Persistence of a pinch in a pipe

TL;DR

This paper reveals that a localized pinch in an elastic pipe persists over a surprisingly long distance, with the persistence length diverging as the pipe's thickness decreases, a phenomenon confirmed experimentally and rooted in geometry.

Contribution

It demonstrates a novel geometric effect causing long-range persistence of localized deformations in tubular structures, applicable across various materials.

Findings

Persistence length diverges as pipe thickness approaches zero.

Experimental confirmation of slow, oscillatory decay of the pinch.

Effect is primarily geometric, not material-dependent.

Abstract

The response of low-dimensional solid objects combines geometry and physics in unusual ways, exemplified in structures of great utility such as a thin-walled tube that is ubiquitous in nature and technology. Here we provide a particularly surprising consequence of this confluence of geometry and physics in tubular structures: the anomalously large persistence of a localized pinch in an elastic pipe whose effect decays very slowly as an oscillatory exponential with a persistence length that diverges as the thickness of the tube vanishes, which we confirm experimentally. The result is more a consequence of geometry than material properties, and is thus equally applicable to carbon nanotubes as it is to oil pipelines.