Analytical solution for the Doppler broadening function using the Kaniadakis distribution

Abreu, Willian Vieira de; Gonçalves, Alessandro C.; Martinez, Aquilino Senra

doi:10.1016/j.anucene.2018.11.023

Cited by 14 publications

(10 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…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%

See 1 more Smart Citation

Doppler Broadening of Neutron Cross-Sections Using Kaniadakis Entropy

Abreu

Maciel

Martinez

et al. 2022

Entropy

View full text Add to dashboard Cite

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.

show abstract

where,

…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Doppler Broadening of Neutron Cross-Sections Using Kaniadakis Entropy

Abreu

Maciel

Martinez

et al. 2022

Entropy

View full text Add to dashboard Cite

show abstract

“…For this reason, it has attracted the interest of many researchers over the last two decades who have studied its foundations and mathematical aspects [49][50][51][52][53][54][55][56][57][58], the underlying thermodynamics [59,60], and specific applications of the theory to various fields. A non-exhaustive list of applications includes those in quantum statistics [61][62][63][64], in quantum entanglement [65,66], in plasma physics [67][68][69][70][71][72][73], in nuclear fission [74][75][76][77], in astrophysics [78][79][80][81], in quantum gravity [82][83][84][85][86][87], in geomechanics [88,89], in genomics [90,91], in complex networks [92][93][94], in economy [95]…”

Section: A the κ-Deformed Exponential Functionmentioning

confidence: 99%

The κ-statistics approach to epidemiology

Kaniadakis

Baldi

Deisboeck

et al. 2020

Preprint

View full text Add to dashboard Cite

A great variety of complex physical, natural and artificial systems are governed by statistical distributions, which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced κ-statistics framework predicts distribution functions with this feature. A growing number of applications in different fields of investigation are beginning to prove the relevance and effectiveness of κ-statistics in fitting empirical data. In this paper, we use κ-statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived κ-Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement between theoretical predictions and empirical observations. For these countries we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic are successfully described by the same theoretical model, even though the two events are caused by different diseases and they are separated by more than 600 years, is evidence that the κ-Weibull model has universal features.

show abstract

“…For this reason, it has attracted the interest of many researchers over the last two decades who have studied its foundations and mathematical aspects [49][50][51][52][53][54][55][56][57][58] , the underlying thermodynamics 59,60 , and specific applications of the theory to various fields. A non-exhaustive list of applications includes those in quantum statistics [61][62][63][64] , in quantum entanglement 65,66 , in plasma physics [67][68][69][70][71][72][73] , in nuclear fission [74][75][76][77] , in astrophysics [78][79][80][81] , in quantum gravity [82][83][84][85][86][87] , in geomechanics 88,89 , in genomics 90,91 , in complex networks [92][93][94] , in economy [95]…”

mentioning

confidence: 99%

The κ-statistics approach to epidemiology

Kaniadakis

Baldi

Deisboeck

et al. 2020

Sci Rep

View full text Add to dashboard Cite

A great variety of complex physical, natural and artificial systems are governed by statistical distributions, which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced $$\kappa $$ κ -statistics framework predicts distribution functions with this feature. A growing number of applications in different fields of investigation are beginning to prove the relevance and effectiveness of $$\kappa $$ κ -statistics in fitting empirical data. In this paper, we use $$\kappa $$ κ -statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived $$\kappa $$ κ -Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement between theoretical predictions and empirical observations. For these countries we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic are successfully described by the same theoretical model, even though the two events are caused by different diseases and they are separated by more than 600 years, is evidence that the $$\kappa $$ κ -Weibull model has universal features.

show abstract

Analytical solution for the Doppler broadening function using the Kaniadakis distribution

Cited by 14 publications

References 6 publications

Doppler Broadening of Neutron Cross-Sections Using Kaniadakis Entropy

Doppler Broadening of Neutron Cross-Sections Using Kaniadakis Entropy

The κ-statistics approach to epidemiology

The κ-statistics approach to epidemiology

Contact Info

Product

Resources

About