  Spatial tailoring of the material constitutive properties is a well-known
strategy to mold the local flow of given observables in different physical
domains. Coordinate-transformation-based methods (e.g., transformation optics)
offer a powerful and systematic approach to design anisotropic,
spatially-inhomogeneous artificial materials ("metamaterials") capable of
precisely manipulating wave-based (electromagnetic, acoustic, elastic) as well
as diffusion-based (heat) phenomena in a desired fashion. However versatile
these approaches have been, most designs have so far been limited to serving
single-target functionalities in a given physical domain. Here we present a
step towards a "transformation multiphysics" framework that allows independent
and simultaneous manipulation of multiple physical phenomena. As a proof of
principle of this new scheme, we design and synthesize (in terms of realistic
material constituents) a metamaterial shell that simultaneously behaves as a
thermal concentrator and an electrical "invisibility cloak". Our numerical
results open up intriguing possibilities in the largely unexplored phase space
of multi-functional metadevices, with a wide variety of potential applications
to electrical, magnetic, acoustic, and thermal scenarios.
