14 research outputs found
Helicoidal instability of a scroll vortex in three-dimensional reaction-diffusion systems
We study the dynamics of scroll vortices in excitable reaction-diffusion
systems analytically and numerically. We demonstrate that intrinsic
three-dimensional instability of a straight scroll leads to the formation of
helicoidal structures. This behavior originates from the competition between
the scroll curvature and unstable core dynamics. We show that the obtained
instability persists even beyond the meander core instability of
two-dimensional spiral wave.Comment: 4 pages, 5 figures, revte
Anomalous relaxation and self-organization in non-equilibrium processes
We study thermal relaxation in ordered arrays of coupled nonlinear elements
with external driving. We find, that our model exhibits dynamic
self-organization manifested in a universal stretched-exponential form of
relaxation. We identify two types of self-organization, cooperative and
anti-cooperative, which lead to fast and slow relaxation, respectively. We give
a qualitative explanation for the behavior of the stretched exponent in
different parameter ranges. We emphasize that this is a system exhibiting
stretched-exponential relaxation without explicit disorder or frustration.Comment: submitted to PR
Universal Scaling of Wave Propagation Failure in Arrays of Coupled Nonlinear Cells
We study the onset of the propagation failure of wave fronts in systems of
coupled cells. We introduce a new method to analyze the scaling of the critical
external field at which fronts cease to propagate, as a function of
intercellular coupling. We find the universal scaling of the field throughout
the range of couplings, and show that the field becomes exponentially small for
large couplings. Our method is generic and applicable to a wide class of
cellular dynamics in chemical, biological, and engineering systems. We confirm
our results by direct numerical simulations.Comment: 4 pages, 3 figures, RevTe
-kinks in strongly ac driven sine-Gordon systems
We demonstrate that -kinks exist in non-parametrically ac driven
sine-Gordon systems if the ac drive is sufficiently fast. It is found that, at
a critical value of the drive amplitude, there are two stable and two unstable
equilibria in the sine-Gordon phase. The pairwise symmetry of these equilibria
implies the existence of a one-parameter family of -kink solutions in the
reduced system. In the dissipative case of the ac driven sine-Gordon systems,
corresponding to Josephson junctions, the velocity is selected by the balance
between the perturbations. The results are derived from a perturbation analysis
and verified by direct numerical simulations.Comment: 4 pages, 2 figures, revte
Tunable Pinning of Burst-Waves in Extended Systems with Discrete Sources
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 pinned if the diffusive coupling is below a critical value. When the
coupling crosses the critical value the system undergoes a depinning
instability via a saddle-node bifurcation, and the wave begins to move. We
obtain the universal scaling for the mean wave velocity just above threshold.Comment: 4 pages, 5 figures, revte
Parametrically forced sine-Gordon equation and domain walls dynamics in ferromagnets
A parametrically forced sine-Gordon equation with a fast periodic {\em
mean-zero} forcing is considered. It is shown that -kinks represent a
class of solitary-wave solutions of the equation. This result is applied to
quasi-one-dimensional ferromagnets with an easy plane anisotropy, in a rapidly
oscillating magnetic field. In this case the -kink solution we have
introduced corresponds to the uniform ``true'' domain wall motion, since the
magnetization directions on opposite sides of the wall are anti-parallel. In
contrast to previous work, no additional anisotropy is required to obtain a
true domain wall. Numerical simulations showed good qualitative agreement with
the theory.Comment: 3 pages, 1 figure, revte
Dynamics of Wetting Fronts in Porous Media
We propose a new phenomenological approach for describing the dynamics of
wetting front propagation in porous media. Unlike traditional models, the
proposed approach is based on dynamic nature of the relation between capillary
pressure and medium saturation. We choose a modified phase-field model of
solidification as a particular case of such dynamic relation. We show that in
the traveling wave regime the results obtained from our approach reproduce
those derived from the standard model of flow in porous media. In more general
case, the proposed approach reveals the dependence of front dynamics upon the
flow regime.Comment: 4 pages, 2 figures, revte
pi-kinks in Strongly AC Driven Sine-Gordon Systems
We demonstrate that ß-kinks can exist in non-parametrically AC driven sineGordon systems if the AC drive is sufficiently fast. It is found that, at a critical value of the drive amplitude, there are two stable and two unstable fixed points in the sine-Gordon phase. The pairwise symmetry of these fixed points implies the existence of a one-parameter family of ß-kink solutions in the reduced system. In the dissipative case the velocity is selected and only one of the kink solutions survives. The results are derived from a perturbation analysis and verified by direct numerical simulations. 1 Introduction Soliton bearing systems are very important for our understanding of collective phenomena in many physical systems in the one dimensional approximation [1]. Often, such systems are perturbed in one form or another and sometimes these perturbations are temporally periodic [2]. If the perturbations are small, one can approximate the dynamics of the system through the adiabatic perturbation ..