Width scaling of an interface constrained by a membrane

TL;DR

This paper explores how the shape and growth of an interface are affected by a membrane, revealing two different universality classes depending on the membrane's position, with implications for biological membrane and colony growth.

Contribution

It identifies two distinct universality classes for interface growth constrained by a membrane, expanding understanding of interfacial dynamics under geometrical constraints.

Findings

Ahead arrangement exhibits standard KPZ growth.

Behind arrangement shows arrested KPZ with smaller roughness exponent.

Different arrangements lead to fundamentally different surface properties.

Abstract

We investigate the shape of a growing interface in the presence of an impenetrable moving membrane. The two distinct geometrical arrangements of the interface and membrane, obtained by placing the membrane behind or ahead of the interface, are not symmetrically related. On the basis of numerical results and an exact calculation, we argue that these two arrangements represent two distinct universality classes for interfacial growth: whilst the well-established Kardar-Parisi-Zhang (KPZ) growth is obtained in the `ahead' arrangement, we find an arrested KPZ growth with a smaller roughness exponent in the `behind' arrangement. This suggests that the surface properties of growing cell membranes and expanding bacterial colonies, for example, are fundamentally distinct.