skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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 space-time separable solution of the neutron diffusion equation (featuring a single α-eigenvalue) corresponds to time translation and flux scaling symmetries. Additional solutions of this equation are also constructed using its broader symmetry set.

Authors:
ORCiD logo [1];  [2];  [3];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Univ. of Illinois, Urbana, IL (United States). Dept. of Nuclear, Plasma, and Radiological Engineering
  3. 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):
LA-UR-18-21934
Journal ID: ISSN 2399-6528
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Physics Communications
Additional Journal Information:
Journal Volume: 2; Journal Issue: 10; Journal ID: ISSN 2399-6528
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:10.1088/2399-6528/aae2a4.
Ramsey, Scott D., Tellez, Jacob A., Riewski, Eric J., & Temple, Brian A. Symmetry and separability of the neutron diffusion equation. United States. doi:10.1088/2399-6528/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:10.1088/2399-6528/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 space-time separable solution of the neutron diffusion equation (featuring a single α-eigenvalue) corresponds to time translation and flux scaling symmetries. Additional solutions of this equation are also constructed using its broader symmetry set.},
doi = {10.1088/2399-6528/aae2a4},
journal = {Journal of Physics Communications},
issn = {2399-6528},
number = 10,
volume = 2,
place = {United States},
year = {2018},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Figures / Tables:

Figure A1. Figure A1.: Plot of the normalized scalar flux resulting from the space-time separable symmetry solution where Δk is constant, $γ$=ωr and $τ$=$α$t.

Save / Share:

Figures / Tables found in this record:

    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.