| Physics of Fractal Operators 2003 Edition Contributor(s): West, Bruce (Author), Bologna, Mauro (Author), Grigolini, Paolo (Author) |
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ISBN: 0387955542 ISBN-13: 9780387955544 Publisher: Springer OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: January 2003 Annotation: 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; "Physics of 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. Physics of 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. |
| Additional Information |
| BISAC Categories: - Science | Physics - Mathematical & Computational - Mathematics | Differential Equations - General - Science | Physics - Quantum Theory |
| Dewey: 530.155 |
| LCCN: 2002026660 |
| Series: Institute for Nonlinear Science |
| Physical Information: 0.8" H x 6.1" W x 9.2" (1.40 lbs) 354 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The discussion emphasizes physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat transport in heterogeneous materials. |