Domain chaos puzzle and the calculation of the structure factor and its half-width
Abstract
The disagreement of the scaling of the correlation length ξ 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 ξ 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 ξ . For both a Gaussian and a squared SH form, the correlation length ξ¯≡1/σ , determined from the variance σ2 of the SF, has the same dependence on the control parameter ɛ as the length ξ contained explicitly in the functional forms. However, for the SH and the Lorentzian forms we find ξ¯∼ξ1/2 . Results for ξ determined from new experimental data by fitting the functional forms directly to the experimental SF yielded ξ∼ɛ-ν with ν≃(1)/(4) for all four functions in the case of the FT method, but ν≃(1)/(2) , in agreement with the GL prediction, in the case of the MEM. Over a wide range of ɛ and wave number k , the experimental SFs collapsed onto a unique curve when appropriately scaled by ξ .
- Publication:
-
Physical Review E
- Pub Date:
- April 2006
- DOI:
- 10.1103/PhysRevE.73.046209
- arXiv:
- arXiv:nlin/0511065
- Bibcode:
- 2006PhRvE..73d6209B
- Keywords:
-
- 47.54.-r;
- 47.52.+j;
- 47.32.-y;
- Pattern selection;
- pattern formation;
- Chaos in fluid dynamics;
- Vortex dynamics;
- rotating fluids;
- Nonlinear Sciences - Pattern Formation and Solitons;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 15 pages, 26 figures, 1 table