arXiv subjects

Raphaël Assier

Publications and source records attributed to Raphaël Assier.

5 recordsLinked to original sources

arXiv2026

Waves within a network of slowly time-modulated interfaces: time-dependent effective properties, reciprocity and high-order dispersion

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.

math-ph↗

arXiv2025

Scattering of transient waves by an interface with time-modulated jump conditions

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.

math-ph↗

arXiv2024

Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenization

The homogenization procedure developed here is conducted on a laminate with periodic space-time modulation on the fine scale: at leading order, this modulation creates convection in the low-wavelength regime if both parameters are modulated. However, if only one parameter is modulated, which is more realistic, this convective term disappears and one recovers a standard diffusion equation with effective homogeneous parameters; this does not describe the non-reciprocity and the propagation of the field observed from exact dispersion diagrams. This inconsistency is corrected here by considering second-order homogenization which results in a non-reciprocal propagation term that is proved to be non-zero for any laminate and verified via numerical simulation. The same methodology is also applied to the case when the density is modulated in the heat equation, leading therefore to a corrective advective term which cancels out non-reciprocity at the leading order but not at the second order.

math.AP↗

arXiv2023

High-order homogenisation of the time-modulated wave equation: non-reciprocity for a single varying parameter

Laminated media with material properties modulated in space and time in the form of travelling waves have long been known to exhibit non-reciprocity. However, when using the method of low frequency homogenisation, it was so far only possible to obtain non-reciprocal effective media when both material properties are modulated in time, in the form of a Willis-coupling (or bi-anisotropy in electromagnetism) model. If only one of the two properties is modulated in time, while the other is kept constant, it was thought impossible for the method of homogenisation to recover the expected non-reciprocity since this Willis-coupling coefficient then vanishes. Contrary to this belief, we show that effective media with a single time-modulated parameter are non-reciprocal, provided homogenization is pushed to the second order. This is illustrated by numerical experiments (dispersion diagrams and time-domain simulations) for a bilayered modulated medium.

physics.class-ph↗

arXiv2023

High-frequency homogenization for periodic dispersive media

High-frequency homogenization is used to study dispersive media, containing inclusions placed periodically, for which the properties of the material depend on the frequency (Lorentz or Drude model with damping, for example). Effective properties are obtained near a given point of the dispersion diagram in frequency-wavenumber space. The asymptotic approximations of the dispersion diagrams, and the wavefields, so obtained are then cross-validated via detailed comparison with finite element method simulations in both one and two dimensions.

physics.class-ph↗