A Fast Algorithm for Generating Long Self-Affine Profiles

TL;DR

This paper presents a wavelet-based algorithm that efficiently generates long self-affine profiles with consistent long-range correlations, outperforming traditional Fourier filtering methods in speed and scalability.

Contribution

The paper introduces a novel wavelet filtering algorithm that significantly improves the efficiency of generating long self-affine profiles with persistent correlations.

Findings

The wavelet filtering algorithm is faster than Fourier filtering for large systems.

It produces profiles with long-range correlations throughout the entire system.

The method is scalable for generating very long self-affine profiles.

Abstract

We introduce a fast algorithm for generating long self-affine profiles. The algorithm, which is based on the fast wavelet transform, is faster than the conventional Fourier filtering algorithm. In addition to increased performance for large systems, the algorithm, named the wavelet filtering algorithm, a priori gives rise to profiles for which the long-range correlation extends throughout the entire system independently of the length scale.