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Unexpected thermodynamic properties of some exact far-from-equilibrium solutions in molecular dynamics

Monday, August 7, 2017 - 10:00am - 10:45am
Vincent 215
Richard James (University of Minnesota, Twin Cities)
This lecture gives an introduction to the concept of “objective structures” (OS) and also serves to provide elementary background material for the lectures of Kaushik Dayal and Alessia Nota. More specifically, after a quick general introduction to OS, we describe a time-dependent invariant manifold of the equations of molecular dynamics (MD). The manifold is independent of the description of the atomic forces within a general framework: it is exactly the same manifold whether the atoms are those of steel, water or air. Some version of this manifold is inherited by all accepted models of continuum mechanics, as well as the Boltzmann equation. Some of the MD solutions correspond to certain far-from equilibrium, unsteady flows, while others are naturally associated with the dynamics of particular nanostructures. Both simulations and a study of the Boltzmann equation suggest the presence of certain thermodynamic relations that are completely unexpected in these far-from-equilibrium situations. This lecture draws on joint work with Amartya Banerjee, Kaushik Dayal, Stefan Mueller, Alessia Nota and Juan Velazquez.