Related papers: Spiral Waves in Media with Complex Excitable Dynam…
The question of the relative importance of coherent structures and waves has for a long time attracted a great deal of interest in astrophysical plasma turbulence research, with a more recent focus on kinetic scale dynamics. Here we utilize…
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…
Motivated by recent observations that long-range connections (LRC) play a role in various brain phenomena, we have observed two distinct dynamical transitions in the activity of excitable media where waves propagate both between neighboring…
We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.
We study the nonlinear wave dynamics of one-dimensional chains of polycatenated rings. These interlocked structures support amplitude-dependent nonlinear wave propagation driven by tensile activation and internal structural flexibility,…
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…
Astrophysical disks that are sufficiently cold and dense are linearly unstable to the formation of axisymmetric rings as a result of the disk's gravity. In practice, spiral structures are formed, which may in turn produce bound fragments.…
Stable periodic orbits in spiral galactic models that form families of precessing ellipses can create spiral density waves similar to those that are observed in real grand-design galaxies. We study the range in parameter space for which the…
We investigate existence, stability, and instability of anchored rotating spiral waves in a model for geometric curve evolution. We find existence in a parameter regime limiting on a purely eikonal curve evolution. We study stability and…
Spiral density waves dominate several facets of accretion disc dynamics --- planet-disc interactions and gravitational instability (GI) most prominently. Though they have been examined thoroughly in two-dimensional simulations, their…
Spiral waves are ubiquitous spatiotemporal patterns that occur in various excitable systems. In cardiac tissue, the formation of these spiral waves is associated with life-threatening arrhythmias, and, therefore, it is important to study…
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…
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…
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…
It is shown that a new type of the self-similar spherical ionization waves may exist in gases. All spatial scales and the propagation velocity of such waves increase exponentially in time. Conditions for existence of these waves are…
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…
The pattern speeds of spiral galaxies are closely related to the flow of material in their disks. Flows that follow the `precessing ellipses' paradigm (see e.g., Kalnajs 1973) are likely associated with slowly rotating spirals, which have…
Propagating spiral waves have been discovered in various chemical, biological and physical systems. Spiral waves in multicellular organisms are often associated with essential living functions. Although certain eukaryotic microorganisms…
Spiral density wave theory attempts to describe the spiral pattern in spiral galaxies in terms of a long-lived wave structure with a constant pattern speed in order to avoid the winding dilemma. The pattern is consequently a rigidly…
In this paper, we investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional responses. We have carried out the analytical study for both one and two dimensional system in details and found out a…