H. J. Haubold

A heuristic remark on the periodic variation in the number of solar neutrinos detected on Earth

Four operating neutrino observatories confirm the long standing discrepancy between detected and predicted solar neutrino flux. Among these four experiments the Homestake experiment is taking data for almost 25 years. The reliability of the radiochemical method for detecting solar neutrinos has been tested recently by the GALLEX experiment. All efforts to solve the solar neutrino problem by improving solar, nuclear, and neutrino physics have failed so far. This may also mean that the average solar neutrino flux extracted from the four experiments may not be the proper quantity to explain the production of neutrinos in the deep interior of the Sun. Occasionally it has been emphasized that the solar neutrino flux may vary over time. In this paper we do address relations among specific neutrino fluxes produced in the proton-proton chain that are imposed by the coupled systems of nonlinear partial differential equations of solar structure and kinetic equations by focusing our attention on a statistical interpretation of selected kinetic equations of PPII/PPIII branch reactions of the protonproton chain. A fresh look at the statistical implications for the outcome of kinetic equations for nuclear reactions may shed light on recent claims that the7Be-neutrino flux of the Sun is suppressed in comparison to the pp- and8B neutrino fluxes and may hint at that the solar neutrino flux is indeed varying over time as shown by the Homestake experiment.

Analysis of Solar Neutrino Data from Super-Kamiokande I and II

Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur 342004, India;E-Mail: ram.saxena@yahoo.com* Author to whom correspondence should be addressed; E-Mail: hans.haubold@unvienna.org;Tel.: +43-676-4252050; Fax: +43-1-26060-5830.Received: 5 December 2013; in revised form: 16 December 2013 / Accepted: 27 February 2014 /Published: 10 March 2014Abstract: We are going back to the roots of the original solar neutrino problem: theanalysis of data from solar neutrino experiments. The application of standard deviationanalysis (SDA) and diffusion entropy analysis (DEA) to the Super-Kamiokande I and IIdata reveals that they represent a non-Gaussian signal. The Hurst exponent is different fromthe scaling exponent of the probability density function, and both the Hurst exponent andscaling exponent of the probability density function of the Super-Kamiokande data deviateconsiderably from the value of 0.5, which indicates that the statistics of the underlyingphenomenon is anomalous. To develop a road to the possible interpretation of this finding,we utilize Mathai’s pathway model and consider fractional reaction and fractional diffusionas possible explanations of the non-Gaussian content of the Super-Kamiokande data.Keywords: solar neutrinos; Super-Kamiokande; data analysis; standard deviation;diffusion entropy; entropic pathway model, fractional reaction; fractional diffusion;thermonuclear functionsWe are going back to the roots of the original solar neutrino problem: analysis of data from solar neutrino experiments. The application of standard deviation analysis (SDA) and diffusion entropy analysis (DEA) to the SuperKamiokande I and II data reveals that they represent a non-Gaussian signal. The Hurst exponent is different from the scaling exponent of the probability density function and both Hurst exponent and scaling exponent of the probability density function of the SuperKamiokande data deviate considerably from the value of 0.5 which indicates that the statistics of the underlying phenomenon is anomalous. To develop a road to the possible interpretation of this finding we utilize Mathais pathway model and consider fractional reaction and fractional diffusion as possible explanations of the non-Gaussian content of the SuperKamiokande data.

Distributed order reaction-diffusion systems associated with Caputo derivatives

This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. [“The fundamental solution of the space-time fractional diffusion equation,” Fractional Calculus Appl. Anal. 4, 153–202 (2001); Mainardi et al. “Fox H-functions in fractional diffusion,” J. Comput. Appl. Math. 178, 321–331 (2005)] for the fundamental solution of the space-time fractional equation, including Haubold et al. [“Solutions of reaction-diffusion equations in terms of the H-function,” Bull. Astron. Soc. India 35, 681–689 (2007)] and Saxena et al. [“Fractional reaction-diffusio...

The resonant thermonuclear reaction rate

Basic physical principles for the resonant and nonresonant thermonuclear reaction rates are applied to find their standard representations for nuclear astrophysics. Closed‐form representations for the resonant reaction rate are derived in terms of Meijer’s G‐function. Analytic representations of the resonant and nonresonant nuclear reaction rates are compared and the appearance of Meijer’s G‐function is discussed in physical terms.

Solar nuclear energy generation and the chlorine solar neutrino experiment

The study of solar neutrinos may provide important insights into the physics of the central region of the Sun. Four solar neutrino experiments have confirmed the solar neutrino problem but do not clearly indicate whether solar physics, nuclear physics, or neutrino physics have to be improved to solve it. Nonlinear relations among the different neutrino fluxes are imposed by two coupled systems of differential equations governing the internal structure and time evolution of the Sun. We assume that the results of the four neutrino experiments are correct and are concerned not with the discrepancy between the average rate and the predicted rate, but with a possible time dependence of the argon production rate as revealed in the Homestake experiment over a time period of 20 years. Based on the subtlety of the solar neutrino problem we review here qualitatively the physical laws employed for understanding the internal solar structure and conjecture that the interlink between specific nuclear reactions of the P...

The Solar Neutrino Problem as a Probe for Nuclear Astrophysics

In a recently published paper KLAPDOR [1] has shown the central importance of methods for obtaining the shape of the beta strength function in nuclear physics and astrophysics. In addition to the beta strength function determined by the weak interaction there is the reaction rate leading the synthesis of elements in thermonuclear processes determined mainly by strong and electromagnetic interactions of nuclei. In the light of the solar neutrino problem we started the development of a new mathematical approach to the analytic representation of nuclear reaction rates, cp. HAUBOLD and JOHN [2]. The intention to come up with closed form representations of nuclear reaction rates is to take into account first physical principles of a reaction in a thermonuclear plasma as consistent as possible and to avoid mathematical approximations, cp. HAUBOLD and MATHAI [3]. The present status of our programme of the mathematical approach to the representation of nuclear reaction rates is as follows.

Scientific Endeavors of A.M. Mathai: An Appraisal on the Occasion of his Eightieth Birthday, 28 April 2015

A.M. Mathai is Emeritus Professor of Mathematics and Statistics at McGill University, Canada. He is currently the Director of the Centre for Mathematical and Statistical Sciences India. His research contributions cover a wide spectrum of topics in mathematics, statistics, physics, astronomy, and biology. He is a Fellow of the Institute of Mathematical Statistics, National Academy of Sciences of India, and a member of the International Statistical Institute. He is a founder of the Canadian Journal of Statistics and the Statistical Society of Canada. He was instrumental in the implementation of the United Nations Basic Space Science Initiative (1991–2012). This paper highlights research results of A.M. Mathai in the period of time from 1962 to 2015. He published over 300 research papers and over 25 books.