Date of Award
8-2026
Degree Type
Report
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
Committee Chair(s)
Erin Beckman (Committee Chair)
Committee
Erin Beckman
Committee
Luis Gordillo
Committee
Hailei Wang
Abstract
This work studies the stochastic behavior of neutron populations in a one-dimensional rod model using Monte Carlo simulation. The first part of this project reproduces the computational results of Dumonteil, Horton, Kyprianou, and Zoia (2025) by independently implementing the Monte Carlo algorithm described in their article, with the asymptotic behavior of the first moment analyzed in relation to the dominant eigenvalue and adjoint eigenfunction of the neutron transport operator. The model is then extended to a heterogeneous setting by introducing a central region where fission is suppressed. A global expectation over initial positions and directions is used to estimate the effective multiplication factor, and the resulting heterogeneous first-moment results are compared with the homogeneous results of Dumonteil, Horton, Kyprianou, and Zoia, showing how spatial heterogeneity alters the neutron distribution and criticality.
Recommended Citation
Crowford, Samuel Kaleb, "Criticality in a Heterogeneous Neutron Transport Rod Model" (2026). All Graduate Reports and Creative Projects, Fall 2023 to Present. 169.
https://digitalcommons.usu.edu/gradreports2023/169
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