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We consider time-dependence of dynamical transport, following a recent studyof the stadium billiard in which classical transmission and reflectionprobabilities were shown to exhibit exponential or algebraic decay depending onthe choice of the lead or "hole". The system considered here is much moregeneral, having a generic mixed phase space structure, time-dependence of thedynamics, and Fermi acceleration (trajectories with unbounded velocity). Wepropose an efficient numerical scheme for this model, observe the asymmetrictransport effect, and discuss observed stretched exponential decays.

Asymmetric transport in the bouncer model: Mixed, time dependent, noncompact dynamics