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Final Exam

Peter Rudzis
Tuesday, July 26, 2022 - 8:30am
via ZOOM

Advisor: Chris Burdzy

Title: Ergodicity of rough collision dynamics

Abstract: A 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. In this talk, we will consider a rough disk colliding with a fixed rough wall in dimension two. In this setting, the class of rough collision laws has a simple characterization in terms of a reversible measure and a conserved quantity related to "rolling'' collisions. The reversible measure is a variant of Lambertian distribution, studied in geometric optics, and is universal in the sense that it does not depend on the shape of the microscopic rough features on the surface of each body. We will consider the Markov process obtained by allowing the rough disk to bounce randomly between two parallel rough walls, stating general conditions under which Lambertian distribution is the unique non-singular ergodic measure for the process.

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