A novel analytical solution of the deformed Doppler broadening function using the Kaniadakis distribution and the comparison of computational efficiencies with the numerical solution

Abreu, Willian Vieira de; Martinez, Aquilino Senra; Carmo, Eduardo D. do; Gonçalves, Alessandro C.

doi:10.1016/j.net.2021.10.003

Cited by 5 publications

(10 citation statements)

References 35 publications

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“…In order to see more closely and compare the standard Maxwell-Boltzmann behavior with the Kaniadakis, we selected two different resonance peaks—apart from each other—at three different temperatures ( Figure 6 , Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 , Figure 12 and Figure 13 ) to confirm the expected curve attenuation illustrated in previous works [ 13 , 14 , 29 , 45 ]:…”

Section: Resultsmentioning

confidence: 85%

“…Calculating the numerical deformed Doppler broadening function using the Kaniadakis entropy can be very computationally costly. In fact, in a recently published paper [ 14 ], the analytical solution provided by Equation (9) was approximately 4.6 times faster than the numerical one.…”

Section: Resultsmentioning

confidence: 99%

“…As mentioned earlier, the analytical solution of the Doppler broadening function using the Kaniadakis statistics, proposed by Abreu et al [ 13 ] is obtained through a differential equation and its respective resolution [ 14 ], given by:

where,

…”

Section: Methodsmentioning

confidence: 99%

“…However, the numerical calculation of Equation (1) can represent a considerable additional amount of computer processing time, especially when inserted in nuclear data processing codes. In order to surpass this issue, Abreu et al [ 13 ] proposed an analytical solution based on obtaining a differential equation and its solution to represent the deformed Doppler broadening function using the Kaniadakis distribution [ 14 ]. This analytical solution proved to be up to five times faster than the numerical one [ 14 ].…”

Section: Introductionmentioning

confidence: 99%

“…In order to surpass this issue, Abreu et al [ 13 ] proposed an analytical solution based on obtaining a differential equation and its solution to represent the deformed Doppler broadening function using the Kaniadakis distribution [ 14 ]. This analytical solution proved to be up to five times faster than the numerical one [ 14 ]. Analytical solutions were also successfully applied in order to obtain faster methods for the Doppler broadening function considering the standard Maxwell-Boltzmann statistics [ 15 ] and Tsallis statistics [ 16 ].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Doppler Broadening of Neutron Cross-Sections Using Kaniadakis Entropy

Abreu

Maciel

Martinez

et al. 2022

Entropy

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In the last seven years, Kaniadakis statistics, or κ-statistics, have been applied in reactor physics to obtain generalized nuclear data, which can encompass, for instance, situations that lie outside thermal equilibrium. In this sense, numerical and analytical solutions were developed for the Doppler broadening function using the κ-statistics. However, the accuracy and robustness of the developed solutions contemplating the κ distribution can only be appropriately verified if applied inside an official nuclear data processing code to calculate neutron cross-sections. Hence, the present work inserts an analytical solution for the deformed Doppler broadening cross-section inside the nuclear data processing code FRENDY, developed by the Japan Atomic Energy Agency. To do that, we applied a new computational method called the Faddeeva package, developed by MIT, to calculate error functions present in the analytical function. With this deformed solution inserted in the code, we were able to calculate, for the first time, deformed radiative capture cross-section data for four different nuclides. The usage of the Faddeeva package brought more accurate results when compared to other standard packages, reducing the percentage errors in the tail zone in relation to the numerical solution. The deformed cross-section data agreed with the expected behavior compared to the Maxwell–Boltzmann.

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Section: Resultsmentioning

confidence: 85%

Section: Resultsmentioning

confidence: 99%

where,

…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Doppler Broadening of Neutron Cross-Sections Using Kaniadakis Entropy

Abreu

Maciel

Martinez

et al. 2022

Entropy

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Jeans analysis with κ-deformed Kaniadakis distribution in f (R) gravity

2022

Phys. Scr.

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The influence of the κ-deformed Kaniadakis distribution on Jeans instability in the background of f(R) gravity is investigated, the dispersion relation considering the κ-deformed Kaniadakis distribution is derived by exploiting the kinetic theory. The cases of high and low frequency perturbations are analyzed, respectively, it is found that the range of the unstable modes and the growth rates decrease with the increased distribution index κ in both of high and low frequency regime. Finally, based on the derivation of effective temperature, the relation between Jeans mass and temperature is studied, it is found that lower Jeans mass means that the system is more likely to collapse due to gravitational instability, the system is unstable for lower distribution index κ.

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The Scientific Contribution of the Kaniadakis Entropy to Nuclear Reactor Physics: A Brief Review

Martinez

Abreu

2023

Entropy

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In nuclear reactors, tracking the loss and production of neutrons is crucial for the safe operation of such devices. In this regard, the microscopic cross section with the Doppler broadening function is a way to represent the thermal agitation movement in a reactor core. This function usually considers the Maxwell–Boltzmann statistics for the velocity distribution. However, this distribution cannot be applied on every occasion, i.e., in conditions outside the thermal equilibrium. In order to overcome this potential limitation, Kaniadakis entropy has been used over the last seven years to generate generalised nuclear data. This short review article summarises what has been conducted so far and what has to be conducted yet.

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A novel analytical solution of the deformed Doppler broadening function using the Kaniadakis distribution and the comparison of computational efficiencies with the numerical solution

Cited by 5 publications

References 35 publications

Doppler Broadening of Neutron Cross-Sections Using Kaniadakis Entropy

Doppler Broadening of Neutron Cross-Sections Using Kaniadakis Entropy

Jeans analysis with κ-deformed Kaniadakis distribution in f (R) gravity

The Scientific Contribution of the Kaniadakis Entropy to Nuclear Reactor Physics: A Brief Review

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