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