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Domain chaos puzzle and the calculation of the structure factor and its half-width Nathan Becker* and Guenter Ahlers
 

Summary: Domain chaos puzzle and the calculation of the structure factor and its half-width
Nathan Becker* and Guenter Ahlers
Department of Physics and iQCD, University of California, Santa Barbara, California 93106, USA
Received 28 November 2005; published 27 April 2006
The disagreement of the scaling of the correlation length between experiment and the Ginzburg-Landau
GL model for domain chaos was resolved. The Swift-Hohenberg SH domain chaos model was integrated
numerically to acquire test images to study the effect of a finite image size on the extraction of
from the structure factor SF . The finite image size had a significant effect on the SF determined with the
Fourier-transform FT method. The maximum entropy method MEM was able to overcome this finite
image-size problem and produced fairly accurate SFs for the relatively small image sizes provided by experi-
ments. Correlation lengths often have been determined from the second moment of the SF of chaotic patterns
because the functional form of the SF is not known. Integration of several test functions provided analytic
results indicating that this may not be a reliable method of extracting . For both a Gaussian and a squared
SH form, the correlation length 1/ , determined from the variance 2
of the SF, has the same dependence
on the control parameter as the length contained explicitly in the functional forms. However, for the SH
and the Lorentzian forms we find 1/2
. Results for determined from new experimental data by fitting
the functional forms directly to the experimental SF yielded -
with

  

Source: Ahlers, Guenter - Department of Physics, University of California at Santa Barbara

 

Collections: Physics