2005/11/30 by Nathan Becker, Guenter Ahlers
Agricultural and Biological Sciences · Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Plant and animal studies #Spectroscopy and Quantum Chemical Studies #nlin.CD #nlin.PS
paper · pdf · doi:10.1103/physreve.73.046209
15 pages, 26 figures, 1 table
arxiv created 2005/11/30 · openalex publication_date 2006/04/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The disagreement of the scaling of the correlation length \ensuremathξ 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 \ensuremathξ 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 \ensuremathξ. For both a Gaussian and a squared SH form, the correlation length \ensuremathξ\ensuremath≡1∕\ensuremathσ, determined from the variance \ensuremathσ2 of the SF, has the same dependence on the control parameter \ensuremathε as the length \ensuremathξ contained explicitly in the functional forms. However, for the SH and the Lorentzian forms we find \ensuremathξ\ensuremath∼\ensuremathξ1∕2. Results for \ensuremathξ determined from new experimental data by fitting the functional forms directly to the experimental SF yielded \ensuremathξ\ensuremath∼\ensuremathε^\ensuremath-\ensuremathν with \ensuremathν\ensuremath≃(1)/(4) for all four functions in the case of the FT method, but \ensuremathν\ensuremath≃(1)/(2), in agreement with the GL prediction, in the case of the MEM. Over a wide range of \ensuremathε and wave number k, the experimental SFs collapsed onto a unique curve when appropriately scaled by \ensuremathξ.