Comptes Rendus
Research article
Scattering of transient waves by an interface with time-modulated jump conditions
Michaël Darche1 ; Raphaël Assier2; Sébastien Guenneau3, 4; Bruno Lombard1 ; Marie Touboul3, 5, 6
1 Aix Marseille Université, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, France
2 Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK
3 UMI 2004 Abraham de Moivre-CNRS, Imperial College London, London SW7 2AZ, UK
4 Department of Physics, The Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
5 Department of Mathematics, Imperial College London, Huxley Building, Queen’s Gate, London SW7 2AZ, UK
6 POEMS, ENSTA, CNRS, INRIA, Institut Polytechnique de Paris, 91120 Palaiseau, France
Comptes Rendus. Mécanique, Volume 353 (2025), pp. 923-951

Time modulation of the physical parameters offers interesting new possibilities for wave control. Examples include amplification of waves, harmonic generation and non-reciprocity, without resorting to non-linear mechanisms. Most of the recent studies focus on the time-modulation of the bulk physical properties. However, as the temporal modulation of these properties is difficult to achieve experimentally, we will concentrate here on the special case of an interface with time-varying jump conditions, which is simpler to implement. This work is focused on wave propagation in a one-dimensional medium containing one modulated interface. Properties of the scattered waves are investigated theoretically: energy balance, generation of harmonics, impedance matching and non-reciprocity. A fourth-order numerical method is also developed to simulate transient scattering. Numerical experiments are conducted to validate the numerical scheme and to illustrate the theoretical findings.

La modulation temporelle des propriétés d’un milieu de propagation offre de nouvelles possibilités intéressantes pour le contrôle des ondes. Les exemples incluent l’amplification des ondes, la génération d’harmoniques et la non-réciprocité, sans avoir recours à des mécanismes non linéaires. La plupart des études récentes se concentrent sur la modulation temporelle des propriétés physiques volumiques d’un milieu de propagation. Cependant, cette modulation étant difficile à réaliser expérimentalement, on se concentre ici sur le cas particulier d’une interface avec des conditions de saut variables en temps, plus simple à mettre en œuvre. Ce travail se concentre sur la propagation des ondes dans un milieu monodimensionnel contenant une interface modulée. On étudie théoriquement de nombreuses propriétés des ondes diffusées : bilan d’énergie, génération d’harmoniques, adaptation d’impédance et non-réciprocité. Une méthode numérique d’ordre 4 est développée pour simuler les ondes transitoires diffractées. Des expériences numériques sont menées pour valider le schéma numérique et illustrer les résultats théoriques attendus.

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DOI: 10.5802/crmeca.317
Keywords: Elastic waves, imperfect jump conditions, time-varying media, non-reciprocity, numerical methods for hyperbolic equations
Mots-clés : Ondes élastiques, conditions de sauts imparfaites, milieux modulés en temps, non-réciprocité, méthodes numériques pour les équations hyperboliques

Michaël Darche 1; Raphaël Assier 2; Sébastien Guenneau 3, 4; Bruno Lombard 1; Marie Touboul 3, 5, 6

1 Aix Marseille Université, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, France
2 Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK
3 UMI 2004 Abraham de Moivre-CNRS, Imperial College London, London SW7 2AZ, UK
4 Department of Physics, The Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
5 Department of Mathematics, Imperial College London, Huxley Building, Queen’s Gate, London SW7 2AZ, UK
6 POEMS, ENSTA, CNRS, INRIA, Institut Polytechnique de Paris, 91120 Palaiseau, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     author = {Micha\"el Darche and Rapha\"el Assier and S\'ebastien Guenneau and Bruno Lombard and Marie Touboul},
     title = {Scattering of transient waves by an interface with time-modulated jump conditions},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {923--951},
     year = {2025},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {353},
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     language = {en},
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Michaël Darche; Raphaël Assier; Sébastien Guenneau; Bruno Lombard; Marie Touboul. Scattering of transient waves by an interface with time-modulated jump conditions. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 923-951. doi: 10.5802/crmeca.317

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