Rafael Rangel

Dynamics and chaos of a current driven two-dimensional Josephson junctions array under 13Φ0 magnetic field

We derive the equations of motion for a two-dimensional capacitive Josephson junctions array in the presence of both a DC current and a magnetic field f=13 of the quantum flux Φ0 . The ground state symmetry of an N×N array is assumed to hold for all currents, then by using the resistively and capacitively shunted junction equations, a model system of four-coupled non-linear second-order differential equations is derived. The system has the form βcx″+x′+∇U=0, where U is a four-dimensional potential and βc is the Stewart–McCumber parameter. The dynamics can be viewed as the motion of a massive particle sliding under the action of the potential in a four-dimensional configuration space with a friction proportional to its speed. There are three distinct branches: one below the critical current Ic where the static zero voltage solution is stable; the second branch which originates from the static solution through a Hopf bifurcation and where a total voltage develops along the direction of the applied current and across the array (instantaneous Hall voltage), (the latter means vortices moving perpendicular to the current and constitutes a flux-flow like regime); and a third branch above the synchronization current Is, where the motion of the junctions synchronizes and the motion of the vortices ceases with zero Hall voltage. For a wide range of βc, the second branch shows chaotic dynamics of extremely rich complexity. A pervasive feature is the presence of antimonotonicity, i.e., reversals of period doubling cascades.

Roughening transition in a thermal sine-Gordon system

Abstract We relate the appearance of noise induced solitons in a sine-Gordon system with the roughening exponent, defined as the scaling exponent of the length of the ensemble average of the standard deviation of the height of the spatiotemporal profile. We find that before the onset of the noise-induced transition to the solitonic regime, the roughening exponent is zero as would correspond for a white noise signal. After the activation of solitons this exponent exhibits a crossover from ∼0.70 to ∼0.50. We point out the connection of our results to models for surface growth and random deposition, particularly, the stochastic Kardar-Parisi-Zhang model.

Cooperative effects due to interpore surface tension in unstable displacement in porous media

Abstract We model fluid-fluid displacement in d = 2 by a diffusion limited aggregation (DLA) algorithm which takes interpore surface tension and capillary forces into account. The invading fluid is non-viscous. Cooperative effects are important when the ratio between capillary forces and tension forces q is ≅ 1. In that case we introduce a simple rule that considers the wetting displacement (invading fluid wets more) and the non wetting case (displaced fluid wets more). We find qualitative agreement with the experiments of Stokes et. al. (Phys.Rev. Lett. 57, 1718 (1986)). Furthermore, we study the tree trunk thickness of the patterns generated as a function of the control parameter r ∞ Ca−1, (Ca = the capillary number) and study the geometry of the interface. We compare the results with the experiments.

Noise-Induced Organization in a sine-Gordon chain

Abstract The appearance of thermally activated solitons in a sine-Gordon system is related to the roughening exponent ζ, defined as the scaling exponent of the length of the ensemble average of the standard deviation of the height of the spatiotemporal profile. Before the onset of the noise-induced transition to the solitonic regime, the roughening exponent is zero as it is for a white noise signal. After the activation of solitons, there is a very interesting crossover from non-KPZ behavior (ζ ∼ 0.70) to KPZ behavior (ζ ∼ 0.50); additionally, for sufficiently large scales, a crossover to a zero roughening exponent takes place. In this paper we precise the underlying dynamics of the different regimes that appear at different scales via geometric characterization as the size of the system and the friction coefficient are varied.