Dynamic Scaling of Non-Euclidean Interfaces

TL;DR

This paper investigates how curved interfaces, especially on spherical surfaces, exhibit unique dynamic scaling behaviors differing from flat interfaces, highlighting the need to reexamine experimental scaling analyses in such contexts.

Contribution

It introduces a theoretical framework for understanding the dynamic scaling of non-Euclidean interfaces, emphasizing differences from planar cases and implications for experimental analysis.

Findings

Spherical interfaces are effectively flat due to irrelevant noise.

Kinetic roughening on curved surfaces is characterized by marginal logarithmic fluctuations.

Standard scaling analysis may be inadequate for curved interface experiments.

Abstract

The dynamic scaling of curved interfaces presents features that are strikingly different from those of the planar ones. Spherical surfaces above one dimension are flat because the noise is irrelevant in such cases. Kinetic roughening is thus a one-dimensional phenomenon characterized by a marginal logarithmic amplitude of the fluctuations. Models characterized by a planar dynamical exponent $z>1$, which include the most common stochastic growth equations, suffer a loss of correlation along the interface, and their dynamics reduce to that of the radial random deposition model in the long time limit. The consequences in several applications are discussed, and we conclude that it is necessary to reexamine some experimental results in which standard scaling analysis was applied.