Related papers: Solvable Model of Spiral Wave Chimeras
Three-dimensional excitable systems can selforganize vortex patterns that rotate around one-dimensional phase singularities called filaments. In experiments with the Belousov-Zhabotinsky reaction and numerical simulations, we pin these…
Generic wave dislocations (phase singularities, optical vortices) in three dimensions have anisotropic local structure, which is analysed, with emphasis on the twist of surfaces of equal phase along the singular line, and the rotation of…
Harmonically modulated complex solitary waves which are a generalized type of envelope soliton (herein coined oscillatory solitons) are studied for the two U(1)-invariant integrable generalizations of the modified Korteweg-de Vries…
Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological nature. A small perturbation causes gradual change in spatial location of spiral's rotation center and…
The analysis of wave patterns in a structure which possesses periodicity in the spatial and temporal dimensions is presented. The topic of imperfect chiral interfaces is also considered. Although causality is fundamental for physical…
In a weakly excitable medium, characterized by a large threshold stimulus, the free end of an isolated broken plane wave (wave tip) can either rotate (steadily or unsteadily) around a large excitable core, thereby producing a spiral…
We study the influence of nonuniform motion of oscillators in a ring chain with nonlocal coupling on their collective dynamics and reveal the mechanism behind the emergence of an atypical chimera state in such systems. The mechanism relies…
Formation of diverse patterns in spatially extended reaction-diffusion systems is an important aspect of study which is pertinent to many chemical and biological processes. Of special interest is the peculiar phenomenon of chimera state…
The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier-Stokes equations. The mean swimming velocity and the mean rate of dissipation…
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…
Target waves and spiral waves were discovered in the Belousov-Zhabotinsky (BZ) reaction around 50 years ago. Many biological systems demonstrate such rotating spiral patterns. Spiral waves are widely encountered in the glycolytic activity…
Excitable media are a generic class of models used to simulate a wide variety of natural systems including cardiac tissue. Propagation of excitation waves in this medium results in the formation of characteristic patterns such as rotating…
It is shown, by means of numerical simulations, that intercellular spiral waves of calcium can be initiated in a network of coupled cells as a result of a de-synchronization between Ca2+ oscillations in two domains. No artificial…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
Pinning and depinning of wavefronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…
A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating…
N-body simulations of disc galaxies that display recurrent transient spiral patterns are comparatively easy to construct, but are harder to understand. In this paper, I summarise the evidence from such experiments that the spiral patterns…
The purpose of this article is the study of the symmetries in a circular and linear harmonic oscillator chains system, and consequently use them as a means to find the eigenvalues of these configurations. Furthermore, a hidden…
This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem…
We study the dynamics of waves in a system of diffusively coupled discrete nonlinear sources. We show that the system exhibits burst waves which are periodic in a traveling-wave reference frame. We demonstrate that the burst waves are…