  We generalize the compact group approach to conducting systems to give a
self-consistent analytical solution to the problem of the effective quasistatic
electrical conductivity of macroscopically homogeneous and isotropic
dispersions of hard-core--penetrable-shell particles. The shells are in general
inhomogeneous and characterized by a radially-symmetrical, piecewise-continuous
conductivity profile. The local value of the conductivity is determined by the
shortest distance from the point of interest to the nearest particle. The
effective conductivity is expressed in terms of the constituents'
conductivities and volume concentrations; the latter account for the
statistical microstructure of the system. The theory effectively incorporates
many-particle effects and is expected to be rigorous in the static limit. Using
the well-tested statistical physics results for the shell volume concentration,
this conclusion is backed up by mapping the theory on available 3D random
resistor network simulations for hard spheres coated with fully penetrable
concentric shells. Finally, the theory is shown to fit experimental data for
real composite solid electrolytes. The fitting results indicate that the effect
of enhanced electrical conduction is generally contributed to by several
mechanisms. These are effectively taken into account through the shell
conductivity profile.
