Here, U ∞ ∞ is the velocity of the bulk shear flow evaluated at the particle center, E ∞ ∞ is the symmetric part of the velocity-gradient tensor; R F U and R F E are the configuration-dependent resistance matrices that give the hydrodynamic force/torque on the particles due to their motion relative to the fluid ( R F U ) and due to the imposed shear flow ( R F E ). Note that the subscripts on the matrices indicate the coupling between kinematic ( U ) and dynamic ( F ) quantities.