Scaling Properties of a Moving Polymer

TL;DR

This paper models a moving, weakly self-avoiding polymer using an SPDE and finds that its effective radius scales as J^{5/3}, indicating stretching for large intrinsic length J, contrasting with the equilibrium case.

Contribution

The paper introduces an SPDE model for a moving polymer and establishes its effective radius scaling law, revealing stretching behavior not seen in equilibrium models.

Findings

Effective radius scales as J^{5/3} for the model in R^2.

Contrasts with equilibrium case where radius scales as J.

Conjecture that in R^2, the radius scales as J^{5/4}.

Abstract

We set up an SPDE model for a moving, weakly self-avoiding polymer with intrinsic length $J$ taking values in $(0,\infty)$. Our main result states that the effective radius of the polymer is approximately $J^{5/3}$; evidently for large $J$ the polymer undergoes stretching. This contrasts with the equilibrium situation without the time variable, where many earlier results show that the effective radius is approximately $J$. For such a moving polymer taking values in $\mathbf{R}^2$, we offer a conjecture that the effective radius is approximately $J^{5/4}$.