Olivier Merlo

Exponential growth of electrochemical double layer capacitance in glassy carbon during thermal oxidation

The evolution of the electrochemical double layer capacitance of glassy carbon during thermochemical gas phase oxidation was studied with electrochemical impedance spectroscopy. Particular attention was paid to the initial oxidation stage, during which the capacitance grows exponentially. This stage could be experimentally assessed by lowering the reaction temperature and oxidant partial pressure. After a specific oxidation time the capacitance growth experiences a cross-over to a logistic growth.

The chaotic set and the cross section for chaotic scattering in three degrees of freedom

This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step towards a more general understanding of chaotic scattering in higher dimensions. Despite the strong restrictions, it breaks the essential simplicity implicit in any two-dimensional time-independent scattering problem. Introducing the third degree of freedom by breaking a continuous symmetry, we first explore the topological structure of the homoclinic/heteroclinic tangle and the structures in the scattering functions. Then we work out the implications of these structures for the doubly differential cross section. The most prominent structures in the cross section are rainbow singularities. They form a fractal pattern that reflects the fractal structure of the chaotic invariant set. This allows us to determine structures in the cross section from the invariant set and, conversely, to obtain information about the topology of the invariant set from the cross section. The latter is a contribution to the inverse scattering problem for chaotic systems.

Self-pulsing effect in chaotic scattering

We study the quantum and classical scattering of Hamiltonian systems whose chaotic saddle is described by binary or ternary horseshoes. We are interested in situations for which a stable island, associated with the inner fundamental periodic orbit of the system exists and is large, but chaos around this island is well developed. Such situations are quite common as they correspond typically to the near-integrable domain in the transition from integrable to chaotic scattering. Both classical and quantum dynamics are analysed and in both cases, the most surprising effect is a periodic response to an incoming wave packet. The period of this self-pulsing effect or scattering echoes coincides with the mean period, by which the scattering trajectories rotate around the stable orbit. This period of rotation is directly related to the development stage of the underlying horseshoe. Therefore the predicted echoes will provide experimental access to topological information. We numerically test these results in kicked one-dimensional models and in open billiards.

Characterization of the new NSLS infrared microspectroscopy beamline U10B

The first of several new infrared beamlines, built on a modified bending magnet port of the NSLS VUV ring, is now operational for mid-infrared microspectroscopy. The port simultaneously delivers 40 mrad by 40 mrad to two separate beamlines and spectrometer endstations designated U10A and U10B. The latter is equipped with a scanning infrared microspectrometer. The combination of this instrument and high brightness synchrotron radiation makes diffraction- limited microspectroscopy practical. This paper describes the beamlines performance and presents quantitative information on the diffraction-limited resolution.

Strands and braids in narrow planetary rings: a scattering system approach

We address the occurrence of narrow planetary rings and some of their structural properties, in particular when the rings are shepherded. We consider the problem as Hamiltonian scattering of a large number of non-interacting massless point particles in an effective potential. Using the existence of stable motion in scattering regions in this set up, we describe a mechanism in phase space for the occurrence of narrow rings and some consequences in their structure. We illustrate our approach with three examples. We find eccentric narrow rings displaying sharp edges, variable width and the appearance of distinct ring components (strands) which are spatially organized and entangled (braids). We discuss the relevance of our approach for narrow planetary rings.

Phase-Space Structure for Narrow Planetary Rings

We address the occurrence of narrow planetary rings under the interaction with shepherds. Our approach is based on a Hamiltonian framework of non–interacting particles where open motion (escape) takes place, and includes the quasi–periodic perturbations of the shepherd’s Kepler motion with small and zero eccentricity. We concentrate in the phase–space structure and establish connections with properties like the eccentricity, sharp edges and narrowness of the ring. Within our scattering approach, the organizing centers necessary for the occurrence of the rings are stable periodic orbits, or more generally, stable tori. In the case of eccentric motion of the shepherd, the rings are narrower and display a gap which defines different components of the ring.

Multiple components in narrow planetary rings.

The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with 2 degrees of freedom, respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed at specific values of a control parameter. Using the stability resonances we show that they, and not the mean-motion resonances, account for the position of these gaps. For more degrees of freedom, exciting these resonances divides the regions of trapped motion. For planetary rings, we demonstrate that this mechanism yields rings with multiple components.

Symmetry properties of periodic orbits extracted from scattering data.

Discrete symmetries of a system are reflected in the properties of the shortest periodic orbits. By applying a recent method to extract these from the scaling of the fractal structure in scattering functions, we show how the symmetries can be extracted from scattering data simultaneously with the periods and the Lyapunov exponents. We pay particular attention to the change of scattering data under a small symmetry breaking.

Symmetry breaking: a tool to unveil the topology of chaotic scattering with three degrees of freedom

We shall use symmetry breaking as a tool to attack the problem of identifying the topology of chaotic scatteruing with more then two degrees of freedom. specifically we discuss the structure of the homoclinic/heteroclinic tangle and the connection between the chaotic invariant set, the scattering functions and the singularities in the cross section for a class of scattering systems with one open and two closed degrees of freedom.