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We establish the well-posedness, the finite speed propagation, and a regularity result for Maxwell's equations in media consisting of dispersive (frequency dependent) metamaterials. Two typical examples for such metamaterials are materials…
One cannot pull an open, curved string along itself. This fact is clearly reflected in the unwrapping motion of a string or chain as it is dragged around an object, and implies strong consequences for slender structures in passive…
We investigate the dissipative dynamics of linear and nonlinear waves in harmonic traps by means of engineered complex non-Hermitian potentials. By combining an analytical mapping between real and complex Schr\"odinger equations with direct…
We present and review several models of fractional viscous stresses from the literature, which generalise classical viscosity theories to fractional orders by replacing total strain derivatives in time with fractional time derivatives. We…
Small amplitude inhomogeneous plane waves are studied as they propagate on the free surface of a predeformed semi-infinite body made of Bell constrained material. The predeformation corresponds to a finite static pure homogeneous strain.…
An effective medium theory for resonant and non-resonant metamaterials for flexural waves in thin plates is presented. The theory provides closed-form expressions for the effective parameters of arrangement of inclusions or resonators in…
The normal modes of a continuum solid endowed with a random distribution of line defects that behave like elastic strings are described. These strings interact with elastic waves in the bulk, generating wave dispersion and attenuation. As…
A class of isotropic and scale invariant strain energy functions is given for which the corresponding spherically symmetric elastic motion includes bodies whose diameter becomes infinite with time or collapses to zero in finite time,…
Transformation elasticity, by analogy with transformation acoustics and optics, converts material domains without altering wave properties, thereby enabling cloaking and related effects. By noting the similarity between transformation…
We investigate the collective excitations of anisotropic dipolar supersolids in planar confinement, focusing on triangular and stripe phases in situations where the dipoles are titled to have a component in the plane. Using Bogoliubov-de…
The standing surface waves in a rectangular vertically oscillating vessel filled with water (Faraday waves) in the presence of a floating elastic sheet are studied experimentally and theoretically. The threshold amplitude of the instability…
We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent, and rigorous manner. The scalar…
We study the nonlinear wave dynamics of one-dimensional chains of polycatenated rings. These interlocked structures support amplitude-dependent nonlinear wave propagation driven by tensile activation and internal structural flexibility,…
In recent work, we have proposed a theory for the derivation of an exact nonlinear dispersion relation for elastic wave propagation which here we consider for a thin rod (linearly nondispersive) and a thick rod (linearly dispersive). The…
We theoretically demonstrate the concept of metadamping in dissipative metamaterials. We consider an infinite mass-spring chain with repeated local resonators and a statically equivalent periodic chain whose wave propagation characteristics…
A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency…
Fluids confined in nanopores are ubiquitous in nature and technology. In recent years, the interest in confined fluids has grown, driven by research on unconventional hydrocarbon resources -- shale gas and shale oil, much of which are…
In this paper we consider a wave model with non-effective mass and dissipation terms and provide asymptotic descriptions of its representation of solutions. In particular we conclude sharp estimates for a corresponding energy and estimates…
We study the tidal forcing, propagation and dissipation of linear inertial waves in a rotating fluid body. The intentionally simplified model involves a perfectly rigid core surrounded by a deep ocean consisting of a homogeneous…
Layered media can be used as acoustic filters, allowing only waves of certain frequencies to propagate. In soft magneto-active laminates, the shear wave band gaps (i.e., the frequency intervals for which shear waves cannot propagate) can be…