Related papers: Spiral waves: linear and nonlinear theory

The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the…

Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…

In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements,…

Species diversity in ecosystems is often accompanied by the self-organisation of the population into fascinating spatio-temporal patterns. Here, we consider a two-dimensional three-species population model and study the spiralling patterns…

Heteroclinic-induced spiral waves may arise in systems of partial differential equations that exhibit robust heteroclinic cycles between spatially uniform equilibria. Robust heteroclinic cycles arise naturally in systems with invariant…

This article discusses the description of wall-bounded turbulence as a deterministic high-dimensional dynamical system of interacting coherent structures, defined as eddies with enough internal dynamics to behave relatively autonomously…

Spiral waves are considered to be one of the potential mechanisms that maintains complex arrhythmias such as atrial and ventricular fibrillation. The aim of the present study was to quantify the complex dynamics of spiral waves as the…

A long-standing controversy in studies of spiral structure has concerned the lifetimes of individual spiral patterns. Much theoretical work has sought quasi-stationary spiral modes while N-body simulations have consistently displayed…

In the first part of this article, we review the observational evidence for spirals in the accretion discs of cataclysmic variables. It is shown that with the increasing amount of data available, spirals appear to be an omnipresent feature…

A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…

This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary…

The article summarizes the studies of wave fields in structured non-equilibrium media describing by means of nonlocal hydrodynamic models. Due to the symmetry properties of models, we derived the invariant wave solutions satisfying…

Stability, bifurcation properties, and the spatiotemporal behavior of different nonlinear combination structures of spiral vortices in the counter rotating Taylor-Couette system are investigated by full numerical simulations and by coupled…

We argue that self-excited instabilities are the cause of spiral patterns in simulations of unperturbed stellar discs. In previous papers, we have found that spiral patterns were caused by a few concurrent waves, which we claimed were…

Pattern formation in ultra-cold quantum systems has recently received a great deal of attention.In this work, we investigate a two-dimensional model system accounting for the dynamics of trapped ions. We find a novel spiral wave which is…

We analyze the spiral structure that results in a numerical simulation of a galactic disk with stellar and gaseous components evolving in a potential that includes an axisymmetric halo and bulge. We perform a second simulation without the…

We consider a particle that is subject to a constant force and scatters inelastically on a vibrating periodically corrugated floor. At small friction and small radius of the circular scatterers the dynamics is dominated by resonances…

We study existence, asymptotics, and stability of spiral waves in a driven curvature approximation, supplemented with an anchoring condition on a circle of finite radius. We analyze the motion of curves written as graphs in polar…

It has long been established that turbulent jets comprise large-scale coherent structures, now more commonly referred to as "wavepackets". These structures exhibit a remarkable spatio-temporal organisation, despite turbulence. In this work…

A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…