Harmonic and transient scattering from time varying obstacles

Transient scattering as a tool for identification of objects and their physical properties through their natural (resonance) complex frequencies is now under intensive investigation by mathematicians and engineers. This promising method of inverse scattering is pertinent to mechanical as well as electromagnetic waves. Presently this problem is considered in the context of acoustics for time varying objects, such as pulsating cylinders and spheres. Together with a choice of a reasonably simple physical model and boundary conditions, this provides a framework for discussing a few canonical problems. Mathematically, the method employed here is essentially a perturbation technique. The representation in terms of compact symbolic differential operators which are manipulated algebraically helps to avoid a lot of cumbersome detail. The results display the creation of new spectral components and the associated new poles (i.e., new resonance frequencies) due to the time variation of the objects. The additional new features, when compared to the presumably known signature of the original object at rest, facilitate the identification of the details of the motion.