Philippe Richetti

From quasiperiodicity to chaos in the Belousov–Zhabotinskii reaction. I. Experiment

We report on the experimental observation of both a primary and a secondary Hopf bifurcation leading to quasiperiodicity in the Belousov–Zhabotinskii reaction. When taking the BZ system away from these local conditions, we witness the occurrence of chaos which comes with the breaking of the underlying torus into a fractal object. We emphasize that most of the alternating periodic–chaotic sequences studied in the literature are reminiscent of such two‐frequency dynamics. We argue about the controversal existence of deterministic chaos in such sequences. We anticipate the results of a numerical and theoretical investigation of these sequences which discards definitely any stochastic objection to chemical chaos.

From quasiperiodicity to chaos in the Belousov–Zhabotinskii reaction. II. Modeling and theory

We discuss the quasiperiodic behavior experimentally observed in the Belousov–Zhabotinskii reaction as the result of the interaction of two elementary instabilities, namely the Hopf bifurcation at the origin of the oscillating nature of this reaction and the hysteresis bifurcation which accounts for the phenomenom of bistability. We use a normal form approach to understand the evolution of the dynamics when the BZ system is moved away from the local situation where both these instabilities are competing. We first discuss the transition to chaos which comes with the breaking up of the underlying torus into a fractal object. Then we emphasize that nonlocally such a two‐frequency dynamics manifests through alternating periodic–chaotic sequences which look very much like the sequences observed in bench experiments. We propose a seven‐variable Oregonator type model which not only accounts for these sequences but also for those which involve only one fundamental frequency as observed in the 1980 Texas experimen...

Experimental evidence for homoclinic chaos in the Belousov-Zhabotinskii reaction

Abstract Experiments on the Belousov-Zhabotinskii reaction in a continuous flow reactor reveal a spiraling strange attractor which arises from the interaction of a local subcritical Hopf bifurcation with a global homoclinic bifurcation. The proximity of these two bifurcations justifies the application of a theorem by Shilnikov which ensures the existence of chaos. An iteration scheme deduced from the data appears to be consistent (within the experimental resolution) with the symbolic dynamics predicted by the theory.

Hierarchical self-assembly of a bulk metamaterial enables isotropic magnetic permeability at optical frequencies

Raspberry-like magnetic nanoclusters are synthesized and subsequently self-assembled to form a bulk metamaterial exhibiting strong isotropic optical magnetism in visible light. The magnetic response of the nanoclusters (metamolecules) and of the final assembled material are measured by independent optical experiments. The validity of the effective permeability parameter is probed by spectroscopic ellipsometry at variable incidence. Numerical simulations confirm the measurements.

Boundary lubricant films under shear: effect of roughness and adhesion

The normal interaction and the behavior under shear of mica surfaces covered by two different triblock copolymers of polylysine-polydimethysiloxane-polylysine were studied by combining the capabilities of the surface forces apparatus and the atomic force microscopy. At low pH values these copolymers spontaneously adsorb on the negatively charged mica surfaces from aqueous solutions as a consequence of the positive charge of the polylysine moieties. The morphology of the adsorbed layer is determined by the molecular structure of the particular copolymer investigated. This morphology plays a fundamental role on the behavior of the adsorbed layers under shear and compression. While nonadhesive smooth layers oppose an extremely small resistance to sliding, the presence of asperities even at the nanometric scale originates a frictional resistance to the motion. The behavior of uniform nonadhesive nanorough surfaces under shear can be quantitatively understood in terms of a simple multistable thermally activated junction model. The electric charge of the adsorbed copolymer molecules and hence the adhesion energy between the coated surfaces can be modified by varying the pH of the surrounding media. In the presence of an adhesive interaction between the surfaces the behavior under shear is strongly modified. Time-dependent mechanisms of energy dissipation have to be evoked in order to explain the changes observed.

Triblock copolymer lubricant films under shear : Effect of molecular Cross-Linking

The normal interaction and the behavior under shear of mica surfaces covered by a triblock copolymer of poly(L-lysine)-b-polydimethysiloxane-b-poly(L-lysine) (Plys40-b-PDMS40-b-Plys40) before and after cross-linking reaction with two dicarboxylic acids were studied, combining the capabilities of the surface forces apparatus and atomic force microscopy (AFM). At low pH values, this copolymer spontaneously adsorbed on the negatively charged mica surfaces from aqueous solutions as a consequence of the positive charge of the polylysine moieties, forming an extremely smooth boundary layer. This smooth layer displays a very small resistance to shear under small loads, exhibiting outstanding lubrication properties. Nevertheless, the fusion of two contacting layers can be induced by compression at a certain pressure, a process that causes a marked increase in the friction forces. Cross-linking of the adsorbed polymer molecules by covalent bond formation with dicarboxylic acids increases the mechanical stability of the adsorbed layers and hinders the fusion of the boundary layers under pressure but impairs its lubrication properties to a certain extent.

Isotropic Huygens dipoles and multipoles with colloidal particles

Huygens sources are elements that scatter light in the forward direction as used in the Huygens-Fresnel principle. They have remained fictitious until recently when experimental systems have been fabricated. In this Rapid Communication, we propose isotropic meta-atoms that act as Huygens sources. Using clusters of plasmonic or dielectric colloidal particles, Huygens dipoles that resonate at visible frequencies can be achieved with scattering cross sections as high as five times the geometric cross section of the particle surpassing anything achievable with a hypothetical simple spherical particle. Examples are given that predict extremely broadband scattering in the forward direction over a 1000 nm wavelength range at optical frequencies. These systems are important to the fields of nanoantennas, metamaterials, and wave physics in general as well as any application nthat requires local control over the radiation properties of a system as in solar cells or biosensing.

Nonlinear Interactions Between Instabilities Leading to Chaos in the Belousov-Zhabotinsky Reaction

The occurrence of well-odered structures in physical systems submitted to some forcing is a manifestation of an instability which affects one of their normal modes. The dissipative structure which appears results from a nonlinear saturation of this instability. Such a transition presents some analogy with phase — transition phenomena[l]. When the value of the control parameter is close to the critical transition value, the temporal evolution of the amplitude of the mode is governed by an “universal” (normal form) first order equation like that given by Landau for the initial development of instability in fluids[2,3]. In more complicated cases, there will exist, in parameter space, polycritical surfaces on which several modes may simultaneously become marginally unstable [4,5]. In neighborhoods of such surfaces, the dynamics is governed by coupled ordinary differential equations for the amplitude of the nearly marginal modes, which generalize the Landau equation to problems of competing instabilities [6–10]. In such cases the temporal evolution of the system may become increasingly complex, e.g. relaxation oscillations, quasiperiodic and even chaotic behavior [5].