Front reversals, wave traps, and twisted spirals in periodically forced oscillatory media

A new kind of nonlinear nonequilibrium patterns —twisted spiral waves—is predicted for periodically forced oscillatory reaction-diffusion media. We show, furthermore, that, in such media, spatial regions with modified local properties may act as traps where propagating waves can be stored and released in a controlled way. Underlying both phenomena is the effect of the wavelength-dependent propagation reversal of traveling phase fronts, always possible when homogeneous oscillations are modulationally stable without forcing. The analysis is performed using as a model the complex Ginzburg-Landau equation, applicable for reaction-diffusion systems in the vicinity of a supercritical Hopf bifurcation

On the back-firing instability

The onset of the back-firing instability is studied in a one-dimensional spatially extended and dissipative system, where propagating localized solutions become unstable. It corresponds to the emission in the tail of a solitary wave of a new wave propagating in the opposite direction. We describe in geometrical term the transition, using a normal form equation as example. We relate the instability scenario to a mechanism of spatio-temporal chaos

Self-generated nonlinear oscillations in multilayer semiconductor heterostructures

Nonlinear charge transport parallel to the layers of modulation-doped GaAs/AlxGa1-xAs heterostructures is studied theoretically and experimentally. In the field regime of about 2 kV cm-1 we find DC-induced current oscillations associated with N-shaped negative differential resistance. We develop a dynamic model based on real space transfer of hot electrons from the undoped high-mobility GaAs layers to the adjacent n-doped low-mobility AlxGa1-xAs layers. In particular, we extend previous models to multilayer structures and investigate the dependence of the self-generated oscillations upon circuit conditions and the lattice temperature in the range TL=77-200 K. In the light of the experimental results the theoretical predictions are analysed and discussed

Formation and control of Turing patterns and phase fronts in photonics and chemistry

We review the main mechanisms for the formation of regular spatial structures (Turing patterns) and phase fronts in photonics and chemistry driven by either diffraction or diffusion. We first demonstrate that the so-called 'off-resonance' mechanism leading to regular patterns in photonics is a Turing instability. We then show that negative feedback techniques for the control of photonic patterns based on Fourier transforms can be extended and applied to chemical experiments. The dynamics of phase fronts leading to locked lines and spots are also presented to outline analogies and differences in the study of complex systems in these two scientific disciplines