5 papers
Band-Edge Homogenization and the Sound-Soft Limit of Finite Bubbly Crystals
Habib Ammari, Yuxin Du, Xin Fu +2
We establish a quantitative sound-soft scattering limit for a finite bubbly crystal near the upper edge of the first Bloch band of the corresponding infinite crystal. The inclusion…
Minnaert resonances and higher-order acoustic modes for bubbles in a viscous fluid with surface tension
Habib Ammari, Xin Fu, Wenjia Jing +1
The aim of this paper is to account for viscosity, surface tension, and interactions between micro-bubbles in approximating their resonant behavior in the ultrasonic regime. Origin…
Perturbative Approach to Nonlinear Capacitance Matrix Formulations
Habib Ammari, Clemens Thalhammer
We study a nonlinear Helmholtz system with cubic nonlinearity on high-contrast inclusions in three dimensions, and the solitons that emerge as the contrast tends to zero. Using…
Nonlinear subwavelength resonances in three dimensions
Habib Ammari, Thea Kosche
In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelen…
Wave packets propagation in the subwavelength regime near the Dirac point
Habib Ammari, Xin Fu, Wenjia Jing
In [Ammari et al., SIAM J Math Anal., 52 (2020), pp. 5441--5466], the first author with collaborators proved the existence of Dirac dispersion cones at subwavelength scales in bubb…