Transition to spatiotemporal chaos in the fronts dynamics of a subcritical state

The evolution of the isolated domains of a bifurcated structure in a subcritical state is experimentally studied along the hysteresis branch, up to the critical point at which a chaotic regime is found to develop. The width of the domains is unstable and the fronts dynamics exhibit a cascade of bifurcations as the constraint increases. The chaotic regime is initiated by a splitting of the isolated domains, controlled by a width-selection mechanism. Most of these results are qualitatively reproduced in a fifth-order Ginzburg-Landau model.     

Entrainment of a spatially extended nonlinear structure under selective forcing

The response of a nonlinear state to a variable forcing periodic in space is studied in an extended dynamical system consisting of a liquid crystal layer driven to convection. Both the statics and the dynamics of the entrainment and the locking effects are analyzed. The dynamics of the evolution are controlled by topological singularities that allow a diffusion of the phase. The mechanisms involved are related to the role of the defects in systems undergoing spontaneous symmetry breakings.     

Application of weigert effect to the pseudocoloration of a black and white signal

We propose here a method to transform the grey levels of a black and white transparency into different colours. The transparency to be processed, illuminated by a beam of linearly polarized white light, is twice recorded on a photograph silver-chloride emulsion. The direction of the light vector is rotated through π/2 between the exposures. The resulting plate is characterized by a spatially varying anisotropy. The main point is that the wavelength λ_B and λ_D, respectively corresponding to the cancellation of birefringence and dichroism, are function of the irradiance of the signal and of the successive exposure times. The plate is then illuminated in white light and observed between two polarizers P and A. It reconstructs an achromatic image of T when the respective axes of P and A are mutually perpendicular. A rotation of A from its setting crossed with P generate a colour distribution on the plate.     

A discrete carleson theorem along the primes with a restricted supremum

Mathematische Zeitschrift - Consider the discrete maximal function acting on finitely supported functions on the integers, $$\begin{aligned} \mathcal {C}_\Lambda f(n) := \sup _{\lambda \in \Lambda...     

Anisotropy induced in a silver chloride emulsion by two successive beams of white light perpendicularly polarized

This paper is a study of the anisotropy induced in a silver chloride photographic emulsion by two successive beams of white light, linearly polarized at right angle. After the first exposure, the colloidal medium contains silver ellipsoids e generated by the photolysis of silver chloride and silver ellipsoids e_b resulting of the partial destruction of some of the previous ones by long wavelengths. This medium is then illuminated by the second beam linearly polarized at right angle of the first beam. Short wavelengths induced silver ellipsoids e′ identical to the ellopsoids e but rotated through π/2 with respect to them. As in the first exposure, some of them are partly broken up and transformed into ellipsoids e′_b identical to ellipsoids e_b but the direction of their major axis. Moreover, the long wavelengths of second exposure transform some of the particles e and e_b generated during the first exposure, into smaller ellipsoids e_eb and e_bb. Finally, the colloidal medium resulting of these two exposures, contains silver chloride and six sorts of silver particles. By calculating the indices of the medium, we show that the wavelengths characterizing the zero birefringence and zero dichroism of the emulsion are dependent on the energies recorded during each of the exposures.