The extraordinary properties of second harmonic generation in negative-index metamaterials, where the Poynting vector and the wavevector have opposite directions are investigated. The ”backward” phase-matching condition results in significant changes in the Manley-Rowe relations and in spatial distributions of the field intensities of the coupled waves. 0 0 z RHM

Based on a recent study of the linearized Bianchi equations by Buchman and Sarbach, we construct and implement a hierarchy of absorbing boundary conditions for the Einstein equations in generalized harmonic gauge. As a test problem, we demonstrate that we can evolve multipolar gravitational waves without any spurious reflections at linear order in perturbation theory.

We present a new method to solve an inverse scattering problem for time-harmonic electromagnetic waves. The method is based on an equivalence relation of the inverse problem to a system of two integral equations. This system can be solved numerically by a recently developed spectral method for the direct scattering problem.

We recount some of Ralph Kleinman's scientiic achievements in obstacle scattering for time harmonic waves by reporting on two topics where R.K. and R.K. interacted mathematically. The rst topic is the problem of nonuniqueness for the classical boundary integral equations for the direct scattering problem and the second is the development of numerical methods for the inverse scattering problem.

Colloidal spheres localized in an array of harmonic wells form a thermally excited, viscously damped dynamical system capable of supporting propagating elastic waves. Experimentally realized with micrometer-scale polystyrene spheres localized in a line of holographic optical traps, the hydrodynamically coupled array's behavior is quantitatively explained by a model based on the Oseen superposit...

Collisions between bright solitary waves in the 1D Gross-Pitaevskii equation with a harmonic potential, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. A particle analogy for the solitary waves is formulated and shown to be integrable for a two-particle system. The extension to three particles is shown to support chaotic regimes. Good agreement is found b...

We investigate the transmission properties of a metallic layer with narrow slits. We consider (time-harmonic) Maxwell's equations in the H-parallel case with a fixed incident wavelength. We denote η > 0 as the typical size of the complex structure and obtain the effective equations by letting η → 0. For metallic permittivities with negative real part, plasmonic waves can be excited on the surfa...

Acoustic waves interact with the human body, head and ears, before reaching the tympanic membranes in the ear canals. In this project we will develop an analytical method to calculate how these acoustic interactions occur. This is a highly nontrivial problem, because the acoustic wave equation (or, for harmonic waves, the Helmholtz equation) has to be solved on the complex geometry of the bound...

However, in reality most interfaces are not planar on both micro and macro scales. The purpose of this study is to investigate the interaction between elastic waves and a slightIy non-planar interface. The method of asymptotic analysis is used to derive elose form solutions for the problem of reflection and scattering of a time-harmonic SH-wave at a slightly, but otherwise arbitrarily, non-plan...

The nolinear hydrodynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging from small harmonic oscillations (linearized model), to nonlinear oscillations, up through solitary waves. These non-axis-symmetric localized shapes are also d...