The pressure exerted by adsorbing directed lattice paths and staircase polygons

A directed path in the vicinity of a hard wall exerts pressure on the wall because of loss of entropy. The pressure at a particular point may be estimated by estimating the loss of entropy if the point is excluded from the path. In this paper we determine asymptotic expressions for the pressure on t...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2013-03, Vol.46 (11), p.115202-20
Main Authors: van Rensburg, E J Janse, Prellberg, T
Format: Article
Language:English
Subjects:
adsorbing polymer
Approximation
asymptotic approximations
Asymptotic properties
directed lattice paths
Entropy
generating functions
Lattices
Mathematical analysis
Mathematical models
Polygons
Staircases
Walls
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Summary:A directed path in the vicinity of a hard wall exerts pressure on the wall because of loss of entropy. The pressure at a particular point may be estimated by estimating the loss of entropy if the point is excluded from the path. In this paper we determine asymptotic expressions for the pressure on the X-axis in models of adsorbing directed paths in the first quadrant. Our models show that the pressure vanishes in the limit of long paths in the desorbed phase, but there is a non-zero pressure in the adsorbed phase. We determine asymptotic approximations of the pressure for finite length Dyck paths and directed paths, as well as for a model of adsorbing staircase polygons with both ends grafted to the X-axis.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/46/11/115202