Advanced search
Publication Cover
Nuclear Science and Engineering Volume 155, 2007 - Issue 1
Submit an article Journal homepage
54
Views
30
CrossRef citations to date
0
Altmetric
Technical Note

Polynomial Chaos Functions and Neutron Diffusion

M. M. R. WilliamsImperial College of Science, Technology and EngineeringDepartment of Earth Science and Engineering Computational Physics and Geophysics Prince Consort Road, London SW72BP, United Kingdom
Pages 109-118 | Published online: 10 Apr 2017

Citations (30)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (3)

Patrick Behne, Jan Vermaak & Jean Ragusa. (2023) Parametric Model-Order Reduction for Radiation Transport Simulations Based on an Affine Decomposition of the Operators. Nuclear Science and Engineering 197:2, pages 233-261.
Read now
Jagjit Singh Matharu & Vidya Devi. (2019) Uncertainty Propagation in Neutron Activation Cross-Section Measurement Using Unscented Transformation Method. Nuclear Science and Engineering 193:3, pages 314-324.
Read now
L. Gilli, D. Lathouwers, J. L. Kloosterman & T. H. J. J. van der Hagen. (2013) Development of an Adaptive Nonintrusive Spectral Technique for Uncertainty Quantification and Application to a Multiphysics Problem. Nuclear Science and Engineering 175:2, pages 172-187.
Read now

Articles from other publishers (27)

Nicolò Abrate, Sandra Dulla & Nicola Pedroni. (2023) A non-intrusive reduced order model for the characterisation of the spatial power distribution in large thermal reactors. Annals of Nuclear Energy 184, pages 109674.
Crossref
Patrick Behne, Jan Vermaak & Jean C. Ragusa. (2022) Minimally-invasive parametric model-order reduction for sweep-based radiation transport. Journal of Computational Physics 469, pages 111525.
Crossref
Jagjit Singh Matharu & Vidya Devi. (2020) A modified unscented transformation method for uncertainty propagation in neutron induced cross section measurement. Annals of Nuclear Energy 149, pages 107777.
Crossref
A. V. Kuzmin & T. N. Korbut. (2019) Adaptation of the Polynomial Chaos Method for the Uncertainty Analysis of Critical Experiments. Physics of Atomic Nuclei 81:10, pages 1404-1407.
Crossref
Dongli Huang, Hany Abdel-Khalik, Cristian Rabiti & Frederick Gleicher. (2017) Dimensionality reducibility for multi-physics reduced order modeling. Annals of Nuclear Energy 110, pages 526-540.
Crossref
Xu Wu & Tomasz Kozlowski. (2017) Inverse uncertainty quantification of reactor simulations under the Bayesian framework using surrogate models constructed by polynomial chaos expansion. Nuclear Engineering and Design 313, pages 29-52.
Crossref
Hu Ze-Hua, Ye Tao, Liu Xiong-Guo & Wang Jia. (2017) Uncertainty quantification in the calculation of keff using sensitity and stochastic sampling method. Acta Physica Sinica 66:1, pages 012801.
Crossref
Zoltán Perkó, Danny Lathouwers, Jan Leen Kloosterman & Tim van der Hagen. (2014) Large scale applicability of a Fully Adaptive Non-Intrusive Spectral Projection technique: Sensitivity and uncertainty analysis of a transient. Annals of Nuclear Energy 71, pages 272-292.
Crossref
D. Ayres, S. Park & M.D. Eaton. (2014) Propagation of input model uncertainties with different marginal distributions using a hybrid polynomial chaos expansion. Annals of Nuclear Energy 66, pages 1-4.
Crossref
Zoltán Perkó, Luca Gilli, Danny Lathouwers & Jan Leen Kloosterman. (2014) Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis. Journal of Computational Physics 260, pages 54-84.
Crossref
D. Ayres, M.M.R. Williams & M.D. Eaton. (2013) Time and static eigenvalues of the stochastic transport equation by the methods of polynomial chaos. Progress in Nuclear Energy 67, pages 33-55.
Crossref
L. Gilli, D. Lathouwers, J.L. Kloosterman, T.H.J.J. van der Hagen, A.J. Koning & D. Rochman. (2013) Uncertainty quantification for criticality problems using non-intrusive and adaptive Polynomial Chaos techniques. Annals of Nuclear Energy 56, pages 71-80.
Crossref
M.M.R. Williams. (2013) Static and dynamic criticality with uncertainty. Annals of Nuclear Energy 52, pages 22-27.
Crossref
M.M.R. Williams. (2013) A method for solving stochastic eigenvalue problems II. Applied Mathematics and Computation 219:9, pages 4729-4744.
Crossref
M.M.R. Williams. (2012) Uncertainty quantification in resonance absorption. Annals of Nuclear Energy 47, pages 124-133.
Crossref
D.A.F. Ayres, M.D. Eaton, A.W. Hagues & M.M.R. Williams. (2012) Uncertainty quantification in neutron transport with generalized polynomial chaos using the method of characteristics. Annals of Nuclear Energy 45, pages 14-28.
Crossref
M.M.R. Williams. (2012) Uncertainty quantification in aerosol dynamics. Annals of Nuclear Energy 43, pages 136-141.
Crossref
L. Gilli, D. Lathouwers, J.L. Kloosterman & T.H.J.J. van der Hagen. (2012) Performing uncertainty analysis of a nonlinear Point-Kinetics/Lumped Parameters problem using Polynomial Chaos techniques. Annals of Nuclear Energy 40:1, pages 35-44.
Crossref
Erin D. Fichtl & Anil K. Prinja. (2011) The stochastic collocation method for radiation transport in random media. Journal of Quantitative Spectroscopy and Radiative Transfer 112:4, pages 646-659.
Crossref
Matthew Eaton & M.M.R. Williams. (2010) A probabilistic study of the influence of parameter uncertainty on solutions of the neutron transport equation. Progress in Nuclear Energy 52:6, pages 580-588.
Crossref
M.M.R. Williams. (2010) A method for solving a stochastic eigenvalue problem applied to criticality. Annals of Nuclear Energy 37:6, pages 894-897.
Crossref
M.M.R. Williams & Matthew Eaton. (2010) A probabilistic study of the influence of parameter uncertainty on solutions of the radiative transfer equation. Journal of Quantitative Spectroscopy and Radiative Transfer 111:5, pages 696-707.
Crossref
M.M.R. Williams. (2010) A probabilistic study of the influence of parameter uncertainty on thermal radiation heat transfer. International Journal of Heat and Mass Transfer 53:7-8, pages 1461-1472.
Crossref
M.M.R. Williams. (2010) A method for solving stochastic eigenvalue problems. Applied Mathematics and Computation 215:11, pages 3906-3928.
Crossref
M.M.R. Williams. (2009) On some matters concerning the backward and forward equations of probability balance for neutrons in a medium with randomly time-varying properties. Progress in Nuclear Energy 51:6-7, pages 663-671.
Crossref
M.M.R. Williams. (2008) An approximate method for solving radiation transport problems in temporally and spatially stochastic media. Journal of Quantitative Spectroscopy and Radiative Transfer 109:10, pages 1778-1790.
Crossref
J.S. Cassell & M.M.R. Williams. (2008) An approximate method for solving radiation and neutron transport problems in spatially stochastic media. Annals of Nuclear Energy 35:5, pages 790-803.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.