We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. Standard boundary or finite element methods, with a piecewise polynomial approximation space, have a computational cost that grows linearly with respect to the frequency of the incident wave. Recently ChandlerWilde and Langdon proposed a novel Galerkin boundary element method fo...

We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound ...

This paper considers a progressive solitary wave of permanent form in an ideal fluid of constant depth and explores Davies’ approximation [Proc. R. Soc. Lond. A, 208 (1951), pp. 475– 486] with high-order corrections to Levi-Civita’s surface condition for the logarithmic hodograph variable. Using a complex plane that was originally introduced by Packham [Proc. R. Soc. Lond. A, 213 (1952), pp. 23...

We report a first-principles theoretical study of the surface relaxation and lattice dynamics of the Cu~211! surface using the plane-wave pseuodopotential method. We find large atomic relaxations for the first several atomic layers near the step edges on this surface, and a substantial step-induced renormalization of the surface harmonic force constants. We use the results to study the harmonic...

In the present paper, the problem of light reflection from a birefringent medium and thin film is considered. First, the analytical equations governing the propagation of a plane and harmonic electromagnetic wave in an infinite, birefringent, linear, non-dispersive, non-absorbing, and non-magnetic medium is derived from Maxwell equations. Then, using phase matching condition and boundary condit...

An approximation technique is considered for computing transmission and reflection coefficients for plane waves propagating through stratified slabs. The propagation of elastic pulse through a planar slab is derived from first principles using straightforward time-dependent method. The paper ends with calculations of enhancement factor for the elastic plane wave and it is shown that it depends ...

The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency. Each standing wave consists of two eigenwaves with different complex amplitudes and opposite directions of propagation....

Magnetic resonance elastography (MRE) is an increasingly used noninvasive modality for diagnosing diseases using the response of soft tissue to harmonic shear waves. We present a study on the algebraic Helmholtz inversion (AHI) applied to planar MRE, demonstrating that the deduced phase speed of shear waves depends strongly on the relative orientations of actuator polarization, motion encoding ...

An approximation technique is considered for computing transmission and reflection coefficients for propagation of an elastic pulse through a planar slab of finite width. The propagation of elastic pulse through a planar slab is derived from first principles using straightforward time-dependent method. The paper ends with calculations of enhancement factor for the elastic plane wave and it is s...