arXiv subjects

H. J. Haubold

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

At least 55 records · Page 3Linked to original sources

arXiv2010

A Pathway from Bayesian Statistical Analysis to Superstatistics

Superstatistics and Tsallis statistics in statistical mechanics is given an interpretation in terms of Bayesian statistical analysis. Subsequently superstatistics is extended by replacing each component of the conditional and marginal densities by Mathai's pathway model and further both components are replaced by Mathai's pathway models. This produces a wide class of mathematically and statistically interesting functions for prospective applications in statistical physics. It is pointed out that the final integral is a particular case of a general class of integrals introduced by the authors earlier. Those integrals are also connected to Kraetzel integrals in applied analysis, inverse Gaussian densities in stochastic processes, reaction rate integrals in the theory of nuclear astrophysics and Tsallis statistics in nonextensive statistical mechanics. The final results are obtained in terms of Fox's H-function. Matrix variate analogue of one significant specific case is also pointed out.

cond-mat.stat-mech↗

arXiv2010

Contributions of the United Nations Office for Outer Space Affairs to the International Space Weather Initiative (ISWI)

In 2010, the United Nations Committee on the Peaceful Uses of Outer Space began consideration of a new agenda item under a three-year work plan on the International Space Weather Initiative (ISWI). The main objectives of ISWI are to contribute to the development of the scientific insight necessary to improve understanding and forecasting capabilities of space weather as well as to education and public outreach. The United Nations Programme on Space Applications, implemented by the Office for Outer Space Affairs, is implementing ISWI in the framework of its United Nations Basic Space Science Initiative (UNBSSI), a long-term effort, launched in 1991, for the development of basic space science and for international and regional cooperation in this field on a worldwide basis, particularly in developing countries. UNBSSI encompassed a series of workshops, held from 1991 to 2004, which addressed the status of basic space science in Africa, Asia and the Pacific, Latin America and the Caribbean, and Western Asia. As a result several small astronomical research facilities have been inaugurated and education programmes at the university level were established. Between 2005 and 2009, the UNBSSI activities were dedicated to promoting activities related to the International Heliophysical Year 2007 (IHY), which contributed to the establishment of a series of worldwide ground-based instrument networks, a node of which is also operated by the Office for Outer Space Affairs. Building on these accomplishments, UNBSSI is now focussing on the ISWI.

astro-ph.IM↗

arXiv2010

Fusion yield: Guderley model and Tsallis statistics

The reaction rate probability integral is extended from Maxwell-Boltzmann approach to a more general approach by using the pathway model introduced by Mathai [Mathai A.M.:2005, A pathway to matrix-variate gamma and normal densities, Linear Algebra and Its Applications}, 396, 317-328]. The extended thermonuclear reaction rate is obtained in closed form via a Meijer's G-function and the so obtained G-function is represented as a solution of a homogeneous linear differential equation. A physical model for the hydrodynamical process in a fusion plasma compressed and laser-driven spherical shock wave is used for evaluating the fusion energy integral by integrating the extended thermonuclear reaction rate integral over the temperature. The result obtained is compared with the standard fusion yield obtained by Haubold and John in 1981.[Haubold, H.J. and John, R.W.:1981, Analytical representation of the thermonuclear reaction rate and fusion energy production in a spherical plasma shock wave, Plasma Physics, 23, 399-411]. An interpretation for the pathway parameter is also given.

physics.plasm-ph↗

arXiv2010

Pathway Model and Nonextensive Statistical Mechanics

The established technique of eliminating upper or lower parameters in a general hypergeometric series is profitably exploited to create pathways among confluent hypergeometric functions, binomial functions, Bessel functions, and exponential series. One such pathway, from the mathematical statistics point of view, results in distributions which naturally emerge within nonextensive statistical mechanics and Beck-Cohen superstatistics, as pursued in generalizations of Boltzmann-Gibbs statistics.

cond-mat.stat-mech↗

arXiv2010

Status Report on the United Nations Basic Space Science Initiative (UNBSSI)

Since 1990, the UN Programme on Space Applications leads the United Nations Basic Space Science Initiative by contributing to the international and regional development of astronomy and space science through annual UN/ESA/NASA/JAXA workshops on basic space science, International Heliophysical Year 2007, and the International Space Weather Initiative. Space weather is the conditions on the Sun and in the solar wind, magnetosphere, ionosphere and thermosphere that can influence the performance and reliability of space-borne and ground-based technological systems and can endanger human life or health. The programme also coordinates the development of IHY/ISWI low-cost, ground-based, world-wide instrument arrays. To date, 14 world-wide instrument arrays comprising approximately 1000 instruments (GPS receivers, magnetometers, spectrometers, particle detectors) are operating in more than 71 countries. The most recent workshop was hosted by the Republic of Korea in 2009 for Asia and the Pacific. Annual workshops on the ISWI have been scheduled to be hosted by Egypt in 2010 for Western Asia, Nigeria in 2011 for Africa, and Ecuador in 2012 for Latin America and the Caribbean.

astro-ph.IM↗

arXiv2010

An Alternative Method for Solving a Certain Class of Fractional Kinetic Equations

An alternative method for solving the fractional kinetic equations solved earlier by Haubold and Mathai (2000) and Saxena et al. (2002, 2004a, 2004b) is recently given by Saxena and Kalla (2007). This method can also be applied in solving more general fractional kinetic equations than the ones solved by the aforesaid authors. In view of the usefulness and importance of the kinetic equation in certain physical problems governing reaction-diffusion in complex systems and anomalous diffusion, the authors present an alternative simple method for deriving the solution of the generalized forms of the fractional kinetic equations solved by the aforesaid authors and Nonnenmacher and Metzler (1995). The method depends on the use of the Riemann-Liouville fractional calculus operators. It has been shown by the application of Riemann-Liouville fractional integral operator and its interesting properties, that the solution of the given fractional kinetic equation can be obtained in a straight-forward manner. This method does not make use of the Laplace transform.

math-ph↗

arXiv2010

Extended Reaction Rate Integral as Solutions of Some General Differential Equations

Here an extended form of the reaction rate probability integral, in the case of nonresonant thermonuclear reactions with the depleted tail and the right tail cut off, is considered. The reaction rate integral then can be looked upon as the inverse of the convolution of the Mellin transforms of Tsallis type statistics of nonextensive statistical mechanics and stretched exponential as well as that of superstatistics and stretched exponentials. The differential equations satisfied by the extended probability integrals are derived. The idea used is a novel one of evaluating the extended integrals in terms of some special functions and then by invoking the differential equations satisfied by these special functions. Some special cases of limiting situations are also discussed.

math-ph↗

arXiv2010

Solutions of the Fractional Reaction Equation and the Fractional Diffusion Equation

In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter method based on a result developed by the authors is given to derive the solution of a fractional diffusion equation. Fox functions and Mittag-Leffler functions are used for closed-form representations of the solutions of the respective differential equations.

math-ph↗

arXiv2010

Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

Geometric generalized Mittag-Leffler distributions having the Laplace transform $\frac{1}{1+β\log(1+t^α)},0<α\le 2,β>0$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al (2002, 2004a,b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.

astro-ph.IM↗

arXiv2009

Comment on Inconsistency of the basic nonadditivity of q-nonextensive statistical mechanics, arXiv:0910.3826v1

In a recent paper, Wang. et al. (2009) claim that Tsallis' nonadditivity of q-nonextensive statistical mechanics (Gell-Mann and Tsallis 2004, Tsallis 2009) is mathematically inconsistent and hence one should carefully review Tsallis' ideas and theory in toto. This present comment is to point out that the conclusions of Wang et al. (2009) were arrived at by misinterpreting two basic items and hence the advice of Wang et al. should be carefully reviewed.

cond-mat.stat-mech↗

arXiv2009

Mittag-Leffler Functions to Pathway Model to Tsallis Statistics

In reaction rate theory, in input-output type models and in reaction-diffusion problems when the total derivatives are replaced by fractional derivatives the solutions are obtained in terms of Mittag-Leffler functions and their generalizations. When fractional calculus enters into the picture the solutions of these problems, usually available in terms of hypergeometric functions, G and H-functions, switch to Mittag-Leffler functions and their generalizations into Wright functions. In this paper, connections are established among generalized Mittag-Leffler functions, pathway model, Tsallis statistics, superstatisitcs and power law, and among the corresponding entropic measures.

cond-mat.stat-mech↗

arXiv2009

Mittag-Leffler Functions and Their Applications

Motivated essentially by the success of the applications of the Mittag-Leffler functions in many areas of science and engineering, the authors present in a unified manner, a detailed account or rather a brief survey of the Mittag- Leffler function, generalized Mittag-Leffler functions, Mittag-Leffler type functions, and their interesting and useful properties. Applications of Mittag-Leffler functions in certain areas of physical and applied sciences are also demonstrated. During the last two decades this function has come into prominence after about nine decades of its discovery by a Swedish mathematician G.M. Mittag-Leffler, due its vast potential of its applications in solving the problems of physical, biological, engineering and earth sciences etc. In this survey paper, nearly all types of Mittag-Leffler type functions existing in the literature are presented. An attempt is made to present nearly an exhaustive list of references concerning the Mittag-Leffler functions to make the reader familiar with the present trend of research in Mittag-Leffler type functions and their applications.

math.CA↗

arXiv2009

Functions of Mittag-Leffler and Fox: The Pathway Model to Tsallis Statistics and Beck-Cohen Superstatistics

In reaction rate theory, in production-destruction type models and in reaction-diffusion problems when the total derivatives are replaced by fractional derivatives the solutions are obtained in terms of Mittag-Leffler functions and their generalizations. When fractional calculus enters into the picture the solutions of these problems, usually available in terms of generalized hypergeometric functions, switch to Mittag-Leffler functions and their generalizations into Wright functions and subsequently into Fox functions. In this paper, connections are established among generalized Mittag-Leffler functions, Mathai's pathway model, Tsallis statistics, Beck-Cohen superstatistics, and among corresponding entropic measures. The Mittag-Leffler function, for large values of the parameter, approaches a power-law. For values of the parameter close to zero, the Mittag-Leffler function behaves like a stretched exponential. The Mittag-Leffler function is a generalization of the exponential function and represents a deviation from the exponential paradigm whenever it shows up in solution of physical problems. The paper elucidates the relation between analytic representations of the q-exponential function that is fundamental to Tsallis statistics, Mittag-Leffler, Wright, and Fox functions, respectively, utilizing Mellin-Barnes integral representations.

cond-mat.stat-mech↗

arXiv2009

Special functions and pathways for problems in astrophysics: An essay in honor of A.M. Mathai

The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information and statistical distribution theory. The results presented in the essay cover a period of time in Mathai's research from 1982 to 2008 and are all related to the thematic area of the gravitationally stabilized solar fusion reactor and fractional reaction-diffusion, taking into account concepts of non-extensive statistical mechanics. The time period referred to above coincides also with Mathai's exceptional contributions to the establishment and operation of the Centre for Mathematical Sciences, India, as well as the holding of the United Nations (UN)/European Space Agency (ESA)/National Aeronautics and Space Administration (NASA) of the United States/ Japanese Aerospace Exploration Agency (JAXA) Workshops on basic space science and the International Heliophysical Year 2007, around the world. Professor Mathai's contributions to the latter, since 1991, are a testimony for his social conscience applied to international scientific activity.

astro-ph.SR↗

arXiv2007

A pathway to multivariate Gaussian density

A general principle called "conservation of the ellipsoid of concentration" is introduced and a generalized entropic form of order 'alpha' is optimized under this principle. It is shown that this can produce a density which can act as a pathway to multivariate Gaussian density. The resulting entropic pathway contains as special cases the Boltzmann-Gibbs (Shannon) and Tsallis (Havrda-Charvat) entropic forms.

cond-mat.stat-mech↗

arXiv2007

Solutions of fractional reaction-diffusion equations in terms of Mittag-Leffler functions

This paper deals with the solution of unified fractional reaction-diffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. On account of the most general character of the derived results, numerous results on fractional reaction, fractional diffusion, and fractional reaction-diffusion problems scattered in the literature, including the recently derived results by the authors for reaction-diffusion models, follow as special cases.

math.CA↗

arXiv2007

Extension of thermonuclear functions through the pathway model including Maxwell-Boltzmann and Tsallis distributions

The Maxwell-Boltzmannian approach to nuclear reaction rate theory is extended to cover Tsallis statistics (Tsallis, 1988) and more general cases of distribution functions. An analytical study of respective thermonuclear functions is being conducted with the help of statistical techniques. The pathway model, recently introduced by Mathai (2005), is utilized for thermonuclear functions and closed-form representations are obtained in terms of H-functions and G-functions. Maxwell-Boltzmannian thermonuclear functions become particular cases of the extended thermonuclear functions. A brief review on the development of the theory of analytic representations of nuclear reaction rates is given.

astro-ph↗

arXiv2007

Pathway parameter and thermonuclear functions

In the theory of thermonuclear reaction rates, analytical evaluation of thermonuclear functions for non-resonant reactions, including cases with cut-off and depletion of the tail of the Maxwell-Boltzmann distribution function were considered in a series of papers by Mathai and Haubold (1988). In the present paper we study more general classes of thermonuclear functions by introducing a pathway parameter alpha, so that when alpha --> 1 the thermonuclear functions in the Maxwell-Boltzmannian case are recovered. We will also give interpretations for the pathway parameter alpha in the case of cut-off and in terms of moments.

cond-mat.stat-mech↗