Rattling and freezing in a 1D transport model

Jean Pierre Eckmann, Lai-Sang Young

Research output: Contribution to journalArticle

Abstract

We consider a heat conduction model introduced by Collet and Eckmann (2009 Commun. Math. Phys. 287 1015-38). 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 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.

Original languageEnglish (US)
Pages (from-to)207-226
Number of pages20
JournalNonlinearity
Volume24
Issue number1
DOIs
StatePublished - Jan 2011

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Freezing
freezing
baths
Open systems
Heat conduction
documentation
Momentum
conductive heat transfer
Model
Fluxes
Open Systems
Heat Conduction
Conductor
conductors
momentum
Collision
collisions
Contact
scattering
Unit

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Rattling and freezing in a 1D transport model. / Eckmann, Jean Pierre; Young, Lai-Sang.

In: Nonlinearity, Vol. 24, No. 1, 01.2011, p. 207-226.

Research output: Contribution to journalArticle

Eckmann, Jean Pierre ; Young, Lai-Sang. / Rattling and freezing in a 1D transport model. In: Nonlinearity. 2011 ; Vol. 24, No. 1. pp. 207-226.
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