  Self-powered motion in catalytic colloidal particles provides a compelling
example of active matter, i.e. systems that engage in single-particle and
collective behavior far from equilibrium. The long-time, long-distance behavior
of such systems is of particular interest, since it connects their individual
micro-scale behavior to macro-scale phenomena. In such analyses, it is
important to distinguish motion due to subtle advective effects -- which also
has long time scales and length scales -- from phenomena that derive from
intrinsically powered motion. Here, we develop a methodology to analyze the
statistical properties of the translational and rotational motions of powered
colloids to distinguish, for example, active chemotaxis from passive advection
by bulk flow.
