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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.27641 |
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| _version_ | 1866912986853015552 |
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| author | Darche, Michaël Assier, Raphaël Guenneau, Sébastien Lombard, Bruno Touboul, Marie |
| author_facet | Darche, Michaël Assier, Raphaël Guenneau, Sébastien Lombard, Bruno Touboul, Marie |
| contents | We consider wave propagation through a 1D periodic network of slowly time-modulated interfaces. Each interface is modelled by time-dependent spring-mass jump conditions, where mass and rigidity interface parameters are modulated in time. Low-frequency homogenisation yields a leading-order model described by an effective time-dependent wave equation, i.e.\ a wave equation with effective mass density and Young's modulus which are homogeneous in space but depend on time. This means that time-dependent bulk effective properties can be created by an array where only interfaces are modulated in time. The occurrence of k-gaps in case of a periodic modulation is also analysed. Second-order homogenisation is then performed and leads to an effective model which is reciprocal but encapsulates higher-order dispersive effects. These findings and the limitations of the models are illustrated through time-domain simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27641 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Waves within a network of slowly time-modulated interfaces: time-dependent effective properties, reciprocity and high-order dispersion Darche, Michaël Assier, Raphaël Guenneau, Sébastien Lombard, Bruno Touboul, Marie Mathematical Physics We consider wave propagation through a 1D periodic network of slowly time-modulated interfaces. Each interface is modelled by time-dependent spring-mass jump conditions, where mass and rigidity interface parameters are modulated in time. Low-frequency homogenisation yields a leading-order model described by an effective time-dependent wave equation, i.e.\ a wave equation with effective mass density and Young's modulus which are homogeneous in space but depend on time. This means that time-dependent bulk effective properties can be created by an array where only interfaces are modulated in time. The occurrence of k-gaps in case of a periodic modulation is also analysed. Second-order homogenisation is then performed and leads to an effective model which is reciprocal but encapsulates higher-order dispersive effects. These findings and the limitations of the models are illustrated through time-domain simulations. |
| title | Waves within a network of slowly time-modulated interfaces: time-dependent effective properties, reciprocity and high-order dispersion |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2603.27641 |