Dynamical aspects of inextensible chains

TL;DR

This paper develops a novel Langevin equation-based approach to study the dynamics of inextensible chains, deriving generating functionals for different models and showing their convergence in the continuous limit.

Contribution

It introduces a non-Gaussian Langevin framework for inextensible chains and compares different chain models, highlighting their similarities and differences in the continuous limit.

Findings

Derived the generating functional for a freely hinged chain.

Constructed the generating functional for a freely jointed bar chain.

Showed that different chain models converge to the same functional in the continuous limit.

Abstract

In the present work the dynamics of a continuous inextensible chain is studied. The chain is regarded as a system of small particles subjected to constraints on their reciprocal distances. It is proposed a treatment of systems of this kind based on a set Langevin equations in which the noise is characterized by a non-gaussian probability distribution. The method is explained in the case of a freely hinged chain. In particular, the generating functional of the correlation functions of the relevant degrees of freedom which describe the conformations of this chain is derived. It is shown that in the continuous limit this generating functional coincides with a model of an inextensible chain previously discussed by one of the authors of this work. Next, the approach developed here is applied to a inextensible chain, called the freely jointed bar chain, in which the basic units are small extended objects. The generating functional of the freely jointed bar chain is constructed. It is shown that it differs profoundly from that of the freely hinged chain. Despite the differences, it is verified that in the continuous limit both generating functionals coincide as it is expected.