Extended Self-similarity in Kinetic Surface Roughening

TL;DR

This paper demonstrates that in kinetic surface roughening, extended self-similarity enhances the observable scaling range, indicating that relative exponents may be more fundamental than absolute ones, based on numerical simulations.

Contribution

It introduces the concept of extended self-similarity in kinetic surface roughening and shows its effectiveness in increasing the scaling range in simulations.

Findings

Extended self-similarity enhances the scaling range.

The behavior is observed in both one and two dimensions.

Relative exponents may be more fundamental than absolute exponents.

Abstract

We show from numerical simulations that a limited mobility solid-on-solid model of kinetically rough surface growth exhibits extended self-similarity analogous to that found in fluid turbulence. The range over which scale-independent power-law behavior is observed is significantly enhanced if two correlation functions of different order, such as those representing two different moments of the difference in height between two points, are plotted against each other. This behavior, found in both one and two dimensions, suggests that the `relative' exponents may be more fundamental than the `absolute' ones.