Nuclear reactor with subdiffusive neutron transport: development of linear fractional-order models

Vyawahare, Vishwesh A.; Nataraj, P. S. V.; Espinosa-Paredes, Gilberto; Ramírez, Ricardo Isaac Cázares

doi:10.1007/s40435-016-0272-8

Cited by 18 publications

(3 citation statements)

References 45 publications

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“…Several researchers have contributed to the development of a variety of FO models along with the necessary satisfactory motivation and analysis for the same. The FO neutron diffusion equation models were proposed in [ 7 , 8 , 49 ]. The FO models used in the work are proposed in [ 5 ].…”

Section: Fractional-order Models Of Nuclear Reactormentioning

confidence: 99%

Modeling nonlinear fractional-order subdiffusive dynamics in nuclear reactor with artificial neural networks

Bhusari¹,

Patil²,

Jadhav³

et al. 2022

Int. J. Dynam. Control

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This paper presents the development and analysis of artificial neural network (ANN) models for the nonlinear fractional-order (FO) point reactor kinetics model, FO Nordheim–Fuchs model, inverse FO point reactor kinetics model and FO constant delayed neutron production rate approximation model. These models represent the dynamics of a nuclear reactor with neutron transport modeled as subdiffusion. These FO models are nonlinear in nature, are comprised of a system of coupled fractional differential equations and integral equations, and are considered to be difficult for solving both analytically and numerically. The ANN models were developed using the data generated from these models. The work involves the iterative process of ANN learning with different combinations of layers and neurons. It is shown through extensive simulation studies that the developed ANN models faithfully capture the transient and steady-state dynamics of these FO models, thereby providing a satisfactory representation for the nonlinear subdiffusive process of neutron transport in a nuclear reactor.

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Section: Fractional-order Models Of Nuclear Reactormentioning

confidence: 99%

Modeling nonlinear fractional-order subdiffusive dynamics in nuclear reactor with artificial neural networks

Bhusari¹,

Patil²,

Jadhav³

et al. 2022

Int. J. Dynam. Control

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“…The telegraph equations describe the current and voltage of wave propagation of electric signals in a cable transmission line to find distance and time, and has many applications such as neutron transport [17], random walk of suspension flows [18], signal analysis for transmission, propagation of electrical signals [19] etc. Since the telegraph equation with classical derivatives can not wells match the abnormal diffusion phenomena during the finite long transmit progress, where the voltage or the current wave possibly exists, in modeling of this equation, from the point of view of memory effects, we obtain the fractional telegraph equations with fractional derivatives [20][21][22]. The timefractional telegraph equation can be written as follows:…”

Section: Introductionmentioning

confidence: 99%

Invariant Solutions and Conservation Laws of the Time-Fractional Telegraph Equation

Najafi,

Çelik,

Uyanık

2023

Advances in Mathematical Physics

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In this study, the Lie symmetry analysis is given for the time-fractional telegraph equation with the Riemann–Liouville derivative. This equation is useable to describe the physical processes of models possessing memory. By applying classical and nonclassical Lie symmetry analysis for the telegraph equation with α , β time-fractional derivatives and some technical computations, new infinitesimal generators are obtained. The actual methods give some classical symmetries while the nonclassical approach will bring back other symmetries to these equations. The similarity reduction and conservation laws to the fractional telegraph equation are found.

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“…Das and Biswas [28] developed a constitutive neutron diffusion equation for describing the neutron flux profile by using the concept of fractional divergence. Vyawahare et al [29] studied a fractional-order model of a nuclear reactor, which predicts subdiffusive behaviour for long time. Vyawahare and Nataraj [30] dealt with a fractional-order model of neutron transport process and pointed out that it is a more faithful and realistic representation of neutron movements than the classical model.…”

Section: Introductionmentioning

confidence: 99%

Numerical Approximation for Fractional Neutron Transport Equation

Zhao

Zheng

2021

Journal of Mathematics

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Fractional neutron transport equation reflects the anomalous transport processes in nuclear reactor. In this paper, we will construct the fully discrete methods for this type of fractional equation with Riesz derivative, where the generalized WENO5 scheme is used in spatial direction and Runge–Kutta schemes are adopted in temporal direction. The linear stabilities of the generalized WENO5 schemes with different stages and different order ERK are discussed detailed. Numerical examples show the combinations of forward Euler/two-stage, second-order ERK and WENO5 are unstable and the three-stage, third-order ERK method with generalized WENO5 is stable and can maintain sharp transitions for discontinuous problem, and its convergence reaches fifth order for smooth boundary condition.

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Nuclear reactor with subdiffusive neutron transport: development of linear fractional-order models

Cited by 18 publications

References 45 publications

Modeling nonlinear fractional-order subdiffusive dynamics in nuclear reactor with artificial neural networks

Modeling nonlinear fractional-order subdiffusive dynamics in nuclear reactor with artificial neural networks

Invariant Solutions and Conservation Laws of the Time-Fractional Telegraph Equation

Numerical Approximation for Fractional Neutron Transport Equation

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