Floppy Membranes
M. C. Diamantini, H. Kleinert, C. A. Trugenberger
TL;DR
This paper discusses floppy membranes, tensionless surfaces governed by bending elasticity, which remain smooth and have a Hausdorff dimension of 2, unlike stiffer surfaces that are rough at certain scales.
Contribution
It introduces the concept of floppy membranes and characterizes their smoothness and dimensional properties due to bending elasticity.
Findings
Floppy membranes are tensionless and governed by bending elasticity.
They remain smooth over any distance with Hausdorff dimension D=2.
They contrast with stiffer surfaces that are rough at finite scales.
Abstract
Floppy membranes are tensionless surfaces without extrinsic stiffness, whose fluctuations are governed by fourth-order bending elasticity. This suppresses spiky superstructures and ensures that floppy membranes remain smooth over any distance, with Hausdorff dimension D=2, in contrast to surfaces with stiffness, which are rough on the scale of some finite persistence length.
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