Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

516 Monte Carlo Particle Transport Methods: Neutron and Photon Calculationsin straight-ahead model, 447—455zero-variance schemes, 489—497Pay-off functions in collision density equations,110--119Perturbation calculations, 121 — 125, 307—328, seealso Correlated Monte Carlo analysisby differential games, 344—348Taylor series approach, 344—348Phase space defined, 23Photoelectric effect, analog simulation, 43—44Photon/matter interactions, analog simulation, 43—47Photonuclear absorption, 47Point estimation of flux, 60—61, 378—399, seealso Flux, point estimation ofPower density function, first derivative sampling,16—19Power function selection of sampling probabilitydistributions, 13—14Probability mixing method, 9Quantities and notations, 22—30Quota sampling, 90—91Radiative capture, 48Radioactive activity defined, 23Random vector selection, 19—20Random walk, analog simulation, see Analoggames, simulation of random walkRare events, 62Rare setsestimation of combined variance, 417—419estimation of common mean, 411—417Rayleigh (coherent) scattering, 47Rejection techniques, 9—12in analog simulation of random walk, 36—37in Klein-Nishina energy selection, 66—68in Legendre expansion, 77—78Russian roulette method, 58—59, 107optimization of, 455—458Sample mean estimation, 399—406Samplingof adjoint source, 130—131correlated, 122—123correlation, 92—93importance, 87—89, 203—207, 96—98initial directions, 37—38initial energies, 38mean and variance in straightforward, 86—87quota, 90—91small sets, 406—411, 431—434space coordinates, 35—37systematic, 89—90Sampling probability distributions, 6—8QRSefficient selections from the exponential distribution,16first derivative of the probability density function,16—19inverse distribution method, 8probability mixing method, 9random vector selection, 19—20rejection techniques, 9—12sampling from normal distribution, 14—16selection from power functions, 13—14table look-up method, 12—13two- and three—dimensional random orientations,20—22Scatteringanalog simulation, 43angle selection for anisotropic, 73—75Compton, 44—46defined, 25delta, 222—226direction cosines of particle after, 54elastic, 48—50inelastic, 50—51Rayleigh (coherent), 47straight-ahead model, 236—239, 300—301of thermal neutrons, 51—52Scoringof adjoint Monte Carlo analysis, 134—137in analog simulation of random walk, 54—55in collision density equations, 108—119expected values in analog modifications, 59—62Second-moment equation analysis, 249—250of multiple convolutions, 297—300zero-variance schemes, 250—258, 271—275Self-improving estimator, 280—283Sensitivity analysis, 123—125, 328—346, see alsoDifferential Monte Carlo analysis: sensitivityanalysisSlab transmission, 59—60, 113—114, 508—509Source density defined, 23Source iteration, 347—357Source parameter selection in analog games,34—35Space coordinate sampling, 35—37Splitting, 58—59continuous, 470—486, 186—192optimization of, 462—470in moment equations, 178—182optimization in straight-ahead model, 442—447Statistical considerations in analog games, 62—65Statistical evaluation problemsdetermination of theoretical variances, 426—429estimation of common mean from rare sets,411—417estimation of ratio of expectations, 419—425optimum combination of sample mean, 399—406unbiased estimation of combined variants fromsmall sample sets, 406—411unbiased estimation of criticality reaction rates,430—431Straight-ahead model, 236—239, 300—301optimization