Bistable and dynamic states of parametrically excited ultrasound in a fluid-filled cavity

In this paper we have considered the problem of parametric sound generation in an acoustic resonator flled with a fluid, taking explicitely into account the influence of the nonlinearly generated second harmonic. A simple model is presented, and its stationary solutions obtained. The main feature of these solutions is the appearance of bistable states of the fundamental field resulting from the coupling to the second harmonic. An experimental setup was designed to check the predictions of the theory. The results are consistent with the predicted values for the mode amplitudes and parametric thresholds. At higher driving values a self-modulation of the amplitudes is observed. We identify this phenomenon with a secondary instability previously reported in the frame of the theoretical model.Comment: 5 figures. Submitted to JAS

Self-pulsing dynamics of ultrasound in a magnetoacoustic resonator

A theoretical model of parametric magnetostrictive generator of ultrasound is considered, taking into account magnetic and magnetoacoustic nonlinearities. The stability and temporal dynamics of the system is analized with standard techniques revealing that, for a given set of parameters, the model presents a homoclinic or saddle--loop bifurcation, which predicts that the ultrasound is emitted in the form of pulses or spikes with arbitrarily low frequency.Comment: 5 pages, 5 figure

Excitability in a nonlinear magnetoacoustic resonator

We report a nonlinear acoustic system displaying excitability. The considered system is a magnetostrictive material where acoustic waves are parametrically generated. For a set of parameters, the system presents homoclinic and heteroclinic dynamics, whose boundaries define a excitability domain. The excitable behaviour is characterized by analyzing the response of the system to different external stimuli. Single spiking and bursting regimes have been identified.Comment: 4 pages, 5 figure

Wave focusing using symmetry matching in axisymmetric acoustic gradient index lenses

Copyright 2013 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. The following article appeared in Romero García, V.; Cebrecos Ruiz, A.; Picó Vila, R.; Sánchez Morcillo, VJ.; García-Raffi, LM.; Sánchez Pérez, JV. (2013). Wave focusing using symmetry matching in axisymmetric acoustic gradient index lenses. Applied Physics Letters. 103(26):264106-264106. doi:10.1063/1.4860535 and may be found at http://scitation.aip.org/The symmetry matching between the source and the lens results in fundamental interest for lensing applications. In this work, we have modeled an axisymmetric gradient index (GRIN) lens made of rigid toroidal scatterers embedded in air considering this symmetry matching with radially symmetric sources. The sound amplification obtained in the focal spot of the reported lens (8.24 dB experimentally) shows the efficiency of the axisymmetric lenses with respect to the previous Cartesian acoustic GRIN lenses. The axisymmetric design opens new possibilities in lensing applications in different branches of science and technology.The work was supported by Spanish Ministry of Science and Innovation and European Union FEDER through Project Nos. FIS2011-29734-C02-01 and -02 and PAID 2012/253. V. R. G. is grateful for the support of post-doctoral contracts of the UPV CEI-01-11.Romero García, V.; Cebrecos Ruiz, A.; Picó Vila, R.; Sánchez Morcillo, VJ.; García-Raffi, LM.; Sánchez Pérez, JV. (2013). Wave focusing using symmetry matching in axisymmetric acoustic gradient index lenses. Applied Physics Letters. 103(26):264106-264106. https://doi.org/10.1063/1.4860535S26410626410610326John, S. (1987). Strong localization of photons in certain disordered dielectric superlattices. Physical Review Letters, 58(23), 2486-2489. doi:10.1103/physrevlett.58.2486Yablonovitch, E. (1987). Inhibited Spontaneous Emission in Solid-State Physics and Electronics. Physical Review Letters, 58(20), 2059-2062. doi:10.1103/physrevlett.58.2059Kushwaha, 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). Sound attenuation by sculpture. Nature, 378(6554), 241-241. doi:10.1038/378241a0Pennec, Y., Vasseur, J. O., Djafari-Rouhani, B., Dobrzyński, L., & Deymier, P. A. (2010). Two-dimensional phononic crystals: Examples and applications. Surface Science Reports, 65(8), 229-291. doi:10.1016/j.surfrep.2010.08.002Cervera, F., Sanchis, L., Sánchez-Pérez, J. V., Martínez-Sala, R., Rubio, C., Meseguer, F., … Sánchez-Dehesa, J. (2001). Refractive Acoustic Devices for Airborne Sound. Physical Review Letters, 88(2). doi:10.1103/physrevlett.88.023902Krokhin, A. A., Arriaga, J., & Gumen, L. N. (2003). Speed of Sound in Periodic Elastic Composites. Physical Review Letters, 91(26). doi:10.1103/physrevlett.91.264302Sánchez-Pérez, J. V., Caballero, D., Mártinez-Sala, R., Rubio, C., Sánchez-Dehesa, J., Meseguer, F., … Gálvez, F. (1998). Sound Attenuation by a Two-Dimensional Array of Rigid Cylinders. Physical Review Letters, 80(24), 5325-5328. doi:10.1103/physrevlett.80.5325Sheng, P. (1995). Wave Scattering and the Effective Medium. Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena, 49-113. doi:10.1016/b978-012639845-8/50003-4Mei, J., Liu, Z., Wen, W., & Sheng, P. (2006). Effective Mass Density of Fluid-Solid Composites. Physical Review Letters, 96(2). doi:10.1103/physrevlett.96.024301Lin, S.-C. S., Huang, T. J., Sun, J.-H., & Wu, T.-T. (2009). Gradient-index phononic crystals. Physical Review B, 79(9). doi:10.1103/physrevb.79.094302Zigoneanu, L., Popa, B.-I., & Cummer, S. A. (2011). Design and measurements of a broadband two-dimensional acoustic lens. Physical Review B, 84(2). doi:10.1103/physrevb.84.024305Li, Y., Liang, B., Tao, X., Zhu, X., Zou, X., & Cheng, J. (2012). Acoustic focusing by coiling up space. Applied Physics Letters, 101(23), 233508. doi:10.1063/1.4769984Yang, S., Page, J. H., Liu, Z., Cowan, M. L., Chan, C. T., & Sheng, P. (2004). Focusing of Sound in a 3D Phononic Crystal. Physical Review Letters, 93(2). doi:10.1103/physrevlett.93.024301Luo, C., Johnson, S. G., Joannopoulos, J. D., & Pendry, J. B. (2002). All-angle negative refraction without negative effective index. Physical Review B, 65(20). doi:10.1103/physrevb.65.201104Ke, M., Liu, Z., Qiu, C., Wang, W., Shi, J., Wen, W., & Sheng, P. (2005). Negative-refraction imaging with two-dimensional phononic crystals. Physical Review B, 72(6). doi:10.1103/physrevb.72.064306SAMIMY, M., KIM, J.-H., KEARNEY-FISCHER, M., & SINHA, A. (2010). Acoustic and flow fields of an excited high Reynolds number axisymmetric supersonic jet. Journal of Fluid Mechanics, 656, 507-529. doi:10.1017/s0022112010001357Choe, Y., Kim, J. W., Shung, K. K., & Kim, E. S. (2011). Microparticle trapping in an ultrasonic Bessel beam. Applied Physics Letters, 99(23), 233704. doi:10.1063/1.3665615Baac, H. W., Ok, J. G., Maxwell, A., Lee, K.-T., Chen, Y.-C., Hart, A. J., … Guo, L. J. (2012). Carbon-Nanotube Optoacoustic Lens for Focused Ultrasound Generation and High-Precision Targeted Therapy. Scientific Reports, 2(1). doi:10.1038/srep00989Chang, T. M., Dupont, G., Enoch, S., & Guenneau, S. (2012). Enhanced control of light and sound trajectories with three-dimensional gradient index lenses. New Journal of Physics, 14(3), 035011. doi:10.1088/1367-2630/14/3/035011Sanchis, L., Yánez, A., Galindo, P. L., Pizarro, J., & Pastor, J. M. (2010). Three-dimensional acoustic lenses with axial symmetry. Applied Physics Letters, 97(5), 054103. doi:10.1063/1.3474616Gomez-Reino, C., Perez, M. V., & Bao, C. (2002). Gradient-Index Optics. doi:10.1007/978-3-662-04741-5Romero-García, V., Sánchez-Pérez, J. V., Castiñeira-Ibáñez, S., & Garcia-Raffi, L. M. (2010). Evidences of evanescent Bloch waves in phononic crystals. Applied Physics Letters, 96(12), 124102. doi:10.1063/1.3367739Climente, A., Torrent, D., & Sánchez-Dehesa, J. (2010). Sound focusing by gradient index sonic lenses. Applied Physics Letters, 97(10), 104103. doi:10.1063/1.3488349Martin, T. P., Nicholas, M., Orris, G. J., Cai, L.-W., Torrent, D., & Sánchez-Dehesa, J. (2010). Sonic gradient index lens for aqueous applications. Applied Physics Letters, 97(11), 113503. doi:10.1063/1.348937

Self-organization of ultrasound in viscous fluids

We report the theoretical and experimental demonstration of pattern formation in acoustics. The system is an acoustic resonator containing a viscous fluid. When the system is driven by an external periodic force, the ultrasonic field inside the cavity experiences different pattern-forming instabilities leading to the emergence of periodic structures. The system is also shown to possess bistable regimes, in which localized states of the ultrasonic field develop. The thermal nonlinearity in the viscous fluid, together with the far-from-equilibrium conditions, are is the responsible of the observed effects

Energy localization and shape transformations in semiflexible polymer rings

Shape transformations in driven and damped molecular chains are considered. Closed chains of weakly coupled molecular subunits under the action of spatially homogeneous time-periodic external field are studied. The coupling between the internal excitations and the bending degrees of freedom of the chain modifies the local bending rigidity of the chain. In the absence of driving the array takes a circular shape.When the energy pumped into the system exceeds some critical value the chain undergoes a nonequilibrium phase transition: The circular shape of the aggregate becomes unstable and the chain takes the shape of an ellipse or, in general, of a polygon. The excitation energy distribution becomes spatially nonuniform: It localizes in such places where the chain is more flat. The weak interaction of the chain with a flat surface restricts the dynamics to a flat manifold.Y.B.G. acknowledges partial financial support from a special program of the National Academy of Sciences of Ukraine, and is thankful to the Department of Applied Mathematics and Computer Science and the Department of Physics, Technical University of Denmark as well as the University of Seville for hospitality. J.F.R.A acknowledges Grant No. 2011/FQM-280 from CEICE, Junta de Andalucia Spain. J.F.R.A. and V.J.S.-M. acknowledge financial support from Project No. FIS2015-65998-C2-2-P from MINECO, Spain.Gaididei, YB.; Archilla, JFR.; Sánchez Morcillo, VJ.; Gorria, C. (2016). Energy localization and shape transformations in semiflexible polymer rings. Physical Review E. 93(6):062227-1-062227-9. https://doi.org/10.1103/PhysRevE.93.062227S062227-1062227-993

Natural sonic crystal absorber constituted of seagrass (Posidonia Oceanica) fibrous spheres

[EN] We present a 3-dimensional fully natural sonic crystal composed of spherical aggregates of fibers (called Aegagropilae) resulting from the decomposition of Posidonia Oceanica. The fiber network is first acoustically characterized, providing insights on this natural fiber entanglement due to turbulent flow. The Aegagropilae are then arranged on a principal cubic lattice. The band diagram and topology of this structure are analyzed, notably via Argand representation of its scattering elements. This fully natural sonic crystal exhibits excellent sound absorbing properties and thus represents a sustainable alternative that could outperform conventional acoustic materials.This article is based upon work from COST Action DENORMS CA15125, supported by COST(European Cooperation in Science and Technology). The authors gratefully acknowledge the ANR-RGC METARoom (ANR-18-CE08-0021) project, the project HYPERMETA funded under the program Etoiles Montantes of the Region Pays de la Loire, and the project PID2019-109175GB-C22 funded by the Spanish Ministry of Science and Innovation. N.J. acknowledges financial support from the Spanish Ministry of Science, Innovation and Universities (MICINN) through grant "Juan de la Cierva - Incorporacion" (IJC2018-037897-I). The authors would like to thank V. Pagneux and R. Pico Vila for useful discussions and J. Barber and C. Dordoni for their help in collecting the samples.Barguet, L.; Romero-García, V.; Jimenez, N.; García-Raffi, LM.; Sánchez Morcillo, VJ.; Groby, J. (2021). Natural sonic crystal absorber constituted of seagrass (Posidonia Oceanica) fibrous spheres. Scientific Reports. 11(1):1-8. https://doi.org/10.1038/s41598-020-79982-9S1811

Two and three-dimensional oscillons in nonlinear Faraday resonance

We study 2D and 3D localised oscillating patterns in a simple model system exhibiting nonlinear Faraday resonance. The corresponding amplitude equation is shown to have exact soliton solutions which are found to be always unstable in 3D. On the contrary, the 2D solitons are shown to be stable in a certain parameter range; hence the damping and parametric driving are capable of suppressing the nonlinear blowup and dispersive decay of solitons in two dimensions. The negative feedback loop occurs via the enslaving of the soliton's phase, coupled to the driver, to its amplitude and width.Comment: 4 pages; 1 figur

Second-harmonic generation for dispersive elastic waves in a discrete granular chain

The propagation of nonlinear compressional waves in a one-dimensional granular chain driven at one end by a harmonic excitation is studied. The chain is described by a Fermi-Pasta-Ulam (FPU) lattice model with quadratic nonlinearity (alpha-FPU model), valid for strong initial compression of the chain by an external static force. A successive approximations method is used to obtain the analytical expressions for the amplitudes of the static displacement field and of the fundamental and second harmonics propagating through the lattice. Both propagating and evanescent second harmonics are shown to influence the nonlinear propagation characteristics of the fundamental frequency. The propagating regime is characterized by a periodic energy transfer between first and second harmonics, resulting from dispersion, which disappears when the second harmonic becomes evanescent.The work was financially supported by the MICINN of the Spanish Government, under Grant No. FIS2011-29734-C02-02 and by ANR Project Stabingram No. ANR-2010-BLAN-0927-03. V. S.-M. and I. P.-A. acknowledge financial support from Generalitat Valenciana, the Spanish Ministry of Science and Innovation, and Universitat Politecnica de Valencia. V. R.-G. is grateful for the support of "Programa de Contratos Post-Doctorales conMovilidad UPV del Campus de Eexcelencia Internacional (CEI-01-11)" and of Grant No. BEST2012 of the Generalitat Valenciana.Sánchez Morcillo, VJ.; Pérez Arjona, I.; Romero García, V.; Tournat, V.; Gusev, VE. (2013). Second-harmonic generation for dispersive elastic waves in a discrete granular chain. Physical Review E. 88(4):43203-43203. https://doi.org/10.1103/PhysRevE.88.043203S4320343203884Nesterenko, V. F. (1984). Propagation of nonlinear compression pulses in granular media. Journal of Applied Mechanics and Technical Physics, 24(5), 733-743. doi:10.1007/bf00905892Nesterenko, V. F. (2001). Dynamics of Heterogeneous Materials. doi:10.1007/978-1-4757-3524-6Lazaridi, A. N., & Nesterenko, V. F. (1985). Observation of a new type of solitary waves in a one-dimensional granular medium. Journal of Applied Mechanics and Technical Physics, 26(3), 405-408. doi:10.1007/bf00910379Coste, C., Falcon, E., & Fauve, S. (1997). Solitary waves in a chain of beads under Hertz contact. Physical Review E, 56(5), 6104-6117. doi:10.1103/physreve.56.6104Job, S., Melo, F., Sokolow, A., & Sen, S. (2005). How Hertzian Solitary Waves Interact with Boundaries in a 1D Granular Medium. Physical Review Letters, 94(17). doi:10.1103/physrevlett.94.178002SEN, S., HONG, J., BANG, J., AVALOS, E., & DONEY, R. (2008). Solitary waves in the granular chain. Physics Reports, 462(2), 21-66. doi:10.1016/j.physrep.2007.10.007Campbell, D. K., Flach, S., & Kivshar, Y. S. (2004). Localizing Energy Through Nonlinearity and Discreteness. Physics Today, 57(1), 43-49. doi:10.1063/1.1650069Boechler, N., Theocharis, G., Job, S., Kevrekidis, P. G., Porter, M. A., & Daraio, C. (2010). Discrete Breathers in One-Dimensional Diatomic Granular Crystals. Physical Review Letters, 104(24). doi:10.1103/physrevlett.104.244302Berman, G. P., & Izrailev, F. M. (2005). The Fermi–Pasta–Ulam problem: Fifty years of progress. Chaos: An Interdisciplinary Journal of Nonlinear Science, 15(1), 015104. doi:10.1063/1.1855036Tournat, V., Gusev, V. E., & Castagnède, B. (2004). Self-demodulation of elastic waves in a one-dimensional granular chain. Physical Review E, 70(5). doi:10.1103/physreve.70.056603Korobov, A. I., Brazhkin, Y. A., & Sovetskaya, E. S. (2010). Characteristic features of elastic wave propagation in a one-dimensional model of an unconsolidated medium. Acoustical Physics, 56(4), 446-452. doi:10.1134/s106377101004007xKorobov, A. I., Brazhkin, Y. A., & Shirgina, N. V. (2012). Nonlinear elastic properties of a model one-dimensional granular unconsolidated structure. Acoustical Physics, 58(1), 90-98. doi:10.1134/s1063771011060091Marquie, P., Bilbault, J. M., & Remoissenet, M. (1994). Generation of envelope and hole solitons in an experimental transmission line. Physical Review E, 49(1), 828-835. doi:10.1103/physreve.49.828Geniet, F., & Leon, J. (2002). Energy Transmission in the Forbidden Band Gap of a Nonlinear Chain. Physical Review Letters, 89(13). doi:10.1103/physrevlett.89.134102Khomeriki, R., Lepri, S., & Ruffo, S. (2004). Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model. Physical Review E, 70(6). doi:10.1103/physreve.70.066626Tse Ve Koon, K., Leon, J., Marquié, P., & Tchofo-Dinda, P. (2007). Cutoff solitons and bistability of the discrete inductance-capacitance electrical line: Theory and experiments. Physical Review E, 75(6). doi:10.1103/physreve.75.066604Cabaret, J., Tournat, V., & Béquin, P. (2012). Amplitude-dependent phononic processes in a diatomic granular chain in the weakly nonlinear regime. Physical Review E, 86(4). doi:10.1103/physreve.86.041305Narisetti, R. K., Ruzzene, M., & Leamy, M. J. (2012). Study of wave propagation in strongly nonlinear periodic lattices using a harmonic balance approach. Wave Motion, 49(2), 394-410. doi:10.1016/j.wavemoti.2011.12.005Hladky-Hennion, A.-C., & Billy, M. de. (2007). Experimental validation of band gaps and localization in a one-dimensional diatomic phononic crystal. The Journal of the Acoustical Society of America, 122(5), 2594. doi:10.1121/1.2779130Boechler, N., Theocharis, G., & Daraio, C. (2011). Bifurcation-based acoustic switching and rectification. Nature Materials, 10(9), 665-668. doi:10.1038/nmat3072Maznev, A. A., Every, A. G., & Wright, O. B. (2013). Reciprocity in reflection and transmission: What is a ‘phonon diode’? Wave Motion, 50(4), 776-784. doi:10.1016/j.wavemoti.2013.02.006Dauxois, T., Khomeriki, R., & Ruffo, S. (2007). Modulational instability in isolated and driven Fermi–Pasta–Ulam lattices. The European Physical Journal Special Topics, 147(1), 3-23. doi:10.1140/epjst/e2007-00200-2Bunkin, F. V., Kravtsov, Y. A., & Lyakhov, G. A. (1986). Acoustic analogues of nonlinear-optics phenomena. Soviet Physics Uspekhi, 29(7), 607-619. doi:10.1070/pu1986v029n07abeh003458Dormand, J. R., & Prince, P. J. (1980). A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics, 6(1), 19-26. doi:10.1016/0771-050x(80)90013-3Tournat, V., Pèrez-Arjona, I., Merkel, A., Sanchez-Morcillo, V., & Gusev, V. (2011). Elastic waves in phononic monolayer granular membranes. New Journal of Physics, 13(7), 073042. doi:10.1088/1367-2630/13/7/07304

Acoustically penetrable sonic crystals based on fluid-like scatterers

We propose a periodic structure that behaves as a fluid fluid composite for sound waves, where the building blocks are clusters of rigid scatterers. Such building-blocks are penetrable for acoustic waves, and their properties can be tuned by selecting the filling fraction. The equivalence with a fluid fluid system of such a doubly periodic composite is tested analytical and experimentally. Because of the fluid-like character of the scatterers, sound structure interaction is negligible, and the propagation can be described by scalar models, analogous to those used in electromagnetics. As an example, the case of focusing of evanescent waves and the guided propagation of acoustic waves along an array of penetrable elements is discussed in detail. The proposed structure may be a real alternative to design a low contrast and acoustically penetrable medium where new properties as those shown in this work could be experimentally realized.We acknowledge financial support by Spanish Ministerio de Economia y Competitividad and European Union FEDER through project FIS2011-29731-C02-01 and -02. VRG is grateful for the financial support of the post-doctoral grant from the "Pays de la Loire". ACR is grateful for the support of the Programa de Ayudas e Iniciativas de Investigacin (PAID) of the UPV.Cebrecos Ruiz, A.; Romero García, V.; Picó Vila, R.; Sánchez Morcillo, VJ.; Botey, M.; Herrero, R.; Cheng, YC.... (2015). Acoustically penetrable sonic crystals based on fluid-like scatterers. Journal of Physics D-Applied Physics. 48(2):25501-25510. https://doi.org/10.1088/0022-3727/48/2/025501S255012551048