Exact Solution for a 1-dimensional model for Reptation
Andrzej Drzewinski, J. M. J. van Leeuwen
TL;DR
This paper provides an exact analytical solution for a one-dimensional reptation model, detailing key dynamic properties like drift velocity, diffusion constant, and renewal time, and relating it to the Rubinstein-Duke model.
Contribution
It introduces an exact solution for the necklace model in one dimension, offering precise calculations of dynamic properties and connecting it to existing models.
Findings
Exact expressions for drift velocity, diffusion constant, and renewal time.
The model's properties are related to a special case of the Rubinstein-Duke model.
Provides insights into the dynamics of reptation in one-dimensional systems.
Abstract
We discuss the exact solution for the properties of the recently introduced ``necklace'' model for reptation. The solution gives the drift velocity, diffusion constant and renewal time for asymptotically long chains. Its properties are also related to a special case of the Rubinstein-Duke model in one dimension.
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