### 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 language | English (US) |
---|---|

Pages (from-to) | 207-226 |

Number of pages | 20 |

Journal | Nonlinearity |

Volume | 24 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2011 |

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### ASJC Scopus subject areas

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

### Cite this

*Nonlinearity*,

*24*(1), 207-226. https://doi.org/10.1088/0951-7715/24/1/010

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

Research output: Contribution to journal › Article

*Nonlinearity*, vol. 24, no. 1, pp. 207-226. https://doi.org/10.1088/0951-7715/24/1/010

}

TY - JOUR

T1 - Rattling and freezing in a 1D transport model

AU - Eckmann, Jean Pierre

AU - Young, Lai-Sang

PY - 2011/1

Y1 - 2011/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79251601649&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79251601649&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/24/1/010

DO - 10.1088/0951-7715/24/1/010

M3 - Article

AN - SCOPUS:79251601649

VL - 24

SP - 207

EP - 226

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 1

ER -