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Grains of SAWs: associating quasi-particles to surface acoustic waves. (English) Zbl 1423.82001

Summary: This work aims at showing how to associate quasi-particles in inertial or non-inertial motion with surface-wave solutions, especially for Rayleigh and Bleustein-Gulyaev surface waves on elastic or piezoelectric substrates (by way of examples). Perturbations of various kinds (surface energy, connection to an external fluid or an external electric field, viscosity of the substrate) are also envisaged. The technique employed for this is based on the exploitation of the conservation equations for energy and wave-momentum deduced via Noether’s theorem or by direct computation, and associated with the basic field equations of which we already know the analytic continuum solutions. Volume integration of the conservation laws is then performed over a volume representative of the surface wave motion.

MSC:

82B05 Classical equilibrium statistical mechanics (general)
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[1] Achenbach, J.D., Wave propagation in elastic solids, (1973), North-Holland Amsterdam · Zbl 0268.73005
[2] Bertoni, H.L.; Tamir, T., Unified theory of Rayleigh-angle phenomena for acoustic beams at liquid-solid interfaces, Applied physics A: materials science & processing, 2/4, 157-172, (1973)
[3] Bleustein, J.L., A new surface wave in piezoelectric materials, Applied physics letter, 13, 412-414, (1968)
[4] Brekhovskikh, L.M., Waves in layered media, (1960), Academic Press New York · Zbl 0558.73018
[5] Brenig, W., Besitzen schallwellen einen impuls, Zeit physik, 143, 168-172, (1955)
[6] Caloi, P., Comportement des ondes de Rayleigh dans un milieu firmo-élastique indéfini, Publications du bureau central seismologique international, series A, travaux scientifique, 17, 89-108, (1950)
[7] Curie, P.K.; Hayes, M.A.; O’Leary, P.M., Viscoelastic Rayleigh waves, Quarterly of applied mathematics, 35, 35-53, (1977) · Zbl 0355.73024
[8] Dieulesaint, E.; Royer, D., Elastic waves in solids (translated from the French), (2000), J. Wiley New York · Zbl 0960.74002
[9] Eringen, A.C.; Maugin, G.A., Electrodynamics of continua, Vol. I, (1990), Springer-Verlag New York
[10] Gubanov, A., Rayleigh waves on a boundary between a solid and a liquid, J eksp teoret fiz (USSR), 15, 497, (1945), [in Russian] · Zbl 0063.01778
[11] Gulyaev, Yu.V., Electroacoustic surface waves in solids, Soviet physics JETP letters, 9, 35-38, (1969), [in Russian, 1968]
[12] Henrich, V.E.; Cox, P.A., The surface science of metal oxides, (1994), University Press Cambridge
[13] Kittel, C., Introduction to solid state physics, (2005), Wiley International Edition New York
[14] Lai, C.G.; Rix, G.L., Solution of the Rayleigh eigenproblem in viscoelastic media, Bulletin of the seismological society of America, 92, 2297-2309, (2002)
[15] Ludwig, W., Dynamics at crystal surfaces, surface phonons, International journal of engineering science, 29/3, 345-361, (1991)
[16] Maugin, G.A., Continuum mechanics of electromagnetic solids, (1988), North-Holland Amsterdam · Zbl 0652.73002
[17] Maugin, G.A., On canonical equations of continuum thermomechanics, Mechanics research communications, 33, 705-710, (2006) · Zbl 1192.74006
[18] Maugin, G.A., Configurational forces: thermomechanics* physics* mathematics and numerics, (2011), CRC/Taylor and Francis Boca Raton, Florida · Zbl 1234.74002
[19] Maugin, G.A.; Christov, C.I., Nonlinear waves and conservation laws (nonlinear duality between elastic waves and quasi-particles), (), 101-147
[20] Maugin, G.A.; Hadouaj, H., Solitary surface transverse waves on an elastic substrate coated with a thin film, Physical review, B44, 1266-1280, (1991)
[21] Maugin, G.A.; Rousseau, M., On two insufficiently exploited conservation laws in continuum mechanics: canonical momentum and action, (), 251-268, [ISBN: 978-3-642-11444-1]
[22] Maugin, G.A.; Rousseau, M., Bleustein – gulyaev SAW and its associated quasi-particle, International journal of engineering science, 48, 1462-1469, (2010) · Zbl 1231.74124
[23] Maynard, J.D., Phonons in crystals, (), 657-672, [Chapter 57]
[24] Rousseau, M., & Maugin, G. A. (2011c). Influence of viscosity on the motion of quasi-particles associated with surface acoustic waves. International Journal of Engineering Science. http://dx.doi.org/10.1016/j.ijengsci.2011.09.008; Rousseau, M., & Maugin, G. A. (2011c). Influence of viscosity on the motion of quasi-particles associated with surface acoustic waves. International Journal of Engineering Science. http://dx.doi.org/10.1016/j.ijengsci.2011.09.008 · Zbl 1423.74437
[25] Rousseau, M., & Maugin, G. A. (2011d). Quasi-particles associated with Bleustein-Gulyaev SAWs: Perturbations by elastic nonlinearities. International Journal of Non-Linear Mechanics. http://dx.doi.org/10.1016/j.ijnonlinmech.2011.08.014; Rousseau, M., & Maugin, G. A. (2011d). Quasi-particles associated with Bleustein-Gulyaev SAWs: Perturbations by elastic nonlinearities. International Journal of Non-Linear Mechanics. http://dx.doi.org/10.1016/j.ijnonlinmech.2011.08.014
[26] Rousseau, M.; Maugin, G.A., Rayleigh SAW and its canonically associated quasi-particle, Proceedings of the royal society London A, 467, 495-507, (2011) · Zbl 1219.74023
[27] Rousseau, M.; Maugin, G.A., Bleustein – gulyaev SAWS with low losses: approximate direct solution, Journal of electromagnetic analysis and applications, 3, 122-127, (2011)
[28] Scholte, J.G., On Rayleigh waves in visco-elastic media, Physica (Utrecht), 13, 245-250, (1947)
[29] Tsai, Y.M.; Kolsky, H., Surface wave propagation for linear viscoelastic solids, J.mech.math.solids, 16, 99-109, (1968)
[30] Vardoulakis, I.; Georgiadis, H.G., SH surface waves in a homogeneous gradient-elastic half-space with surface energy, Journal of elasticity, 47, 147-165, (1997) · Zbl 0912.73016
[31] Vlasie-Belloncle, V.; Rousseau, M., Effect of surface free energy on the behaviour of surface and guided waves, Ultrasonics, 45, 188-195, (2006)
[32] Whitham, G.B., Linear and nonlinear waves, (1974), Interscience-John Wiley New York · Zbl 0373.76001
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