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A.C. Cadavid, J.K. Lawrence (California State University, Northridge), A.A. Ruzmaikin (Jet Propulsion Laboratory)
The diffusion properties of photospheric bright points associated with magnetic elements (MBP's) in the granulation network are analyzed. We find that the transport is subdiffusive for times less than 20 minutes but normal for times larger than 25 minutes. The subdiffusive transport is caused by the walkers being trapped at stagnation points in the intercellular pattern. We find that the distribution of waiting times at the trap sites obeys a truncated Lévy type (power law) distribution. The fractal dimension of the pattern of sites available to the random walk is less than 2 for the subdiffusive range and tends to 2 in the normal diffusion range. We show how the continuous time random walk formalism can give an analytical explanation of the observations. We simulate this random walk by using a version of a phenomenological model of renewing cells introduced originally for supergranules by Simon, Title and Weiss (1995). We find that the traps which cause the subdiffusive transport arise when the renewed convection cell pattern is neither fixed nor is it totally uncorrelated from the old pattern as required in Leighton's model, but in some intermediate state between these extremes. (Work supported in part by NSF grant ATM-9628882).
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