Special Seminar in honor of the opening of the

Carolina Center for Interdisciplinary Applied Mathematics (C²IAM)

Please note the special time and place:

Thursday, January 24th
Reception to begin at 4pm in the Math Lounge, Phillips 330
The seminar will begin at 5pm in Phillips 215

Louis Howard

Mathematics Department, MIT (Emeritus)
Adjunct Professor, Department of Mathematics, Duke University

Title: Some effects of bottom corrugations on surface water waves.

Abstract:

When a beam of x-rays impinges on a crystal, it usually mostly passes right through, but a small amount is scattered by each of the nuclei in the crystal. In certain directions, which depend on the wave length of the x-rays and the atomic spacings in the crystal, the scattered waves from the various nuclei add up constructively, providing greatly enhanced scattering in those directions. The resulting x-ray diffraction patterns, first extensively studied by the Braggs, can be interpreted to determine crystal structures and even much information about the molecular structure of any compounds which can be crystallized.

An analogous phenomenon occurs when water waves pass over a periodically varying bottom, for example a series of parallel sandbars, as are indeed to be found on some beaches. In the simplest case, a plane wave train passing over a regular array of bottom corrugations whose crests are parallel to those of the water waves, the enhanced Bragg reflection occurs when the corrugation spacing is nearly half the water wave length. Several interesting and sometimes surprising consequences of this will be described, together with the main ideas of the mathematics which has been found useful in studying them.