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Fractals in Engineering - New Trends in Theory and Applications (Hardcover, 2005 ed.)
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Fractals in Engineering - New Trends in Theory and Applications (Hardcover, 2005 ed.)
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This volume is a sequel to the books Fractals: Theory and
Applications in Engineering (Springer-Verlag, 1999) and Fractals in
Engineering. From Theory to Industrial Applications
(Springer-Verlag, 1997), presenting some of the most recent
advances in the ?eld. It is a fascinating exercise to follow the
progress of knowledge in this interdisciplinary area, as witnessed
by these three volumes.
First,con?rmingprevioustrendsobservedin1997and1999,appliedma-
ematical research on fractals has now reached a mature level, where
beautiful theories are developed in direct contact with engineering
concerns. The four papers in the Mathematical Aspects section
constitute valuable additions to the set of tools needed by the
engineer: Synthetic pictures modelling and rendering in computer
graphics (Theory and Applications of Fractal Tops, by Michael
Barnsley), curve approximation and "fractal B-splines" (Splines,
Fractal Functions, and Besov and Triebel-Lizorkin Spaces, by Peter
Mas- pust), deep understanding of the Hol .. derian properties of
certain stochastic processes useful in a large number of
applications (H.. olderian random fu- tions, by Antoine Ayache et
al. ), and study of the invariant measure of a coupled discrete
dynamical system (Fractal Stationary Density in Coupled
Maps,byJu..rgen Jost et al. ). The second section of the book
describes novel physical applications as well as recent progress on
more classical ones. The paper A Network of Fr- tal Force Chains
and Their E?ect in Granular Materials under Compression by Luis E.
Vallejo et al.
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