I will describe a circle of results on the Smoluchowski-Kramers limit in
systems of stochastic differential equations.  Some of them were directly
motivated by experiments, others suggest further laboratory work.  In each
case we identify a noise-induced drift which significantly changes the
observed properties of the system.  This is a joint work with experimental
physicists:  Giovanni Volpe (Bilkent University, Ankara) and Giuseppe
Pesce (University of Naples)  and with Scott Hottovy and Austin
McDaniel---graduate students at the University of Arizona.