Transverse instabilities in chemical Turing patterns of stripes

We present a theoretical and experimental study of the sideband instabilities in Turing patterns of stripes. We compare numerical computations of the Brusselator model with experiments in a chlorine dioxide–iodine– malonic acid ~CDIMA! reaction in a thin gel layer reactor in contact with a continuously refreshed reservoir of reagents. Spontaneously evolving Turing structures in both systems typically exhibit many defects that break the symmetry of the pattern. Therefore, the study of sideband instabilities requires a method of forcing perfect, spatially periodic Turing patterns with the desired wave number. This is easily achieved in numerical simulations. In experiments, the photosensitivity of the CDIMA reaction permits control and modulation of Turing structures by periodic spatial illumination with a wave number outside the stability region. When a too big wave number is imposed on the pattern, the Eckhaus instability may arise, while for too small wave numbers an instability sets in forming zigzags. By means of the amplitude equation formalism we show that, close to the hexagon-stripe transitions, these sideband instabilities may be preceded by an amplitude instability that grows transient spots locally before reconnecting with stripes. This prediction is tested in both the reaction-diffusion model and the experiment

Percolation thresholds in chemical disordered excitable media

The behavior of chemical waves advancing through a disordered excitable medium is investigated in terms of percolation theory and autowave properties in the framework of the light-sensitive Belousov-Zhabotinsky reaction. By controlling the number of sites with a given illumination, different percolation thresholds for propagation are observed, which depend on the relative wave transmittances of the two-state medium considered

Spiral anchoring in anisotropic media with multiple inhomogeneities: a dynamical system approach

Various PDE models have been suggested in order to explain and predict the dynamics of spiral waves in excitable media. In two landmark papers, Barkley noticed that some of the behaviour could be explained by the inherent Euclidean symmetry of these models. LeBlanc and Wulff then introduced forced Euclidean symmetry-breaking (FESB) to the analysis, in the form of individual translational symmetry-breaking (TSB) perturbations and rotational symmetry-breaking (RSB) perturbations; in either case, it is shown that spiral anchoring is a direct consequence of the FESB. In this article, we provide a characterization of spiral anchoring when two perturbations, a TSB term and a RSB term, are combined, where the TSB term is centered at the origin and the RSB term preserves rotations by multiples of $\frac{2\pi}{\jmath^*}$, where $\jmath^*\geq 1$ is an integer. When $\jmath^*>1$ (such as in a modified bidomain model), it is shown that spirals anchor at the origin, but when $\jmath^* =1$ (such as in a planar reaction-diffusion-advection system), spirals generically anchor away from the origin.Comment: Revised versio

Wave competition in excitable modulated media.

The propagation of an initially planar front is studied within the framework of the photosensitive Belousov-Zhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steady-state velocity are experimentally validated

Lifetime enhancement of scroll rings by spatiotemporal fluctuations

The dynamics of three-dimensional scroll rings with spatiotemporal random excitability is investigated numerically using the FitzHugh-Nagumo model. Depending on the correlation time and length scales of the fluctuations, the lifetime of the ring filament is enlarged and a resonance effect between the time scale of the scroll ring and the time correlation of the noise is observed. Numerical results are interpreted in terms of a simplified stochastic model derived from the kinematical equations for three-dimensional excitable waves

Lifetime enhancement of scroll rings by spatiotemporal fluctuations

The dynamics of three-dimensional scroll rings with spatiotemporal random excitability is investigated numerically using the FitzHugh-Nagumo model. Depending on the correlation time and length scales of the fluctuations, the lifetime of the ring filament is enlarged and a resonance effect between the time scale of the scroll ring and the time correlation of the noise is observed. Numerical results are interpreted in terms of a simplified stochastic model derived from the kinematical equations for three-dimensional excitable waves

Rationale, design, and baseline characteristics in Evaluation of LIXisenatide in Acute Coronary Syndrome, a long-term cardiovascular end point trial of lixisenatide versus placebo

Background: Cardiovascular (CV) disease is the leading cause of morbidity and mortality in patients with type 2 diabetes mellitus (T2DM). Furthermore, patients with T2DM and acute coronary syndrome (ACS) have a particularly high risk of CV events. The glucagonlike peptide 1 receptor agonist, lixisenatide, improves glycemia, but its effects on CV events have not been thoroughly evaluated. Methods: ELIXA (www.clinicaltrials.gov no. NCT01147250) is a randomized, double-blind, placebo-controlled, parallelgroup, multicenter study of lixisenatide in patients with T2DM and a recent ACS event. The primary aim is to evaluate the effects of lixisenatide on CV morbidity and mortality in a population at high CV risk. The primary efficacy end point is a composite of time to CV death, nonfatal myocardial infarction, nonfatal stroke, or hospitalization for unstable angina. Data are systematically collected for safety outcomes, including hypoglycemia, pancreatitis, and malignancy. Results: Enrollment began in July 2010 and ended in August 2013; 6,068 patients from 49 countries were randomized. Of these, 69% are men and 75% are white; at baseline, the mean ± SD age was 60.3 ± 9.7 years, body mass index was 30.2 ± 5.7 kg/m2, and duration of T2DM was 9.3±8.2 years. The qualifying ACS wasamyocardial infarctionin83% and unstableangina in 17%. The study will continue until the positive adjudication of the protocol-specified number of primary CV events. Conclusion: ELIXA will be the first trial to report the safety and efficacy of a glucagon-like peptide 1 receptor agonist in people with T2DM and high CV event risk. © 2015 Elsevier Inc. All rights reserved