Dipolar localization of waves in twisted phononic crystal plates

The localization of waves in two-dimensional clusters of scatterers arranged in relatively twisted lattices is studied by multiple scattering theory. It is found that, for a given frequency, it is always possible to nd localized modes for a discrete set of rotation angles, analogous to the so-called \magic angles" recently found in two-dimensional materials like graphene. Similarly, for small rotations of the lattices, a large number of resonant frequencies is found, whose position strongly depends on the rotation angle. Moreover, for angles close to those that make the two lattices commensurable a single mode appears that can be easily tuned by the rotation angle. Unlike other twisted materials, where the properties of the bilayers are mainly explained in terms of the dispersion relation of the individual lattices, the special angles in these clusters happen because of the formation of dipolar scatterers due to the relative rotation between the two lattices, enhancing therefore their interaction. While the presented results are valid for any type of wave, the speci c case of exural waves in thin elastic plates is numerically studied, and the di erent modes found are comprehensively explained in terms of the interaction between pairs of scatterers. The analysis presented here shows that these structures are promising candidates for the inverse design of tunable wave-trapping devices for classical waves

Edge modes for flexural waves in quasi-periodic linear arrays of scatterers

We present a multiple scattering analysis of robust interface states for flexural waves in thin elastic plates. We show that finite clusters of linear arrays of scatterers built on a quasi-periodic arrangement support bounded modes in the two-dimensional space of the plate. The spectrum of these modes plotted against the modulation defining the quasi-periodicity has the shape of a Hofstadter butterfly, which as suggested by previous works might support topologically protected modes. Some interface states appear inside the gaps of the butterfly, which are enhanced when one linear cluster is merged with its mirror reflected version. The robustness of these modes is verified by numerical experiments in which different degrees of disorder are introduced in the scatterers, showing that neither the frequency nor the shape of the modes is altered. Since the modes are at the interface between two one-dimensional arrays of scatterers deposited on a two-dimensional space, these modes are not fully surrounded by bulk gaped materials so that they are more suitable for their excitation by propagating waves. The generality of these results goes beyond flexural waves since similar results are expected for acoustic or electromagnetic waves.D.T. acknowledges financial support from the “Ramón y Cajal” Fellowship under Grant No. RYC-2016-21188 and the Ministry of Science, Innovation and Universities through Project No. RTI2018-093921-A-C42. M.M.-S. acknowledges financial support from the FPU program under Grant No. FPU18/02725

Towards the full control of sound with sonic crystals and acoustic metamaterials

El objetivo de este trabajo ha sido obtener expresiones matemáticas para los parámetros elásticos y acústicos efectivos de sistemas heterogéneos en el límite de homogeneización, lo que ha permitido el diseño de nuevos dispositivos acústicos y elásticos funcionales en un amplio rango de longitudes de onda. Los sistemas heterogéneos estudiados han sido, principalmente, estructuras de cilindros elásticos inmersos en un medio fluido no-viscoso, aunque otras geometrías han sido comentadas. La periodicidad de estas estructuras permite reducir el problema al estudio de la "celda unidad"; es decir, a la región del espacio que se repite. Sin embargo, el método desarrollado en el presente trabajo ha permitido analizar el comportamiento cuando la periodicidad se ve alterada por defectos estructurales. Matemáticamente este problema ha sido tratado mediante la teoría de dispersión múltiple, ya que las geometrías del problema son principalmente circulares y dicha teoría ha demostrado ser la más adecuada en ese caso. Se ha utilizado la citada teoría de dispersión múltiple para analizar el comportamiento de un sólo cilindro y de un conjunto de cilindros. Este conjunto de cilindros ha sido ordenado, por un lado, en filas infinitas, dando lugar a expresiones para la reflectancia y transmitancia. Por otro lado, la extensión a todo el plano de las redes de cilindros ha permitido obtener resultados para la estructura de bandas. Para obtener los parámetros efectivos se han desarrollado dos métodos de homogeneización que, si bien coinciden en resultados para los casos elementales, han demostrado ser complementarios para calcular situaciones más complejas. El primero se basa en la propagación de ondas elásticas a través de medios periódicos. Se ha demostrado que, en el límite de baja frecuencia, la propagación de estas ondas presenta una relación de dispersión lineal, de cuya pendiente se ha podido obtener la velocidad de propagación efectiva del medio uniforme asociado. El segundoTorrent Martí, D. (2008). Towards the full control of sound with sonic crystals and acoustic metamaterials [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/3061Palanci

Bound states in the continuum in circular clusters of scatterers

In this work, we study the localization of flexural waves in highly symmetric clusters of scatterers. It is shown that when the scatterers are placed regularly in the perimeter of a circumference the quality factor of the resonances strongly increases with the number of scatterers in the cluster. It is also found that in the continuous limit, that is to say, when the number of scatterers tends to infinite, the quality factor is infinite so that the modes belong to the class of the so called bound states in the continuum or BICs, and an analytical expression for the resonant frequency is found. These modes have different multipolar symmetries, and we show that for high multipolar orders the modes tend to localize at the border of the circumference, forming therefore a whishpering gallery mode with an extraordinarily high quality factor. Numerical experiments are performed to check the robustness of these modes under different types of disorder and also to study their excitation from the far field. Although we have focused our study to flexural waves, the methodology presented in this work can be applied to other classical waves, like electromagnetic or acoustic waves, being therefore a promissing approach for the design of high quality resonators based on finite clusters of scatterers

Radial Photonic Crystal Shells and Their Application as Resonant and Radiating Elements

Radial photonic crystals (RPCs) are a class of microstructured media that possess very particular electromagnetic features. Their properties are driven by radially dependent permittivity and permeability profiles that are also anisotropic. A two dimensional RPC structure is designed and analyzed in order to assess its principal characteristics. This is done through the study of the dispersion diagram of the periodic multilayered structure and also through the analysis of a finite size device. In the later case, research is performed in view of possible applications of RPCs as resonant devices and also when they are combined with line sources. Finally, a device with reduced complexity is designed and implemented by means of a microstructured resonator array. This device is numerically analyzed and the comparison of two independent models shows very good agreement. Potential use of RPCs as frequency and location sensors is pointed out.Carbonell Olivares, J.; Torrent Martí, D.; Sánchez-Dehesa Moreno-Cid, J. (2013). Radial Photonic Crystal Shells and Their Application as Resonant and Radiating Elements. IEEE Transactions on Antennas and Propagation. 61(2):755-767. doi:10.1109/TAP.2012.2225015S75576761

Analysis of flexural wave cloaks

This work presents a comprehensive study of the cloak for bending waves theoretically proposed by Farhat et al. [see Phys. Rev. Lett. 103, 024301 (2009)] and later on experimentally realized by Stenger et al. [see Phys. Rev. Lett. 108, 014301 (2012)]. This study uses a semi-analytical approach, the multilayer scattering method, which is based in the Kirchoff-Love wave equation for flexural waves in thin plates. Our approach was unable to reproduce the predicted behavior of the theoretically proposed cloak. This disagreement is here explained in terms of the simplified wave equation employed in the cloak design, which employed unusual boundary conditions for the cloaking shell. However, our approach reproduces fairly well the measured displacement maps for the fabricated cloak, indicating the validity of our approach. Also, the cloak quality has been here analyzed using the so called averaged visibility and the scattering cross section. The results obtained from both analysis let us to conclude that there is room for further improvements of this type of flexural wave cloak by using better design procedures. (C) 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).This work has been supported by the Spanish Ministerio de Economia y Competitividad and the European Union Fondo Europeo para el Desarrollo Regional (FEDER) under Grant with Ref. TEC2014-53088-C3-1-R. We gratefully acknowledge Nicolas Stenger for providing us the parameters listed in Table I.Climente Alarcón, A.; Torrent Martí, D.; Sánchez-Dehesa Moreno-Cid, J. (2016). Analysis of flexural wave cloaks. AIP Advances. 6(12):121704-1-121705-16. https://doi.org/10.1063/1.4968611S121704-1121705-1661

Gradient index lenses for flexural waves based on thickness variations

Copyright (2014) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics along with the following message: The following article appeared in Applied Physics Letters 105, (6) and may be found at http://dx.doi.org/10.1063/1.4893153. Authors own version of final article on e-print serversThis work presents a method for the realization of gradient index devices for flexural waves in thin plates. Unlike recent approaches based on phononic crystals, the present approach is based on the thickness-dependence of the dispersion relation of flexural waves, which is used to create gradient index devices by means of local variations of the plate's thickness. Numerical simulations of known circularly symmetrical gradient index lenses have been performed. These simulations have been done using the multilayer multiple scattering method and the results prove their broadband efficiency and omnidirectional properties. Finally, finite element simulations employing the full three-dimensional elasticity equations also support the validity of the designed approach. (c) 2014 AIP Publishing LLC.This work has been supported by the U.S. Office of Naval Research under Grant No. N000140910554.Climente Alarcón, A.; Torrent Martí, D.; Sánchez-Dehesa Moreno-Cid, J. (2014). Gradient index lenses for flexural waves based on thickness variations. Applied Physics Letters. 105(6). https://doi.org/10.1063/1.4893153S1056Norris, A. N., & Vemula, C. (1995). Scattering of flexural waves on thin plates. Journal of Sound and Vibration, 181(1), 115-125. doi:10.1006/jsvi.1995.0129SQUIRE, V. A., & DIXON, T. W. (2000). SCATTERING OF FLEXURAL WAVES FROM A COATED CYLINDRICAL ANOMALY IN A THIN PLATE. Journal of Sound and Vibration, 236(2), 367-373. doi:10.1006/jsvi.2000.2953Movchan, A. ., Movchan, N. ., & McPhedran, R. . (2007). Bloch–Floquet bending waves in perforated thin plates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463(2086), 2505-2518. doi:10.1098/rspa.2007.1886Lee, W.-M., & Chen, J.-T. (2010). Scattering of flexural wave in a thin plate with multiple circular holes by using the multipole Trefftz method. International Journal of Solids and Structures, 47(9), 1118-1129. doi:10.1016/j.ijsolstr.2009.12.002Parnell, W. J., & Martin, P. A. (2011). Multiple scattering of flexural waves by random configurations of inclusions in thin plates. Wave Motion, 48(2), 161-175. doi:10.1016/j.wavemoti.2010.10.004McPhedran, R. C., Movchan, A. B., & Movchan, N. V. (2009). Platonic crystals: Bloch bands, neutrality and defects. Mechanics of Materials, 41(4), 356-363. doi:10.1016/j.mechmat.2009.01.005Hsu, J.-C., & Wu, T.-T. (2006). Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates. Physical Review B, 74(14). doi:10.1103/physrevb.74.144303Huang, C.-Y., Sun, J.-H., & Wu, T.-T. (2010). A two-port ZnO/silicon Lamb wave resonator using phononic crystals. Applied Physics Letters, 97(3), 031913. doi:10.1063/1.3467145Farhat, M., Guenneau, S., & Enoch, S. (2010). High directivity and confinement of flexural waves through ultra-refraction in thin perforated plates. EPL (Europhysics Letters), 91(5), 54003. doi:10.1209/0295-5075/91/54003Wu, T.-T., Chen, Y.-T., Sun, J.-H., Lin, S.-C. S., & Huang, T. J. (2011). Focusing of the lowest antisymmetric Lamb wave in a gradient-index phononic crystal plate. Applied Physics Letters, 98(17), 171911. doi:10.1063/1.3583660Pierre, J., Boyko, O., Belliard, L., Vasseur, J. O., & Bonello, B. (2010). Negative refraction of zero order flexural Lamb waves through a two-dimensional phononic crystal. Applied Physics Letters, 97(12), 121919. doi:10.1063/1.3491290Farhat, M., Guenneau, S., Enoch, S., Movchan, A. B., & Petursson, G. G. (2010). Focussing bending waves via negative refraction in perforated thin plates. Applied Physics Letters, 96(8), 081909. doi:10.1063/1.3327813Bramhavar, S., Prada, C., Maznev, A. A., Every, A. G., Norris, T. B., & Murray, T. W. (2011). Negative refraction and focusing of elastic Lamb waves at an interface. Physical Review B, 83(1). doi:10.1103/physrevb.83.014106Wang, C. H. (2003). Plate-Wave Diffraction Tomography for Structural Health Monitoring. AIP Conference Proceedings. doi:10.1063/1.1570323Fromme, P., Wilcox, P. D., Lowe, M. J. S., & Cawley, P. (2006). On the development and testing of a guided ultrasonic wave array for structural integrity monitoring. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 53(4), 777-785. doi:10.1109/tuffc.2006.1621505Berryman, J. G. (1980). Long‐wavelength propagation in composite elastic media I. Spherical inclusions. The Journal of the Acoustical Society of America, 68(6), 1809-1819. doi:10.1121/1.385171Krokhin, A. A., Arriaga, J., & Gumen, L. N. (2003). Speed of Sound in Periodic Elastic Composites. Physical Review Letters, 91(26). doi:10.1103/physrevlett.91.264302Torrent, D., Håkansson, A., Cervera, F., & Sánchez-Dehesa, J. (2006). Homogenization of Two-Dimensional Clusters of Rigid Rods in Air. Physical Review Letters, 96(20). doi:10.1103/physrevlett.96.204302Stenger, N., Wilhelm, M., & Wegener, M. (2012). Experiments on Elastic Cloaking in Thin Plates. Physical Review Letters, 108(1). doi:10.1103/physrevlett.108.014301Krylov, V. V., & Tilman, F. J. B. S. (2004). Acoustic ‘black holes’ for flexural waves as effective vibration dampers. Journal of Sound and Vibration, 274(3-5), 605-619. doi:10.1016/j.jsv.2003.05.010O’Boy, D. J., Krylov, V. V., & Kralovic, V. (2010). Damping of flexural vibrations in rectangular plates using the acoustic black hole effect. Journal of Sound and Vibration, 329(22), 4672-4688. doi:10.1016/j.jsv.2010.05.019Krylov, V. V., & Winward, R. E. T. B. (2007). Experimental investigation of the acoustic black hole effect for flexural waves in tapered plates. Journal of Sound and Vibration, 300(1-2), 43-49. doi:10.1016/j.jsv.2006.07.035Georgiev, V. B., Cuenca, J., Gautier, F., Simon, L., & Krylov, V. V. (2011). Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect. Journal of Sound and Vibration, 330(11), 2497-2508. doi:10.1016/j.jsv.2010.12.001Climente, A., Torrent, D., & Sánchez-Dehesa, J. (2013). Omnidirectional broadband insulating device for flexural waves in thin plates. Journal of Applied Physics, 114(21), 214903. doi:10.1063/1.4839375Šarbort, M., & Tyc, T. (2012). Spherical media and geodesic lenses in geometrical optics. 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Anisotropic Metamaterials as sensing devices in acoustics and electromagnetism

We analyze the properties of acoustic and electromagnetic metamaterials with anisotropic constitutive parameters. Particularly, we analyze the so-called Radial Wave Crystals, which are radially periodic structures verifying the Bloch theorem. This type of crystals can be designed and implemented in acoustics as well as in electromagnetism by using anisotropic metamaterials. In acoustics, we have previously predicted that they can be employed as acoustic cavities with huge quality factors and also like dynamically driven antennas. Similar functionalities are here proven in the electromagnetic domain with, in particular, an analysis of the functionality of practical devices operating in the microwave regime. Starting from our recent works on anisotropic structures and their comparison in both application fields, we present a complete discussion concerning their properties in acoustics and electromagnetics.Sánchez-Dehesa Moreno-Cid, J.; Torrent Martí, D.; Carbonell Olivares, J. (2012). Anisotropic Metamaterials as sensing devices in acoustics and electromagnetism. Proceedings of SPIE. 8346:1-11. doi:10.1117/12.916043S111834

Majorana-like Zero Modes in Kekule Distorted Sonic Lattices

[EN] Topological phases have recently been realized in bosonic systems. The associated boundary modes between regions of distinct topology have been used to demonstrate robust waveguiding, protected from defects by the topology of the surrounding bulk. A related type of topologically protected state that is not propagating but is bound to a defect has not been demonstrated to date in a bosonic setting. Here we demonstrate numerically and experimentally that an acoustic mode can be topologically bound to a vortex fabricated in a two-dimensional, Kekul¿e-distorted triangular acoustic lattice. Such lattice realizes an acoustic analog of the Jackiw-Rossi mechanism that topologically binds a bound state in a p-wave superconductor vortex. The acoustic bound state is thus a bosonic analog of a Majorana bound state, where the two valleys replace particle and hole components. We numerically show that it is topologically protected against arbitrary symmetry-preserving local perturbations, and remains pinned to the Dirac frequency of the unperturbed lattice regardless of parameter variations. We demonstrate our prediction experimentally by 3D printing the vortex pattern in a plastic matrix and measuring the spectrum of the acoustic response of the device. Despite viscothermal losses, the measured topological resonance remains robust, with its frequency closely matching our simulations.J. C. acknowledges support from the European Research Council (ERC) through the Starting Grant No. 714577 PHONOMETA and from the MINECO through a Ramon y Cajal grant (No. RYC-2015-17156). J. S.-D. acknowledges support from the Ministerio de Economia y Competitividad of the Spanish Government and the European Union "Fondo Europeo de Desarrollo Regional (FEDER)" through Project No. TEC2014-53088-C3-1-R. P. S.-J. acknowledges support from MINECO/FEDER under Grant No. FIS2015-65706-P. D. T. acknowledges financial support through the Ramon y Cajal fellowship under Grant No. RYC-2016-21188 and to the Ministry of Science, Innovation and Universities through Project No. RTI2018-093921-A-C42.Gao, P.; Torrent Martí, D.; Cervera Moreno, FS.; San-Jose, P.; Sánchez-Dehesa Moreno-Cid, J.; Christensen, J. (2019). Majorana-like Zero Modes in Kekule Distorted Sonic Lattices. Physical Review Letters. 123(19):196601-1-196601-4. https://doi.org/10.1103/PhysRevLett.123.196601S196601-1196601-412319Hasan, M. Z., & Kane, C. L. (2010). Colloquium: Topological insulators. Reviews of Modern Physics, 82(4), 3045-3067. doi:10.1103/revmodphys.82.3045Elliott, S. R., & Franz, M. (2015). Colloquium: Majorana fermions in nuclear, particle, and solid-state physics. Reviews of Modern Physics, 87(1), 137-163. doi:10.1103/revmodphys.87.137Acín, A., Bloch, I., Buhrman, H., Calarco, T., Eichler, C., Eisert, J., … Wilhelm, F. K. (2018). The quantum technologies roadmap: a European community view. New Journal of Physics, 20(8), 080201. doi:10.1088/1367-2630/aad1eaAlicea, J. (2012). New directions in the pursuit of Majorana fermions in solid state systems. Reports on Progress in Physics, 75(7), 076501. doi:10.1088/0034-4885/75/7/076501Nayak, C., Simon, S. H., Stern, A., Freedman, M., & Das Sarma, S. (2008). Non-Abelian anyons and topological quantum computation. Reviews of Modern Physics, 80(3), 1083-1159. doi:10.1103/revmodphys.80.1083Kushwaha, M. S., Halevi, P., Dobrzynski, L., & Djafari-Rouhani, B. (1993). Acoustic band structure of periodic elastic composites. Physical Review Letters, 71(13), 2022-2025. doi:10.1103/physrevlett.71.2022Martínez-Sala, R., Sancho, J., Sánchez, J. V., Gómez, V., Llinares, J., & Meseguer, F. (1995). 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Morphological and molecular characterization of local varieties, modern cultivars and wild relatives of an emerging vegetable crop, the pepino (Solanum muricatum), provides insight into its diversity, relationships and breeding history

Availability of standardized morphological and molecular characterization data is essential for the efficient development of breeding programmes in emerging crops. Pepino (Solanum muricatum) is an increasingly important vegetatively propagated vegetable crop for which concurrent data on morphological descriptors and molecular markers are not available. We evaluated 58 morphological traits, using a collection of 14 accessions of pepinos (including local Andean varieties and modern cultivars) and 8 of wild relatives, using the IPGRI and COMAV descriptors lists coupled with 20 EST-SSRs from tomato. High morphological diversity was found in both cultivated and wild accessions; all morphological traits except three were variable. Cultivated pepino and wild relatives were significantly different for 26 traits. Also, local varieties and modern cultivars of pepino were different from each other for 13 morphological traits and were clearly separated in a principal components analysis. Fourteen of the 20 tomato EST-SSRs were polymorphic, with an average number of alleles per locus of 4.07 and a polymorphic information content value of 0.4132. This revealed a high degree of transferability from tomato to pepino and wide molecular diversity in the collection. Cultivated materials manifest high levels of observed heterozygosity, suggesting that it is related to heterosis for yield associated with heterozygosis. SSR data clearly differentiated cultivated and wild materials. Furthermore, for pepinos, the modern varieties were genetically much less diverse than the traditional local varieties. However, both groups of cultivated material expressed a low degree of genetic differentiation. A strong correlation (r = 0.673) between morphological and molecular distances was found. Our results provide foundational information for programmes of germplasm conservation, and that can be used to enhance breeding for this emerging crop.Herraiz García, FJ.; Vilanova Navarro, S.; Andújar, I.; Torrent Martí, D.; Plazas Ávila, MDLO.; Gramazio, P.; Prohens Tomás, J. (2015). Morphological and molecular characterization of local varieties, modern cultivars and wild relatives of an emerging vegetable crop, the pepino (Solanum muricatum), provides insight into its diversity, relationships and breeding history. Euphytica. 206(2):301-318. doi:10.1007/s10681-015-1454-8S3013182062Abouelnasr H, Li YY, Zhang ZY, Liu JY, Li SF, Li W, Yu JL, McBeath JH, Han CG (2014) First report of Potato virus H on Solanum muricatum in China. Plant Dis 98:1016Anderson GJ (1975) The variation and evolution of selected species of Solanum section Basarthrum. Brittonia 27:209–222Anderson GJ (1979) Systematic and evolutionary consideration of Solanum section Basarthrum. 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