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The main objective of this Report is to formulate the general theoreticalframework of electromagnetic scattering by discrete random media rooted in theMaxwell-Lorentz electromagnetics and discuss its immediate analytical andnumerical consequences. Starting from the microscopic Maxwell-Lorentzequations, we trace the development of the first-principles formalism enablingaccurate calculations of monochromatic and quasi-monochromatic scattering bystatic and randomly varying multiparticle groups. We illustrate how thisgeneral framework can be coupled with state-of-the-art computer solvers of theMaxwell equations and applied to direct modeling of electromagnetic scatteringby representative random multi-particle groups with arbitrary packingdensities. This first-principles modeling yields general physical insightsunavailable with phenomenological approaches. We discuss how thefirst-order-scattering approximation, the radiative transfer theory, and thetheory of weak localization of electromagnetic waves can be derived asimmediate corollaries of the Maxwell equations for very specific andwell-defined kinds of particulate medium. These recent developments confirm themesoscopic origin of the radiative transfer, weak localization, andeffective-medium regimes and help evaluate the numerical accuracy of widelyused approximate modeling methodologies.

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media