Domain chaos puzzle and the calculation of the structure factor and its half-width

Abstract

The disagreement of the scaling of the correlation length xi 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 experiments. 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 xi. For both a Gaussian and a squared SH form, the correlation length xi[triple bond]1/sigma, determined from the variance sigma2 of the SF, has the same dependence on the control parameter epsilon as the length xi contained explicitly in the functional forms. However, for the SH and the Lorentzian forms we find xi approximately xi (1/2). Results for xi determined from new experimental data by fitting the functional forms directly to the experimental SF yielded xi approximately epsilon(-v) with v approximately equal to 1/4 for all four functions in the case of the FT method, but v approximately equal to 1/2, in agreement with the GL prediction, in the case of the MEM. Over a wide range of epsilon and wave number k, the experimental SFs collapsed onto a unique curve when appropriately scaled by xi.