On the power spectrum of undulations of simulated bilayers

TL;DR

This paper compares Fourier analysis methods for bilayer undulations, showing they produce consistent structure factors with key physical features, and discusses the Laurent series approach.

Contribution

It demonstrates the equivalence of Fourier series and direct summation methods for analyzing bilayer surface undulations and explores the Laurent series approach.

Findings

Fourier series and direct summation yield identical structure factors.

Structure factors exhibit key physical features like divergence and peaks.

Laurent series analysis is also discussed.

Abstract

The best finite Fourier Series for a smooth surface $h(x,y)$ closest to the positions of heads of amphiphiles in the least-square sense, agrees fully with the Fourier coefficients obtained by a direct summation over raw data points. Both metods produce structure factors $S(q)$ containing all necessary features: small-q divergence, a minimum, the raise to the ubiquitous nearest neighbor peak near $q=2\pi/$(coll.diameter) and further peaks. The Laurent series is also discussed.