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Starting from a fine-scale dissipative particle dynamics (DPD) model ofself-motile point particles, we derive meso-scale continuum equations byapplying a spatial averaging version of the Irving--Kirkwood--Noll procedure.Since the method does not rely on kinetic theory, the derivation is valid forhighly concentrated particle systems. Spatial averaging yields a stochasticcontinuum equations similar to those of Toner and Tu. However, our theory alsoinvolves a constitutive equation for the average fluctuation force. Accordingto this equation, both the strength and the probability distribution vary withtime and position through the effective mass density. The statistics of thefluctuation force also depend on the fine scale dissipative force equation, thephysical temperature, and two additional parameters which characterizefluctuation strengths. Although the self-propulsion force entering our DPDmodel contains no explicit mechanism for aligning the velocities of neighboringparticles, our averaged coarse-scale equations include the commonly encounteredcubically nonlinear (internal) body force density.

Spatial averaging of a dissipative particle dynamics model for active suspensions