Fractional-space law for the neutron current density

Espinosa-Paredes, Gilberto; Vázquez-Rodríguez, R.; Gallegos, Edmundo del Valle; Alonso, Gustavo; Moghaddam, Nader Maleki

doi:10.1016/j.anucene.2012.12.009

Cited by 20 publications

(4 citation statements)

References 21 publications

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“…In recent work alpha was estimated with plant data using Detrended Fluctuation Analysis (DFA) [9], which was applied to a neutronic power signal of the Forsmark stability benchmark and Laguna Verde Nuclear Power Plant. According with these DFA results, a ranges between 0.1881 and 0.9399 were found, which consider different operation of the reactor, such as stationary operation, load changes and unstable conditions due to wave density phenomena.…”

Section: Fractional Calculusmentioning

confidence: 99%

“…In order to model the anomalous diffusion process, a new version of the diffusion equation has been developed based on the fractional derivatives. Neutron fractional diffusion equation was derived by Espinosa-Paredes [9]:…”

Section: Fractional Calculusmentioning

confidence: 99%

“…Moreover, the numerical solution of conservation equations, with variable coefficients in a heterogeneous media, need to be matured. In order to core calculation in nuclear reactors, there is a new version of the neutron diffusion equation, which is established on the fractional space derivatives [9]. Neutron fractional diffusion equation, NFDE, uses a non-local gradient of Fick's law (J a ¼ ÀD a r a /) where the fractional derivative operator r a can be defined in the Riemann-Liouville, Caputo and http://dx.doi.org/10.1016/j.apm.2014.12.036 0307-904X/Ó 2014 Elsevier Inc. All rights reserved.…”

Section: Introductionmentioning

confidence: 99%

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Development of a 2D-Multigroup Code (NFDE-2D) based on the neutron spatial-fractional diffusion equation

Moghaddam

Afarideh

Espinosa-Paredes

2015

Applied Mathematical Modelling

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a b s t r a c tThe first aim of this work is the numerical solution of the neutron spatial-fractional diffusion equation in two-dimension for energy multigroups using the shifted Grünwald-Letnikov approximation in the fractional derivatives. The second aim is related to illustrate a real application of fractional derivatives in the nuclear reactors. The novelty of this work is the discretization method of the neutron fractional diffusion equation in multigroup form for high heterogeneous multiplicative media where the effective multiplication factor (K eff ) was rigorously calculated. When the classical Laplacian is converted to fractional Laplacian, the jump length statistics are unrestricted. For neutron population in the nuclear reactors there is a new version of the neutron diffusion equation which is established on the fractional space derivatives, called in this work as neutron fractional diffusion equation (NFDE). We have developed the NFDE-2D as a nuclear reactors core calculation code, which is validated with some numerical experiments where different orders of fractional derivative are considered. The results demonstrate that reactors exhibit the complex behavior against order of fractional derivative which is depended on the competition between neutron absorption and super-diffusion phenomena, which is comparable with the neutron transport theory.

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Section: Fractional Calculusmentioning

confidence: 99%

Section: Fractional Calculusmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Development of a 2D-Multigroup Code (NFDE-2D) based on the neutron spatial-fractional diffusion equation

Moghaddam

Afarideh

Espinosa-Paredes

2015

Applied Mathematical Modelling

View full text Add to dashboard Cite

show abstract

“…Moreover numerical solutions of conservation equations, with variable coefficients in the heterogeneous media, need to be matured. In order to core calculation in the nuclear reactors there is a new version of the neutron diffusion equation which is established on the fractional space derivatives (Maleki Moghaddam et al, 2014;Espinosa-Paredes et al, 2013).The neutron fractional diffusion equation, NFDE, uses the non-local gradient of Fick's law (J = ÀD a r a /) where the fractional derivative operator, r a , can be defined in the Riemann-Liouville, Caputo and Grünwald-Letnikov sense (Das, 2012;Oldham and Spanier, 1974;Hilfer, 2000;Miller and Ross, 1993) and a is the order of fractional derivatives. In the limit a ?…”

Section: Introductionmentioning

confidence: 99%