Related papers: Wave scattering by many small particles embedded i…
We use boundary element simulations to study the interaction of model microswimmers with a neutrally buoyant spherical particle. The ratio of the size of the particle to that of the swimmer is varied from $R^\mathrm{P} / R^\mathrm{S} \ll…
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…
Disorder is more the rule than the exception in natural and synthetic materials. Nonetheless, wave propagation within inhomogeneously disordered materials has received scant attention. We combine microwave experiments and theory to find the…
A method is proposed to create materials with a desired refraction coefficient, possibly negative one. The method consists of embedding into a given material small particles. Given $n_0(x)$, the refraction coefficient of the original…
We study one- and two-photon scattering from a qubit embedded in a one-dimensional waveguide in the presence of modal dispersion. We use a resolvent based analysis and utilize techniques borrowed from the Lee model studies. Modal dispersion…
It is proposed to create materials with a desired refraction coefficient in a bounded domain $D\subset \R^3$ by embedding many small balls with constant refraction coefficients into a given material. The number of small balls per unit…
An integral-differential equation is derived for the self-consistent (effective) field in the medium consisting of many small bodies randomly distributed in some region. Acoustic and electromagnetic fields are considered in such a medium.…
Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary…
In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a…
We calculate the differential, total, and transport cross-sections for scattering of two-dimensional massless Dirac electrons by a circular barrier. For scatterer of a small radius, the cross-sections are dominated by quantum effects such…
We study the diffusion of monochromatic classical waves in a disordered acoustic medium by scattering theory. In order to avoid artifacts associated with mathematical point scatterers, we model the randomness by small but finite insertions.…
Seismic coda waves, once regarded as noise, are now recognized as key indicators of wave scattering in seismograms. Aki (1969) first proposed that these waves result from small-scale heterogeneities in the Earth's interior, spurring…
Refraction and diffraction of waves in natural crystals and artificial crystals formed by anisotropically scattering centers are considered. A detailed study of the electromagnetic wave refraction in a two-dimensional photonic crystal…
A classical way for exploring the scattering behavior of a small sphere is to approximate Mie coefficients with a Taylor series expansion. This ansatz delivered a plethora of insightful results, mostly for small spheres supporting localized…
We study theoretically the scattering of light by an ensemble of $N$ resonant atoms in a sub-wavelength volume. We consider the low intensity regime so that each atom responds linearly to the field. While $N$ non-interacting atoms would…
The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this…
A transport theory for atomic matter waves in low-dimensional waveguides is outlined. The thermal fluctuation spectrum of magnetic near fields leaking out of metallic microstructures is estimated. The corresponding scattering rate for…
We study the time-dependent scattering of a quantum mechanical wave packet at a barrier for energies larger than the barrier height, in the semi-classical regime. More precisely, we are interested in the leading order of the exponentially…
We present an explicit numerical scheme to solve the variable coefficient wave equation in one space dimension with minimal restrictions on the coefficient and initial data.
We derive from first principles a one-way radiative transfer equation for the wave intensity resolved over directions (Wigner transform of the wave field) in random media. It is an initial value problem with excitation from a source which…