Abstract:

An acoustic cloak is a region enclosing an object such that acoustic waves from all directions pass through and around the cloak as though the object was not present in the fluid. The object has zero scattering strength and is therefore acoustically invisible. Several researchers have proposed using fluids with anisotropic inertia for the cloaking material, but this has been shown by the author to require a cloak with infinite mass. An alternative framework is to use pentamodal materials, which guarantees finite mass and, under certain circumstances, isotropic inertia. The acoustic cloaking theory recently proposed by the author for acoustics is but one element in a class of cloaking theories for pentamodal materials. The main result is that pentamodal materials with anisotropic inertia form an invariant set of materials under arbitrary finite deformation and under the condition that the deformed material is cloaked. The general theory is explained using the language of finite deformations, common in continuum mechanics. The group properties follow by considering finite deformation in combination with gauge transformations. The talk will attempt to explain the meaning of pentamodal materials and show that the mathematics of transformation is related to simple physical requirements of transparency.