  The acoustic cloaking theory of Norris (2008) permits considerable freedom in
choosing the transformation function f from physical to virtual space. The
standard process for defining cloak materials is to first define f and then
evaluate whether the materials are practically realizable. In this paper, this
process is inverted by defining desirable material properties and then deriving
the appropriate transformations which guarantee the cloaking effect.
Transformations are derived which result in acoustic cloaks with special
properties such as 1) constant density 2) constant radial stiffness 3) constant
tangential stiffness 4) power-law density 5) power-law radial stiffness 6)
power-law tangential stiffness 7) minimal elastic anisotropy.
