**AAS Meeting #194 - Chicago, Illinois, May/June 1999**

*Session 93. Quiet Photosphere, Chromosphere and Transition Region*

Display, Thursday, June 3, 1999, 9:20am-4:00pm, Southeast Exhibit Hall
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## [93.01] Scaling Universality Classes and Analysis of Solar Data

*J.K. Lawrence, A.C. Cadavid (CSUN), A.A. Ruzmaikin (JPL)*

Many solar phenomena display a scaling symmetry associated
with random multiplicative cascades. Here a physical
measure, initially uniform on a spatial, temporal, or
space-time set, is divided among subsets according to
randomly determined fractions. This division is repeated on
smaller and smaller sub-subsets, so that the resulting
measure at the smallest scale is given at any point by the
product of a string of random fractions comprising its
fragmentation history. Such measures are highly
intermittent. They characterize such solar phenomena as the
spatial distribution of magnetic flux in an active region
and the time distribution of global X-ray emission.

The probability distribution functions (PDFs) governing the
random fractions fall into universality classes with robust
properties (Hentschel 1994). For example, all PDFs which
allow for zero fractions lead to measures with local peaks
of unlimited strengths which are progressively less and less
space filling. The GOES-2 X-ray data belong to this class,
which indicates the presence of critical behavior associated
with flares (Lu & Hamilton 1991). We investigate a number
of time series for the presence or absence of this property.

Multifractals in nature may fall into a narrow universality
class described by just 3 parameters (Schertzer, et al.
1997). We find that at least some examples of active region
magnetic fields do indeed have the conjectured form.
Further, we apply a causal space-time version of this class
of multiplicative cascade processes to forecasting the
evolution of solar velocity fields.

This work was supported in part by NSF grant ATM-9628882.

Hentschel, H.G.E. 1994, Phys. Rev. E, 50, 243. Lu, E.T. &
Hamilton, R.J. 1991, ApJ, 380, L89. Schertzer, D., Lovejoy,
S., Schmitt, F., Chigirinskaya, Y. & Marsan, D. 1997,
Fractals, 5, 427.

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