On Radlow's quarter-plane diffraction solution

Corner Diffraction Coefficients for the Quarter Plane

The current near a right-angled comer on a perfectly conducting flat scatterer illuminated by a plane wave is expressed as a sum of three currents. The first is the physical optics (PO) current, which describes the surface effect. The second is the fringe wave (FW) current, which is found from the half-plane solution and accounts for the distortion of the current caused by the edges. The third ...

A new solution representation for the BBM equation in a quarter plane and the eventual periodicity

The initialand boundary-value problem for the Benjamin-Bona-Mahony (BBM) equation is studied in this paper. The goal is to understand the periodic behavior (termed as eventual periodicity) of its solutions corresponding to periodic boundary condition or periodic forcing. To this aim, we derive a new formula representing solutions of this initialand boundary-value problem by inverting the operat...

Optical Diffraction in Close Proximity to Plane Apertures. II. Comparison of Half-Plane Diffraction Theories

The accuracy and physical significance of the classical Rayleigh-Sommerfeld and Kirchhoff diffraction integrals are assessed in the context of Sommerfeld's rigorous theory of half-plane diffraction and Maxwell's equations. It is shown that the Rayleigh-Sommerfeld integrals are in satisfactory agreement with Sommerfeld's theory in most of the positive near zone, except at sub-wavelength distance...

Toeplitz Operators in a Quarter-plane by Gilbert Strang

Classifying lattice walks restricted to the quarter plane

This work considers lattice walks restricted to the quarter plane, with steps taken from a set of cardinality three. We present a complete classification of the generating functions of these walks with respect to the classes algebraic, transcendental holonomic and non-holonomic. The principal results are a new algebraic class related to Kreweras’ walks; two new non-holonomic classes; and enumer...