Extremal maps of the universal hyperbolic solenoid

We show that the set of points in the Teichmuller space of the universal hyperbolic solenoid which do not have a Teichmuller extremal representative is generic (that is, its complement is the set of the first kind in the sense of Baire). This is in sharp contrast with the Teichmuller space of a Riemann surface where at least an open, dense subset has Teichmuller extremal representatives. In addition, we provide a sufficient criteria for the existence of Teichmuller extremal representatives in the given homotopy class. These results indicate that there is an interesting theory of extremal (and uniquely extremal) quasiconformal mappings on hyperbolic solenoids.Comment: LaTeX, 15 page

Lie groupoids and algebroids applied to the study of uniformity and homogeneity of material bodies

A Lie groupoid, called \textit{material Lie groupoid}, is associated in a natural way to any elastic material. The corresponding Lie algebroid, called \textit{material algebroid}, is used to characterize the uniformity and the homogeneity properties of the material. The relation to previous results in terms of $G-$structures is discussed in detail. An illustrative example is presented as an application of the theory

Leaky-Wave antennas with arbitrary radiation based on bianisotropic Huygens’ metasurfaces

In this contribution, we present the application of Huygens’ metasurfaces (HMS) to the arbitrary design of leaky-wave antennas (LWAs). These metasurfaces have demonstrated their capabiity to tailor the electromagnetic waves at will. We use them to design LWAs consisting on a parallel-plate waveguide in which the top cover is replaced by a HMS, which implements the desired field transformation. By introducing bianisotropy of the omega type into the metasurface, we have the required degrees of freedom to achieve arbitrary control of the LWA radiation parameters: leakage factor and pointing angle (phase constant). The theoretical derivation of the concept and the design methodology will be described. Moreover, the flexibility in the design will be highlighted with results of two examples of broadside radiation with different directivities.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 706334

Application of Huygens’ Metasurfaces to the Arbitrary Design of a Leaky-Wave Antenna

Leaky-wave antennas are guiding structures that leak power along their length. Their radiation is mainly characterized by the propagation constant (leakage factor and phase constant) of the traveling wave. In this contribution, a leakywave antenna based on parallel-plate waveguide is proposed. Arbitrary control of the leakage factor and the phase constant is achieved by replacing the top plate by an omega-type bianisotropic Huygens’ metasurface, which implements the desired field transformation. The theoretical derivation and design methodology are briefly described. Several designs with different pointing angles (phase constants) and leakage rates have been carried out. Electromagnetic simulation results validate the theoretical derivation, highlight the capabilities of the structure and confirm the flexibility in the design parameters.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech