Author name code: balke
ADS astronomy entries on 2022-09-14
author:"Balke, A. Christiaan" 
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Title: Percolation theory and the geometry of photospheric magnetic
    flux concentrations
Authors: Balke, A. C.; Schrijver, C. J.; Zwaan, C.; Tarbell, T. D.
Bibcode: 1993SoPh..143..215B
Altcode:
  The magnetic field in solar active regions forms a highly structured
  pattern without an apparent length scale. We study this pattern in
  detail for a plage and its surroundings observed with the Swedish Solar
  Observatory on La Palma. The magnetogram has a resolution of about
  1/3″, after image optimisation. We analysed the geometric properties
  of isolated patches of magnetic flux. Patches with a linear size up to
  3″ appear to be statistically self-similar, with a fractal dimension
  ofD<SUB>f</SUB> = 1.54 ± 0.05 for the relation between area and linear
  size. This value agrees very well with the dimensionD<SUB>f</SUB>
  = 1.56 which is found in percolation theory for clusters of tracers
  placed randomly on a lattice with a tracer density below a critical
  threshold. The distribution of observed cluster areas also agrees
  with that of clusters on such a random lattice. The correspondence
  between properties of observations and of clusters on randomly filled
  lattices suggests that- well after emergence - the magnetic flux on
  the Sun is randomly distributed at least up to sizes of about 3″
  and possibly larger.

Title: Patterns in the photospheric magnetic field and percolation
    theory
Authors: Schrijver, C. J.; Zwaan, C.; Balke, A. C.; Tarbell, T. D.;
   Lawrence, J. K.
Bibcode: 1992A&A...253L...1S
Altcode:
  The magnetic field in solar plages forms a highly structured pattern
  with no apparent characteristic length scale. This pattern appears
  to be a fractal with a dimension between 1.45 and 1.60. Small-scale
  displacements of concentrations of magnetic flux in the network
  are consistent with a random walk on a fractal with a similar
  dimension. Percolation theory offers an effective explanation for
  observed geometric properties of small-scale flux concentrations
  in the solar photosphere, by demonstrating the close correspondence
  with clusters formed by randomly placed tracers on a 2D (irregular)
  lattice. Percolation theory also offers a model for the subdiffusive
  behavior of tracers performing a random walk on clusters formed
  by bonded sites. The geometry of flux concentrations and of the
  displacement of magnetic flux as a function of time are equivalent
  to situations in percolation theory below a critical value, called
  'the percolation threshold'.

Title: Fractals in Magnetograms
Authors: Schrijver, C. J.; Zwaan, C.; Balke, A. C.; Tarbell, T. D.;
   Lawrence, J. K.
Bibcode: 1992ASPC...27...67S
Altcode: 1992socy.work...67S
  No abstract at ADS

Title: Short Term Evolution of Fine Scale Magnetic Structures
Authors: Topka, K.; Frank, Z.; Shine, R.; Tarbell, T.; Title, A.;
   Scharmer, G.; Balke, A.
Bibcode: 1989BAAS...21..842T
Altcode:
  No abstract at ADS

