URI Physics Colloquium

Interacting rods in a heterogeneous environment

Gerhard Müller
University of Rhode Island
November 7, 2014

Abstract

We consider linear arrays of cells of volume Vc populated by rods of one size, sVc, s=1,2,… subject to a hardcore exclusion interaction. Each rod experiences a position-dependent external potential. In some applications the rods also interact via a contact force, in others by a special kind of long-range force.

We employ two distinct methods of exact analysis with complementary strengths to calculate profiles of pressure, mass density, and entropy density on mesoscopic and microscopic length scales at thermal equilibrium. One method uses density functionals and the other statistically interacting vacancy particles. The applications worked out include gravity, power-law traps, and centrifuges. For rods of size s>1 the profiles exhibit spatial oscillations on a microscopic length scale.

The continuum limit reveals significant differences between lattice and continuum versions of the same model. Generalizations to dimensions two (cylindrical symmetry) and three (spherical symmetry), relying on additional assumptions, are demonstrated.