  We have studied the effective response of composites of spherical particles
each having a dielectric profile which varies along the radius of the
particles. We developed a first-principles approach to compute the dipole
moment of the individual spherical particle and hence the effective dielectric
response of a dilute suspension. The approach has been applied to two model
dielectric profiles, for which exact solutions are available. Moreover, we used
the exact results to validate the results from the differential effective
dipole approximation, recently developed to treat graded spherical particles of
an arbitrary dielectric profile. Excellent agreement between the two approaches
were obtained. While the focus of this work has been on dielectric responses,
the approach is equally applicable to analogous systems such as the
conductivity and elastic problems.
