9 research outputs found
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
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
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