Condensed Matter Theory

Abstract:

A lattice Boltzmann algorithm is used to simulate the slow spreading of drops on a surface patterned with slanted micro-posts. Gibb's pinning of the interface on the sides or top of the posts leads to unidirectional spreading over a wide range of contact angles and inclination angles of the posts. Regimes for spreading in no, one or two directions are identified, and shown to agree well with a two-dimensional theory proposed in Chu, Xiao and Wang. A more detailed numerical analysis of the contact line shapes allows us to understand deviations from the two dimensional model, and to identify the shapes of the pinned interfaces. © 2013 The Royal Society of Chemistry.

Abstract:

Statistical lattice ensembles of loops in three or more dimensions typically have phases in which the longest loops fill a finite fraction of the system. In such phases it is natural to ask about the distribution of loop lengths. We show how to calculate moments of these distributions using $CP^{n-1}$ or $RP^{n-1}$ and O(n) $\sigma$ models together with replica techniques. The resulting joint length distribution for macroscopic loops is Poisson-Dirichlet with a parameter $\theta$ fixed by the loop fugacity and by symmetries of the ensemble. We also discuss features of the length distribution for shorter loops, and use numerical simulations to test and illustrate our conclusions.