A stochastic, four energy group model of a nuclear assembly

The formulation of a stochastic, four energy group, space-independent model of a nuclear assembly was studied. The model included one group of delayed neutron precursors and an extraneous source. The model treated the evolutionary birth and death processes of a neutron chain in a nuclear assembly as a multi-dimensional Markovian process. The probability balance equation was derived by accounting for all the birth and death processes occurring in the assembly and then was changed into its differential-difference form. Using the probability generating function technique, the differential-difference equation was transformed into a first order partial differential equation in the probability generating function. Equations for the neutron and delayed neutron precursor population probability distribution functions, the deterministic functions (means, variances, and covariances), and the extinction probabilities of the neutron chains were derived from the characteristic equations for the various moments of the first order P.D.E. for the probability generating function.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Nuclear Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Myers, William Leon

Contributors dc:contributor

• Axford, Roy A.

• Engineering, Nuclear

Statement dc:rights

• Copyright 1995 Myers, William Leon

Language dc:language

eng

Identifier

AAI9543681
(UMI)AAI9543681

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F21654