Résumé: A time-domain effective model for acoustic wave propagation through a two-dimensional periodic array of gas bubbles embedded in a liquid is presented. The model is expressed as transmission conditions: pressure remains continuous, whereas the normal velocity exhibits a jump induced by the internal pressure of the bubbles. This internal pressure follows a damped mass–spring equation, with damping arising solely from radiative coupling to the surrounding liquid, which makes the resonance frequency and quality factor of the array emerge unambiguously. Aside from the bubble density in the lattice, these quantities are fully governed by two independent geometric parameters: a dimensionless capacitance, depending solely on bubble shape, and a lattice coefficient, depending solely on lattice geometry. For plane wave scattering, comparisons with direct numerical simulations demonstrate that the model accurately reproduces the resonant behavior of bubble screens across a range of configurations, including spherical, spheroidal, and cylindrical bubbles, as well as square and rectangular lattices. This generalizes the classical model of Leroy et al. [Eur. Phys. J. E 29(1), 123–130 (2009)] for spherical bubbles in square lattices. Notably, the model reveals—and simulations confirm—that the resonance frequency shift relative to an isolated bubble, usually positive (blue shift), can become negative (red shift) in rectangular lattices with aspect ratios exceeding seven.

Résumé: We derive effective Boussinesq and Korteweg–de Vries equations governing nonlinear wave propagation over a structured bathymetry using a three-scale homogenization approach. The model captures the anisotropic effects induced by the bathymetry, leading to significant modifications in soliton dynamics. Homogenized parameters, determined from elementary cell problems, reveal strong directional dependencies in wave speed and dispersion. Our results provide new insights into nonlinear wave propagation in structured shallow-water environments, and consequently motivate further fundamental and applied studies in wave hydrodynamics and coastal engineering.

Résumé: The shear resistance of the shear zone governs the behavior of many landslides. Among the factors influencing shear resistance, the velocity dependence of the shear zone can give rise to rapid catastrophic failure (velocity-weakening) or exert a deceleration effect (velocity-strengthening). In this study, we investigated the shear-velocity dependence of shear zone in clayey soil from the Baige landslide in Tibet, China, across a broad range of velocities (3.3 × 10⁻⁸ to 6 m/s), at typical landslide stress levels (200 to 2000 kPa), to simulate the whole lifespan of the landslide, from creep deformation to rapid catastrophic failure. We found that the shear velocity dependence of clayey soils could be classified into three regimes: slight weakening at slow velocities, substantial velocity-strengthening at intermediate velocities, and rapid weakening at high velocities once a critical velocity was attained. The mechanisms for the first and second regimes were explained by the alignment (entropy) change of clay particles along the shear surface. At very slow shear velocities, clay particles become aligned parallel to the shear surface, causing slight weakening and a drop in entropy. As the shear velocity increased, the clay particles became less aligned and more randomly distributed, interlocking with each other, giving rise to strong velocity-strengthening. The rapid weakening in the third regime was associated with frictional heating, independent of entropy. Across the slow to intermediate velocity range, clay particle entropy controls velocity-weakening and velocity-strengthening frictional behavior of shear zones, potentially influencing landslide slow creep. In contrast, rapid shearing causes frictional weakening in clayey shear zones, which may trigger landslide rapid failure. This study offers new insights into landslide dynamics and the transition from creep to rapid failure.