Exact solutions of lattice polymer models |
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| Authors: | R Brak A L Owczarek A Rechnitzer |
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| Institution: | (1) Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, 3052, Australia;(2) Department of Mathematics, University of British Columbia, Vancouver, BC, Canada, V6T-1Z2 |
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| Abstract: | We consider directed path models of a selection of polymer and vesicle problems. Each model is used to illustrate an important
method of solving lattice path enumeration problems. In particular, the Temperley method is used for the polymer collapse
problem. The ZL method is used to solve the semi-continuous vesicle model. The Constant Term method is used to solve a set
of partial difference equations for the polymer adsorption problem. The Kernel method is used to solve the functional equation
that arises in the polymer force problem. Finally, the Transfer Matrix method is used to solve a problem in colloid dispersions.
All these methods are combinatorially similar as they all construct equations by considering the action of adding an additional
column to the set of objects. |
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| Keywords: | Interacting self-avoiding walks Directed paths Polymer adsorption Polymer collapse Vesicles Exact solution Combinatorics |
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