Effective Radius of a Discrete Moving Polymer

TL;DR

This paper introduces a discrete SPDE model for weakly self-avoiding polymers, demonstrating that the root mean squared radius scales linearly with the intrinsic length, contrasting continuous model predictions.

Contribution

The paper develops a novel discrete SPDE framework with a tailored penalty factor, providing new insights into polymer scaling behavior in lattice environments.

Findings

Root mean squared radius scales linearly with intrinsic length J

Discrete model differs from continuous law by Mueller and Neuman

Analytical tractability for lattice-like polymer environments

Abstract

We present a discrete space-time stochastic partial differential equation (SPDE) model to describe the dynamics of a weakly self-avoiding polymer with intrinsic length $J$. By introducing a penalty factor tailored to the discrete setting, we establish that the polymer's root mean squared radius scales linearly with $J$. This scaling behavior differs from the law derived by Mueller and Neuman \cite{mueller2022scaling} in the continuous framework, highlighting both the distinct nature of the discrete model and its analytical tractability for studying polymer behavior in lattice-like environments.