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Recently, it was shown that strongly driven micromechanical resonators show mode shapes that strongly differ from the eigenmodes. This raises the question of the origin of this nonlinear behavior. We measure the spatial dependence of the…
The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the…
The diffraction problem of a plane wave impinging on a grating formed by nested cavities is solved by means of the modal method, for $s$ and $p$ polarization modes. The cavities are formed by perfectly conducting sheets that describe…
For over 70 years it has been assumed that scalar wave propagation in (ensemble-averaged) random particulate materials can be characterised by a single effective wavenumber. Here, however, we show that there exist many effective…
We introduce a direct, linear sampling approach to imaging in an acoustic waveguide with sound hard walls. The waveguide terminates at one end and has unknown geometry due to compactly supported wall deformations. The goal of imaging is to…
In this paper, we present a mathematical study of wave scattering by a hard elastic obstacle embedded in a soft elastic body in three dimensions. Our contributions are threefold. First, we characterize subwavelength resonances using the…
The wide application of the modern resonant measurement techniques makes all the steps of the measuring process, including data acquisition more efficient and reliable. Here we investigate the multidimensional space of the parameters to…
We give a detailed analysis of long range cumulative scattering effects from rough boundaries in waveguides. We assume small random fluctuations of the boundaries and obtain a quantitative statistical description of the wave field. The…
Decades of work on beam deformation on reflection, and especially on lateral shifts, have spread the idea that a reflected beam is larger than the incident beam. However, when the right conditions are met, a beam reflected by a multilayered…
A radial transverse resonance model for two cylindrical concentric layers with different complex dielectric constants is presented. An inverse problem with four unknowns - 3 physical material parameters and one dimensional dielectric layer…
This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…
We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…
The transfer matrix method remains a simple yet powerful tool for modeling acoustic systems, particularly in a closed waveguide geometry. Here we present a generalisation of this method based on the theory of mode matching, that…
A method for designing plasmonic particles with desired resonance spectra is presented. The method is based on repetitive perturbations of an initial particle shape while calculating the eigenvalues of the various quasistatic resonances.…
We study the scattering of surface water waves with irrotational draining vortices. At small depth, this system is a mathematical analogue of a rotating black hole and can be used to mimic some of its peculiar phenomenon. Using ray-tracing…
The basic ideas of a homotopy-based multiple-variable method is proposed and applied to investigate the nonlinear interactions of periodic traveling waves. Mathematically, this method does not depend upon any small physical parameters at…
This paper presents and compares three analytical methods for calculating low frequency band gap boundaries in doubly periodic arrays of resonating thin elastic shells. It is shown that both lattice sum expansions in the vicinity of its…
In some underwater acoustic waveguides with specially selected sound speed profiles striations or fringes of the interference pattern are determined by a single parameter \beta\ called the waveguide (or Chuprov) invariant. In the present…
As an alternative to atomistic calculations of long-wavelength acoustic modes of atomically thin layers, which are known to converge very slowly, we propose a quantitatively predictive and physically intuitive approach based on continuum…
Resonant coupling of coplanar waveguides is explored by wrapping proximate shorted ends of the waveguides with micron size ferromagnetic Co90Ta5Zr5 tubes. Ferromagnetic resonance and up to 7 outer surface modes are identified. Experimental…