Fronts and patterns in a spatially forced CDIMA reaction

Abstract

We use the CDIMA chemical reaction and the Lengyel-Epstein model of this reaction to study resonant responses of a pattern-forming system to time-independent spatial periodic forcing. We focus on the 2 : 1 resonance, where the wavenumber of a one-dimensional periodic forcing is about twice the wavenumber of the natural stripe pattern that the unforced system tends to form. Within this resonance, we study transverse fronts that shift the phase of resonant stripe patterns by p. We identify phase fronts that shift the phase discontinuously, and pairs of phase fronts that shift the phase continuously, clockwise and anti-clockwise. We further identify a front bifurcation that destabilizes the discontinuous front and leads to a pair of continuous fronts. This bifurcation is the spatial counterpart of the nonequilibrium Ising-Bloch (NIB) bifurcation in temporally forced oscillatory systems. The spatial NIB bifurcation that we find occurs as the forcing strength is increased, unlike earlier studies of the NIB bifurcation. Furthermore, the bifurcation is subcritical, implying a range of forcing strength where both discontinuous Ising fronts and continuous Bloch fronts are stable. Finally, we find that both Ising fronts and Bloch fronts can form discrete families of bound pairs, and we relate arrays of these front pairs to extended rectangular and oblique patterns.

Non-monotonic resonance in a spatially forced Lengyel-Epstein model

“…26 The motivation for this study is a recent finding of a reversed NIB bifurcation in a spatially forced variant of the LE model. 24 We show that, unlike the picture that has emerged from earlier studies, 6,23 the effect of increasing the forcing strength is not necessarily monotonic; the resonance tongue can narrow and the NIB bifurcation can be reversed at sufficiently strong forcing.…”

“…Equation (2) with p ¼ 1 represents the first and largest term in a Fourier cosine series of a square-wave forcing normally used in experiments on the CDIMA reaction. 4,24 The form (2) preserves an inherent property of forcing by periodic illumination, namely, that the spatial mean increases with the forcing amplitude. The value p ¼ 0 represents constant illumination with no periodic modulations.…”

“…[20][21][22] A similar front bifurcation in 2D spatially forced non-oscillatory systems 23 has been related recently to a transition from oblique to rectangular patterns. 24 In this paper, we study the 2:1 spatial resonance in the LE model, 25 which describes the dynamics of the CDIMA reaction. 26 The motivation for this study is a recent finding of a reversed NIB bifurcation in a spatially forced variant of the LE model.…”

Turing Patterns in Chemical Systems

“…Embora a combinação desses padrões possa resultar em superestruturas, suas simetrias inerentes permanecem inalteradas nestas estruturas mais complexas. 99 Alguns exemplos obtidos experimentalmente por Feldman et al 38 são visualizados na Figura 6. Em intensidades de luz relativamente baixas, os padrões alinham-se com as bandas projetadas, i.e.…”

Modulation of Turing Patterns in the CDIMA Reaction by Ultraviolet and Visible Light

“…Turing patterns (TPs) have been thoroughly studied in the chlorine dioxide–iodine–malonic acid (CDIMA) reaction–diffusion system for more than two decades. − The photosensitivity of this reaction is conveniently used to control and modify the pattern formation . Most of these studies have employed visible white light (VWL) with weak and intermediate intensities. − Although it is well understood that the absorption of photons by molecular iodine and its photodissociation to very reactive atomic iodine trigger the system photosensitivity, the details of the photochemistry in this system are not completely understood. − In addition to molecular iodine, there are other species present, both initial reagents and intermediates, that can absorb light in the visible spectrum and thus may contribute to the photosensitivity of the reaction.…”