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H. J. Haubold

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

At least 73 records · Page 4Linked to original sources
arXiv2007

Solutions of fractional reaction-diffusion equations in terms of the H-function

This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation associated with the Caputo derivative as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the Laplace and Fourier transforms in closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by many authors, notably by Mainardi et al. (2001, 2005) for the fundamental solution of the space-time fractional diffusion equation, and Saxena et al. (2006a, b) for fractional reaction- diffusion equations. The advantage of using 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 neutral fractional diffusion, space-fractional 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-functions in compact form.

math.PR↗
arXiv2007

On generalized entropy measures and pathways

Product probability property, known in the literature as statistical independence, is examined first. Then generalized entropies are introduced, all of which give generalizations to Shannon entropy. It is shown that the nature of the recursivity postulate automatically determines the logarithmic functional form for Shannon entropy. Due to the logarithmic nature, Shannon entropy naturally gives rise to additivity, when applied to situations having product probability property. It is argued that the natural process is non-additivity, important, for example, in statistical mechanics, even in product probability property situations and additivity can hold due to the involvement of a recursivity postulate leading to a logarithmic function. Generalizations, including Mathai's generalized entropy are introduced and some of the properties are examined. Situations are examined where Mathai's entropy leads to pathway models, exponential and power law behavior and related differential equations. Connection of Mathai's entropy to Kerridge's measure of "inaccuracy" is also explored.

math.ST↗
arXiv2007

Generalized Measure of Entropy, Mathai's Distributional Pathway Model, and Tsallis Statistics

The pathway model of Mathai (2005) mainly deals with the rectangular matrix-variate case. In this paper the scalar version is shown to be associated with a large number of probability models used in physics. Different families of densities are listed here, which are all connected through the pathway parameter 'alpha', generating a distributional pathway. The idea is to switch from one functional form to another through this parameter and it is shown that basically one can proceed from the generalized type-1 beta family to generalized type-2 beta family to generalized gamma family when the real variable is positive and a wider set of families when the variable can take negative values also. For simplicity, only the real scalar case is discussed here but corresponding families are available when the variable is in the complex domain. A large number of densities used in physics are shown to be special cases of or associated with the pathway model. It is also shown that the pathway model is available by maximizing a generalized measure of entropy, leading to an entropic pathway. Particular cases of the pathway model are shown to cover Tsallis statistics (Tsallis, 1988) and the superstatistics introduced by Beck and Cohen (2003).

cond-mat.stat-mech↗
arXiv2007

Solutions of certain fractional kinetic equations and a fractional diffusion equation

In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic 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.

math.CA↗
arXiv2007

A certain class of Laplace transforms with applications to reaction and reaction-diffusion equations

A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables and the concept of Laplacianness in statistics, alpha-Laplace and Mittag-Leffler stochastic processes, the concepts of infinite divisibility and geometric infinite divisibility problems in probability theory and certain fractional integrals and fractional derivatives. A number of applications are pointed out with special reference to solutions of fractional reaction and reaction-diffusion equations and their generalizations.

math.CA↗
arXiv2007

Fractional reaction-diffusion equations

In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen, Metzler, and Fogedby (1999) for anomalous diffusion and del-Castillo-Negrete, Carreras, and Lynch (2003) for reaction-diffusion systems with Lévy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation.

math.CA↗
arXiv2007

Reaction-diffusion systems and nonlinear waves

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. The importance of the derived results lies in the fact that numerous results on fractional reaction, fractional diffusion, anomalous diffusion problems, and fractional telegraph equations scattered in the literature can be derived, as special cases, of the results investigated in this article.

math.CA↗
arXiv2007

Solution of generalized fractional reaction-diffusion equations

This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.

math.CA↗
arXiv2006

The United Nations Basic Space Science Initiative: The TRIPOD concept

Since 1990, the United Nations is annually holding a workshop on basic space science for the benefit of the worldwide development of astronomy. Additional to the scientific benefits of the workshops and the strengthening of international cooperation, the workshops lead to the establishment of astronomical telescope facilities through the Official Development Assistance (ODA) of Japan. Teaching material, hands-on astrophysics material, and variable star observing programmes had been developed for the operation of such astronomical telescope facilities in an university environment. This approach to astronomical telescope facility, observing programme, and teaching astronomy has become known as the basic space science TRIPOD concept. Currently, a similar TRIPOD concept is being developed for the International Heliophysical Year 2007, consisting of an instrument array, data taking and analysis, and teaching space science.

physics.soc-ph↗
arXiv2006

Pathway Model, Superstatistics, Tsallis Statistics, and a Generalized Measure of Entropy

The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This entropy is a variant of the generalized entropy of order 'alpha', considered in Mathai and Rathie (1975), and it is also associated with Shannon, Boltzmann-Gibbs, Renyi, Tsallis, and Havrda-Charvat entropies. The generalized entropy measure introduced here is also shown to haveinteresting statistical properties and it can be given probabilistic interpretations in terms of inaccuracy measure, expected value, and information content in a scheme. Particular cases of the pathway model are shown to be Tsallis statistics (Tsallis, 1988) and superstatistics introduced by Beck and Cohen (2003). The pathway model's connection to fractional calculus is illustrated by considering a fractional reaction equation.

cond-mat.stat-mech↗
arXiv2006

Report on the Twelfth United Nations/European Space Agency Workshop on Basic Space Science

Pursuant to recommendations of the United Nations Conference on the Exploration and Peaceful Uses of Outer Space (UNISPACE III) and deliberations of the United Nations Committee on the Peaceful Uses of Outer Space (UNCOPUOS), annual UN/European Space Agency workshops on basic space science have been held around the world since 1991. These workshops contributed to the development of astrophysics and space science, particularly in developing nations. Following a process of prioritization, the workshops identified the following elements as particularly important for international cooperation in the field: (i) operation of astronomical telescope facilities implementing TRIPOD, (ii) virtual observatories, (iii) astrophysical data systems, (iv) concurrent design capabilities for the development of international space missions, and (v) theoretical astrophysics such as applications of nonextensive statistical mechanics. Beginning in 2005, the workshops focus on preparations for the International Heliophysical Year 2007 (IHY2007). The workshops continue to facilitate the establishment of astronomical telescope facilities as pursued by Japan and the development of low-cost, ground-based, world-wide instrument arrays as lead by the IHY secretariat.

physics.soc-ph↗
arXiv2004

World Space Observatory/Ultraviolet (WSO/UV): Progress Report

The World Space Observatory/Ultraviolet (WSO/UV) represents a new mission implementation model for large space missions for astrophysics. The process has been brought up to enable, fully scientific needs driven, a logic to be applied to the demands for large collection powers required to undertake space missions which are complementary to the continuously increasing sensitivity of ground-based telescopes. One of the assumptions associated with the idea of a WSO is to avoid the excessive complexity required for multipurpose missions. Although there may exist purely technological or programmatic policy issues, which would suggest such more complex missions to be more attractive, many other aspects, which do not need to be explored in this report, may argue against such a mission model. Following this precept and other reasons, the first implementation model for a WSO has been done for the ultraviolet domain WSO/UV. WSO/UV is a follow-up project of the UN/ESA Workshops on Basic Space Science, organised annually since 1991.

physics.pop-ph↗
arXiv2004

Developing Basic Space Science World Wide: Progress Report

The UN/ESA Workshops on Basic Space Science is a long-term effort for the development of astronomy and regional and international co-operation in this field on a world wide basis, particularly in developing nations. The first four workshops in this series (India 1991, Costa Rica and Colombia 1992, Nigeria 1993, and Egypt 1994) addressed the status of astronomy in Asia and the Pacific, Latin America and the Caribbean, Africa, and Western Asia, respectively. One major recommendation that emanated from the first four workshops was that small astronomical facilities should be established in developing nations for research and education programmes at the university level and that such facilities should be networked. Subsequently, material for teaching and observing programmes for small optical telescopes were developed or recommended and astronomical telescope facilities have been inaugurated at UN/ESA Workshops on Basic Space Science in Sri Lanka (1995), Honduras (1997), and Jordan (1999). UN/ESA Workshops on Basic Space Science in Germany (1996), France (2000), Mauritius (2001), Argentina (2002), and P.R. China (2004) emphasised the particular importance of astrophysical data systems and the virtual observatory concept for the development of astronomy on a world wide basis. Since 1996, the workshops are contributing to the development of the World Space Observatory concept. Achievements of the series of workshops are briefly summarised in this report.

physics.soc-ph↗
arXiv2004

Boltzmann-Gibbs Entropy Versus Tsallis Entropy: Recent Contributions to Resolving the Argument of Einstein Concerning "Neither Herr Boltzmann nor Herr Planck has given a definition of W"?

Classical statistical mechanics of macroscopic systems in equilibrium is based on Boltzmann's principle. Tsallis has proposed a generalization of Boltzmann-Gibbs statistics. Its relation to dynamics and nonextensivity of statistical systems are matters of intense investigation and debate. This essay review has been prepared at the occasion of awarding the 'Mexico Prize for Science and Technology 2003'to Professor Constantino Tsallis from the Brazilian Center for Research in Physics.

physics.class-ph↗
arXiv2004

On Generalized Fractional Kinetic Equations

In a recent paper, Saxena et al. [1] developed the solutions of three generalized fractional kinetic equations in terms of Mittag-Leffler functions. The object of the present paper is to further derive the solution of further generalized fractional kinetic equations. The results are obtained in a compact form in terms of generalized Mittag-Leffler functions. Their relation to fundamental laws of physics is briefly discussed.

math-ph↗
arXiv2004

Unified Fractional Kinetic Equation and a Fractional Diffusion Equation

In earlier papers Saxena et al. (2002, 2003) derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which extended the work of Haubold and Mathai (2000). The object of the present paper is to investigate the solution of a unified form of fractional kinetic equation in which the free term contains any integrable function f(t), which provides the unification and extension of the results given earlier recently by Saxena et al. (2002, 2003). The solution has been developed in terms of the Wright function in a closed form by the method of Laplace transform. Further we derive a closed-form solution of a fractional diffusion equation. The asymptotic expansion of the derived solution with respect to the space variable is also discussed. The results obtained are in a form suitable for numerical computation.

math-ph↗
arXiv2002

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

Since 1988, the United Nations, through the Programme on Space Applications, is supporting the establishment and operation of regional Centres for Space Science and Technology Education in Africa, Asia and the Pacific, Latin America and the Caribbean, and Western Asia. Simultaneously, education curricula have been developed for remote sensing and geographic information system, satellite communications, satellite meteorology and global climate, and space and atmospheric science. The paper reviews briefly these developments and highlights the most recent updated education curricula in the four disciplines that are made available in 2002, in the six official languages of the United Nations, for implementation at the regional Centres and beyond.

physics.ed-ph↗