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arXiv · 1007.0582

Rattling and freezing in a 1-D transport model

Jean-Pierre Eckmann·Lai-Sang Young
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Abstract

We consider a heat conduction model introduced in \cite{Collet-Eckmann 2009}. This is an open system in which particles exchange momentum with a row of (fixed) scatterers. We assume simplified bath conditions throughout, and give a qualitative description of the dynamics extrapolating from the case of a single particle for which we have a fairly clear understanding. The main phenomenon discussed is {\it freezing}, or the slowing down of particles with time. As particle number is conserved, this means fewer collisions per unit time, and less contact with the baths; in other words, the conductor becomes less effective. Careful numerical documentation of freezing is provided, and a theoretical explanation is proposed. Freezing being an extremely slow process, however, the system behaves as though it is in a steady state for long durations. Quantities such as energy and fluxes are studied, and are found to have curious relationships with particle density.

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Jean-Pierre Eckmann, Lai-Sang Young. 2010-07-04. Rattling and freezing in a 1-D transport model. https://doi.org/10.1088/0951-7715%2F24%2F1%2F010

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