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" Monte Carlo methods for particle transport "
Alireza Haghighat.
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BL
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753835
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b573796
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| Main Entry
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Alireza Haghighat.
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| Title & Author
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Monte Carlo methods for particle transport\ Alireza Haghighat.
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| Edition Statement
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1st
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| Publication Statement
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Boca Raton : CRC Press, 2014
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: illustrations (black and white).
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| ISBN
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1466592540
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: 9781466592544
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<P>Acknowledgments</P><P>About the Author</P><B><P>Introduction</P></B><P>History of Monte Carlo Simulation</P><P>Status of Monte Carlo Codes</P><P>Motivation for Writing This Book</P><P>Overview of the Book</P><P>Recommendations to Instructors</P><P>Author's Expectation</P><P>References</P><B><P>Random Variables and Sampling</P></B><P>Introduction</P><P>Random Variables</P><I><P>Discrete Random Variable</P><P>Continuous Random Variable</P><P>Notes on pdf and cdf Characteristics</P></I><P>Random Numbers</P><P>Derivation of the Fundamental Formulation of Monte Carlo (FFMC)</P><P>Sampling One-Dimensional Density Functions</P><I><P>Analytical Inversion</P><P>Numerical Inversion</P><P>Probability Mixing Method</P><P>Rejection Technique</P><P>Numerical Evaluation</P><P>Table Lookup</P></I><P>Sampling Multidimensional Density Functions</P><P>Example Procedures for Sampling a Few Commonly Used Distributions</P><I><P>Normal Distribution</P><P>Watt Spectrum</P><P>Cosine and Sine Function Sampling</P></I><P>Remarks</P><P>References</P><P>Problems</P><B><P>Random Number Generation (RNG)</P></B><P>Introduction</P><P>Random Number Generation Approaches</P><P>Pseudorandom Number Generators (PRNGs)</P><I><P>Congruential Generators</P><P>Multiple Recursive Generator</P></I><P>Testing Randomness</P><I><P>x2-Test</P><P>Frequency Test</P><P>Serial Test </P><P>Gap Test </P><P>Poker Test </P><P>Moment Test </P><P>Serial Correlation Test </P><P>Serial Test via Plotting </P></I><P>Examples for PRNG Tests </P><I><P>Evaluation of PRNG Based on Period and Average </P><P>Serial Test via Plotting </P></I><P>Remarks </P><P>References </P><P>Problems</P><B><P>Fundamentals of Probability and Statistics </P></B><P>Introduction</P><P>Expectation Value</P><I><P>One-Dimensional Density Function</P><P>Multidimensional Density Function</P><P>Useful Theorems Associated with the "True Variance"</P></I><P>Definition of Sample Expectation Values Used in Statistics</P><I><P>Sample Mean</P><P>Expected Value of the Sample Variance</P></I><P>Precision and Accuracy of a Statistical Process</P><I><P>Uniform Distribution </P><P>Bernoulli and Binomial Distributions </P><P>Geometric Distribution </P><P>Poisson Distribution</P><P>Normal ("Gaussian") Distribution</P></I><P>Limit Theorems and Their Applications </P><I><P>Corollary to the de Moivre-Laplace Limit Theorem</P><P>Central Limit Theorem </P></I><P>Formulations of Uncertainty and Relative Error for a Random Process</P><I><P>General Random Process </P><P>Special Case of Bernoulli Process</P></I><P>Confidence Interval for Finite Sampling </P><I><P>Introduction to Student's t-Distribution </P><P>Determination of Confidence Interval and Application of the t-Distribution </P></I><P>Test of Normality of Distribution </P><I><P>Test of Skewness Coefficient </P><P>Shapiro-Wilk Test for Normality </P></I><P>References </P><P>Problems </P><B><P>Integrals and Associated Variance Reduction Techniques </P></B><P>Introduction </P><P>Estimation of Integrals </P><P>Variance Reduction Techniques Associated with Integrals </P><I><P>Importance Sampling </P><P>Correlation Sampling Technique </P><P>Stratified Sampling Technique </P><P>Combined Sampling </P></I><P>Remarks</P><P>References </P><P>Problems </P><B><P>Fixed-Source Monte Carlo Particle Transport</P></B><P>Introduction </P><P>Introduction to the Linear Boltzmann Equation</P><P>Introduction the Monte Carlo Method</P><I><P>Determination of Free Flight, i.e., Path-Length</P><P>Selection of Interaction Type </P><P>Selection of Scattering Angle </P></I><P>A Monte Carlo Algorithm for Estimation of Transmitted Particles </P><P>Perturbation Calculations via Correlated Sampling </P><P>Analysis of Monte Carlo Results</P><P>Remarks </P><P>References </P><P>Problems </P><B><P>Variance Reduction Techniques in Particle Transport</P></B><P>Introduction </P><P>Effectiveness of Variance Reduction Algorithms</P><P>Biasing of Density Functions</P><I><P>Implicit Capture (or Survival Biasing) </P><P>Russian Roulette </P><P>Biasing the Path-Length to the Next Collision </P><P>Exponential Transformation </P><P>Forced Collision </P></I><P>Splitting Techniques </P><I><P>Geometric Splitting with Russian Roulette </P><P>Energy Splitting with Russian Roulette</P><P>Angular Splitting with Russian Roulette </P><P>Weight-Window Technique</P></I><P>Application of Combination of Importance Sampling, pdf biasing, and Splitting Technique in Particle Transport </P><I><P>Importance (Adjoint) Function Methodology in Deterministic Transport Theory </P><P>Determination of Detector Response </P><P>Use of Deterministic Importance (Adjoint) Function for Importance Sampling </P></I><P>Remarks </P><P>References </P><P>Problems </P><B><P>Tallying </P></B><P>Introduction </P><P>Major Quantities in a Particle Transport Simulation </P><P>Tallying in a Steady-State System</P><I><P>Collision Estimator</P><P>Path-Length Estimator </P><P>Surface-Crossing Estimator </P><P>Analytical Estimator </P></I><P>Tallying in a Time-Dependent System</P><P>Tallies in Nonanalog Simulations </P><P>Estimation of Relative Error Associated Physical Quantities</P><P>Propagation of Error </P><P>Remarks</P><P>References </P><P>Problems</P><B><P>Geometry and Particle Tracking</P></B><P>Introduction </P><P>Discussion on a Combinatorial Geometry Approach </P><I><P>Definition of Surfaces </P><P>Definition of Cells </P><P>Examples </P></I><P>Description of Boundary Conditions </P><P>Particle Tracking </P><P>Remarks</P><P>References </P><P>Problems </P><B><P>Eigenvalue or Criticality Monte Carlo Particle Transport</P></B><P>Introduction </P><P>Theory of Power-Iteration for Eigenvalue Problems </P><P>Monte Carlo Eigenvalue Calculation</P><I><P>Random Variables Associated with a Fission Process </P><P>Direction of Fission Neutrons </P><P>Monte Carlo Simulation of a Criticality Problem </P><P>Estimators for Sampling Fission Neutrons </P></I><P>Issues Associated with the Standard Eigenvalue Calculation Procedure </P><I><P>Diagnostic Methods for Source Convergence</P><P>Fission Matrix (FM) Methodology </P><P>Issues Associated with the FM Method </P></I><P>Remarks </P><P>References </P><P>Problems </P><B><P>Vector and Parallel Processing of Monte Carlo Methods </P></B><P>Introduction</P><P>Vector Processing </P><I><P>Vector Performance </P></I><P>Parallel Processing</P><I><P>Parallel Performance </P></I><P>Vectorization of Monte Carlo Methods </P><P>Parallelization of the Monte Carlo Methods</P><I><P>Other Possible Parallel Monte Carlo Algorithms </P></I><P>Development of a Parallel Algorithm Using MPI </P><P>Remarks </P><P>References</P><P>Problems</P><P>Appendices One to Six</P>
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| Contents
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Introduction. Random Variables and Sampling. Random Number Generation (RNG). Fundamentals of Probability and Statistics. Integrals and Associated Variance Reduction Techniques. Fixed-Source Monte Carlo Particle Transport. Variance Reduction Techniques in Particle Transport. Tallying. Geometry and Particle Tracking. Eigenvalue or Criticality Monte Carlo Particle Transport. Vector and Parallel Processing of Monte Carlo Methods.
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| Subject
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Monte Carlo method.
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Transport theory.
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| LC Classification
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QC20.7.M65A457 2014
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| Added Entry
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Alireza Haghighat
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