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The Foldy-Lax equation is generalized for a medium which consists ofparticles with both electric and magnetic responses. The result is used tocompute fields scattered from ensembles of particles. The computationalcomplexity is reduced by hierarchical clustering techniques to enablesimulations with on the order of 10^10 particles. With so many particles we areable to see the transition to bulk media behavior of the fields. Fornon-magnetic materials, the observable index, permittivity, and permeability ofthe effective bulk medium are in good agreement with the Clausius-Mossottirelation. The fields simulated for particles with both electric and magneticresponses are in good agreement with new analytical results for a generalizedeffective medium theory.

Clustering Diffused-Particle Method for Scattering from Large Ensembles of Electromagnetically Polarizable Particles