Faraday-Talbot effect: Alternating phase and circular arrays.

A hydrodynamic analog to the optical Talbot effect may be realized on the surface of a vertically shaken fluid bath when a periodic array of pillars protrudes from the fluid surface. When the pillar spacing is twice or one and a half times the Faraday wavelength, we observe repeated images of the pillars projected in front of the array. Sloshing inter-pillar ridges act as sources of Faraday waves, giving rise to self-images. Here, we explore the emergence of Faraday-Talbot patterns when the sloshing ridges between pillars have alternating phases. We present a simple model of linear wave superposition and use it to calculate the expected self-image locations, comparing them to experimental observations. We explore how alternating phase sources affect the Faraday-Talbot patterns for linear and circular arrays of pillars, where curvature allows for magnification and demagnification of the self-imaging pattern. The use of an underlying wavefield is a subject of current interest in hydrodynamic quantum analog experiments, as it may provide a means to trap walking droplets.

Comparison of single neuron models in terms of synchronization propensity.

A plausible model for coherent perception is the synchronization of chaotically distributed neural spike trains over wide cortical areas. A recently introduced propensity criterion provides a tool for a quantitative comparison of different neuron models in terms of their ability to synchronize to an applied perturbation. We explore the propensity of several systems and indicate the requirements to be satisfied by a plausible candidate for modeling neuronal activity. Our results show that the conflicting requirements of stability and sensitivity leading to high propensity to synchronization can be satisfied by a strongly nonuniform attractor made of two distinct regions: a saddle focus plus a sufficiently separated saddle node.

Pattern stabilization through parameter alternation in a nonlinear optical system.

We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are used for both numerical simulations and a weakly nonlinear analysis of the patterned states. The simulations show excellent agreement with the experiment. The nonlinear analysis provides an explanation of the patterning under alternation and accurately predicts both the observed dependence of the patterning on the frequency of alternation and the measured spatial frequencies of the patterns.

Stochastic resonance on two-dimensional arrays of bistable oscillators in a nonlinear optical system.

We describe an experimental realization of stochastic resonance in two-dimensional arrays of coupled nonlinear oscillators. The experiment is implemented using an optoelectronic system composed of a liquid crystal light valve in a feedback loop with external, spatially variable noise being added through a liquid crystal display. The behavior of the system differs from previously studied uniform arrays, showing a high signal-to-noise ratio at the output for a broad range of input noise. We show that this behavior is qualitatively the same as that exhibited by computer models where the nonlinear elements of the array have a distribution of biases applied to their switching thresholds.

Stochastic resonance in two-dimensional arrays of coupled nonlinear oscillators

In this Brief Report we report the results of computer simulations on the periodic and noise driving of two-dimensional square arrays of coupled nonlinear oscillators. We find significant improvement in the output of these arrays over their one-dimensional counterparts (quantified by signal-to-noise ratio in the power spectrum at the frequency of the periodic driving). We also find that, within the limited resolution of our simulations, the one-dimensional scaling laws proposed by Lindner et al. [Phys. Rev. E 53, 2081 (1996)] seem to hold quite well for two-dimensional arrays.