Superposition of Harmonic Surfaces: Helical Motifs in Lamellar Structures

TL;DR

This paper explores harmonic surfaces in three-dimensional space, establishing a superposition principle and applying it to model complex lamellar structures with helical motifs.

Contribution

It introduces a superposition principle for harmonic surfaces and demonstrates its use in constructing and analyzing lamellar structures with helical features.

Findings

Harmonic surfaces can be decomposed into harmonic components.

Constructed configurations of helical motifs in lamellar structures.

Provided asymptotic analysis using multipole expansions.

Abstract

We study harmonic surfaces in $\mathbb{R}^3$ through the framework of harmonic Enneper immersions and prove a superposition principle for such surfaces. We prove that minimal and maximal surfaces admit a decomposition into harmonic components. Applications include the construction of finite and infinite configurations of helical motifs, an asymptotic analysis via multipole expansions, and the modelling of twist grain boundary phases in lamellar systems.