14 research outputs found
Domain-size control by global feedback in bistable systems
We study domain structures in bistable systems such as the Ginzburg-Landau
equation. The size of domains can be controlled by a global negative feedback.
The domain-size control is applied for a localized spiral pattern
The Saffman-Taylor problem on a sphere
The Saffman-Taylor problem addresses the morphological instability of an
interface separating two immiscible, viscous fluids when they move in a narrow
gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend
the classic Saffman-Taylor situation, by considering the flow between two
curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We
derive the mode-coupling differential equation for the interface perturbation
amplitudes and study both linear and nonlinear flow regimes. The effect of the
spherical cell (positive) spatial curvature on the shape of the interfacial
patterns is investigated. We show that stability properties of the fluid-fluid
interface are sensitive to the curvature of the surface. In particular, it is
found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw
flow on weakly negative, curved surfaces is briefly discussed.Comment: 26 pages, 4 figures, RevTex, accepted for publication in Phys. Rev.
Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states
Scroll waves are three-dimensional analogs of spiral waves. The linear
stability spectrum of untwisted and twisted scroll waves is computed for a
two-variable reaction-diffusion model of an excitable medium. Different bands
of modes are seen to be unstable in different regions of parameter space. The
corresponding bifurcations and bifurcated states are characterized by
performing direct numerical simulations. In addition, computations of the
adjoint linear stability operator eigenmodes are also performed and serve to
obtain a number of matrix elements characterizing the long-wavelength
deformations of scroll waves.Comment: 30 pages 16 figures, submitted to Phys. Rev.
Spiral anchoring in anisotropic media with multiple inhomogeneities: a dynamical system approach
Various PDE models have been suggested in order to explain and predict the
dynamics of spiral waves in excitable media. In two landmark papers, Barkley
noticed that some of the behaviour could be explained by the inherent Euclidean
symmetry of these models. LeBlanc and Wulff then introduced forced Euclidean
symmetry-breaking (FESB) to the analysis, in the form of individual
translational symmetry-breaking (TSB) perturbations and rotational
symmetry-breaking (RSB) perturbations; in either case, it is shown that spiral
anchoring is a direct consequence of the FESB.
In this article, we provide a characterization of spiral anchoring when two
perturbations, a TSB term and a RSB term, are combined, where the TSB term is
centered at the origin and the RSB term preserves rotations by multiples of
, where is an integer. When
(such as in a modified bidomain model), it is shown that spirals
anchor at the origin, but when (such as in a planar
reaction-diffusion-advection system), spirals generically anchor away from the
origin.Comment: Revised versio
Untersuchungen der gasdynamischen Reaktion des Kohlenfloezes
Translated from Russian. Published in Bezop. Tr. Prom-sti. (1982) v. 51(4) p. 47-49Available from Steinkohlenbergbauverein, Essen (Germany, F.R.) (St 6919) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman
Wave competition in excitable modulated media.
The propagation of an initially planar front is studied within the framework of the photosensitive Belousov-Zhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steady-state velocity are experimentally validated
Education as a factor of social differentiation and mobility: (A roundtable)
[No abstract available