Rattling and freezing in a 1-D transport model

TL;DR

This paper investigates a 1-D heat conduction model where particles slow down over time, leading to reduced system effectiveness, with detailed numerical and theoretical analysis of the freezing phenomenon and its impact on energy and fluxes.

Contribution

It provides a qualitative and numerical analysis of freezing in a 1-D transport model, offering a theoretical explanation for the slowdown phenomenon.

Findings

Particles exhibit freezing, significantly reducing collisions and system contact with baths.

Energy and fluxes show unusual relationships with particle density.

Freezing occurs as an extremely slow process, making the system appear steady for long periods.

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.