Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1908.08751

Threaded rings that swim in excitable media

Antonio Cincotti·Fabian Maucher·David Evans·Brette M. Chapin·Kate Horner·Elizabeth Bromley·Andrew Lobb·Jonathan W. Steed·Paul Sutcliffe
View original source ↗Read source document ↗Export metadata ↓

Abstract

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 configuration in which a closed filament loop, known as a scroll ring, is threaded by a pair of counter-rotating filaments that are perpendicular to the plane of the ring and end on the boundary of a thin medium. We simulate the dynamics of this threaded ring (thring) in the photosensitive Belousov-Zhabotinsky excitable medium, using the modified Oregonator reaction-diffusion equations. These computations reveal that the threading topology induces an exotic motion in which the thring swims in the plane of the ring. We propose a light templating protocol to create a thring in the photosensitive Belousov-Zhabotinsky medium and provide experimental confirmation that this protocol indeed yields a thring.

Explore related subjects

nlin.PScond-mat.soft

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Antonio Cincotti, Fabian Maucher, David Evans, Brette M. Chapin, Kate Horner, Elizabeth Bromley, Andrew Lobb, Jonathan W. Steed, Paul Sutcliffe. 2019-11-08. Threaded rings that swim in excitable media. https://doi.org/10.1103/physrevlett.123.258102

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Duck hunting with quantum mechanics

We bridge two sides of singular perturbation theory: the classical theory of slow-fast systems and the semi-classical approach to quantum mechanical systems. For a specific but physically important class of dynamical systems, we show that purely classical and exotic objects, so-called canard solutions, are shadows of instantons in the corresponding quantum system. We demonstrate that canard solutions exist in a domain of parameter space whose boundaries are determined by an instanton action. We illustrate our statements analytically for the relevant example, the overdamped Josephson junction, and confirm them numerically. For the Josephson junction, the canard window is the exponentially narrow gap between consecutive Shapiro steps.

nlin.PS↗
arXiv2026

Rolls and Snaking in a Swift-Hohenberg Equation with Non-smooth Nonlinearity

We study rolls and homoclinic snaking in a variation of the one-dimensional Swift-Hohenberg equation, whose standard forms are prototypical order-parameter models for pattern formation in the sciences. Motivated by classes of differential equation models that involve continuous non-smooth low order nonlinear terms, we replace the standard quadratic-cubic nonlinearity by $ν|u|^α-u^3$, $α\in [1,2]$ with $ν> 0$. In the vicinity of zero, for $α<2$ this nonlinearity falls outside the scope of classical Taylor expansion and bifurcation analysis. Our partially analytical and partially numerical results highlight that the non-smooth term modifies the criticality of pattern-forming bifurcations and alters the associated branches of solutions. In particular, $α\in(1,2)$ implies subcriticality of roll bifurcations for any $ν>0$. At $α=1$ differentiability is lost, which has a strong impact on the bifurcations of sign-changing rolls including the disappearance of homoclinic snaking. Homoclinic snaking thus emerges non-smoothly as $α$ increases from $α=1$, and persists when retaining an additional, e.g., quadratic term.

nlin.PS↗