Physics of Fractal Operators

Bruce J. West, Mauro Bologna, Paolo Grigolini

364 pages, parution le 18/02/2003

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Résumé

This text describes how fractal phenomena, both deterministic and random, change over time, using the fractional calculus. The intent is to identify those characteristics of complex physical phenomena that require fractional derivatives or fractional integrals to describe how the process changes over time. The discussion emphasizes the properties of physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory.

In many cases, classic analytic function theory cannot serve for modeling complex phenomena; "Fractal Operators" shows how classes of less familiar functions, such as fractals, can serve as useful models in such cases. Because fractal functions, such as the Weierstrass function (long known not to have a derivative), do in fact have fractional derivatives, they can be cast as solutions to fractional differential equations. The traditional techniques for solving differential equations, including Fourier and Laplace transforms as well as Green's functions, can be generalized to fractional derivatives.

Fractal Operators addresses a general strategy for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of various forms of transport in heterogeneous materials. This strategy builds on traditional approaches and explains why the historical techniques fail as phenomena become more and more complicated.

Contents

Non-differentiable Processes
Failure of Traditional Models
Fractional Dynamics
Fractional Fourier Transforms
Fractional Laplace Transforms
Fractional Randomness
Fractional Rheology
Fractional Stochastics
The Ant in the Gurge Metaphor
Appendices

L'auteur - Bruce J. West

Duke University, Triangle, NC, USA

L'auteur - Mauro Bologna

University of North Texas, Denton, TX, USA

L'auteur - Paolo Grigolini

University of North Texas, Denton, TX, USA

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Bruce J. West, Mauro Bologna, Paolo Grigolini
Parution	18/02/2003
Nb. de pages	364
Format	16 x 24
Couverture	Relié
Poids	630g
Intérieur	Noir et Blanc
EAN13	9780387955544
ISBN13	978-0-387-95554-4