Condensation of hard rods under gravity: Exact results in one dimension
Abstract
We present exact results for the density profile of a one dimensional array of N hard rods of diameter D and mass m under gravity g. For a strictly one dimensional system, the liquidsolid transition occurs at zero temperature, because the closepacked density φ_{c} is 1. However, if we relax this condition slightly such that φ_{c}=1δ, we find a series of critical temperatures T^{(i)}_{c}=mgD(N+1i)/μ_{0} with μ_{0}=1/δ1, at which the ith particle undergoes the liquidsolid transition. The functional form of the onset temperature, T^{(1)}_{c}=mgDN/μ_{0}, is consistent with the previous result [Physica A 271, 192 (1999)] obtained by the Enskog equation. We also show that the increase in the center of mass is linear in T before the transition, but it becomes quadratic in T after the transition because of the formation of solid near the bottom.
 Publication:

Physical Review E
 Pub Date:
 May 2001
 DOI:
 10.1103/PhysRevE.63.051506
 arXiv:
 arXiv:condmat/0007494
 Bibcode:
 2001PhRvE..63e1506H
 Keywords:

 64.70.Dv;
 51.30.+i;
 45.70.Vn;
 Solidliquid transitions;
 Thermodynamic properties equations of state;
 Granular models of complex systems;
 traffic flow;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Materials Science
 EPrint:
 doi:10.1103/PhysRevE.63.051506