Symmetry and separability of the neutron diffusion equation
Abstract
Separation of variables is one of the oldest techniques for solving certain classes of partial differential equations (PDEs). As is the case with many other solution techniques for differential equations, separation of variables may be codified within the broader framework of symmetry analysis. Though the separation of variables technique is frequently used in the nuclear engineering context with various equations describing neutron transport, its connection to the symmetries of those equations has not yet been thoroughly established. It is thus the purpose of this work to establish that connection using neutron diffusion as both an initial step toward analysis of more generally applicable equations, and as a connection to previous results in related problems. Using Lie group analysis, it is found that the traditional spacetime separable solution of the neutron diffusion equation (featuring a single αeigenvalue) corresponds to time translation and flux scaling symmetries. Additional solutions of this equation are also constructed using its broader symmetry set.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Univ. of Illinois, Urbana, IL (United States). Dept. of Nuclear, Plasma, and Radiological Engineering
 Univ. of Wisconsin, Madison, WI (United States). Dept. of Engineering Physics
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1482936
 Report Number(s):
 LAUR1821934
Journal ID: ISSN 23996528
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of Physics Communications
 Additional Journal Information:
 Journal Volume: 2; Journal Issue: 10; Journal ID: ISSN 23996528
 Publisher:
 IOP Publishing
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; neutron diffusion; symmetry analysis; separation of variables
Citation Formats
Ramsey, Scott D., Tellez, Jacob A., Riewski, Eric J., and Temple, Brian A. Symmetry and separability of the neutron diffusion equation. United States: N. p., 2018.
Web. doi:10.1088/23996528/aae2a4.
Ramsey, Scott D., Tellez, Jacob A., Riewski, Eric J., & Temple, Brian A. Symmetry and separability of the neutron diffusion equation. United States. doi:10.1088/23996528/aae2a4.
Ramsey, Scott D., Tellez, Jacob A., Riewski, Eric J., and Temple, Brian A. Wed .
"Symmetry and separability of the neutron diffusion equation". United States. doi:10.1088/23996528/aae2a4. https://www.osti.gov/servlets/purl/1482936.
@article{osti_1482936,
title = {Symmetry and separability of the neutron diffusion equation},
author = {Ramsey, Scott D. and Tellez, Jacob A. and Riewski, Eric J. and Temple, Brian A.},
abstractNote = {Separation of variables is one of the oldest techniques for solving certain classes of partial differential equations (PDEs). As is the case with many other solution techniques for differential equations, separation of variables may be codified within the broader framework of symmetry analysis. Though the separation of variables technique is frequently used in the nuclear engineering context with various equations describing neutron transport, its connection to the symmetries of those equations has not yet been thoroughly established. It is thus the purpose of this work to establish that connection using neutron diffusion as both an initial step toward analysis of more generally applicable equations, and as a connection to previous results in related problems. Using Lie group analysis, it is found that the traditional spacetime separable solution of the neutron diffusion equation (featuring a single αeigenvalue) corresponds to time translation and flux scaling symmetries. Additional solutions of this equation are also constructed using its broader symmetry set.},
doi = {10.1088/23996528/aae2a4},
journal = {Journal of Physics Communications},
issn = {23996528},
number = 10,
volume = 2,
place = {United States},
year = {2018},
month = {9}
}