摘要:

A review is given of singular eigenfunction techniques which have been developed in the past few years to deal with linear transport problems having a spatially dependent single scatter albedo. Both analytic and numerical aspects are discussed.

ISSN:0041-1450    

DOI:10.1080/00411458508211674

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Geometrical surface splitting is used extensively in deep penetration Monte Carlo calculations for the purpose of variance reduction. For many years this method has been used on a rather intuitive basis. No detailed statistical model existed to support the unbiasedness of the method, although it is quite obvious that it is unbiased, or to provide a starting point for analytic evaluation of the second moment which is essential for optimization of the method. In the following, we develop such a statistical model for a general case of any number of routes from the source to the detector and Russian Roulette. The model involves the description of a general independent source paricle event along with the probabilistic quantities accompanying such an event. The detector contribution of such an event is established together with its probability density. Folding the detector contribution with the probability density and averaging over all possible source particle events yields the first momqt or the detector response. We also briefly discuss the possibility of obtaining the second moment by this direct statistical approach.

ISSN:0041-1450    

DOI:10.1080/00411458508211675

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

In part I, the statistical model for transport of neutrons in terms of surface to surface probability densities was described and the first moment was derived by averaging the general contribution of a source particle with its probability density over all possible source particle events. In the following we derive an analytic expression for the second moment based on the model described in I.

ISSN:0041-1450    

DOI:10.1080/00411458508211676

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

The critical eiaenvalues of the monoeneraetic time-independent neutron transport equation are compared for spheres, cylinders and slabs. Strict monotonicity properties are derived and the generalization to the energy-dependent case is discussed.

ISSN:0041-1450    

DOI:10.1080/00411458508211677

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor