The shape of cleaved tethered membranes

TL;DR

This study investigates how systematic internal cleaving affects the morphology of flexible elastic membranes, revealing controlled collapse into complex shapes and a universal behavior in certain cases.

Contribution

It introduces a novel numerical analysis of how internal bond cleaving influences membrane shapes, highlighting controllable morphological transitions.

Findings

Cleaving leads to controlled collapse into complex morphologies.

Membranes with bending rigidity exhibit a universal radius of gyration curve.

Random bond removal does not disrupt membrane extension.

Abstract

A remarkable property of flexible self-avoiding elastic surfaces (membranes) is that they remain flat at all temperatures, even in the absence of a bending rigidity or in the presence of active fluctuations. Here, we report numerical results of these surfaces wherein we alter their topology by systematically cleaving internal bonds. While it is known that a random removal of membrane bonds does not disrupt the overall extended shape of the membrane, we find that cleaving an elastic surface with longitudinal parallel cuts leads to its systematic collapse into a number of complex morphologies that can be controlled by altering the number and length of the inserted cuts. For the simpler case of membranes with bending rigidity but in the absence of self-avoidance, we find that the radius of gyration of the surface as a function of number of cuts is represented by a universal master curve when the variables are appropriately rescaled.