Abstract
We solve analytically for the perimeter-area generating functions for two models of vesicles. While from the solution of the first model, staircase polygons, one can easily extract the asymptotic scaling behavior, the exact solution of the second, column-convex polygons, is difficult to analyze. This leads us to apply a recently developed method for deriving the scaling behavior indirectly, utilizing a set of nonlinear differential equations. One result of this work is a nontrivial confirmation of the scaling/universality hypothesis.
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Brak, R., Owczarek, A.L. & Prellberg, T. Exact scaling behavior of partially convex vesicles. J Stat Phys 76, 1101–1128 (1994). https://doi.org/10.1007/BF02187057
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DOI: https://doi.org/10.1007/BF02187057