Two-Point
Statistics of Multifractal Measures
C. Meneveau*
and A. Chhabra+
Mason Laboratory | Yale University | New Haven, CT 06520
*Present Address: Department of Mechanical Engineering
The Johns Hopkins University | Baltimore, MD 21218
+Present Address: Morgan Stanley | New York, NY
ABSTRACT: The relationship between the f(a)
function of a multifractal and the spatial correlations of
its singularity strengths is examined. An expression to compute
the probability of observing two different singularities a'
and a'' within a distance r is derived
for measures arising from isotropic random multiplicative processes.
the correlation of 's is shown to decay logarithmically with
distance. Possible applications to turbulence models are discussed,
and the results are illustrated for a binomial measure, where the scaling of two-point correlation functions is shown to exhibit a phase transition.
Physica
A, 164, pp. 564-574
DOI: 10.1016/0378-4371(90)90223-F | Full PDF
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