Meanders: A Direct Enumeration Approach

Abstract

We study the statistics of semi-meanders, i.e. configurations of a set of roads crossing a river through n bridges, and possibly winding around its source, as a toy model for compact folding of polymers. By analyzing the results of a direct enumeration up to n=29, we perform on the one hand a large n extrapolation and on the other hand we reformulate the available data into a large q expansion, where q is a weight attached to each road. We predict a transition at q=2 between a low-q regime with irrelevant winding, and a large-q regime with relevant winding.

uses harvmac (l), epsf, 16 figs included, uuencoded, tar compressed

References in corpus (4)

• Meanders and the Temperley-Lieb algebra
• Meander, Folding and Arch Statistics
• Fermionic Matrix Models
• Supersymmetric Matrix Models and the Meander Problem

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• Folding Transitions of the Square-Diagonal Lattice
• Asymptotics for a Class of Meandric Systems, via the Hasse Diagram of NC(n)
• Vertex Models on Feynman Diagrams
• Geometrically Constrained Statistical Models on Fixed and Random Lattices: From Hard Squares to Meanders
• Asymptotic behavior of two-terminal series-parallel networks