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The Mathematics of Granular Media

Peter Rudzis
Monday, November 2, 2020 - 2:30pm to 3:30pm

Granular media equations are variants of the Boltzmann equation which model a fluid of particles in which particle-to-particle interactions are energy-dissipative. An active area of research with many open questions, a number of mathematical techniques have been leveraged to understand granular media, ranging from the traditional analytical techniques of moment analysis and Fourier analysis to more modern approaches such as studying the Wasserstein gradient flow structure found in some of the equations. We will present the basic models for granular media, discussing physical assumptions and motivation, survey the range of techniques used to study these models, and along the way ponder some of the big open questions and surprising results in this field. The material for this talk is taken from a survey paper by Cédric Villani of the same name.

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