Complete band gaps including non-local effects occur only in the relaxed micromorphic model

In this paper we substantiate the claim implicitly made in previous works that the relaxed micromorphic model is the only linear, isotropic, reversibly elastic, nonlocal generalized continuum model able to describe complete band-gaps on a phenomenological level. To this end, we recapitulate the response of the standard Mindlin-Eringen micromorphic model with the full micro-distortion gradient of P, the relaxed micromorphic model depending only on the Curl P of the micro-distortion P, and a variant of the standard micromorphic model in which the curvature depends only on the divergence Div P of the micro distortion. The Div-model has size-effects but the dispersion analysis for plane waves shows the incapability of that model to even produce a partial band gap. Combining the curvature to depend quadratically on Div P and Curl P shows that such a model is similar to the standard Mindlin-Eringen model which can eventually show only a partial band gap

Homogenization of corrugated interfaces in electromagnetics

A surface with periodic corrugations of suffciently small periodicity is shown to be electromagnetically equivalent to an inhomogeneous transition region (slab). Explicit expressions for the inhomogeneous transition region are found for one-dimensional corrugations and for two-dimensional corrugations a local elliptic problem has to be solved in order to find the equivalent electromagnetic properties. The homogenized surface can be characterized by its surface impedance dyadic or its reflection dyadic. A few numerical examples illustrate the theory

On chemiluminescent emission from an infiltrated chiral sculptured thin film

The theory describing the far-field emission from a dipole source embedded inside a chiral sculptured thin film (CSTF), based on a spectral Green function formalism, was further developed to allow for infiltration of the void regions of the CSTF by a fluid. In doing so, the extended Bruggeman homogenization formalism--which accommodates constituent particles that are small compared to wavelength but not vanishingly small--was used to estimate the relative permittivity parameters of the infiltrated CSTF. For a numerical example, we found that left circularly polarized (LCP) light was preferentially emitted through one face of the CSTF while right circularly polarized (RCP) light was preferentially emitted through the opposite face, at wavelengths within the Bragg regime. The centre wavelength for the preferential emission of LCP/RCP light was red shifted as the refractive index of the infiltrating fluid increased from unity, and this red shift was accentuated when the size of the constituent particles in our homogenization model was increased. Also, the bandwidth of the preferential LCP/RCP emission regime decreased as the refractive index of the infiltrating fluid increased from unity

Wave propagation in relaxed micromorphic continua: modelling metamaterials with frequency band-gaps

In this paper the relaxed micromorphic model proposed in [Patrizio Neff, Ionel-Dumitrel Ghiba, Angela Madeo, Luca Placidi, Giuseppe Rosi. A unifying perspective: the relaxed linear micromorphic continuum, submitted, 2013, arXiv:1308.3219; and Ionel-Dumitrel Ghiba, Patrizio Neff, Angela Madeo, Luca Placidi, Giuseppe Rosi. The relaxed linear micromorphic continuum: existence, uniqueness and continuous dependence in dynamics, submitted, 2013, arXiv:1308.3762] has been used to study wave propagation in unbounded continua with microstructure. By studying dispersion relations for the considered relaxed medium, we are able to disclose precise frequency ranges (band-gaps) for which propagation of waves cannot occur. These dispersion relations are strongly nonlinear so giving rise to a macroscopic dispersive behavior of the considered medium. We prove that the presence of band-gaps is related to a unique elastic coefficient, the so-called Cosserat couple modulus $\mu_{c}$, which is also responsible for the loss of symmetry of the Cauchy force stress tensor. This parameter can be seen as the trigger of a bifurcation phenomenon since the fact of slightly changing its value around a given threshold drastically changes the observed response of the material with respect to wave propagation. We finally show that band-gaps cannot be accounted for by classical micromorphic models as well as by Cosserat and second gradient ones. The potential fields of application of the proposed relaxed model are manifold, above all for what concerns the conception of new engineering materials to be used for vibration control and stealth technology

Two-layer model of wind-driven circulation in the Antarctic Ocean

In this study, we investigate the wind-driven circulation in the Antarctic Ocean using a primitive two-layer model with realistic topography. A prominent feature of steady circulation driven by the annual mean wind stress is a clockwise(cyclonic) circulation in the lower layer at the Weddell Basin and the Australia Antarctic Basin. In particular, the circulation pattern in the Australia Antarctic Basin agrees with the observations. In these basins, negative vorticity input from the wind stress is transmitted to the lower layer through the diffusion term(Gent and McWilliams term) and causes prominent cyclonic gyres within closed geostrophic contours of f/H(f: Coriolis parameter, H: water depth). The model result forced by the seasonal wind stress shows that variations of the Antarctic Coastal Current are explained by wind stress variations along the coast. The transport of this current is determined by the integration of onshore Ekman transport along the coast. It is also shown that this Antarctic Coastal Current can be a part of the western boundary current in the Weddell Sea. On a time scale of 10 to 100 days, the variation of the upper layer thickness coincides with the sea level variation at Syowa Station. This variation might be attributed to coastal trapped waves driven by the alongshore wind stress