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In elastic wave systems, combining the powerful concepts of resonance and spatial grading within structured surface arrays enable resonant metasurfaces to exhibit broadband wave focusing, mode conversion from surface (Rayleigh) waves to…
A coupled system consisting of a quasilinear parabolic equation and a semilinear hyperbolic equation is considered. The problem arises as a small aspect ratio limit in the modeling of a MEMS device taking into account the gap width of the…
Control of the electromagnetic waves in nano-scale structured materials is central to the development of next generation photonic circuits and devices. In this context, hyperbolic metamaterials, where elliptical isofrequency surfaces are…
For optimal application, pressure-sensitive adhesives must have rheological properties in between those of a viscoplastic solid and those of a viscoelastic liquid. Such adhesives can be produced by emulsion polymerisation, resulting in…
Mechanical nonlinearities dominate the motion of nanoresonators already at relatively small oscillation amplitudes. Although single and coupled two-degrees-of-freedom models have been used to account for experimentally observed nonlinear…
We consider a Glauber dynamics associated with the Ising model on a large two-dimensional box with with minus boundary conditions and in the limit of a vanishing positive external magnetic field. The volume of this box increases…
A number of physical phenomena are described by nonlinear hyperbolic equations. Presence of discontinuous solutions motivates the necessity of development of reliable numerical methods based on the fundamental mathematical properties of…
We study the vibrational motion of membrane resonators upon strong drive in the strongly nonlinear regime. By imaging the vibrational state of rectangular siliconnitride membrane resonators and by analyzing the frequency response using…
We present a solution method which combines the method of matched asymptotics with the method of multipole expansions to determine the band structure of cylindrical Helmholtz resonators arrays in two dimensions. The resonator geometry is…
We are interested in the resonant electromagnetic (EM) scattering by all-dielectric metasurfaces made of a two-dimensional lattice of nanoparticles with high refractive indices. In [Ammari et al., Trans. AMS, 376 (2023), 39-90], it has been…
We investigate singularly perturbed elliptic problems with multiplicative nonlocal diffusion terms subject to Robin boundary conditions. The diffusion depends on a global quantity of the solution, which introduces a nonlocal coupling…
Using a combination of multipole methods and the method of matched asymptotics, we present a solution procedure for acoustic plane wave scattering by a single Helmholtz resonator in two dimensions. Closed-form representations for the…
Context: The Rayleigh-Taylor instabilities generated by the deceleration of a supernova remnant during the ejecta-dominated phase are known to produce finger-like structures in the matter distribution which modify the geometry of the…
The resonant excitation of an electromagnetic guided mode of a slab structure by exterior radiation results in anomalous scattering behavior, including sharp energy-transmission anomalies and field amplification around the frequency of the…
The edge of torn elastic sheets and growing leaves often form a hierarchical buckling pattern. Within non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian…
Propagation of the surface waves on the interface between an uniaxial hyperbolic material and an isotopical topological insulator is studied. The cases of the anisotropy axes is normal to interface or one is coplanar to interface are…
We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which allows for the modeling of the dynamics of interfaces between…
Transformation methods have stimulated many interesting applications of manipulating electromagnetic and acoustic waves by using metamaterials, such as super-lens imaging and cloaking. These successes are mainly due to the form-invariant…
By an idealized quantum mechanical model, we formally describe the dispersion of nonretarded electromagnetic waves that express charge density oscillations near a fixed plane in three spatial dimensions (3D) at zero temperature. Our goal is…
This paper presents a study of nonlinear superpositions of Riemann wave solutions admitted by quasilinear hyperbolic first-order systems of partial differential equations. In particular, we focus on the Euler system and non-elastic wave…