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We study the interaction of highly nonlinear solitary waves in granular crystals, with an adjacent linear elastic medium. We investigate the effects of interface dynamics on the reflection of incident waves and on the formation of primary…
This article presents experimental results on properties of waves propagating in an unbounded and a bounded photonic crystal consisting of metallic cylinders which are arranged in a triangular lattice. First, we present transmission…
To date, the influence of non-linear stratifications and two layer stratifications on internal wave propagation has been studied for two-dimensional wave fields in a cartesian geometry. Here, we use a novel wave generator configuration to…
The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one…
We present a propagation model showing that a transmitter randomly positioned in space generates unbounded peaks in the histogram of the resulting power, provided the signal strength is an oscillating or non-monotonic function of distance.…
We illustrate properties of guided waves in terms of a superposition of body waves. In particular, we consider the Love and SH waves. Body-wave propagation at postcritical angles--required for a total reflection--results in the speed of the…
The transmission lines we consider are constructed from the nonlinear inductors and the nonlinear capacitors. In the first part of the paper we additionally include linear ohmic resistors. Thus, the dissipation being taken into account…
Large arrays of wave-absorbing structures could serve the double objective of coastal protection against erosion and clean, renewable electrical power production. In this work, the principle of an artificial canopy is explored, which…
Rate of convergence is studied for a diffusion process on the half line with a non-sticky reflection to a heavy-tailed 1D invariant distribution which density on the half line has a polynomial decay at infinity. Starting from a standard…
The paper presents new results on localisation and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, surface waves are identified and studied at the interface…
In this paper, we initiate the study of wave propagation in a recently proposed mathematical model for stretch-limited elastic strings. We consider the longitudinal motion of a simple class of uniform, semi-infinite, stretch-limited strings…
Fundamental concepts in the quasi-one-dimensional geometry of disordered wires and random waveguides in which ideas of scaling and the transmission matrix were first introduced are reviewed. We discuss the use of the transmission matrix to…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their…
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…
This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…
We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding…
A numerical study of the statistics of transmission ($t$) and reflection ($r$) of quasi-particles from a one-dimensional disordered lasing or amplifying medium is presented. The amplification is introduced via a uniform imaginary part in…
We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the…
Superscattering, induced by degenerate resonances, breaks the fundamental single-channel limit of scattering cross section of subwavelength structures; in principle, an arbitrarily large total cross section can be achieved via…