter 9: Geometry and particle tracking -- 9.1 INTRODUCTION -- 9.2 COMBINATORIAL GEOMETRY APPROACH -- 9.2.1 Definition of a surface -- 9.2.2 Definition of cells -- 9.2.3 Examples for irregular cells -- 9.3 DESCRIPTION OF BOUNDARY CONDITIONS -- 9.4 PARTICLE TRACKING -- 9.5 REMARKS.
505	8		\|a Chapter 10: Eigenvalue (criticality) Monte Carlo method for particle transport -- 10.1 INTRODUCTION -- 10.2 THEORY OF POWER ITERATION FOR EIGENVALUE PROBLEMS -- 10.3 MONTE CARLO EIGENVALUE CALCULATION -- 10.3.1 Random variables for sampling fission neutrons -- 10.3.1.1 Number of fission neutrons -- 10.3.1.2 Energy of fission neutrons -- 10.3.1.3 Direction of fission neutrons -- 10.3.2 Procedure for Monte Carlo Eigenvalue simulation -- 10.3.2.1 Estimators for sampling fission neutrons -- 10.3.3 A method to combine the estimators -- 10.4 ISSUES ASSOCIATED WITH THE STANDARD EIGENVALUE MONTE CARLO SIMULATION PROCEDURE -- 10.5 DIAGNOSTIC TESTS FOR SOURCE CONVERGENCE -- 10.5.1 Shannon entropy technique -- 10.5.1.1 Concept of Shannon entropy -- 10.5.1.2 Application of the Shannon entropy to the fission neutron source -- 10.5.2 Center of Mass (COM) technique -- 10.6 STANDARD EIGENVALUE MONTE CARLO CALCULATION PERFORMANCE, ANALYSIS, SHORTCOMINGS -- 10.6.1 A procedure for selection of appropriate eigenvalue parameters -- 10.6.2 Demonstration of the shortcomings of the standard eigenvalue Monte Carlo calculation -- 10.6.2.1 Example problem -- 10.6.2.2 Results and analysis -- 10.7 REMARKS -- Chapter 11: Fission matrix methods for eigenvalue Monte Carlo simulation -- 11.1 INTRODUCTION -- 11.2 DERIVATION OF FORMULATION OF THE FISSION MATRIX METHODOLOGY -- 11.2.1 Implementation of the FM method - Approach 1 -- 11.2.2 Implementation of the FM method - Approach 2 -- 11.2.2.1 Issues associated with the FMBMC approach -- 11.3 APPLICATION OF THE FM METHOD - APPROACH 1 -- 11.3.1 Modeling spent fuel facilities -- 11.3.1.1 Problem description -- 11.3.1.2 FM coefficient pre-calculation -- 11.3.1.3 Comparison of RAPID to Serpent - Accuracy and Performance -- 11.3.2 Reactor cores -- 11.3.3 A few innovative techniques for generation or correction of FM coeffiicients
505	8		\|a 11.3.3.1 Geometric similarity -- 11.3.3.2 Boundary correction -- 11.3.3.3 Material discontinuity -- 11.3.4 Simulation of the OECD/NEA benchmark -- 11.4 DEVELOPMENT OF OTHER FM MATRIX BASED FORMULATIONS -- 11.5 REMARKS -- Chapter 12: Vector and parallel processing of Monte Carlo particle transport -- 12.1 INTRODUCTION -- 12.2 VECTOR PROCESSING -- 12.2.0.1 Scalar computer -- 12.2.0.2 Vector computer -- 12.2.1 Vector performance -- 12.3 PARALLEL PROCESSING -- 12.3.1 Parallel performance -- 12.3.1.1 Factors affecting the parallel performance -- 12.4 VECTORIZATION OF THE MONTE CARLO PARTICLE TRANSPORT METHODS -- 12.5 PARALLELIZATION OF THE MONTE CARLO PARTICLE TRANSPORT METHODS -- 12.5.1 Other possible parallel Monte Carlo particle transport algorithms -- 12.6 DEVELOPMENT OF A PARALLEL ALGORITHM USING MPI -- 12.7 REMARKS -- Appendix A: Appendix 1 -- A.1 INTEGER OPERATIONS ON A BINARY COMPUTER -- Appendix B: Appendix 2 -- B.1 DERIVATION OF A FORMULATION FOR THE SCATTERING DIRECTION IN A 3 D DOMAIN -- Appendix C: Appendix 3 -- C.1 SOLID ANGLE FORMULATION -- Appendix D: Appendix 4 -- D.1 ENERGY DEPENDENT NEUTRON NUCLEAR INTERACTIONS IN MONTE CARLO SIMULATION -- D.2 INTRODUCTION -- D.3 ELASTIC SCATTERING -- D.4 INELASTIC SCATTERING -- D.5 SCATTERING AT THERMAL ENERGIES -- Appendix E: Appendix 5 -- E.1 SHANNON ENTROPY -- E.1.1 Derivation of the Shannon entropy - Approach 1 -- E.1.2 Derivation of the Shannon entropy - Approach 2 -- Bibliography -- Index
650		4	\|a Monte Carlo method..
650		4	\|a Particles (Nuclear physics)-Mathematical models..
650		4	\|a Radiative transfer
776	0	8	\|i Erscheint auch als \|a Haghighat, Alireza \|t Monte Carlo Methods for Particle Transport \|d Milton : Taylor & Francis Group,c2020 \|n Druck-Ausgabe, Hardcover \|z 978-0-367-18805-4
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999			\|a oai:aleph.bib-bvb.de:BVB01-032843945
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contents	Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Acknowledgement -- About the Author -- Chapter 1: Introduction -- 1.1 HISTORY OF MONTE CARLO SIMULATION -- 1.2 STATUS OF MONTE CARLO CODES -- 1.3 MOTIVATION FOR WRITING THIS BOOK -- 1.4 AUTHOR'S MESSAGE TO INSTRUCTORS -- Chapter 2: Random Variables and Sampling -- 2.1 INTRODUCTION -- 2.2 RANDOM VARIABLES -- 2.2.1 Discrete random variable -- 2.2.2 Continuous random variable -- 2.2.3 Notes on pdf and cdf characteristics -- 2.3 RANDOM NUMBERS -- 2.4 DERIVATION OF THE FUNDAMENTAL FORMULATION OF MONTE CARLO (FFMC) -- 2.5 SAMPLING ONE DIMENSIONAL DENSITY FUNCTIONS -- 2.5.1 Analytical inversion -- 2.5.2 Numerical inversion -- 2.5.3 Probability mixing method -- 2.5.4 Rejection technique -- 2.5.5 Numerical evaluation -- 2.5.6 Table lookup -- 2.6 SAMPLING MULTIDIMENSIONAL DENSITY FUNCTIONS -- 2.7 EXAMPLE PROCEDURES FOR SAMPLING A FEW COMMONLY USED DISTRIBUTIONS -- 2.7.1 Normal distribution -- 2.7.2 Watt spectrum -- 2.7.3 Cosine and sine functions sampling -- 2.8 REMARKS -- Chapter 3: Random Number Generator (RNG) -- 3.1 INTRODUCTION -- 3.2 RANDOM NUMBER GENERATION APPROACHES -- 3.3 PSEUDO RANDOM NUMBER GENERATORS (PRNGS) -- 3.3.1 Congruential Generators -- 3.3.2 Multiple Recursive Generator -- 3.4 TESTING RANDOMNESS -- 3.4.1 χ2 − Test -- 3.4.1.1 χ2 − distribution -- 3.4.1.2 Procedure for the use of χ2 − test -- 3.4.2 Frequency test -- 3.4.3 Serial test -- 3.4.4 Gap test -- 3.4.5 Poker test -- 3.4.6 Moment test -- 3.4.7 Serial correlation test -- 3.4.8 Serial test via plotting -- 3.5 EXAMPLE FOR TESTING A PRNG -- 3.5.1 Evaluation of PRNG based on period and average -- 3.5.2 Serial test via plotting -- 3.6 REMARKS -- Chapter 4: Fundamentals of Probability and Statistics -- 4.1 INTRODUCTION -- 4.2 EXPECTATION VALUE -- 4.2.1 Single variable 4.2.2 Useful formulation for the expectation operator -- 4.2.3 Multivariable -- 4.3 SAMPLE EXPECTATION VALUES IN STATISTICS -- 4.3.1 Sample mean -- 4.3.2 Sample variance -- 4.4 PRECISION AND ACCURACY OF A SAMPLE AVERAGE -- 4.5 COMMONLY USED DENSITY FUNCTIONS -- 4.5.1 Uniform density function -- 4.5.2 Binomial density function -- 4.5.2.1 Bernoulli process -- 4.5.2.2 Derivation of the Binomial density function -- 4.5.3 Geometric density function -- 4.5.4 Poisson density function -- 4.5.5 Normal ( -- 4.6 LIMIT THEOREMS AND THEIR APPLICATIONS -- 4.6.1 Corollary to the de Moivre-Laplace limit theorem -- 4.6.2 Central limite theorem -- 4.6.2.1 Demonstration of the Central Limit Theorem -- 4.7 GENERAL FORMULATION OF THE RELATIVE UNCERTAINTY -- 4.7.1 Special case of a Bernoulli random process -- 4.8 CONFIDENCE LEVEL FOR FINITE SAMPLING -- 4.8.1 Student's t-distribution -- 4.8.2 Determination of confidence level and application of the t-distribution -- 4.9 TEST OF NORMALITY OF DISTRIBUTION -- 4.9.1 Test of skewness coefficient -- 4.9.2 Shapiro-Wilk test for normality -- Chapter 5: Integrals and Associated Variance Reduction Techniques -- 5.1 INTRODUCTION -- 5.2 EVALUATION OF INTEGRALS -- 5.3 VARIANCE REDUCTION TECHNIQUES FOR DETERMINATION OF INTEGRALS -- 5.3.1 Importance sampling -- 5.3.2 Control variates technique -- 5.3.3 Stratified sampling technique -- 5.3.4 Combined sampling -- 5.4 REMARKS -- Chapter 6: Fixed-Source Monte Carlo Particle Transport -- 6.1 INTRODUCTION -- 6.2 INTRODUCTION TO THE LINEAR BOLTZMANN EQUATION -- 6.3 MONTE CARLO METHOD FOR SIMPLIFIED PARTICLE TRANSPORT -- 6.3.1 Sampling path length -- 6.3.2 Sampling interaction type -- 6.3.2.1 Procedure for N (&gt -- 2) interaction type -- 6.3.2.2 Procedure for a discrete random variable with N outcomes of equal probabilities -- 6.3.3 Selection of scattering angle 6.4 A 1-D MONTE CARLO ALGORITHM -- 6.5 PERTURBATION VIA CORRELATED SAMPLING -- 6.6 HOW TO EXAMINE STATISTICAL RELIABILITY OF MONTE CARLO RESULTS -- 6.7 REMARKS -- Chapter 7: Variance reduction techniques for fixed-source particle transport -- 7.1 INTRODUCTION -- 7.2 OVERVIEW OF VARIANCE REDUCTION FOR FIXED SOURCE PARTICLE TRANSPORT -- 7.3 PDF BIASING WITH RUSSIAN ROULETTE -- 7.3.1 Implicit capture or survival biasing with Russian roulette -- 7.3.1.1 Russian roulette technique -- 7.3.2 Path-length biasing -- 7.3.3 Exponential transformation biasing -- 7.3.4 Forced collision biasing -- 7.4 PARTICLE SPLITTING WITH RUSSIAN ROULETTE -- 7.4.1 Geometric splitting -- 7.4.2 Energy splitting -- 7.4.3 Angular splitting -- 7.5 WEIGHT-WINDOW TECHNIQUE -- 7.6 INTEGRAL BIASING -- 7.6.1 Importance (adjoint) function methodology -- 7.6.2 Source biasing based on the importance sampling -- 7.7 HYBRID METHODOLOGIES -- 7.7.1 CADIS methodology -- 7.7.1.1 FW-CADIS technique -- 7.8 REMARKS -- Chapter 8: Scoring/Tallying -- 8.1 INTRODUCTION -- 8.2 MAJOR PHYSICAL QUANTITIES IN PARTICLE TRANSPORT -- 8.3 TALLYING IN A STEADY STATE SYSTEM -- 8.3.1 Collision estimator -- 8.3.2 Path-length estimator -- 8.3.3 Surface-crossing estimator -- 8.3.3.1 Estimation of partial and net currents -- 8.3.3.2 Estimation of flux on a surface -- 8.3.4 Analytical estimator -- 8.4 TIME DEPENDENT TALLYING -- 8.5 FORMULATION OF TALLIES WHEN VARIANCE REDUCTION USED -- 8.6 ESTIMATION OF RELATIVE UNCERTAINTY OF TALLIES -- 8.7 UNCERTAINTY IN A RANDOM VARIABLE DEPENDENT ON OTHER RANDOM VARIABLES -- 8.8 REMARKS -- Chapter 9: Geometry and particle tracking -- 9.1 INTRODUCTION -- 9.2 COMBINATORIAL GEOMETRY APPROACH -- 9.2.1 Definition of a surface -- 9.2.2 Definition of cells -- 9.2.3 Examples for irregular cells -- 9.3 DESCRIPTION OF BOUNDARY CONDITIONS -- 9.4 PARTICLE TRACKING -- 9.5 REMARKS. Chapter 10: Eigenvalue (criticality) Monte Carlo method for particle transport -- 10.1 INTRODUCTION -- 10.2 THEORY OF POWER ITERATION FOR EIGENVALUE PROBLEMS -- 10.3 MONTE CARLO EIGENVALUE CALCULATION -- 10.3.1 Random variables for sampling fission neutrons -- 10.3.1.1 Number of fission neutrons -- 10.3.1.2 Energy of fission neutrons -- 10.3.1.3 Direction of fission neutrons -- 10.3.2 Procedure for Monte Carlo Eigenvalue simulation -- 10.3.2.1 Estimators for sampling fission neutrons -- 10.3.3 A method to combine the estimators -- 10.4 ISSUES ASSOCIATED WITH THE STANDARD EIGENVALUE MONTE CARLO SIMULATION PROCEDURE -- 10.5 DIAGNOSTIC TESTS FOR SOURCE CONVERGENCE -- 10.5.1 Shannon entropy technique -- 10.5.1.1 Concept of Shannon entropy -- 10.5.1.2 Application of the Shannon entropy to the fission neutron source -- 10.5.2 Center of Mass (COM) technique -- 10.6 STANDARD EIGENVALUE MONTE CARLO CALCULATION PERFORMANCE, ANALYSIS, SHORTCOMINGS -- 10.6.1 A procedure for selection of appropriate eigenvalue parameters -- 10.6.2 Demonstration of the shortcomings of the standard eigenvalue Monte Carlo calculation -- 10.6.2.1 Example problem -- 10.6.2.2 Results and analysis -- 10.7 REMARKS -- Chapter 11: Fission matrix methods for eigenvalue Monte Carlo simulation -- 11.1 INTRODUCTION -- 11.2 DERIVATION OF FORMULATION OF THE FISSION MATRIX METHODOLOGY -- 11.2.1 Implementation of the FM method - Approach 1 -- 11.2.2 Implementation of the FM method - Approach 2 -- 11.2.2.1 Issues associated with the FMBMC approach -- 11.3 APPLICATION OF THE FM METHOD - APPROACH 1 -- 11.3.1 Modeling spent fuel facilities -- 11.3.1.1 Problem description -- 11.3.1.2 FM coefficient pre-calculation -- 11.3.1.3 Comparison of RAPID to Serpent - Accuracy and Performance -- 11.3.2 Reactor cores -- 11.3.3 A few innovative techniques for generation or correction of FM coeffiicients 11.3.3.1 Geometric similarity -- 11.3.3.2 Boundary correction -- 11.3.3.3 Material discontinuity -- 11.3.4 Simulation of the OECD/NEA benchmark -- 11.4 DEVELOPMENT OF OTHER FM MATRIX BASED FORMULATIONS -- 11.5 REMARKS -- Chapter 12: Vector and parallel processing of Monte Carlo particle transport -- 12.1 INTRODUCTION -- 12.2 VECTOR PROCESSING -- 12.2.0.1 Scalar computer -- 12.2.0.2 Vector computer -- 12.2.1 Vector performance -- 12.3 PARALLEL PROCESSING -- 12.3.1 Parallel performance -- 12.3.1.1 Factors affecting the parallel performance -- 12.4 VECTORIZATION OF THE MONTE CARLO PARTICLE TRANSPORT METHODS -- 12.5 PARALLELIZATION OF THE MONTE CARLO PARTICLE TRANSPORT METHODS -- 12.5.1 Other possible parallel Monte Carlo particle transport algorithms -- 12.6 DEVELOPMENT OF A PARALLEL ALGORITHM USING MPI -- 12.7 REMARKS -- Appendix A: Appendix 1 -- A.1 INTEGER OPERATIONS ON A BINARY COMPUTER -- Appendix B: Appendix 2 -- B.1 DERIVATION OF A FORMULATION FOR THE SCATTERING DIRECTION IN A 3 D DOMAIN -- Appendix C: Appendix 3 -- C.1 SOLID ANGLE FORMULATION -- Appendix D: Appendix 4 -- D.1 ENERGY DEPENDENT NEUTRON NUCLEAR INTERACTIONS IN MONTE CARLO SIMULATION -- D.2 INTRODUCTION -- D.3 ELASTIC SCATTERING -- D.4 INELASTIC SCATTERING -- D.5 SCATTERING AT THERMAL ENERGIES -- Appendix E: Appendix 5 -- E.1 SHANNON ENTROPY -- E.1.1 Derivation of the Shannon entropy - Approach 1 -- E.1.2 Derivation of the Shannon entropy - Approach 2 -- Bibliography -- Index
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"><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Description based on publisher supplied metadata and other sources</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Acknowledgement -- About the Author -- Chapter 1: Introduction -- 1.1 HISTORY OF MONTE CARLO SIMULATION -- 1.2 STATUS OF MONTE CARLO CODES -- 1.3 MOTIVATION FOR WRITING THIS BOOK -- 1.4 AUTHOR'S MESSAGE TO INSTRUCTORS -- Chapter 2: Random Variables and Sampling -- 2.1 INTRODUCTION -- 2.2 RANDOM VARIABLES -- 2.2.1 Discrete random variable -- 2.2.2 Continuous random variable -- 2.2.3 Notes on pdf and cdf characteristics -- 2.3 RANDOM NUMBERS -- 2.4 DERIVATION OF THE FUNDAMENTAL FORMULATION OF MONTE CARLO (FFMC) -- 2.5 SAMPLING ONE DIMENSIONAL DENSITY FUNCTIONS -- 2.5.1 Analytical inversion -- 2.5.2 Numerical inversion -- 2.5.3 Probability mixing method -- 2.5.4 Rejection technique -- 2.5.5 Numerical evaluation -- 2.5.6 Table lookup -- 2.6 SAMPLING MULTIDIMENSIONAL DENSITY FUNCTIONS -- 2.7 EXAMPLE PROCEDURES FOR SAMPLING A FEW COMMONLY USED DISTRIBUTIONS -- 2.7.1 Normal distribution -- 2.7.2 Watt spectrum -- 2.7.3 Cosine and sine functions sampling -- 2.8 REMARKS -- Chapter 3: Random Number Generator (RNG) -- 3.1 INTRODUCTION -- 3.2 RANDOM NUMBER GENERATION APPROACHES -- 3.3 PSEUDO RANDOM NUMBER GENERATORS (PRNGS) -- 3.3.1 Congruential Generators -- 3.3.2 Multiple Recursive Generator -- 3.4 TESTING RANDOMNESS -- 3.4.1 χ2 − Test -- 3.4.1.1 χ2 − distribution -- 3.4.1.2 Procedure for the use of χ2 − test -- 3.4.2 Frequency test -- 3.4.3 Serial test -- 3.4.4 Gap test -- 3.4.5 Poker test -- 3.4.6 Moment test -- 3.4.7 Serial correlation test -- 3.4.8 Serial test via plotting -- 3.5 EXAMPLE FOR TESTING A PRNG -- 3.5.1 Evaluation of PRNG based on period and average -- 3.5.2 Serial test via plotting -- 3.6 REMARKS -- Chapter 4: Fundamentals of Probability and Statistics -- 4.1 INTRODUCTION -- 4.2 EXPECTATION VALUE -- 4.2.1 Single variable</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">4.2.2 Useful formulation for the expectation operator -- 4.2.3 Multivariable -- 4.3 SAMPLE EXPECTATION VALUES IN STATISTICS -- 4.3.1 Sample mean -- 4.3.2 Sample variance -- 4.4 PRECISION AND ACCURACY OF A SAMPLE AVERAGE -- 4.5 COMMONLY USED DENSITY FUNCTIONS -- 4.5.1 Uniform density function -- 4.5.2 Binomial density function -- 4.5.2.1 Bernoulli process -- 4.5.2.2 Derivation of the Binomial density function -- 4.5.3 Geometric density function -- 4.5.4 Poisson density function -- 4.5.5 Normal ( -- 4.6 LIMIT THEOREMS AND THEIR APPLICATIONS -- 4.6.1 Corollary to the de Moivre-Laplace limit theorem -- 4.6.2 Central limite theorem -- 4.6.2.1 Demonstration of the Central Limit Theorem -- 4.7 GENERAL FORMULATION OF THE RELATIVE UNCERTAINTY -- 4.7.1 Special case of a Bernoulli random process -- 4.8 CONFIDENCE LEVEL FOR FINITE SAMPLING -- 4.8.1 Student's t-distribution -- 4.8.2 Determination of confidence level and application of the t-distribution -- 4.9 TEST OF NORMALITY OF DISTRIBUTION -- 4.9.1 Test of skewness coefficient -- 4.9.2 Shapiro-Wilk test for normality -- Chapter 5: Integrals and Associated Variance Reduction Techniques -- 5.1 INTRODUCTION -- 5.2 EVALUATION OF INTEGRALS -- 5.3 VARIANCE REDUCTION TECHNIQUES FOR DETERMINATION OF INTEGRALS -- 5.3.1 Importance sampling -- 5.3.2 Control variates technique -- 5.3.3 Stratified sampling technique -- 5.3.4 Combined sampling -- 5.4 REMARKS -- Chapter 6: Fixed-Source Monte Carlo Particle Transport -- 6.1 INTRODUCTION -- 6.2 INTRODUCTION TO THE LINEAR BOLTZMANN EQUATION -- 6.3 MONTE CARLO METHOD FOR SIMPLIFIED PARTICLE TRANSPORT -- 6.3.1 Sampling path length -- 6.3.2 Sampling interaction type -- 6.3.2.1 Procedure for N (&gt -- 2) interaction type -- 6.3.2.2 Procedure for a discrete random variable with N outcomes of equal probabilities -- 6.3.3 Selection of scattering angle</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">6.4 A 1-D MONTE CARLO ALGORITHM -- 6.5 PERTURBATION VIA CORRELATED SAMPLING -- 6.6 HOW TO EXAMINE STATISTICAL RELIABILITY OF MONTE CARLO RESULTS -- 6.7 REMARKS -- Chapter 7: Variance reduction techniques for fixed-source particle transport -- 7.1 INTRODUCTION -- 7.2 OVERVIEW OF VARIANCE REDUCTION FOR FIXED SOURCE PARTICLE TRANSPORT -- 7.3 PDF BIASING WITH RUSSIAN ROULETTE -- 7.3.1 Implicit capture or survival biasing with Russian roulette -- 7.3.1.1 Russian roulette technique -- 7.3.2 Path-length biasing -- 7.3.3 Exponential transformation biasing -- 7.3.4 Forced collision biasing -- 7.4 PARTICLE SPLITTING WITH RUSSIAN ROULETTE -- 7.4.1 Geometric splitting -- 7.4.2 Energy splitting -- 7.4.3 Angular splitting -- 7.5 WEIGHT-WINDOW TECHNIQUE -- 7.6 INTEGRAL BIASING -- 7.6.1 Importance (adjoint) function methodology -- 7.6.2 Source biasing based on the importance sampling -- 7.7 HYBRID METHODOLOGIES -- 7.7.1 CADIS methodology -- 7.7.1.1 FW-CADIS technique -- 7.8 REMARKS -- Chapter 8: Scoring/Tallying -- 8.1 INTRODUCTION -- 8.2 MAJOR PHYSICAL QUANTITIES IN PARTICLE TRANSPORT -- 8.3 TALLYING IN A STEADY STATE SYSTEM -- 8.3.1 Collision estimator -- 8.3.2 Path-length estimator -- 8.3.3 Surface-crossing estimator -- 8.3.3.1 Estimation of partial and net currents -- 8.3.3.2 Estimation of flux on a surface -- 8.3.4 Analytical estimator -- 8.4 TIME DEPENDENT TALLYING -- 8.5 FORMULATION OF TALLIES WHEN VARIANCE REDUCTION USED -- 8.6 ESTIMATION OF RELATIVE UNCERTAINTY OF TALLIES -- 8.7 UNCERTAINTY IN A RANDOM VARIABLE DEPENDENT ON OTHER RANDOM VARIABLES -- 8.8 REMARKS -- Chapter 9: Geometry and particle tracking -- 9.1 INTRODUCTION -- 9.2 COMBINATORIAL GEOMETRY APPROACH -- 9.2.1 Definition of a surface -- 9.2.2 Definition of cells -- 9.2.3 Examples for irregular cells -- 9.3 DESCRIPTION OF BOUNDARY CONDITIONS -- 9.4 PARTICLE TRACKING -- 9.5 REMARKS.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Chapter 10: Eigenvalue (criticality) Monte Carlo method for particle transport -- 10.1 INTRODUCTION -- 10.2 THEORY OF POWER ITERATION FOR EIGENVALUE PROBLEMS -- 10.3 MONTE CARLO EIGENVALUE CALCULATION -- 10.3.1 Random variables for sampling fission neutrons -- 10.3.1.1 Number of fission neutrons -- 10.3.1.2 Energy of fission neutrons -- 10.3.1.3 Direction of fission neutrons -- 10.3.2 Procedure for Monte Carlo Eigenvalue simulation -- 10.3.2.1 Estimators for sampling fission neutrons -- 10.3.3 A method to combine the estimators -- 10.4 ISSUES ASSOCIATED WITH THE STANDARD EIGENVALUE MONTE CARLO SIMULATION PROCEDURE -- 10.5 DIAGNOSTIC TESTS FOR SOURCE CONVERGENCE -- 10.5.1 Shannon entropy technique -- 10.5.1.1 Concept of Shannon entropy -- 10.5.1.2 Application of the Shannon entropy to the fission neutron source -- 10.5.2 Center of Mass (COM) technique -- 10.6 STANDARD EIGENVALUE MONTE CARLO CALCULATION PERFORMANCE, ANALYSIS, SHORTCOMINGS -- 10.6.1 A procedure for selection of appropriate eigenvalue parameters -- 10.6.2 Demonstration of the shortcomings of the standard eigenvalue Monte Carlo calculation -- 10.6.2.1 Example problem -- 10.6.2.2 Results and analysis -- 10.7 REMARKS -- Chapter 11: Fission matrix methods for eigenvalue Monte Carlo simulation -- 11.1 INTRODUCTION -- 11.2 DERIVATION OF FORMULATION OF THE FISSION MATRIX METHODOLOGY -- 11.2.1 Implementation of the FM method - Approach 1 -- 11.2.2 Implementation of the FM method - Approach 2 -- 11.2.2.1 Issues associated with the FMBMC approach -- 11.3 APPLICATION OF THE FM METHOD - APPROACH 1 -- 11.3.1 Modeling spent fuel facilities -- 11.3.1.1 Problem description -- 11.3.1.2 FM coefficient pre-calculation -- 11.3.1.3 Comparison of RAPID to Serpent - Accuracy and Performance -- 11.3.2 Reactor cores -- 11.3.3 A few innovative techniques for generation or correction of FM coeffiicients</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">11.3.3.1 Geometric similarity -- 11.3.3.2 Boundary correction -- 11.3.3.3 Material discontinuity -- 11.3.4 Simulation of the OECD/NEA benchmark -- 11.4 DEVELOPMENT OF OTHER FM MATRIX BASED FORMULATIONS -- 11.5 REMARKS -- Chapter 12: Vector and parallel processing of Monte Carlo particle transport -- 12.1 INTRODUCTION -- 12.2 VECTOR PROCESSING -- 12.2.0.1 Scalar computer -- 12.2.0.2 Vector computer -- 12.2.1 Vector performance -- 12.3 PARALLEL PROCESSING -- 12.3.1 Parallel performance -- 12.3.1.1 Factors affecting the parallel performance -- 12.4 VECTORIZATION OF THE MONTE CARLO PARTICLE TRANSPORT METHODS -- 12.5 PARALLELIZATION OF THE MONTE CARLO PARTICLE TRANSPORT METHODS -- 12.5.1 Other possible parallel Monte Carlo particle transport algorithms -- 12.6 DEVELOPMENT OF A PARALLEL ALGORITHM USING MPI -- 12.7 REMARKS -- Appendix A: Appendix 1 -- A.1 INTEGER OPERATIONS ON A BINARY COMPUTER -- Appendix B: Appendix 2 -- B.1 DERIVATION OF A FORMULATION FOR THE SCATTERING DIRECTION IN A 3 D DOMAIN -- Appendix C: Appendix 3 -- C.1 SOLID ANGLE FORMULATION -- Appendix D: Appendix 4 -- D.1 ENERGY DEPENDENT NEUTRON NUCLEAR INTERACTIONS IN MONTE CARLO SIMULATION -- D.2 INTRODUCTION -- D.3 ELASTIC SCATTERING -- D.4 INELASTIC SCATTERING -- D.5 SCATTERING AT THERMAL ENERGIES -- Appendix E: Appendix 5 -- E.1 SHANNON ENTROPY -- E.1.1 Derivation of the Shannon entropy - Approach 1 -- E.1.2 Derivation of the Shannon entropy - Approach 2 -- Bibliography -- Index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Monte Carlo method..</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Particles (Nuclear physics)-Mathematical models..</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Radiative transfer</subfield></datafield><datafield 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illustrated	Not Illustrated
index_date	2024-07-03T18:01:23Z
indexdate	2024-07-10T09:12:16Z
institution	BVB
isbn	9780429582202 9780429198397
language	English
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spelling	Haghighat, Alireza Verfasser (DE-588)1065692617 aut Monte Carlo methods for particle transport Alireza Haghighat Second edition Boca Raton ; London ; New York CRC Press 2021 ©2021 1 Online-Ressource Illustrationen, Diagramme txt rdacontent c rdamedia cr rdacarrier Description based on publisher supplied metadata and other sources Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Acknowledgement -- About the Author -- Chapter 1: Introduction -- 1.1 HISTORY OF MONTE CARLO SIMULATION -- 1.2 STATUS OF MONTE CARLO CODES -- 1.3 MOTIVATION FOR WRITING THIS BOOK -- 1.4 AUTHOR'S MESSAGE TO INSTRUCTORS -- Chapter 2: Random Variables and Sampling -- 2.1 INTRODUCTION -- 2.2 RANDOM VARIABLES -- 2.2.1 Discrete random variable -- 2.2.2 Continuous random variable -- 2.2.3 Notes on pdf and cdf characteristics -- 2.3 RANDOM NUMBERS -- 2.4 DERIVATION OF THE FUNDAMENTAL FORMULATION OF MONTE CARLO (FFMC) -- 2.5 SAMPLING ONE DIMENSIONAL DENSITY FUNCTIONS -- 2.5.1 Analytical inversion -- 2.5.2 Numerical inversion -- 2.5.3 Probability mixing method -- 2.5.4 Rejection technique -- 2.5.5 Numerical evaluation -- 2.5.6 Table lookup -- 2.6 SAMPLING MULTIDIMENSIONAL DENSITY FUNCTIONS -- 2.7 EXAMPLE PROCEDURES FOR SAMPLING A FEW COMMONLY USED DISTRIBUTIONS -- 2.7.1 Normal distribution -- 2.7.2 Watt spectrum -- 2.7.3 Cosine and sine functions sampling -- 2.8 REMARKS -- Chapter 3: Random Number Generator (RNG) -- 3.1 INTRODUCTION -- 3.2 RANDOM NUMBER GENERATION APPROACHES -- 3.3 PSEUDO RANDOM NUMBER GENERATORS (PRNGS) -- 3.3.1 Congruential Generators -- 3.3.2 Multiple Recursive Generator -- 3.4 TESTING RANDOMNESS -- 3.4.1 χ2 − Test -- 3.4.1.1 χ2 − distribution -- 3.4.1.2 Procedure for the use of χ2 − test -- 3.4.2 Frequency test -- 3.4.3 Serial test -- 3.4.4 Gap test -- 3.4.5 Poker test -- 3.4.6 Moment test -- 3.4.7 Serial correlation test -- 3.4.8 Serial test via plotting -- 3.5 EXAMPLE FOR TESTING A PRNG -- 3.5.1 Evaluation of PRNG based on period and average -- 3.5.2 Serial test via plotting -- 3.6 REMARKS -- Chapter 4: Fundamentals of Probability and Statistics -- 4.1 INTRODUCTION -- 4.2 EXPECTATION VALUE -- 4.2.1 Single variable 4.2.2 Useful formulation for the expectation operator -- 4.2.3 Multivariable -- 4.3 SAMPLE EXPECTATION VALUES IN STATISTICS -- 4.3.1 Sample mean -- 4.3.2 Sample variance -- 4.4 PRECISION AND ACCURACY OF A SAMPLE AVERAGE -- 4.5 COMMONLY USED DENSITY FUNCTIONS -- 4.5.1 Uniform density function -- 4.5.2 Binomial density function -- 4.5.2.1 Bernoulli process -- 4.5.2.2 Derivation of the Binomial density function -- 4.5.3 Geometric density function -- 4.5.4 Poisson density function -- 4.5.5 Normal ( -- 4.6 LIMIT THEOREMS AND THEIR APPLICATIONS -- 4.6.1 Corollary to the de Moivre-Laplace limit theorem -- 4.6.2 Central limite theorem -- 4.6.2.1 Demonstration of the Central Limit Theorem -- 4.7 GENERAL FORMULATION OF THE RELATIVE UNCERTAINTY -- 4.7.1 Special case of a Bernoulli random process -- 4.8 CONFIDENCE LEVEL FOR FINITE SAMPLING -- 4.8.1 Student's t-distribution -- 4.8.2 Determination of confidence level and application of the t-distribution -- 4.9 TEST OF NORMALITY OF DISTRIBUTION -- 4.9.1 Test of skewness coefficient -- 4.9.2 Shapiro-Wilk test for normality -- Chapter 5: Integrals and Associated Variance Reduction Techniques -- 5.1 INTRODUCTION -- 5.2 EVALUATION OF INTEGRALS -- 5.3 VARIANCE REDUCTION TECHNIQUES FOR DETERMINATION OF INTEGRALS -- 5.3.1 Importance sampling -- 5.3.2 Control variates technique -- 5.3.3 Stratified sampling technique -- 5.3.4 Combined sampling -- 5.4 REMARKS -- Chapter 6: Fixed-Source Monte Carlo Particle Transport -- 6.1 INTRODUCTION -- 6.2 INTRODUCTION TO THE LINEAR BOLTZMANN EQUATION -- 6.3 MONTE CARLO METHOD FOR SIMPLIFIED PARTICLE TRANSPORT -- 6.3.1 Sampling path length -- 6.3.2 Sampling interaction type -- 6.3.2.1 Procedure for N (&gt -- 2) interaction type -- 6.3.2.2 Procedure for a discrete random variable with N outcomes of equal probabilities -- 6.3.3 Selection of scattering angle 6.4 A 1-D MONTE CARLO ALGORITHM -- 6.5 PERTURBATION VIA CORRELATED SAMPLING -- 6.6 HOW TO EXAMINE STATISTICAL RELIABILITY OF MONTE CARLO RESULTS -- 6.7 REMARKS -- Chapter 7: Variance reduction techniques for fixed-source particle transport -- 7.1 INTRODUCTION -- 7.2 OVERVIEW OF VARIANCE REDUCTION FOR FIXED SOURCE PARTICLE TRANSPORT -- 7.3 PDF BIASING WITH RUSSIAN ROULETTE -- 7.3.1 Implicit capture or survival biasing with Russian roulette -- 7.3.1.1 Russian roulette technique -- 7.3.2 Path-length biasing -- 7.3.3 Exponential transformation biasing -- 7.3.4 Forced collision biasing -- 7.4 PARTICLE SPLITTING WITH RUSSIAN ROULETTE -- 7.4.1 Geometric splitting -- 7.4.2 Energy splitting -- 7.4.3 Angular splitting -- 7.5 WEIGHT-WINDOW TECHNIQUE -- 7.6 INTEGRAL BIASING -- 7.6.1 Importance (adjoint) function methodology -- 7.6.2 Source biasing based on the importance sampling -- 7.7 HYBRID METHODOLOGIES -- 7.7.1 CADIS methodology -- 7.7.1.1 FW-CADIS technique -- 7.8 REMARKS -- Chapter 8: Scoring/Tallying -- 8.1 INTRODUCTION -- 8.2 MAJOR PHYSICAL QUANTITIES IN PARTICLE TRANSPORT -- 8.3 TALLYING IN A STEADY STATE SYSTEM -- 8.3.1 Collision estimator -- 8.3.2 Path-length estimator -- 8.3.3 Surface-crossing estimator -- 8.3.3.1 Estimation of partial and net currents -- 8.3.3.2 Estimation of flux on a surface -- 8.3.4 Analytical estimator -- 8.4 TIME DEPENDENT TALLYING -- 8.5 FORMULATION OF TALLIES WHEN VARIANCE REDUCTION USED -- 8.6 ESTIMATION OF RELATIVE UNCERTAINTY OF TALLIES -- 8.7 UNCERTAINTY IN A RANDOM VARIABLE DEPENDENT ON OTHER RANDOM VARIABLES -- 8.8 REMARKS -- Chapter 9: Geometry and particle tracking -- 9.1 INTRODUCTION -- 9.2 COMBINATORIAL GEOMETRY APPROACH -- 9.2.1 Definition of a surface -- 9.2.2 Definition of cells -- 9.2.3 Examples for irregular cells -- 9.3 DESCRIPTION OF BOUNDARY CONDITIONS -- 9.4 PARTICLE TRACKING -- 9.5 REMARKS. Chapter 10: Eigenvalue (criticality) Monte Carlo method for particle transport -- 10.1 INTRODUCTION -- 10.2 THEORY OF POWER ITERATION FOR EIGENVALUE PROBLEMS -- 10.3 MONTE CARLO EIGENVALUE CALCULATION -- 10.3.1 Random variables for sampling fission neutrons -- 10.3.1.1 Number of fission neutrons -- 10.3.1.2 Energy of fission neutrons -- 10.3.1.3 Direction of fission neutrons -- 10.3.2 Procedure for Monte Carlo Eigenvalue simulation -- 10.3.2.1 Estimators for sampling fission neutrons -- 10.3.3 A method to combine the estimators -- 10.4 ISSUES ASSOCIATED WITH THE STANDARD EIGENVALUE MONTE CARLO SIMULATION PROCEDURE -- 10.5 DIAGNOSTIC TESTS FOR SOURCE CONVERGENCE -- 10.5.1 Shannon entropy technique -- 10.5.1.1 Concept of Shannon entropy -- 10.5.1.2 Application of the Shannon entropy to the fission neutron source -- 10.5.2 Center of Mass (COM) technique -- 10.6 STANDARD EIGENVALUE MONTE CARLO CALCULATION PERFORMANCE, ANALYSIS, SHORTCOMINGS -- 10.6.1 A procedure for selection of appropriate eigenvalue parameters -- 10.6.2 Demonstration of the shortcomings of the standard eigenvalue Monte Carlo calculation -- 10.6.2.1 Example problem -- 10.6.2.2 Results and analysis -- 10.7 REMARKS -- Chapter 11: Fission matrix methods for eigenvalue Monte Carlo simulation -- 11.1 INTRODUCTION -- 11.2 DERIVATION OF FORMULATION OF THE FISSION MATRIX METHODOLOGY -- 11.2.1 Implementation of the FM method - Approach 1 -- 11.2.2 Implementation of the FM method - Approach 2 -- 11.2.2.1 Issues associated with the FMBMC approach -- 11.3 APPLICATION OF THE FM METHOD - APPROACH 1 -- 11.3.1 Modeling spent fuel facilities -- 11.3.1.1 Problem description -- 11.3.1.2 FM coefficient pre-calculation -- 11.3.1.3 Comparison of RAPID to Serpent - Accuracy and Performance -- 11.3.2 Reactor cores -- 11.3.3 A few innovative techniques for generation or correction of FM coeffiicients 11.3.3.1 Geometric similarity -- 11.3.3.2 Boundary correction -- 11.3.3.3 Material discontinuity -- 11.3.4 Simulation of the OECD/NEA benchmark -- 11.4 DEVELOPMENT OF OTHER FM MATRIX BASED FORMULATIONS -- 11.5 REMARKS -- Chapter 12: Vector and parallel processing of Monte Carlo particle transport -- 12.1 INTRODUCTION -- 12.2 VECTOR PROCESSING -- 12.2.0.1 Scalar computer -- 12.2.0.2 Vector computer -- 12.2.1 Vector performance -- 12.3 PARALLEL PROCESSING -- 12.3.1 Parallel performance -- 12.3.1.1 Factors affecting the parallel performance -- 12.4 VECTORIZATION OF THE MONTE CARLO PARTICLE TRANSPORT METHODS -- 12.5 PARALLELIZATION OF THE MONTE CARLO PARTICLE TRANSPORT METHODS -- 12.5.1 Other possible parallel Monte Carlo particle transport algorithms -- 12.6 DEVELOPMENT OF A PARALLEL ALGORITHM USING MPI -- 12.7 REMARKS -- Appendix A: Appendix 1 -- A.1 INTEGER OPERATIONS ON A BINARY COMPUTER -- Appendix B: Appendix 2 -- B.1 DERIVATION OF A FORMULATION FOR THE SCATTERING DIRECTION IN A 3 D DOMAIN -- Appendix C: Appendix 3 -- C.1 SOLID ANGLE FORMULATION -- Appendix D: Appendix 4 -- D.1 ENERGY DEPENDENT NEUTRON NUCLEAR INTERACTIONS IN MONTE CARLO SIMULATION -- D.2 INTRODUCTION -- D.3 ELASTIC SCATTERING -- D.4 INELASTIC SCATTERING -- D.5 SCATTERING AT THERMAL ENERGIES -- Appendix E: Appendix 5 -- E.1 SHANNON ENTROPY -- E.1.1 Derivation of the Shannon entropy - Approach 1 -- E.1.2 Derivation of the Shannon entropy - Approach 2 -- Bibliography -- Index Monte Carlo method.. Particles (Nuclear physics)-Mathematical models.. Radiative transfer Erscheint auch als Haghighat, Alireza Monte Carlo Methods for Particle Transport Milton : Taylor & Francis Group,c2020 Druck-Ausgabe, Hardcover 978-0-367-18805-4
spellingShingle	Haghighat, Alireza Monte Carlo methods for particle transport Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Acknowledgement -- About the Author -- Chapter 1: Introduction -- 1.1 HISTORY OF MONTE CARLO SIMULATION -- 1.2 STATUS OF MONTE CARLO CODES -- 1.3 MOTIVATION FOR WRITING THIS BOOK -- 1.4 AUTHOR'S MESSAGE TO INSTRUCTORS -- Chapter 2: Random Variables and Sampling -- 2.1 INTRODUCTION -- 2.2 RANDOM VARIABLES -- 2.2.1 Discrete random variable -- 2.2.2 Continuous random variable -- 2.2.3 Notes on pdf and cdf characteristics -- 2.3 RANDOM NUMBERS -- 2.4 DERIVATION OF THE FUNDAMENTAL FORMULATION OF MONTE CARLO (FFMC) -- 2.5 SAMPLING ONE DIMENSIONAL DENSITY FUNCTIONS -- 2.5.1 Analytical inversion -- 2.5.2 Numerical inversion -- 2.5.3 Probability mixing method -- 2.5.4 Rejection technique -- 2.5.5 Numerical evaluation -- 2.5.6 Table lookup -- 2.6 SAMPLING MULTIDIMENSIONAL DENSITY FUNCTIONS -- 2.7 EXAMPLE PROCEDURES FOR SAMPLING A FEW COMMONLY USED DISTRIBUTIONS -- 2.7.1 Normal distribution -- 2.7.2 Watt spectrum -- 2.7.3 Cosine and sine functions sampling -- 2.8 REMARKS -- Chapter 3: Random Number Generator (RNG) -- 3.1 INTRODUCTION -- 3.2 RANDOM NUMBER GENERATION APPROACHES -- 3.3 PSEUDO RANDOM NUMBER GENERATORS (PRNGS) -- 3.3.1 Congruential Generators -- 3.3.2 Multiple Recursive Generator -- 3.4 TESTING RANDOMNESS -- 3.4.1 χ2 − Test -- 3.4.1.1 χ2 − distribution -- 3.4.1.2 Procedure for the use of χ2 − test -- 3.4.2 Frequency test -- 3.4.3 Serial test -- 3.4.4 Gap test -- 3.4.5 Poker test -- 3.4.6 Moment test -- 3.4.7 Serial correlation test -- 3.4.8 Serial test via plotting -- 3.5 EXAMPLE FOR TESTING A PRNG -- 3.5.1 Evaluation of PRNG based on period and average -- 3.5.2 Serial test via plotting -- 3.6 REMARKS -- Chapter 4: Fundamentals of Probability and Statistics -- 4.1 INTRODUCTION -- 4.2 EXPECTATION VALUE -- 4.2.1 Single variable 4.2.2 Useful formulation for the expectation operator -- 4.2.3 Multivariable -- 4.3 SAMPLE EXPECTATION VALUES IN STATISTICS -- 4.3.1 Sample mean -- 4.3.2 Sample variance -- 4.4 PRECISION AND ACCURACY OF A SAMPLE AVERAGE -- 4.5 COMMONLY USED DENSITY FUNCTIONS -- 4.5.1 Uniform density function -- 4.5.2 Binomial density function -- 4.5.2.1 Bernoulli process -- 4.5.2.2 Derivation of the Binomial density function -- 4.5.3 Geometric density function -- 4.5.4 Poisson density function -- 4.5.5 Normal ( -- 4.6 LIMIT THEOREMS AND THEIR APPLICATIONS -- 4.6.1 Corollary to the de Moivre-Laplace limit theorem -- 4.6.2 Central limite theorem -- 4.6.2.1 Demonstration of the Central Limit Theorem -- 4.7 GENERAL FORMULATION OF THE RELATIVE UNCERTAINTY -- 4.7.1 Special case of a Bernoulli random process -- 4.8 CONFIDENCE LEVEL FOR FINITE SAMPLING -- 4.8.1 Student's t-distribution -- 4.8.2 Determination of confidence level and application of the t-distribution -- 4.9 TEST OF NORMALITY OF DISTRIBUTION -- 4.9.1 Test of skewness coefficient -- 4.9.2 Shapiro-Wilk test for normality -- Chapter 5: Integrals and Associated Variance Reduction Techniques -- 5.1 INTRODUCTION -- 5.2 EVALUATION OF INTEGRALS -- 5.3 VARIANCE REDUCTION TECHNIQUES FOR DETERMINATION OF INTEGRALS -- 5.3.1 Importance sampling -- 5.3.2 Control variates technique -- 5.3.3 Stratified sampling technique -- 5.3.4 Combined sampling -- 5.4 REMARKS -- Chapter 6: Fixed-Source Monte Carlo Particle Transport -- 6.1 INTRODUCTION -- 6.2 INTRODUCTION TO THE LINEAR BOLTZMANN EQUATION -- 6.3 MONTE CARLO METHOD FOR SIMPLIFIED PARTICLE TRANSPORT -- 6.3.1 Sampling path length -- 6.3.2 Sampling interaction type -- 6.3.2.1 Procedure for N (&gt -- 2) interaction type -- 6.3.2.2 Procedure for a discrete random variable with N outcomes of equal probabilities -- 6.3.3 Selection of scattering angle 6.4 A 1-D MONTE CARLO ALGORITHM -- 6.5 PERTURBATION VIA CORRELATED SAMPLING -- 6.6 HOW TO EXAMINE STATISTICAL RELIABILITY OF MONTE CARLO RESULTS -- 6.7 REMARKS -- Chapter 7: Variance reduction techniques for fixed-source particle transport -- 7.1 INTRODUCTION -- 7.2 OVERVIEW OF VARIANCE REDUCTION FOR FIXED SOURCE PARTICLE TRANSPORT -- 7.3 PDF BIASING WITH RUSSIAN ROULETTE -- 7.3.1 Implicit capture or survival biasing with Russian roulette -- 7.3.1.1 Russian roulette technique -- 7.3.2 Path-length biasing -- 7.3.3 Exponential transformation biasing -- 7.3.4 Forced collision biasing -- 7.4 PARTICLE SPLITTING WITH RUSSIAN ROULETTE -- 7.4.1 Geometric splitting -- 7.4.2 Energy splitting -- 7.4.3 Angular splitting -- 7.5 WEIGHT-WINDOW TECHNIQUE -- 7.6 INTEGRAL BIASING -- 7.6.1 Importance (adjoint) function methodology -- 7.6.2 Source biasing based on the importance sampling -- 7.7 HYBRID METHODOLOGIES -- 7.7.1 CADIS methodology -- 7.7.1.1 FW-CADIS technique -- 7.8 REMARKS -- Chapter 8: Scoring/Tallying -- 8.1 INTRODUCTION -- 8.2 MAJOR PHYSICAL QUANTITIES IN PARTICLE TRANSPORT -- 8.3 TALLYING IN A STEADY STATE SYSTEM -- 8.3.1 Collision estimator -- 8.3.2 Path-length estimator -- 8.3.3 Surface-crossing estimator -- 8.3.3.1 Estimation of partial and net currents -- 8.3.3.2 Estimation of flux on a surface -- 8.3.4 Analytical estimator -- 8.4 TIME DEPENDENT TALLYING -- 8.5 FORMULATION OF TALLIES WHEN VARIANCE REDUCTION USED -- 8.6 ESTIMATION OF RELATIVE UNCERTAINTY OF TALLIES -- 8.7 UNCERTAINTY IN A RANDOM VARIABLE DEPENDENT ON OTHER RANDOM VARIABLES -- 8.8 REMARKS -- Chapter 9: Geometry and particle tracking -- 9.1 INTRODUCTION -- 9.2 COMBINATORIAL GEOMETRY APPROACH -- 9.2.1 Definition of a surface -- 9.2.2 Definition of cells -- 9.2.3 Examples for irregular cells -- 9.3 DESCRIPTION OF BOUNDARY CONDITIONS -- 9.4 PARTICLE TRACKING -- 9.5 REMARKS. Chapter 10: Eigenvalue (criticality) Monte Carlo method for particle transport -- 10.1 INTRODUCTION -- 10.2 THEORY OF POWER ITERATION FOR EIGENVALUE PROBLEMS -- 10.3 MONTE CARLO EIGENVALUE CALCULATION -- 10.3.1 Random variables for sampling fission neutrons -- 10.3.1.1 Number of fission neutrons -- 10.3.1.2 Energy of fission neutrons -- 10.3.1.3 Direction of fission neutrons -- 10.3.2 Procedure for Monte Carlo Eigenvalue simulation -- 10.3.2.1 Estimators for sampling fission neutrons -- 10.3.3 A method to combine the estimators -- 10.4 ISSUES ASSOCIATED WITH THE STANDARD EIGENVALUE MONTE CARLO SIMULATION PROCEDURE -- 10.5 DIAGNOSTIC TESTS FOR SOURCE CONVERGENCE -- 10.5.1 Shannon entropy technique -- 10.5.1.1 Concept of Shannon entropy -- 10.5.1.2 Application of the Shannon entropy to the fission neutron source -- 10.5.2 Center of Mass (COM) technique -- 10.6 STANDARD EIGENVALUE MONTE CARLO CALCULATION PERFORMANCE, ANALYSIS, SHORTCOMINGS -- 10.6.1 A procedure for selection of appropriate eigenvalue parameters -- 10.6.2 Demonstration of the shortcomings of the standard eigenvalue Monte Carlo calculation -- 10.6.2.1 Example problem -- 10.6.2.2 Results and analysis -- 10.7 REMARKS -- Chapter 11: Fission matrix methods for eigenvalue Monte Carlo simulation -- 11.1 INTRODUCTION -- 11.2 DERIVATION OF FORMULATION OF THE FISSION MATRIX METHODOLOGY -- 11.2.1 Implementation of the FM method - Approach 1 -- 11.2.2 Implementation of the FM method - Approach 2 -- 11.2.2.1 Issues associated with the FMBMC approach -- 11.3 APPLICATION OF THE FM METHOD - APPROACH 1 -- 11.3.1 Modeling spent fuel facilities -- 11.3.1.1 Problem description -- 11.3.1.2 FM coefficient pre-calculation -- 11.3.1.3 Comparison of RAPID to Serpent - Accuracy and Performance -- 11.3.2 Reactor cores -- 11.3.3 A few innovative techniques for generation or correction of FM coeffiicients 11.3.3.1 Geometric similarity -- 11.3.3.2 Boundary correction -- 11.3.3.3 Material discontinuity -- 11.3.4 Simulation of the OECD/NEA benchmark -- 11.4 DEVELOPMENT OF OTHER FM MATRIX BASED FORMULATIONS -- 11.5 REMARKS -- Chapter 12: Vector and parallel processing of Monte Carlo particle transport -- 12.1 INTRODUCTION -- 12.2 VECTOR PROCESSING -- 12.2.0.1 Scalar computer -- 12.2.0.2 Vector computer -- 12.2.1 Vector performance -- 12.3 PARALLEL PROCESSING -- 12.3.1 Parallel performance -- 12.3.1.1 Factors affecting the parallel performance -- 12.4 VECTORIZATION OF THE MONTE CARLO PARTICLE TRANSPORT METHODS -- 12.5 PARALLELIZATION OF THE MONTE CARLO PARTICLE TRANSPORT METHODS -- 12.5.1 Other possible parallel Monte Carlo particle transport algorithms -- 12.6 DEVELOPMENT OF A PARALLEL ALGORITHM USING MPI -- 12.7 REMARKS -- Appendix A: Appendix 1 -- A.1 INTEGER OPERATIONS ON A BINARY COMPUTER -- Appendix B: Appendix 2 -- B.1 DERIVATION OF A FORMULATION FOR THE SCATTERING DIRECTION IN A 3 D DOMAIN -- Appendix C: Appendix 3 -- C.1 SOLID ANGLE FORMULATION -- Appendix D: Appendix 4 -- D.1 ENERGY DEPENDENT NEUTRON NUCLEAR INTERACTIONS IN MONTE CARLO SIMULATION -- D.2 INTRODUCTION -- D.3 ELASTIC SCATTERING -- D.4 INELASTIC SCATTERING -- D.5 SCATTERING AT THERMAL ENERGIES -- Appendix E: Appendix 5 -- E.1 SHANNON ENTROPY -- E.1.1 Derivation of the Shannon entropy - Approach 1 -- E.1.2 Derivation of the Shannon entropy - Approach 2 -- Bibliography -- Index Monte Carlo method.. Particles (Nuclear physics)-Mathematical models.. Radiative transfer
title	Monte Carlo methods for particle transport
title_auth	Monte Carlo methods for particle transport
title_exact_search	Monte Carlo methods for particle transport
title_exact_search_txtP	Monte Carlo methods for particle transport
title_full	Monte Carlo methods for particle transport Alireza Haghighat
title_fullStr	Monte Carlo methods for particle transport Alireza Haghighat
title_full_unstemmed	Monte Carlo methods for particle transport Alireza Haghighat
title_short	Monte Carlo methods for particle transport
title_sort	monte carlo methods for particle transport
topic	Monte Carlo method.. Particles (Nuclear physics)-Mathematical models.. Radiative transfer
topic_facet	Monte Carlo method.. Particles (Nuclear physics)-Mathematical models.. Radiative transfer
work_keys_str_mv	AT haghighatalireza montecarlomethodsforparticletransport

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