Friction mediated by transient elastic linkages : asymptotic expansions and fat tails

TL;DR

This paper extends adhesive models by allowing fat-tailed distributions of linkages, enabling the analysis of stronger adhesions with less frequent breakage, and develops systematic asymptotic expansions without requiring fast decay properties.

Contribution

It weakens the exponential tail assumption in adhesive models and provides a systematic method for asymptotic expansions with fat-tailed distributions.

Findings

Allows for fat-tailed linkage distributions in models

Constructs asymptotic expansions at any order

Overcomes decay property limitations in kernel functions

Abstract

Several results in previous works, strongly depend on the exponential tail of the linkages' distribution in our adhesive models. The purpose of this paper is to weaken this hypothesis and to allow more fat tails for large ages. From the biological point of view this means that we allow adhesions to be stronger, because linkages break less often. Moreover, in our previous articles, the asymptotic expansion of adhesion site's position and the corresponding error estimates also used some fast decay properties of the kernel, we show, when the kernel is a given function of age but constant in time, how to overcome this problem and construct asymptotic expansions in a systematic way at any order with respect to a small parameter $\epsilon$ representing the linkages' turnover.