Evidence for directed percolation universality at the onset of spatiotemporal intermittency in coupled circle maps

We consider a lattice of coupled circle maps, a model arising naturally in descriptions of solid state phenomena such as Josephson junction arrays. We find that the onset of spatiotemporal intermittency (STI) in this system is analogous to directed percolation (DP), with the transition being to an unique absorbing state for low nonlinearities, and to weakly chaotic absorbing states for high nonlinearities. We find that the complete set of static exponents and spreading exponents at all critical points match those of DP very convincingly. Further, hyperscaling relations are fulfilled, leading to independent controls and consistency checks of the values of all the critical exponents. These results lend strong support to the conjecture that the onset of STI in deterministic models belongs to the DP universality class.Comment: Submitted to Physical Review

Breakdown of universality in transitions to spatiotemporal chaos

We show that the transition from laminar to active behavior in extended chaotic systems can vary from a continuous transition in the universality class of directed percolation with infinitely many absorbing states to what appears as a first-order transition. The latter occurs when finite lifetime nonchaotic structures, called "solitons," dominate the dynamics. We illustrate this scenario in an extension of the deterministic Chaté-Manneville coupled map lattice model and in a soliton including variant of the stochastic Domany-Kinzel cellular automaton

Typologie et gestion des boisements spontanes : analyse du foncier et des usages en vue de comprendre les blocages. Application a la partie sud de la Chaine des Puys

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : GR 1696 (1); GR 1696 (2) / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Surface instabilities of ferrofluids

We report on recent progress in understanding the formation of surface protuberances on a planar layer of ferrofluid in a magnetic field oriented normally to the surface. This normal field or Rosensweig instability can be tackled by a linear and a nonlinear description. In the linear regime of small amplitudes we focus on the wave number of maximal growth, its corresponding growth rate and the oscillatory decay of metastable pattern, accessible via a pulse technique. A quantitative comparison of measurements with predictions of the linear stability analysis is performed, whereby the viscosity and the finite depth of the liquid layer are taken into account. In the nonlinear regime the fully developed peak pattern can be predicted by a minimization of the free energy and by numerics employing the finite element method. For a comparison with the results of both methods, the three-dimensional surface profile is recorded by a radioscopic measurement technique. In the bistable regime of the flat and patterned state we generate localized states (ferrosolitons) which are recovered in analytical and numerical model descriptions. For higher fields an inverse hysteretic transition from hexagonal to square planforms is measured. % Via a horizontal field component the symmetry can be broken in the experiment, resulting in liquid ridges and distorted hexagons, as predicted by theory. Replacing ferrofluid by ferrogel also an elastic energy contribution has to be taken into account for a proper model description, yielding a linear shift of the threshold and an increased bistability range. Parametric excitation in combination with magnetic fields is widening the horizon of pattern formation even further. For the mono-spike oscillator harmonic and subharmonic response as well as deterministic chaos is observed and modeled. In a ring of spikes the formation of domains of different wavelengths and spatio-temporal intermittency is quantitatively studied. For an extended layer of ferrofluid we predict that a stabilizing horizontal field counteracted by vertical vibrations will result in oblique rolls with preselected orientation