Transition From Turing Stripe Patterns To Hexagonal Patterns Induced By Polarized Electric Fields

With the development of suitable chemical systems whose kinetics includes a positive feedback and effective diffusion coefficients of the reactants can be made to vary widely under specific conditions, the unambiguous experimental evidences on Turing pattern were established in the early 1990s. Since then, the dynamics of Turing structures have been investigated in great detail. External forcing provides a powerful tool to analyze the response behavior of nonlinear pattern-forming systems, allowing, for instance, the study of their inherently nonlinear mechanism of self-organization. During the past few years, a lot of attention had focused on the corresponding behavior of Turing pattern under purely temporal or spatial steady or spatiotemporal illumination and external constant electric field.We have studied the effect of a circularly polarized electric field on the Turing stripe patterns. An approximate linear stability analysis has shown that Reλis increased after we apply a circularly polarized electric field. The analysis is based onω<<1; thus the results obtained from this linear analysis cannot predict our main numerical results (theωvalues are of order 1 in the numerical simulations) but only show that the system becomes more unstable. We have numerically studied the response of Turing stripe patterns to a circularly polarized electric field. The results reveal an interesting phenomenon that intrinsic stripe patterns change to hexagonal wave patterns for suitable values of intensity and frequency of the applied circularly polarized electric field. The intensity of the electric field 0E and the angular frequency of the electric fieldωare both playing an important role in the competition between stripe wave pattern and hexagonal wave pattern. In addition, we also find that the wavelength of the hexagonal wave pattern increases with 0E which is predicted in linear stability analysis. In order to give a complete description about the patterns controlled by circularly polarized electric fields, we present distributions of patterns in the-ω0E plane.Our results indicate that patterns tend to organize itself to the patterns with the same symmetry of the applied polarized electric field with the fact that hexagonal wave patterns possess hexagonal symmetry that is close to the rotation symmetry of the circularly polarized electric field, while stripe patterns possess stripe symmetry that is far from the rotation symmetry.The transitions from hexagonal patterns to stripe wave patterns induced by a dc electric field and by a linearly polarized electric field have also been observed; the symmetries of the dc electric field and the linearly polarized electric field are close to those of stripe wave patterns, but far from those of hexagonal patterns. These phenomena are related to the resonant behaviors of Turing patterns that have been observed under spatial steady and spatiotemporal illumination. At last, we hope that our theoretical results will be observed in experiments,such as the CDIMA reaction.In the Chapter 1, we reviewed the background of the Turing pattern and introduced some interesting work in the past few years.We did the linear stability analysis of the effect of a circularly polarized electric field on Turing stripe patterns in the Chapter 2, and the corresponding numerical simulations in the Chapter 3.In the chapter 4, we studied the situation of circularly polarized electric field on Turing 0H andπH hexagonal patterns.In the chapter 5 and 6, we studied the results of DC and elliptically polarized electric fields on Turing patterns.We made conclusion in the last chapter.