Invisible obstacles

TL;DR

This paper proves that it is possible to choose boundary controls on an obstacle to make its total radiation arbitrarily small for a fixed incident wave, effectively rendering it invisible in that context.

Contribution

It introduces a method to control boundary functions on obstacles to achieve near invisibility for fixed incident waves and wave numbers.

Findings

Total radiation can be minimized arbitrarily by boundary control.

Existence of boundary functions that make obstacles effectively invisible.

Control can be applied on arbitrarily small boundary subsets.

Abstract

It is proved that one can choose a control function on an arbitrary small open subset of the boundary of an obstacle so that the total radiation from this obstacle for a fixed direction of the incident plane wave and for a fixed wave number will be as small as one wishes. The obstacle is called "invisible" in this case.