Biharmonic Split Ring Resonator Metamaterial: Artificially dispersive effective density in thin periodically perforated plates

We present in this paper a theoretical and numerical analysis of bending waves localized on the boundary of a platonic crystal whose building blocks are split ring resonators (SRR). We first derive the homogenized parameters of the structured plate using a three-scale asymptotic expansion in the linearized biharmonic equation. In the limit when the wavelength of the bending wave is much larger than the typical heterogeneity size of the platonic crystal, we show that it behaves as an artificial plate with an anisotropic effective Young modulus and a dispersive effective mass density. We then analyze dispersion diagrams associated with bending waves propagating within an infinite array of SRR, for which eigen-solutions are sought in the form of Floquet-Bloch waves. We finally demonstrate that this structure displays the hallmarks of All-Angle-Negative-Refraction(AANR) and it leads to superlensing and ultrarefraction effects, interpreted thanks to our homogenization model as a consequence of negative and vanishing effective density, respectively.Comment: 17 pages, 6 figure

Finite elements modelling of scattering problems for flexural waves in thin plates: Application to elliptic invisibility cloaks, rotators and the mirage effect

We propose a finite elements algorithm to solve a fourth order partial differential equation governing the propagation of time-harmonic bending waves in thin elastic plates. Specially designed perfectly matched layers are implemented to deal with the infinite extent of the plates. These are deduced from a geometric transform in the biharmonic equation. To numerically illustrate the power of elastodynamic transformations, we analyse the elastic response of an elliptic invisibility cloak surrounding a clamped obstacle in the presence of a cylindrical excitation i.e. a concentrated point force. Elliptic cloaking for flexural waves involves a density and an orthotropic Young's modulus which depend on the radial and azimuthal positions, as deduced from a coordinates transformation for circular cloaks in the spirit of Pendry et al. [Science {\bf 312}, 1780 (2006)], but with a further stretch of a coordinate axis. We find that a wave radiated by a concentrated point force located a couple of wavelengths away from the cloak is almost unperturbed in magnitude and in phase. However, when the point force lies within the coating, it seems to radiate from a shifted location. Finally, we emphasize the versatility of transformation elastodynamics with the design of an elliptic cloak which rotates the polarization of a flexural wave within its core.Comment: 14 pages, 5 figure

Numerical Analysis of Three-dimensional Acoustic Cloaks and Carpets

We start by a review of the chronology of mathematical results on the Dirichlet-to-Neumann map which paved the way towards the physics of transformational acoustics. We then rederive the expression for the (anisotropic) density and bulk modulus appearing in the pressure wave equation written in the transformed coordinates. A spherical acoustic cloak consisting of an alternation of homogeneous isotropic concentric layers is further proposed based on the effective medium theory. This cloak is characterised by a low reflection and good efficiency over a large bandwidth for both near and far fields, which approximates the ideal cloak with a inhomogeneous and anisotropic distribution of material parameters. The latter suffers from singular material parameters on its inner surface. This singularity depends upon the sharpness of corners, if the cloak has an irregular boundary, e.g. a polyhedron cloak becomes more and more singular when the number of vertices increases if it is star shaped. We thus analyse the acoustic response of a non-singular spherical cloak designed by blowing up a small ball instead of a point, as proposed in [Kohn, Shen, Vogelius, Weinstein, Inverse Problems 24, 015016, 2008]. The multilayered approximation of this cloak requires less extreme densities (especially for the lowest bound). Finally, we investigate another type of non-singular cloaks, known as invisibility carpets [Li and Pendry, Phys. Rev. Lett. 101, 203901, 2008], which mimic the reflection by a flat ground.Comment: Latex, 21 pages, 7 Figures, last version submitted to Wave Motion. OCIS Codes: (000.3860) Mathematical methods in physics; (260.2110) Electromagnetic theory; (160.3918) Metamaterials; (160.1190) Anisotropic optical materials; (350.7420) Waves; (230.1040) Acousto-optical devices; (160.1050) Acousto-optical materials; (290.5839) Scattering,invisibility; (230.3205) Invisibility cloak

Scattering cancellation of the magnetic dipole field from macroscopic spheres

Based on the scattering cancellation technique we suggest a cloak that allows to conceal macroscopic objects, i.e. objects with an optical size comparable to wavelengths in the visible and whose scattering response is dominated by a magnetic dipole contribution. The key idea in our approach is to use a shell of polaritonic spheres around the object to be cloaked. These spheres exhibit an artificial magnetism. In a systematic investigation, where we progressively increase the complexity of the considered structure, we devise the requirements imposed on the shell and outline how it can be implemented with natural available materials

Resistance to ondansetron: Role of pharmacogenetics in post-operative nausea and vomiting

Post-operative nausea and vomiting is the most annoying and at the same time a dangerous side effect of general anaesthesia. Ondansetron is a routinely used anti emetic drug which is being administered by the trial and error principle. Though it did revolutionized the management of this condition but by and large failed to completely eliminate the problem. Recently an important factor possibly elucidating this failure is said to be the differing expression of genes controlling proteins that are involved in transport and receptors related to this drug. Quite surprisingly these transporter and receptor pathways have been found to be polymorphic and at the same time shown to be related to efficacy of the drug. The differentiation between those responding to treatment and those not responding may pave a way to individualize treatment for emesis to a greater extent. This review highlights the pharmacogenetics related to this commonly used anti-emetic drug in anaesthesia. It is visualized as a promising way to achieve the target of individualized therapy. It seems obvious that pharmacogenetics will become an important field of anaesthesia research in the future.Keywords: 5-Hydroxytryptamine type 3 receptor antagonists; Ondansetron; Post-operative nausea and vomiting; Polymorphism; Pharmacogenetic

BDDC and FETI-DP under Minimalist Assumptions

The FETI-DP, BDDC and P-FETI-DP preconditioners are derived in a particulary simple abstract form. It is shown that their properties can be obtained from only on a very small set of algebraic assumptions. The presentation is purely algebraic and it does not use any particular definition of method components, such as substructures and coarse degrees of freedom. It is then shown that P-FETI-DP and BDDC are in fact the same. The FETI-DP and the BDDC preconditioned operators are of the same algebraic form, and the standard condition number bound carries over to arbitrary abstract operators of this form. The equality of eigenvalues of BDDC and FETI-DP also holds in the minimalist abstract setting. The abstract framework is explained on a standard substructuring example.Comment: 11 pages, 1 figure, also available at http://www-math.cudenver.edu/ccm/reports

A noble approach of ACO algorithm for WSN

In energy compelled wireless sensor networks (WSNs), the means by which to perform effectual routing is among the main focuses. A noble approach of ant colony optimization (ACO) algorithm for discovering the optimum route in the WSNs for data transmission is proposed here for enhancement and optimization considering the issue of path selection to reach the nodes. Using the proposed ACO algorithm and considering both the node mobility and the existing energy of the nodes, an optimum route and best cost from the originating node to the target node can be detected. The proposed algorithm has been simulated and verified utilizing MATLAB and the simulation results demonstrate that new ant colony optimization based algorithm can achieve better performance and faster convergence to determine the best cost route

Energy-efficient scalable routing protocol based on ACO for WSNS

Efficient routing is an essential requirement for the design of wireless sensor network (WSN) protocols to overcome inherent challenges and to meet hardware and resource constraints. An energy-efficient scalable routing algorithm based on ant colony optimization (ACO) for WSNs is presented here to find the optimal path of data transmission while consuming less energy leading to increase of network’s lifetime. Most of the existing ACO based routing algorithms are designed on the assumption that the sensor nodes and the sinks are stationary and do not consider the overhead of mobility and the current node energy is not considered, which will prompt sudden passing of certain nodes. To overcome the existing problem of accommodating node mobility, reducing initialization time for ant based routing algorithm and to maintain scalability in WSN for time critical applications, an ACO based WSN routing algorithm has been proposed and analyzed in this paper. The proposed algorithm has been simulated and verified utilizing MATLAB. The evaluation results demonstrate that it has reduced energy consumption, almost 50% less consumed energy even with the increasing number of nodes, compared with the traditional ACO and an existing ant-based routing algorithm. Moreover, it increases the nodes’ lifetime and lifetime of the network