We present the basic ideas and further developments of a new many-particle homogenization theory  for the electrical parameters (quasistatic conductivity, dielectric permittivity, and dielectric loss coefficient) of statistically homogeneous and isotropic particulate systems. The system’s microstructure is formulated in terms of the model of hard-core–penetrable-shell spheres. The cores are associated with particles. The shells account for different types of interfacial and matrix effects and are in general inhomogeneous. The desired parameters are calculated using the compact groups approach (CGA)  and internally-closed homogenization procedure. The former allows one to efficiently estimate many-particle polarization and correlation contributions without explicit detailing of the processes involved. The latter follows immediately from the requirement that the CGA and the boundary conditions for the complex electric field be consistent.
The theory has been used to process experimental data  for paraffin-based dispersed systems with embedded semiconductor (Fe2O3, CuO) or conductor (thermographite, Fe, Al) filler particles. It proves to describe the experiment surprisingly well in the entire range of filler particle concentrations. The physical nature of the effects incorporated by the shells is discussed. These may include: irregularities of particles’ shapes; contact resistance; formation and destruction of oxide layers; impurification of the host in the course of sample preparation; and others.
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Sushko M. Ya., Effective dielectric response of dispersions of graded particles // Phys Rev E.-2017.-96, N. 6.- P. 062121-1-6.
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