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Monte Carlo Primer A Practical Approach to Radiation Transport

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ISBN-10: 0306467488

ISBN-13: 9780306467486

Edition: 2002

Authors: Stephen A. Dupree, Stanley K. Fraley

List price: $279.99
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Description:

This book introduces the reader to the use of Monte Carlo methods for solving practical problems in radiation transport, and will also serve as a reference work for practitioners in the field. It assumes the reader has a general knowledge of calculus and radiation physics, and a knowledge of Fortran programming, but assumes no prior knowledge of stochastic methods or statistical physics. The subject is presented by a combination of theoretical development and practical calculations. Because Monte Carlo methods are closely linked to the use of computers, from the beginning the reader is taught to convert the theoretical constructs developed in the text into functional software for use on a personal computer. Example problems provide the reader with an in-depth understanding of the concepts presented and lead to the production of a unique learning tool, a probabilistic framework code that models in a simple manner the features of production of Monte Carlo transport codes. This framework code is developed in stages such that every function is understood, tested, and demonstrated - random sampling, generating random numbers, implementing geometric models, using variance reduction, tracking particles in a random walk, testing the thoroughness with which the problem phase space is sampled, scoring detectors, and obtaining estimates of uncertainty in results. Advanced topics covered include criticality, correlated sampling, adjoint transport, and neutron thermalization. Monte Carlo codes can produce highly precise wrong answers. The probability of this occurring is increased if production codes are run as opaque, `black boxes' of software. This text attempts to make Monte Carlo into a comprehensible, usable tool for solving practical transport problems. It is suitable for advanced undergraduate and graduate students and researchers who wish to expand their knowledge of the Monte Carlo technique.
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Book details

List price: $279.99
Copyright year: 2002
Publisher: Springer
Publication date: 12/31/2001
Binding: Hardcover
Pages: 341
Size: 7.00" wide x 10.00" long x 1.25" tall
Weight: 1.892
Language: English

Introduction
The Monte Carlo Method
The Evaluation of Random Processes
Predicting the average outcome of a physical process
Another Monte Carlo estimate of [pi]
Monte Carlo Evaluation of Definite Integrals
Evaluation of a definite integral using Monte Carlo
Exercises
Monte Carlo Sampling Techniques
Probability Theory and Statistics
Random Variables and Sample Spaces
Distributions
Sampling
Sampling from the Inverse of the Cumulative Distribution Function
Uniform sampling inside a sphere
The Rejection Technique
Means and Variances
Estimations of Means and Variances
Calculation of mean and variance of a distribution
Introduction to Variance Reduction Techniques
Variance reduction by repeated samples
Stratified Sampling
Use of stratified sampling to evaluate a definite integral
Biased Sampling Schemes
Biasing a Monte Carlo estimate of a definite integral
Exercises
Monte Carlo Modeling of Neutron Transport
Introduction
Neutron Interactions and Mean Free Path
Neutron Transport
A Mathematical Basis for Monte Carlo Neutron Transport
Monte Carlo Modeling of Neutron Motion
Monoenergetic point source with isotropic scattering
Self-attenuation in a spherical source of gamma rays
Beam of neutrons onto a slab shield
Particle Flight Path in Complex Geometries
Mean distance to the next collision
Multi-Region Problems
Two-region slab with a void
Exercises
Energy-Dependent Neutron Transport
Elastic Scattering of Neutrons
Average number of collisions to thermalize neutrons
Transformation of Post-Collision Direction to Laboratory System
Average direction of travel after two collisions
Energy-Dependent Cross Sections
Neutron slowing down and Fermi age in water
Exercises
A Probabilistic Framework Code
Introduction to PFC
Problem Definition in PFC
Problem Geometry and Tracking
Additional Input and Array Initialization
The Random Walk in PFC
Computing the Response
Using PFC to solve Example 3.1
Exercises
Variance Reduction Techniques
Introduction
Source Biasing
Leakage of particles from a slab
Survival Biasing
Particles passing through a slab
Russian Roulette
Russian roulette in the slab problem of Example 6.2
Splitting
Slab problem with splitting and Russian roulette
Exponential Transform
Transmission through a slab with exponential transform
Exercises
Monte Carlo Detectors
Introduction
The Next-Event Estimator
Next-event flux estimates in an isotropic scattering material
Volumetric Flux Detectors
Collision-density and track-length flux estimates
Surface-Crossing Flux Estimator
Surface-crossing flux estimates
Expectation Surface-Crossing Flux Estimator
Expectation surface-crossing flux estimates
Time-Dependent Detectors
Time-dependence of the flux from a point isotropic source
Time dependence in neutron slowing down
Exercises
Nuclear Criticality Calculations with Monte Carlo
Multiplying Assemblies
The Generation Method
Criticality in a homogeneous sphere by ratio of generations
The Matrix Method
k for a homogeneous sphere using matrix method
Combination of Generation and Matrix Methods
Multi-generation matrix calculation
Criticality Calculations Using Multigroup Cross Sections
Critical mass of the Godiva assembly
Exercises
Advanced Applications of Monte Carlo
Correlated Sampling
Generating correlated strings of random numbers
Sensitivity of the number of particles passing through a slab to the thickness of the slab
Adjoint Monte Carlo
Detector response function using adjoint transport
A point-detector response using adjoint transport
Neutron Thermalization
Neutron spectrum in thermal equilibrium
Exercises
Random Number Generators
Bibliography
Index