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Books > Earth & environment > Geography > Cartography, geodesy & geographic information systems (GIS) > Remote sensing
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Non-Linear Variability in Geophysics - Scaling and Fractals (Paperback, Softcover reprint of the original 1st ed. 1991)
Loot Price: R2,884
Discovery Miles 28 840
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Non-Linear Variability in Geophysics - Scaling and Fractals (Paperback, Softcover reprint of the original 1st ed. 1991)
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consequences of broken symmetry -here parity-is studied. In this
model, turbulence is dominated by a hierarchy of helical
(corkscrew) structures. The authors stress the unique features of
such pseudo-scalar cascades as well as the extreme nature of the
resulting (intermittent) fluctuations. Intermittent turbulent
cascades was also the theme of a paper by us in which we show that
universality classes exist for continuous cascades (in which an
infinite number of cascade steps occur over a finite range of
scales). This result is the multiplicative analogue of the familiar
central limit theorem for the addition of random variables.
Finally, an interesting paper by Pasmanter investigates the scaling
associated with anomolous diffusion in a chaotic tidal basin model
involving a small number of degrees of freedom. Although the
statistical literature is replete with techniques for dealing with
those random processes characterized by both exponentially decaying
(non-scaling) autocorrelations and exponentially decaying
probability distributions, there is a real paucity of literature
appropriate for geophysical fields exhibiting either scaling over
wide ranges (e. g. algebraic autocorrelations) or extreme
fluctuations (e. g. algebraic probabilities, divergence of high
order statistical moments). In fact, about the only relevant
technique that is regularly used -fourier analysis (energy spectra)
-permits only an estimate of a single (power law) exponent. If the
fields were mono-fractal (characterized by a single fractal
dimension) this would be sufficient, however their generally
multifractal character calls for the development of new techniques.
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