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H. J. Haubold

Publications and source records attributed to H. J. Haubold.

At least 91 records · Page 5Linked to original sources
arXiv2002

Review of Mathematical Techniques Applicable in Astrophysical Reaction Rate Theory

An overview is presented on statistical techniques for the analytic evaluation of integrals for non-resonant, non-resonant depleted, non-resonant cut-off, non-resonant sccreened, and resonant thermonuclear reaction rates. The techniques are based on statistical distribution theory and the theory of Meijer's G-function and Fox's H-function. The implementation of Meijer's G-function in Mathematica constituts an additional utility for analytic manipulations and numerical computation of thermonuclear reaction rate integrals. Recent results in the astrophysical literature related to the use of analytic thermonuclear reaction rates are incorporated.

math.CA↗
arXiv2002

On Fractional Kinetic Equations

The subject of this paper is to derive the solution of generalized fractional kinetic equations. The results are obtained in a compact form containing the Mittag-Leffler function, which naturally occurs whenever one is dealing with fractional integral equations. The results derived in this paper provide an extension of a result given by Haubold and Mathai in a recent paper (Haubold and Mathai, 2000).

math.CA↗
arXiv2000

Research and Education in Basic Space Science: The Approach Pursued in the UN/ESA Workshops

Since 1990, the United Nations in cooperation with the European Space Agency is holding annually a workshop on basic space science for the benefit of the worldwide development of astronomy. These workshops have been held in countries of Asia and the Pacific (India, Sri Lanka), Latin America and the Caribbean (Costa Rica, Colombia, Honduras), Africa (Nigeria), Western Asia (Egypt, Jordan), and Europe (Germany, France). Additional to the scientific benefits of the workshops and the strengthening of international cooperation, the workshops lead to the establishment of astronomical telescope facilities in Colombia, Egypt, Honduras, Jordan, Morocco, Paraguay, Peru, Philippines, Sri Lanka, and Uruguay. The annual UN/ESA Workshops continue to pursue an agenda to network these astronomical telescope facilities through similar research and education programmes. Teaching material and hands-on astrophysics material has been developed for the operation of such astronomical telescope facilities in an university environment.

astro-ph↗
arXiv2000

The Fractional Kinetic Equation and Thermonuclear Functions

The paper discusses the solution of a simple kinetic equation of the type used for the computation of the change of the chemical composition in stars like the Sun. Starting from the standard form of the kinetic equation it is generalized to a fractional kinetic equation and its solutions in terms of H-functions are obtained. The role of thermonuclear functions, which are also represented in terms of G- and H-functions, in such a fractional kinetic equation is emphasized. Results contained in this paper are related to recent investigations of possible astrophysical solutions of the solar neutrino problem.

astro-ph↗
arXiv2000

Analytical Study of Thermonuclear Reaction Probability Integrals

An analytic study of the reaction probability integrals corresponding to the various forms of the slowly varying cross-section factor $S(E)$ is attempted. Exact expressions for reaction probability integrals are expressed in terms of the extended gamma functions.

astro-ph↗
arXiv1999

Regional Centres for Space Science and Technology Education (Affiliated to the United Nations)

Education is a prerequisite to master the challenges of space science and technology. Efforts to understand and control space science and technology are necessarily intertwined with social expressions in the cultures where science and technology is carried out. The United Nations is leading an effort to establish regional Centres for Space Science and Technology Education in major regions on Earth. The status of the establishment of such institutions in Asia and the Pacific, Africa, Latin America and the Caribbean, Western Asia, and Eastern Europe is briefly described in this article.

physics.ed-ph↗
arXiv1999

UN/ESA Workshops on Basic Space Science: An Update on Their Achievements

During the second half of the twentieth century, expensive observatories are being erected at La Silla (Chile), Mauna Kea (Hawai), Las Palmas (Canary Island), and Calar Alto (Spain), to name a view. In 1990, at the beginning of The Decade of Discovery in Astronomy and Astrophysics (Bahcall [2]), the UN/ESA Workshops on Basic Space Science initiated the establishment of small astronomical telescope facilities, among them many particularly supported by Japan, in developing countries in Asia and the Pacific (Sri Lanka, Philippines), Latin America and the Caribbean (Colombia, Costa Rica, Honduras, Paraguay), and Western Asia (Egypt, Jordan, Morocco). The annual UN/ESA Workshops continue to pursue an agenda to network these small observatory facilities through similar research and education programmes and at the same time encourage the incorporation of cultural elements predominant in the respective cultures. Cross-cultural integration and multi-lingual scientific cooperation may well be a dominant theme in the new millennium (Pyenson [20]). This trend is supported by the notion that astronomy has deep roots in virtually every human culture, that it helps to understand humanity's place in the vast scale of the Universe, and that it increases the knowledge of humanity about its origins and evolution=2E Two of these Workshops have been organized in Europe (Germany 1996 and France 2000) to strengthen cooperation between developing and industrialized countries.

physics.space-ph↗
arXiv1998

UN/ESA Workshops on Basic Space Science: An Initiative in the Worl dwide Development of Astronomy

In 1990, the United Nations, in cooperation with the European Space Agency, initiated the organization of a series of annual Workshops on Basic Space Science for the benefit of astronomers and space scientists in Asia and the Pacific, Latin American and the Caribbean, Africa, Western Asia, and Europe. This article summarizes accomplishments of these Workshops (1991-1998) and their follow-up projects with a view to enhance the worldwide development of astronomy and space science. The Workshops are being considered unique and a model for such an endeavor.

astro-ph↗
arXiv1998

Wavelet Analysis of the New Solar Neutrino Capture Rate Data for the Homestake Experiment

Wavelet analysis offers an alternative to Fourier based time-series analysis and is particularly useful when spectral features are time dependent. We analyze the solar neutrino capture rate of the radiochemical Homestake chlorine experiment with abbreviated Morlet wavelets, using Foster's (AJ, 111, 1709 (1996)) rescaled wavelet technique. We emphasize the complementarity of wavelet analysis to Fourier analysis. The Homestake data seem to contain a harmonic content with periodicities of 4.76 yr, 1.89 yr, 0.85 yr, and 0.51 yr. Wavelet analysis reveals that the 4.76 yr and 1.89 yr periods show an almost constant behavior over the 25 yr Homestake data record, while the 0.85 yr and 0.51 yr periods exhibit a transient phenomenon. The analysis does not show strong evidence for a period of the solar 11 yr cycle.

astro-ph↗
arXiv1996

Structure of the Universe

An introductory account is given of the understanding of the structure of the universe. At present the most plausible theory of the origin of the universe is that it formed from the explosion of an extremely hot and dense fireball several billion years ago. During the first few seconds after the big bang, the energy density was so great that only fundamental particles (leptons, quarks, gauge bosons) existed. As the universe cooled and expanded after the big bang, nuclei and atoms formed and condensed into galaxies and stars and systems of them. The fundamental particles and a wide range of gravitational aggregates of them constitute the small-scale and large-scale structure of the present universe. The current knowledge of the elements of the structure of the universe based on the standard big bang model and the standard model of fundamental particles is considered.

astro-ph↗
arXiv1996

On Thermonuclear Reaction Rates

Nuclear reactions govern major aspects of the chemical evolution od galaxies and stars. Analytic study of the reaction rates and reaction probability integrals is attempted here. Exact expressions for the reaction rates and reaction probability integrals for nuclear reactions in the case of nonresonant, modified nonresonant, screened nonresonant and resonant cases are given. These are expressed in terms of H-functions, G-functions and in computable series forms. Computational aspects are also discussed.

astro-ph↗
arXiv1995

The Sun

The paper is based on lectures on the internal structure and evolution of the Sun. It contains an outline of observational and theoretical elements of the Standard Solar Model, emphasizing also recent research results on solar rotation, magnetic fields, thermonuclear energy generation, and solar activity.

astro-ph↗
arXiv1995

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 non-linear partial differential equations of solar structure and kinetic equations by focusing our attention on a statistical interpretation of selected kinetic equation of PPII/PPIII branch reactions of the proton-proton chain. A fresh look at the statistical implications for the outcome of kinetic equations for nuclear reactions may shed light on recent claims that the $^7$Be-neutrino flux of the Sun is suppressed in comparison to the pp- and $^8$B neutrino fluxes and may hint at that the solar neutrino flux is indeed varying over time as shown by the Homestake experiment.

astro-ph↗
arXiv1995

Solar Structure in terms of Gauss' Hypergeometric Function

Hydrostatic equilibrium and energy conservation determine the conditions in the gravitationally stabilized solar fusion reactor. We assume a matter density distribution varying non- linearly through the central region of the Sun. The analytic solutions of the differential equations of mass conservation, hydrostatic equilibrium, and energy conservation, together with the equation of state of the perfect gas and a nuclear energy generation rate $ε=ε_0ρ^nT^m$, are given in terms of Gauss' hypergeometric function. This model for the structure of the Sun gives the run of density, mass pressure, temperature, and nuclear energy generation through the central region of the Sun. Because of the assumption of a matter density distribution, the conditions of hydrostatic equilibrium and energy conservation are separated from the mode of energy transport in the Sun.

astro-ph↗
arXiv1994

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 quantitatively the physical laws employed for understanding the internal solar structure and conjecture that the interlink between specific nuclear reactions of the PPIII-branch of the proton-proton chain may allow the high-energy solar neutrino flux to vary over time.

astro-ph↗
arXiv1994

Astrophysical thermonuclear functions

As theoretical knowledge and experimental verification of nuclear cross sections increases it becomes possible to refine analytic representations for nuclear reaction rates. In this paper mathematical/statistical techniques for deriving closed-form representations of thermonuclear functions are summarized and numerical results for them are given.The purpose of the paper is also to compare numerical results for approximate and closed-form representations of thermonuclear functions.

astro-ph↗