Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities

Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a Nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar front unstable and gives rise to a pair of counterpropagating fronts. Near the NIB bifurcation the relation of the front velocity to curvature is highly nonlinear and transitions between counterpropagating fronts become feasible. Nonuniformly curved fronts may undergo local front transitions that nucleate spiral-vortex pairs. These nucleation events provide the ingredient needed to initiate spot splitting and spiral turbulence. Similar spatio-temporal processes have been observed recently in the ferrocyanide-iodate-sulfite reaction.Comment: Text: 14 pages compressed Postscript (90kb) Figures: 9 pages compressed Postscript (368kb

Surface Crystallization in a Liquid AuSi Alloy

X-ray measurements reveal a crystalline monolayer at the surface of the eutectic liquid Au_{82}Si_{18}, at temperatures above the alloy's melting point. Surface-induced atomic layering, the hallmark of liquid metals, is also found below the crystalline monolayer. The layering depth, however, is threefold greater than that of all liquid metals studied to date. The crystallinity of the surface monolayer is notable, considering that AuSi does not form stable bulk crystalline phases at any concentration and temperature and that no crystalline surface phase has been detected thus far in any pure liquid metal or nondilute alloy. These results are discussed in relation to recently suggested models of amorphous alloys.Comment: 12 pages, 3 figures, published in Science (2006

Propagation Failure in Excitable Media

We study a mechanism of pulse propagation failure in excitable media where stable traveling pulse solutions appear via a subcritical pitchfork bifurcation. The bifurcation plays a key role in that mechanism. Small perturbations, externally applied or from internal instabilities, may cause pulse propagation failure (wave breakup) provided the system is close enough to the bifurcation point. We derive relations showing how the pitchfork bifurcation is unfolded by weak curvature or advective field perturbations and use them to demonstrate wave breakup. We suggest that the recent observations of wave breakup in the Belousov-Zhabotinsky reaction induced either by an electric field or a transverse instability are manifestations of this mechanism.Comment: 8 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.htm

Multi-Phase Patterns in Periodically Forced Oscillatory Systems

Periodic forcing of an oscillatory system produces frequency locking bands within which the system frequency is rationally related to the forcing frequency. We study extended oscillatory systems that respond to uniform periodic forcing at one quarter of the forcing frequency (the 4:1 resonance). These systems possess four coexisting stable states, corresponding to uniform oscillations with successive phase shifts of $\pi/2$. Using an amplitude equation approach near a Hopf bifurcation to uniform oscillations, we study front solutions connecting different phase states. These solutions divide into two groups: $\pi$-fronts separating states with a phase shift of $\pi$ and $\pi/2$-fronts separating states with a phase shift of $\pi/2$. We find a new type of front instability where a stationary $\pi$-front ``decomposes'' into a pair of traveling $\pi/2$-fronts as the forcing strength is decreased. The instability is degenerate for an amplitude equation with cubic nonlinearities. At the instability point a continuous family of pair solutions exists, consisting of $\pi/2$-fronts separated by distances ranging from zero to infinity. Quintic nonlinearities lift the degeneracy at the instability point but do not change the basic nature of the instability. We conjecture the existence of similar instabilities in higher 2n:1 resonances (n=3,4,..) where stationary $\pi$-fronts decompose into n traveling $\pi/n$-fronts. The instabilities designate transitions from stationary two-phase patterns to traveling 2n-phase patterns. As an example, we demonstrate with a numerical solution the collapse of a four-phase spiral wave into a stationary two-phase pattern as the forcing strength within the 4:1 resonance is increased

Monovalent Ion Condensation at the Electrified Liquid/Liquid Interface

X-ray reflectivity studies demonstrate the condensation of a monovalent ion at the electrified interface between electrolyte solutions of water and 1,2-dichloroethane. Predictions of the ion distributions by standard Poisson-Boltzmann (Gouy-Chapman) theory are inconsistent with these data at higher applied interfacial electric potentials. Calculations from a Poisson-Boltzmann equation that incorporates a non-monotonic ion-specific potential of mean force are in good agreement with the data.Comment: 4 pages, 4 figure

A Phase Front Instability in Periodically Forced Oscillatory Systems

Multiplicity of phase states within frequency locked bands in periodically forced oscillatory systems may give rise to front structures separating states with different phases. A new front instability is found within bands where $\omega_{forcing}/\omega_{system}=2n$ ($n>1$). Stationary fronts shifting the oscillation phase by $\pi$ lose stability below a critical forcing strength and decompose into $n$ traveling fronts each shifting the phase by $\pi/n$. The instability designates a transition from stationary two-phase patterns to traveling $n$-phase patterns

Initial Conditions for Models of Dynamical Systems

The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with appropriate initial conditions, so that it faithfully reproduces the long-term behaviour of the original high-dimensional dynamical system. Our method involves putting the dynamical system into normal form, which not only generates the low-dimensional model, but also provides the correct initial conditions for the model. We illustrate the method with several examples. Keywords: normal form, isochrons, initialisation, centre manifoldComment: 24 pages in standard LaTeX, 66K, no figure

Excitable media in open and closed chaotic flows

We investigate the response of an excitable medium to a localized perturbation in the presence of a two-dimensional smooth chaotic flow. Two distinct types of flows are numerically considered: open and closed. For both of them three distinct regimes are found, depending on the relative strengths of the stirring and the rate of the excitable reaction. In order to clarify and understand the role of the many competing mechanisms present, simplified models of the process are introduced. They are one-dimensional baker-map models for the flow and a one-dimensional approximation for the transverse profile of the filaments.Comment: 14 pages, 16 figure

Anomalous layering at the liquid Sn surface

X-ray reflectivity measurements on the free surface of liquid Sn are presented. They exhibit the high-angle peak, indicative of surface-induced layering, also found for other pure liquid metals (Hg, Ga and In). However, a low-angle peak, not hitherto observed for any pure liquid metal, is also found, indicating the presence of a high-density surface layer. Fluorescence and resonant reflectivity measurements rule out the assignment of this layer to surface-segregation of impurities. The reflectivity is modelled well by a 10% contraction of the spacing between the first and second atomic surface layers, relative to that of subsequent layers. Possible reasons for this are discussed.Comment: 8 pages, 9 figures; to be submitted to Phys. Rev. B; updated references, expanded discussio

Shallow water marine sediment bacterial community shifts along a natural CO2 gradient in the Mediterranean Sea off Vulcano, Italy.

The effects of increasing atmospheric CO(2) on ocean ecosystems are a major environmental concern, as rapid shoaling of the carbonate saturation horizon is exposing vast areas of marine sediments to corrosive waters worldwide. Natural CO(2) gradients off Vulcano, Italy, have revealed profound ecosystem changes along rocky shore habitats as carbonate saturation levels decrease, but no investigations have yet been made of the sedimentary habitat. Here, we sampled the upper 2 cm of volcanic sand in three zones, ambient (median pCO(2) 419 μatm, minimum Ω(arag) 3.77), moderately CO(2)-enriched (median pCO(2) 592 μatm, minimum Ω(arag) 2.96), and highly CO(2)-enriched (median pCO(2) 1611 μatm, minimum Ω(arag) 0.35). We tested the hypothesis that increasing levels of seawater pCO(2) would cause significant shifts in sediment bacterial community composition, as shown recently in epilithic biofilms at the study site. In this study, 454 pyrosequencing of the V1 to V3 region of the 16S rRNA gene revealed a shift in community composition with increasing pCO(2). The relative abundances of most of the dominant genera were unaffected by the pCO(2) gradient, although there were significant differences for some 5 % of the genera present (viz. Georgenia, Lutibacter, Photobacterium, Acinetobacter, and Paenibacillus), and Shannon Diversity was greatest in sediments subject to long-term acidification (>100 years). Overall, this supports the view that globally increased ocean pCO(2) will be associated with changes in sediment bacterial community composition but that most of these organisms are resilient. However, further work is required to assess whether these results apply to other types of coastal sediments and whether the changes in relative abundance of bacterial taxa that we observed can significantly alter the biogeochemical functions of marine sediments