Resonances in chaotic dynamics

We present a discussion and some numerical results on the actual possibility of making accessible, by numerical techniques, the complex singularities of the power spectrum (resonances) for a chaotic signal. Hénon's transformation is investigated in detail, showing that the position of the leading resonance in the complex frequency plane determines the kind of mixing rate in the time evolution.     

Digital holographic microscopy characterization of superdirective beam by metamaterial

Digital holographic microscopy (DHM) has been successfully applied for the first time to characterize the radiative out-of-plane emission properties of a superdirective device. Complementarily to near-field microscopy, DHM allows us to reconstruct the beam in the far-field region. The angular dispersion of the light beam radiated from a grating composed of air and anti-air metamaterial has been determined, and the proposed technique has highlighted a collimation degree higher than 0.04°, as already evaluated in a previous work. Further considerations on the retrieved phase map of the beam in the acquisition plane are presented.     

Superprism Behaviour of an Array of Photonic Crystal Waveguides

The behaviour of an array of photonic crystal waveguides is numerically investigated. It is shown that high dispersion may be achieved in the telecommunication window around 1550 nm, with a device whose dimensions are in the order of half a mm².     

Effects of shear stiffness,rotatory and axial inertia,and interface stiffness on free vibrations of a two-layer beam

The linear dynamics of a two-layer beam is considered. Each beam is modelled by the Timoshenko kinematics, and all inertia terms are considered. The interface allows normal and tangential detachments, which are linearly proportional to the transmitted stresses. The eigenvalue problem providing the natural frequencies is solved exactly.An extensive study of the natural frequencies and of the normal modes is performed with the aim of understanding how the mechanical parameters of the composite influence the vibration behaviour.The study of the convergence of the solution toward that of a simplified problem obtained by neglecting axial and rotational inertia, shear deformations and by considering interface perfect adherence in the normal direction, constitutes the second objective of the work. This permits to consciously assess when these mechanical terms can actually be neglected, contrarily to what is usually done in practice, where they are disregarded ‘a priori’, without adequate care.     

Large Deviation Techniques Applied to Systems with Long-Range Interactions

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by R.S. Ellis, Physica D 133:106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibrium effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the α-Ising model in one-dimension with 0 ⩽ α < 1.     

The Suzuki homocoupling reaction under high-intensity ultrasound

The Pd-catalysed Suzuki homocoupling of boronic acids was successfully carried out in water under high-intensity ultrasound (HIU). Heterogeneous catalysis with Pd/C, facilitating work up and purification, could be used without adding phosphine ligands. Reaction rates and yields were strongly influenced by the oxidant employed; excellent results were obtained using either molecular oxygen or 3-bromo-4-hydroxycoumarin. 3-Arylation of the latter with the Suzuki procedure had failed, exclusively affording the homocoupling products, symmetric biaryls. Besides offering a number of operational advantages, the use of HIU broadens the field of application for the Suzuki reaction.     

Invariant surfaces of a three-dimensional manifold with constant Gauss curvature

We give a reduction procedure to determine (locally) the surfaces with constant Gauss curvature in a three-dimensional manifold which are invariant under the action of a one-parameter subgroup of the isometry group of the ambient space. We apply this procedure to describe the invariant surfaces with constant Gauss curvature in $H^2\times R$ and in $H_3$.     

Polarization splitter based on a square-lattice photonic-crystal fiber

A three-core polarization splitter based on a square-lattice photonic-crystal fiber is presented. The component separates the input field into two orthogonally polarized beams that are coupled to the horizontal and vertical output ports. The splitter has been designed through modal and beam propagation analysis by employing high-performance codes based on the finite-element method. Results obtained for a device length of 20 mm show extinction ratios as low as -23 dB with bandwidths as great as 90 nm.