A diagrammatic approach to response problems in composite systems

The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple-scattering expansion. A special diagrammatic method is developed for analyzing the structure of the expansion. The concept of irreducibility is discussed in detail and shown to be crucial in obtaining macroscopic equations characterizing the system response with coefficients depending solely on local properties of the medium. Due to the representation of particles by lines in diagrams, irreducibility is given a particularly simple topological interpretation in the diagrammatic language. The method is illustrated by a discussion of response problems in colloidal suspensions in the presence of hydrodynamic interactions.