On hereditary models of polymers

TL;DR

This paper establishes a mathematical equivalence between operators related to polymer models, enabling estimation of solutions and applying wave hierarchy properties to analyze polymer chain behaviors.

Contribution

It introduces an equivalence between integro-differential and evolution operators, facilitating analysis of polymer models like Rouse and reptation.

Findings

Fundamental solutions are estimated using third-order operator behavior.

Wave hierarchy properties are applicable to polymeric materials.

Results are demonstrated on the case n=2, relevant to polymer chain models.

Abstract

An equivalence between an integro-differential operator M and an evolution operator Ln is determined. From this equivalence the fundamental solution of Ln is estimated in terms of the fundamental solution related to the third-order operator L1 whose behavior is now available. Moreover, properties typical of wave hierarchies can be applied to polymeric materials. As an example the case n= 2 is considered and results are applied to the Rouse model and the reptation model which describe different aspects of polymer chains.