Related papers: Spiral, Core-defect and Wave break in a modified O…
Spirals are common in Nature: the snail's shell and the ordering of seeds in the sunflower are amongst the most widely-known occurrences. While these are static, dynamic spirals can also be observed in excitable systems such as heart…
A spiral wave is a macroscopic dynamic of excitable media that plays an important role in several distinct systems, including the Belousov-Zhabotinsky reaction, seizures in the brain, and lethal arrhythmia in the heart. Because spiral wave…
It has become widely accepted that the most dangerous cardiac arrhythmias are due to re- entrant waves, i.e., electrical wave(s) that re-circulate repeatedly throughout the tissue at a higher frequency than the waves produced by the heart's…
In experiments with the photosensitive Belousov-Zhabotinsky reaction (PBZR) we found a stable three-dimensional organizing center that periodically emits trigger waves of chemical concentration. The experiments are performed in a parameter…
We present the first experimental study of unpinning a spiral wave of excitation using a circularly polarized electric field. The experiments are conducted in the Belousov-Zhabotinsky(BZ) reaction, and the system is modeled using the…
Rotating spiral waves with a central core composed of phase-randomized oscillators can arise in reaction-diffusion systems if some of the chemical components involved are diffusion-free. This peculiar phenomenon is demonstrated for a…
Three-dimensional excitable systems can create nonlinear scroll waves that rotate around one-dimensional phase singularities. Recent theoretical work predicts that these filaments drift along step-like height variations. Here we test this…
Cardiac tissue and the Belousov-Zhabotinsky reaction provide two notable examples of excitable media that support scroll waves, in which a filament core is the source of spiral waves of excitation. Here we consider a novel topological…
Re-entrant spiral waves are observed in many different situations in nature, perhaps most importantly in excitable electrophysiological tissue where they are believed to be responsible for pathological conditions such as cardiac…
Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coupled locally by diffusion. At the center of such spirals is a phase singularity, a topological defect where the oscillator amplitude drops to…
In two-dimensional reaction-diffusion systems, local curvature perturbations in the shape of traveling waves are typically damped out and disappear in the course of time. If, however, the inhibitor diffuses much faster than the activator,…
Spiral waves are self-repeating waves that can form in excitable media, propagating outward from their center in a spiral pattern. Spiral waves have been observed in different natural phenomena and have been linked to medical conditions…
In this thesis, we are concerned with the dynamics of spiral wave solutions to Reaction-Diffsion systems of equations, and how they behave when subject to symmetry breaking perturbations. We present an asymptotic theory of the study of…
Spiral wave patterns observed in models of cardiac arrhythmias and chemical oscillations develop alternans and stationary line defects, which can both be thought of as period-doubling instabilities. These instabilities are observed on…
Spiral waves of excitation in cardiac tissue are associated with life-threatening cardiac arrhythmias. It is, therefore, important to study the electrophysiological factors that affect the dynamics of these spiral waves. By using an…
In nature, excitable reaction-diffusion systems found in diverse settings (e.g. chemical reactions, metal rust, yeast, amoeba, heart, brain) generate geometrically similar macroscopic waves(1,2). For the heart and brain, the spatiotemporal…
We study the drift of spiral waves in a simple model of heterogeneous excitable medium, having gradients in local excitability or cellular coupling. For the first time, we report the anomalous drift of spiral waves towards regions having…
Rotors of reaction and diffusion, that revolve around a circular singularity, and the corresponding spiral wave activity around it, influence the nature of several excitable media. Their dynamics are known to be affected by target waves and…
Spiral wave propagation in period-2 excitable media is often accompanied by line-defects, the locus of points with period-1 oscillations. Here we investigate spiral line-defects in cardiac tissue where period-2 behavior has a known…
Spiral and antispiral waves are studied numerically in two examples of oscillatory reaction-diffusion media and analytically in the corresponding complex Ginzburg-Landau equation (CGLE). We argue that both these structures are sources of…