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:
-
- 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):
- LA-UR-18-21934
Journal ID: ISSN 2399-6528
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- 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. https://doi.org/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. https://doi.org/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},
number = 10,
volume = 2,
place = {United States},
year = {Wed Sep 19 00:00:00 EDT 2018},
month = {Wed Sep 19 00:00:00 EDT 2018}
}
Figures / Tables:
Works referenced in this record:
Symmetry and Solution of Neutron Transport Equations in Nonhomogeneous Media
journal, January 2014
- Tsyfra, Ivan; Czyżycki, Tomasz
- Abstract and Applied Analysis, Vol. 2014
Direct functional separation of variables and new exact solutions to axisymmetric unsteady boundary-layer equations
journal, February 2016
- Polyanin, Andrei D.; Zhurov, Alexei I.
- Communications in Nonlinear Science and Numerical Simulation, Vol. 31, Issue 1-3
Separation of variables of a generalized porous medium equation with nonlinear source
journal, November 2002
- Estévez, P. G.; Qu, Changzheng; Zhang, Shunli
- Journal of Mathematical Analysis and Applications, Vol. 275, Issue 1
Geometric Approach to Invariance Groups and Solution of Partial Differential Systems
journal, April 1971
- Harrison, B. Kent; Estabrook, Frank B.
- Journal of Mathematical Physics, Vol. 12, Issue 4
Symmetry groups and separation of variables of a class of nonlinear diffusion-convection equations
journal, August 1999
- Chou, Kai-Seng; Qu, Changzheng
- Journal of Physics A: Mathematical and General, Vol. 32, Issue 35
The Differential Form Method for Finding Symmetries
journal, August 2005
- Harrison, B. Kent
- Symmetry, Integrability and Geometry: Methods and Applications