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

Noise Effects on the Complex Patterns of Abnormal Heartbeats

Patients at high risk for sudden death often exhibit complex heart rhythms in which abnormal heartbeats are interspersed with normal heartbeats. We analyze such a complex rhythm in a single patient over a 12-hour period and show that the rhythm can be described by a theoretical model consisting of two interacting oscillators with stochastic elements. By varying the magnitude of the noise, we show that for an intermediate level of noise, the model gives best agreement with key statistical features of the dynamics.Comment: 4 pages, 4 figures, RevTe

Points, Walls and Loops in Resonant Oscillatory Media

In an experiment of oscillatory media, domains and walls are formed under the parametric resonance with a frequency double the natural one. In this bi-stable system, %phase jumps $\pi$ by crossing walls. a nonequilibrium transition from Ising wall to Bloch wall consistent with prediction is confirmed experimentally. The Bloch wall moves in the direction determined by its chirality with a constant speed. As a new type of moving structure in two-dimension, a traveling loop consisting of two walls and Neel points is observed.Comment: 9 pages (revtex format) and 6 figures (PostScript

Instability and Spatiotemporal Dynamics of Alternans in Paced Cardiac Tissue

We derive an equation that governs the spatiotemporal dynamics of small amplitude alternans in paced cardiac tissue. We show that a pattern-forming linear instability leads to the spontaneous formation of stationary or traveling waves whose nodes divide the tissue into regions with opposite phase of oscillation of action potential duration. This instability is important because it creates dynamically an heterogeneous electrical substrate for inducing fibrillation if the tissue size exceeds a fraction of the pattern wavelength. We compute this wavelength analytically as a function of three basic length scales characterizing dispersion and inter-cellular electrical coupling.Comment: 4 pages, 3 figures, submitted to PR

Remodelling of human atrial K+ currents but not ion channel expression by chronic β-blockade

Chronic β-adrenoceptor antagonist (β-blocker) treatment in patients is associated with a potentially anti-arrhythmic prolongation of the atrial action potential duration (APD), which may involve remodelling of repolarising K+ currents. The aim of this study was to investigate the effects of chronic β-blockade on transient outward, sustained and inward rectifier K+ currents (ITO, IKSUS and IK1) in human atrial myocytes and on the expression of underlying ion channel subunits. Ion currents were recorded from human right atrial isolated myocytes using the whole-cell-patch clamp technique. Tissue mRNA and protein levels were measured using real time RT-PCR and Western blotting. Chronic β-blockade was associated with a 41% reduction in ITO density: 9.3 ± 0.8 (30 myocytes, 15 patients) vs 15.7 ± 1.1 pA/pF (32, 14), p < 0.05; without affecting its voltage-, time- or rate dependence. IK1 was reduced by 34% at −120 mV (p < 0.05). Neither IKSUS, nor its increase by acute β-stimulation with isoprenaline, was affected by chronic β-blockade. Mathematical modelling suggested that the combination of ITO- and IK1-decrease could result in a 28% increase in APD90. Chronic β-blockade did not alter mRNA or protein expression of the ITO pore-forming subunit, Kv4.3, or mRNA expression of the accessory subunits KChIP2, KChAP, Kvβ1, Kvβ2 or frequenin. There was no reduction in mRNA expression of Kir2.1 or TWIK to account for the reduction in IK1. A reduction in atrial ITO and IK1 associated with chronic β-blocker treatment in patients may contribute to the associated action potential prolongation, and this cannot be explained by a reduction in expression of associated ion channel subunits

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

Size-Dependent Transition to High-Dimensional Chaotic Dynamics in a Two-Dimensional Excitable Medium

The spatiotemporal dynamics of an excitable medium with multiple spiral defects is shown to vary smoothly with system size from short-lived transients for small systems to extensive chaos for large systems. A comparison of the Lyapunov dimension density with the average spiral defect density suggests an average dimension per spiral defect varying between three and seven. We discuss some implications of these results for experimental studies of excitable media.Comment: 5 pages, Latex, 4 figure

Characterization of a process for the in-furnace reduction of NOx, SO2, and HCl by carboxylic salts of calcium

Calcium magnesium acetate has been assessed as an agent for the reduction of NOx, SO2, and HCl, at the pilot scale, in a down-fired combustor operating at 80 kWth. In addition to this, the chemical and physical processes that occur during heating have been investigated. Benchmarking of calcium magnesium acetate with a suite of five other carboxylic salts (calcium magnesium acetate, calcium propionate, calcium acetate, calcium benzoate, magnesium acetate, and calcium formate) has been performed. NOx reduction involves the volatile organic content of the carboxylic salt being released at temperatures of >1000 °C, where the reaction of CHi radicals with NO under fuel-rich conditions can result in some of the NO forming N2 in a “reburning” process. Thermogravimetry-Fourier transform infrared (TG-FTIR) studies identified the nature of the decomposition products from the low- and high-temperature decompositions. In addition, the rate of weight losses were studied to investigate the influence of the organic decomposition on NOx reduction by reburning. In-furnace reductions of SO2 and HCl are aided by the highly porous, particulate residue, which results from the in situ drying, pyrolysis, and calcination processes. Simultaneous reduction of all three pollutants was obtained, and a synergy between SO2 and HCl capture was identified. A mechanism for this inter-relationship has been proposed. Sorbent particle characterization has been performed by collecting the calcined powder from a spray pyrolysis reactor and compared with those produced from a suite of pure carboxylic salts. Physical properties (including porosity, surface area, and decomposition behavior) have been discussed, relative to reductions in NOx and acid gas emissions

Analytically Solvable Asymptotic Model of Atrial Excitability

We report a three-variable simplified model of excitation fronts in human atrial tissue. The model is derived by novel asymptotic techniques \new{from the biophysically realistic model of Courtemanche et al (1998) in extension of our previous similar models. An iterative analytical solution of the model is presented which is in excellent quantitative agreement with the realistic model. It opens new possibilities for analytical studies as well as for efficient numerical simulation of this and other cardiac models of similar structure