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H. J. Haubold

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

At least 37 records · Page 2Linked to original sources
arXiv2012

Computational solutions of unified fractional reaction-diffusion equations with composite fractional time derivative

This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized fractional time-derivative defined by Hilfer (2000), the space derivative of second order by the Riesz-Feller fractional derivative and adding the function phi(x,t) which is a nonlinear function overning reaction. The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of the H-function. The main result obtained in this paper provides an elegant extension of the fundamental solution for the space-time fractional diffusion equation obtained earlier by Mainardi et al. (2001, 2005) and a result very recently given by Tomovski et al. (2011). Computational representation of the fundamental solution is also obtained explicitly. Fractional order moments of the distribution are deduced. At the end, mild extensions of the derived results associated with a finite number of Riesz-Feller space fractional derivatives are also discussed.

math.AP↗
arXiv2012

Computational solutions of distributed oder reaction-diffusion systems associated with Riemann-Liouville derivatives

This article is in continuation of our earlier article [37] in which computational solution of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative as space derivative is derived. In this article, we present computational solutions of distributed order fractional reaction-diffusion equations associated with Riemann-Liouville derivatives of fractional orders as the time-derivatives and Riesz-Feller fractional derivatives as the space derivatives. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the familiar Mittag-Leffler function. It provides an elegant extension of the results given earlier by Chen et al. [1], Debnath [3], Saxena et al. [36], Haubold et al. [15] and Pagnini and Mainardi [30]. The results obtained are presented in the form of two theorems. Some interesting results associated with fractional Riesz derivatives are also derived as special cases of our findings. It will be seen that in case of distributed order fractional reaction-diffusion, the solution comes in a compact and closed form in terms of a generalization of the Kampé de Fériet hypergeometric series in two variables, defined by Srivastava and Daoust [46] (also see Appendix B). The convergence of the double series occurring in the solution is also given.

math.AP↗
arXiv2012

Analysis of Solar Neutrino Data from SuperKamiokande I and II: Back to the Solar Neutrino Problem

We 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 Mathai's pathway model and consider fractional reaction and fractional diffusion as possible explanations of the non-Gaussian content of the SuperKamiokande data.

astro-ph.SR↗
arXiv2012

Heliosheath: Diffusion Entropy Analysis and Nonextensivity q-Triplet

In this paper we investigate the scaling behavior, based on Diffusion Entropy Analysis and Standard Deviation Analysis, of the magnetic field strength fluctuations recorded by Voyager-I in the heliosphere. The Voyager-I data set exhibits scaling behavior and may follow Levy-type probability distribution. A general fractional-order spatial and temporal diffusion model could be utilized for the interpretation of this Levy-type behavior in comparison to Gaussian behavior. This result confirms earlier studies of scaling behavior of the heliospheric magnetic field strength fluctuations based on non-extensive statistical mechanics leading to the determination of the nonextensivity q-triplet.

physics.gen-ph↗
arXiv2012

Solar neutrino records: Gauss or non-Gauss is the question

This article discusses the possible variation of the solar neutrino flux over time in the records of Super-Kamiokande-I and the relation to non-equilibrium statistical mechanics and the entropic pathway model. The scaling behavior of the Super-Kamiokande-I time series is investigated utilizing Standard Deviation Analysis and Diffusion Entropy Analysis. The data set exhibit scaling behavior and may follow Levy-type probability distribution function.

physics.gen-ph↗
arXiv2012

Proposal for a United Nations Basic Space Technology Initiative

The United Nations Programme on Space Applications, implemented by the United Nations Office for Outer Space Affairs, promotes the benefits of space-based solutions for sustainable economic and social development. The Programme assists Member States of the United Nations to establish indigenous capacities for the use of space technology and its applications. In the past the Programme has primarily been focusing on the use of space applications and on basic space science activities. However, in recent years there has been a strong interest in a growing number of space-using countries to build space technology capacities, for example, the ability to develop and operate small satellites. In reaction to this development, the United Nations in cooperation with the International Academy of Astronautics has been organizing annual workshops on small satellites in the service of developing countries. Space technology related issues have also been addressed as part of various other activities of the Programme on Space Applications. Building on these experiences, the Office for Outer Space Affairs is now considering the launch of a new initiative, preliminarily titled the United Nations Basic Space Technology Initiative (UNBSTI), to promote basic space technology development. The initiative would be implemented in the framework of the Programme on Space Applications and its aim would be to help building sustainable capacities for basic space technology education and development, thereby advancing the operational use of space technology and its applications.

physics.space-ph↗
arXiv2011

The Variation of the Solar Neutrino Fluxes over Time in the Homestake, GALLEX(GNO) and Super-Kamiokande Experiments

Using the records of the fluxes of solar neutrinos from the Homestake, GALLEX (GNO), and Super-Kamiokande experiments, their statistical analyses were performed to search for whether there existed a time variation of these fluxes. The results of the analysis for the three experiments indicate that these fluxes are varying quasi-biennially. This means that both efficiencies of the initial p-p and the pp-III reactions of the proton-proton chain are varying quasi-biennially together with a period of about 26 months. Since this time variation prospectively generated by these two reactions strongly suggests that the efficiency of the proton-proton chain as the main energy source of the Sun has a tendency to vary quasi-biennially due to some chaotic or non-linear process taking place inside the gravitationally stabilized solar fusion reactor. It should be, however, remarked that, at the present moment, we have no theoretical reasoning to resolve this mysterious result generally referred to as the quasi-biennial periodicity in the time variation of the fluxes of solar neutrinos. There is an urgent need to search for the reason why such a quasi-biennial periodicity is caused through some physical process as related to nuclear fusion deep inside the Sun.

physics.gen-ph↗
arXiv2011

Computable solutions of fractional partial differential equations related to reaction-diffusion systems

The object of this paper is to present a computable solution of a fractional partial differential equation associated with a Riemann-Liouville derivative of fractional order as the time-derivative and Riesz-Feller fractional derivative as the space derivative. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computable form in terms of the H-function. It provides an elegant extension of the results given earlier by Debnath, Chen et al., Haubold et al., Mainardi et al., Saxena et al., and Pagnini et al. The results obtained are presented in the form of four theorems. Some results associated with fractional Schroeodinger equation and fractional diffusion-wave equation are also derived as special cases of the findings.

math-ph↗
arXiv2011

A versatile integral in physics and astronomy

This paper deals with a general class of integrals, the particular cases of which are connected to outstanding problems in astronomy and physics. Reaction rate probability integrals in the theory of nuclear reaction rates, Krätzel integrals in applied analysis, inverse Gaussian distribution, generalized type-1, type-2 and gamma families of distributions in statistical distribution theory, Tsallis statistics and Beck-Cohen superstatistics in statistical mechanics and the general pathway model are all shown to be connected to the integral under consideration. Representations of the integral in terms of generalized special functions such as Meijer's G-function and Fox's H-function are also pointed out.

astro-ph.IM↗
arXiv2011

Analytic representations of standard and extended non-resonant thermonuclear functions with depleted tail through the pathway model

The method for the evaluation of the non-resonant thermonuclear function in the Maxwell-Boltzmann case with depleted tail is discussed. Closed forms of the analytical results are obtained in computational format, and written in terms of the H-function in two variables. The standard non-resonant cases are extended to Tsallis reaction rates through the pathway model. Behavior of the depleted non-resonant thermonuclear function is studied. A comparison of the Maxwell-Boltzmann energy distribution with a more general energy distribution called pathway energy distribution is also done.

astro-ph.SR↗
arXiv2011

Analytical results connecting stellar structure parameters and extended reaction rates

Possible modification in the velocity distribution in the non-resonant reaction rates leads to an extended reaction rate probability integral. The closed form representation for these thermonuclear functions are used to obtain the stellar luminosity and neutrino emission rates. The composite parameter {C} that determines the standard nuclear reaction rate through the Maxwell-Boltzmann energy distribution is extended to {C}^* by the extended reaction rates through a more general distribution than the Maxwell-Boltzmann distribution. The new distribution is obtained by the pathway model introduced by Mathai in 2005 [Linear Algebra and Its Applications, 396, 317-328]. Simple analytic models considered by various authors are utilized for evaluating stellar luminosity and neutrino emission rates and are obtained in generalized special functions such as Meijer's G-function and Fox's H-function. The standard and extended non-resonant thermonuclear functions are compared by plotting them. Behavior of the new energy distribution, more general than Maxwell-Boltzmann is also studied.

astro-ph.SR↗
arXiv2011

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. [23,24], for the fundamental solution of the space-time fractional equation, including Haubold et al. [13] and Saxena et al. [38] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion, and time-fractional diffusion. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-function in compact forms. The convergence conditions for the double series occurring in the solutions are investigated. It is interesting to observe that the double series comes out to be a special case of the Srivastava-Daoust hypergeometric function of two variables given in the Appendix B of this paper.

math-ph↗
arXiv2011

United Nations Basic Space Science Initiative: 2011 Status Report on the International Space Weather Initiative

The UNBSSI is a long-term effort for the development of astronomy and space science through regional and international cooperation in this field on a worldwide basis. A series of workshops on BSS was held from 1991 to 2004 (India 1991, Costa Rica and Colombia 1992, Nigeria 1993, Egypt 1994, Sri Lanka 1995, Germany 1996, Honduras 1997, Jordan 1999, France 2000, Mauritius 2001, Argentina 2002, and China 2004; http://www.seas.columbia.edu/~ah297/un-esa/) and addressed the status of astronomy in Asia and the Pacific, Latin America and the Caribbean, Africa, and Western Asia. One major recommendation that emanated from these workshops was the establishment of astronomical facilities in developing nations for research and education programmes at the university level. Such workshops on BSS emphasized the particular importance of astrophysical data systems and the virtual observatory concept for the development of astronomy on a worldwide basis. Pursuant to resolutions of the United Nations Committee on the Peaceful Uses of Outer Space (UNCOPUOS) and its Scientific and Technical Subcommittee, since 2005, these workshops focused on the International Heliophysical Year 2007 (UAE 2005, India 2006, Japan 2007, Bulgaria 2008, Ro Korea 2009; http://www.unoosa.org/oosa/SAP/bss/ihy2007/index.html). Starting in 2010, the workshops focus on the International Space Weather Initiative (ISWI) as recommended in a three-year-work plan as part of the deliberations of UNCOPUOS (http://www.stil.bas.bg/ISWI/). 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. Currently, 14 IHY/ISWI instrument arrays with > 600 instruments are operational in 95 countries.

physics.space-ph↗
arXiv2011

Further solutions of fractional reaction-diffusion equations in terms of the H-function

This paper is a continuation of our earlier paper in which we have derived the solution of an unified fractional reaction-diffusion equation associated with the Caputo derivative as the time-derivative and the Riesz-Feller fractional derivative as the space-derivative. In this paper, we consider an unified reaction-diffusion equation with Riemann-Liouville fractional derivative as the time-derivative and Riesz-Feller derivative as the space-derivative. The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of the H-function. The results derived are of general character and include the results investigated earlier by Kilbas et al. (2006a), Saxena et al. (2006c), and Mathai et al. (2010). The main result is given in the form of a theorem. A number of interesting special cases of the theorem are also given as corollaries.

cond-mat.stat-mech↗
arXiv2011

On extended thermonuclear functions through pathway model

The major problem in the cosmological nucleosynthesis is the evaluation of the reaction rate. The present scenario is that the standard thermonuclear function in the Maxwell-Boltzmann form is evaluated by using various techniques. The Maxwell-Boltzmannian approach to nuclear reaction rate theory is extended to cover Tsallis statistics (Tsallis, 1988) and more general cases of distribution functions. The main purpose of this paper is to investigate in some more detail the extended reaction probability integral in the equilibrium thermodynamic argument and in the cut-off case. The extended reaction probability integrals will be evaluated in closed form for all convenient values of the parameter by means of residue calculus. A comparison of the standard reaction probability integrals with the extended reaction probability integrals is also done.

cond-mat.stat-mech↗
arXiv2010

Matrix-Variate Statistical Distributions and Fractional Calculus

A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results on matrix-variate statistical densities and their connections to fractional calculus will be established. When considering solutions of fractional differential equations, Mittag-Leffler functions and Fox H-function appear naturally. Some results connected with generalized Mittag-Leffler density and their asymptotic behavior will be considered. Reference is made to applications in physics, particularly superstatistics and nonextensive statistical mechanics.

cond-mat.stat-mech↗