Igor Mitkov

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.

Drift of spiral waves in excitable media

Abstract The motion of a spiral wave in excitable media due to interaction with various kinds of boundaries is considered both in the case of small diffusion of the slow field and for the diffusionless case. The drift of the core and the frequency shift of the spiral due to distant boundaries or inhomogeneities in the media are found to be a superexponentially weak function of the distance from the core. It is shown that for some range of parameters the spiral drifts away from the center of a circular domain. It is also shown that the spiral can form a bound state with a plane boundary as well as with a small topological defect. Numerical simulations are performed demonstrating qualitative agreement with the analytical results.

One- and two-dimensional wave fronts in diffusive systems with discrete sets of nonlinear sources

Abstract We study the dynamics of one-and two-dimensional diffusion systems with sets of discrete nonlinear sources. We show that wave fronts propagating in such systems are pinned if the diffusion constant is below a critical value which corresponds to a saddle-node bifurcation of the dynamics. In two dimensions we find that the dissipation is enhanced and moving plain and circular fronts are stable with respect to any perturbations.

Higher-order effects on Shapiro steps in Josephson junctions

We demonstrate that the well known phase-locking mechanism leading to Shapiro steps in ac-driven Josephson junctions is always accompanied by a higher order phase-locking mechanism similar to that of the parametrically driven pendulum. This effect, resulting in a

Some aspects of head-variance evaluation

\pi

p-Kinks in the parametrically driven sine-Gordon equation and applications

-periodic effective potential for the phase, manifests itself clearly in the parameter regions where the usual Shapiro steps are expected to vanish.

TUNABLE PINNING OF BURST WAVES IN EXTENDED SYSTEMS WITH DISCRETE SOURCES

We compare two methods of evaluating head covariance for two‐dimensional steady‐state flow in mildly heterogeneous bounded rectangular aquifers. The quasi‐analytical approach, widely used in stochastic subsurface hydrology, is based on the Greens function representation, and involves numerical four‐fold integration. We compare this approach with a numerical solution of the two‐dimensional boundary‐value problem for head covariance. We show that the finite differences integration of this problem is computationally less expensive than numerical four‐fold integration of slowly‐convergent infinite series.

Dynamics of wetting fronts in porous media

Abstract Parametrically driven sine-Gordon equation with a mean-zero forcing is considered. It is shown that the system is well approximated by the double sine-Gordon equation using the normal form technique. The reduced equation possesses π-kink solutions, which are also observed numerically in the original system. This result is applied to domain walls dynamics in one-dimensional easy-plane ferromagnets. For such system the existence of π-kinks implies the “true” domain structure in the presence of high-frequency magnetic field.