Abstract:
Research into properties of heterogeneous artificial materials, consisting of arrangements of rigid scatterers embedded in a medium with different elastic properties, has been intense throughout last two decades. The capability to prevent the transmission of waves in predetermined bands of frequencies -called bandgaps- becomes one of the most interesting properties of these systems, and leads to the possibility of designing devices to control wave propagation. The underlying physical mechanism is destructive Bragg interference. Here we show a technique that enables the creation of a wide bandgap in these materials, based on fractal geometries. We have focused our work in the acoustic case where these materials are called Phononic/Sonic Crystals (SC) but, the technique could be applied any types of crystals and wave types in ranges of frequencies where the physics of the process is linear.

Abstract:
We analyze a $t_{2g}$ double-exchange system where the orbital directionality of the itinerant degrees of freedom is a key dynamical feature that self-adjusts in response to doping and leads to a phase diagram dominated by two classes of ground-states with zigzag and checkerboard patterns. The prevalence of distinct orderings is tied to the formation of orbital molecules that in one-dimensional paths make insulating zigzag states kinetically more favorable than metallic stripes, thus allowing for a novel doping-induced metal-to-insulator transition. We find that the basic mechanism that controls the magnetic competition is the breaking of orbital directionality through structural distortions and highlight the consequences of the interorbital Coulomb interaction.

Abstract:
We study the low frequency wave propagation behavior of sandwich beams containing periodically embedded internal resonators. A closed form expression for the propagation constant is obtained using a phased array approach and verified using finite element simulations. We show that local resonance and Bragg bandgaps coexist in such a system and that the width of both bandgaps is a function of resonator parameters as well as their periodicity. The interaction between the two bandgaps is studied by varying the local resonance frequency. We find that a single combined bandgap does not exist for this system and that the Bragg bandgaps transition into sub-wavelength bandgaps when the local resonance frequency is above their associated classical Bragg frequency.

Abstract:
Metamaterials are artificial structures that can be designed to exhibit specific electromagnetic properties that are not in the nature. In this paper, we design a directional coupler, based on the theory of the split-ring resonators (SRRs), and the complementary SRR (CSRRs). The experiments and simulations of the directional coupler are based on the theory of the square structure (and not based on the circular structure) of the SRR and CSRR. The advantage of this circuit is that the area of the coupling is great as regards to the coupler based on the circular structure. The results of simulation and measurement with the miniature structures show the backward-wave phenomenon of the left-handed (LH) material.

Abstract:
We present an extended study of finite-width zigzag graphene ribbons (ZGRs) based on a tight-binding model with hard-wall boundary conditions. We provide an exact analytic solution that clarifies the origin of the predicted width dependence on the conductance through junctions of ribbons with different widths. An analysis of the obtained solutions suggests a new description of ZGRs in terms of coupled chains. We pursue these ideas further by introducing a mapping between the ZGR model and the Hamiltonian for N-coupled quantum chains as described in terms of 2N Majorana fermions. The proposed mapping preserves the dependence of ribbon properties on its width thus rendering metallic ribbons for N odd and zero-gap semiconductor ribbons for N even. Furthermore, it reveals a close connection between the low-energy properties of the ZGR model and a continuous family of square lattice model Hamiltonians with similar width-dependent properties that includes the $\pi-$flux and the trivial square lattice models. As a further extension, we show that this new description makes it possible to identify various aspects of the physics of graphene ribbons with those predicted by models of quantum spin chains (QSCs).

Abstract:
Throughput scaling laws of an ad hoc network equipping directional antennas at each node are analyzed. More specifically, this paper considers a general framework in which the beam width of each node can scale at an arbitrary rate relative to the number of nodes. We introduce an elastic routing protocol, which enables to increase per-hop distance elastically according to the beam width, while maintaining an average signal-to-interference-and-noise ratio at each receiver as a constant. We then identify fundamental operating regimes characterized according to the beam width scaling and analyze throughput scaling laws for each of the regimes. The elastic routing is shown to achieve a much better throughput scaling law than that of the conventional nearest-neighbor multihop for all operating regimes. The gain comes from the fact that more source--destination pairs can be simultaneously activated as the beam width becomes narrower, which eventually leads to a linear throughput scaling law. In addition, our framework is applied to a hybrid network consisting of both wireless ad hoc nodes and infrastructure nodes. As a result, in the hybrid network, we analyze a further improved throughput scaling law and identify the operating regime where the use of directional antennas is beneficial.

Abstract:
Based on the Huygens-Fresnel principle we design a planar lens to efficiently realize the interconversion of the point-like source and Gaussian beam in the air ambience. The lens is constructed by a planar plate drilled elaborately with a nonuniform array of zigzag slits, where the slit exits act as subwavelength-sized secondary sources carrying desired sound responses. The experiments operated at audible regime agree well with the theoretical predictions. This compact device could be useful in daily life applications, such as for medical and detection purposes.

Abstract:
Birefringent magnetophotonic crystals are found to exhibit degeneracy breaking for asymmetric contradirectional coupling in planar waveguides. Fundamental to high-order local normal mode coupling leads to partially overlapping gyrotropic bandgaps inside the Brillouin zone and partial suppression of Bloch mode propagation. A large magneto-optically active reorientation in polarization state is found for allowed Bloch modes at bandgap edges.

Abstract:
The ply elastic constants needed for classical lamination theory analysis of multi-directional laminates may differ from those obtained from unidirectional laminates because of three dimensional effects. In addition, the unidirectional laminates may not be available for testing. In such cases, full-field displacement measurements offer the potential of identifying several material properties simultaneously. For that, it is desirable to create complex displacement fields that are strongly influenced by all the elastic constants. In this work, we explore the potential of using a laminated plate with an open-hole under traction loading to achieve that and identify all four ply elastic constants (E 1, E 2, 12, G 12) at once. However, the accuracy of the identified properties may not be as good as properties measured from individual tests due to the complexity of the experiment, the relative insensitivity of the measured quantities to some of the properties and the various possible sources of uncertainty. It is thus important to quantify the uncertainty (or confidence) with which these properties are identified. Here, Bayesian identification is used for this purpose, because it can readily model all the uncertainties in the analysis and measurements, and because it provides the full coupled probability distribution of the identified material properties. In addition, it offers the potential to combine properties identified based on substantially different experiments. The full-field measurement is obtained by moir\'e interferometry. For computational efficiency the Bayesian approach was applied to a proper orthogonal decomposition (POD) of the displacement fields. The analysis showed that the four orthotropic elastic constants are determined with quite different confidence levels as well as with significant correlation. Comparison with manufacturing specifications showed substantial difference in one constant, and this conclusion agreed with earlier measurement of that constant by a traditional four-point bending test. It is possible that the POD approach did not take full advantage of the copious data provided by the full field measurements, and for that reason that data is provided for others to use (as on line material attached to the article).

Abstract:
The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or layered solids. Various techniques such as Absorbing Boundary Conditions, infinite elements or Absorbing Boundary Layers (e.g. Perfectly Matched Layers) lead to an important reduction of such spurious reflections. In this paper, a simple absorbing layer method is proposed: it is based on a Rayleigh/Caughey damping formulation which is often already available in existing Finite Element softwares. The principle of the Caughey Absorbing Layer Method is first presented (including a rheological interpretation). The efficiency of the method is then shown through 1D Finite Element simulations considering homogeneous and heterogeneous damping in the absorbing layer. 2D models are considered afterwards to assess the efficiency of the absorbing layer method for various wave types and incidences. A comparison with the PML method is first performed for pure P-waves and the method is shown to be reliable in a more complex 2D case involving various wave types and incidences. It may thus be used for various types of problems involving elastic waves (e.g. machine vibrations, seismic waves, etc).