Fractal Cauculus Project

From: Roger Bagula (tftn_at_earthlink.net)
Date: 09/16/04 

Date: Thu, 16 Sep 2004 19:44:47 GMT

          FRACTIONAL CALCULUS PROJECT

Partially supported by research grants DES-9980484, DMS-0139943 and
DMS-0139927 from the National Science Foundation and DE-FG03-98ER14885
from the U.S. Department of Energy.

The Fractional Calculus Project is an interdisciplinary collaboration of
mathematicians, statisticians, physicists and hydrologists to develop
the theory and practical application of fractals, fractional
derivatives, and heavy tailed stochastic processes.

Fractional-order partial differential equations (PDEs) are used by
physicists and hydrologists to model anomalous diffusion and Hamiltonian
chaos. These governing equations describe the asymptotic behavior of
continuous time random walks (CTRWs). Stochastic solutions to the
simplest governing equations are Levy motions, generalizing the Brownian
motion solution to the classical diffusion equation. More generally,
these equations invoke pseudo-differential operators that are
non-local. Fractional PDEs address shortcomings with previous methods
in geophysics, but a number of important problems remain open.

Senior investigators:

Inmaculada B. Aban <http://unr.edu/homepage/aban/>, Department of
Mathematics & Statistics, University of Nevada, Reno
David A. Benson
<http://www.hydro.unr.edu/homepages/benson/current/index.html>, Desert
Research Institute, Reno, NV
Tomasz J. Kozubowski <http://unr.edu/homepage/tkozubow/>, Department of
Mathematics & Statistics, University of Nevada, Reno.
Mark M. Meerschaert <http://unr.edu/homepage/mcubed/>, Department of
Physics, University of Nevada, Reno.
Anna K. Panorska, Department of Mathematics & Statistics, University of
Nevada, Reno.
Stephen W. Wheatcraft <http://www.hydro.unr.edu/homepages/wheatcraft/>,
Department of Geological Sciences, University of Nevada, Reno.

Postdoctoral and graduate students:

Ellen Considine, graduate student, Program in Hydrologic Sciences,
University of Nevada, Reno.
Erich Foster, graduate student, Program in Hydrologic Sciences,
University of Nevada, Reno.
Matt Reeves, graduate student, Program in Hydrologic Sciences,
University of Nevada, Reno.
Charles Tadjeran, Postdoctoral Research Assistant, Department of
Mathematics & Statistics, University of Nevada, Reno.
Yong Zhang, Postdoctoral Research Assistant, Desart Research Institute,
Reno.

Other researchers affiliated with the Fractal Calculus Project:

Boris Baeumer <http://www.maths.otago.ac.nz/%7Ebbaeumer/>, Department of
Mathematics, University of Otago, New Zealand.
Peter Becker-Kern, Department of Mathematics, University of Dortmund,
Germany.
Kristen Bianchi, Department of Mathematics & Statistics, University of
Nevada, Reno.
Jeff Mortensen <http://unr.edu/homepage/jm/>, Department of Mathematics
& Statistics, University of Nevada, Reno.
Hans-Peter Scheffler
<http://www.mathematik.uni-dortmund.de/lsiv/scheffler/scheffler.html>,
Department of Mathematics & Statistics, University of Nevada, Reno.
Rina Schumer, PhD in Hydrology 2002 (advisor David Benson).

http://unr.edu/homepage/mcubed/FRG.html 

-- 
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
URL :  http://home.earthlink.net/~tftn
URL :  http://victorian.fortunecity.com/carmelita/435/

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