David Pine Center for Soft Matter Research Department of Physics New York University Title: Random organization in periodically driven systems   Abstract: Systems governed by time-reversible equations of motion often give rise to irreversible behavior.  The transition from reversible to irreversible behavior is fundamental to statistical physics, but has not been observed experimentally in many-body systems.  In a series of experiments, we show that sheared suspensions of solid particles, governed by time-reversible equations of motion, undergo a transition from irreversible to reversible behavior under periodic shear.  We then introduce a new model that shows how irreversible collisions between the suspended particles can cause such a system to self-organize to avoid future collisions. This can lead to a self-organized non-fluctuating quiescent state, with a dynamical phase transition separating it from fluctuating diffusing states.  Experiments exhibit remarkable agreement with this simple model, and provide new insights into how driven systems can self-organize.