A note on the periodic orbits of a self excited rigid body

The aim of the present paper is to study the periodic orbits of a perturbed self excited rigid body with a fixed point. For studying these periodic orbits we shall use averaging theory of first order.

X-Ray Imaging of SAPO-34 Molecular Sieves at the Nanoscale: Influence of Steaming on the Methanol-to-Hydrocarbons Reaction

The effect of a severe steaming treatment on the physicochemical properties and catalytic performance of H-SAPO-34 molecular sieves during the methanol-to-hydrocarbons (MTH) reaction has been investigated with a combination of scanning transmission X-ray microscopy (STXM), catalytic testing, and bulk characterization techniques, including ammonia temperature programmed desorption and 27Al and 29Si magic angle spinning nuclear magnetic resonance. For this purpose, two samples, namely a calcined and a steamed H-SAPO-34 catalyst powder, have been compared. It has been found that calcined H-SAPO-34 displays a high selectivity towards light olefins, yet shows a poor stability as compared to a zeolite H-ZSM-5 catalyst. Moreover, in situ STXM at the carbon K-edge during the MTH reaction allows construction of nanoscale chemical maps of the hydrocarbon species formed within the H-SAPO-34 aggregates as a function of reaction time and steam post-treatment. It was found that there is an initial preferential formation of coke precursor species within the core of the H-SAPO-34 aggregates. For longer times on stream the formation of the coke precursor species is extended to the outer regions, progressively filling the entire H-SAPO-34 catalyst particle. In contrast, the hydrothermally treated H-SAPO-34 showed similar reaction selectivity, but decreased activity and catalyst stability with respect to its calcined counterpart. These variations in MTH performance are related to a faster and more homogeneous formation of coke precursor species filling up the entire steamed H-SAPO-34 catalyst particle. Finally, the chemical imaging capabilities of the STXM method at the Al and Si K-edge are illustrated by visualizing the silicon islands at the nanoscale before and after steaming H-SAPO-34.

Subwavelength beams with polarization singularities in plasmonic metamaterials

We investigated the diffraction behavior of plasmonic Bessel beams propagating in metal-dielectric stratified materials and wire media. Our results reveal various regimes in which polarization singularities are selectively maintained. This polarization-pass effect can be controlled by appropriately setting the filling factor of the metallic inclusions and its internal periodic distribution. These results may have implications in the development of devices at the nanoscale level for manipulation of polarization and angular momentum of cylindrical vector beams.

Efficient split eld FDTD analysis of third-order nonlinear materials in two-dimensionally periodic media

In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.