Burdzy, KrzysztofRudzis, Peter Francis2022-09-232022-09-232022-09-232022Rudzis_washington_0250E_24785.pdfhttp://hdl.handle.net/1773/49400Thesis (Ph.D.)--University of Washington, 2022A rough collision law describes the limiting contact dynamics of a pair of rough rigid bodies, as the scale of the rough features (asperities) on the surface of each body goes to zero. The class of rough collision laws is quite large and includes random elements. The main results of this work characterize the rough collision laws for a freely moving rough disk and a fixed rough wall in dimension 2. Any collision law which (i) is symmetric with respect to a certain well-known invariant measure from billiards theory, and (ii) conserves the projection of the phase space velocity onto the ``rolling velocity'' is a rough collision law. We provide a method for explicitly constructing rough collision laws for a broad range of choices of microstructure on the disk and wall. Having established the collision dynamics, we also investigate the ergodic properties of the system consisting of a rough disk bouncing between two parallel rough walls. For such a system, we describe necessary and sufficient conditions for when Lambertian measure is ergodic. In our introduction, we review past work in billiards, including characterizations of other rough billiard systems due to Plakhov and to Angel, Burdzy, and Sheffield, which our results build upon.application/pdfen-USnonecontact dynamicsfrictional collisionsinvariant measurerigid bodystochastic billiardsMathematicsMathematicsThesis