Quasicrystalline three-dimensional foams

TL;DR

This paper explores quasiperiodic foam structures generated from Frank-Kasper phases, aiming to address the Kelvin problem by identifying configurations with minimal surface area, and finds structures close to the best known solutions.

Contribution

It introduces a numerical approach to generate quasiperiodic foams and analyzes their potential to solve the Kelvin problem, revealing structures near optimal configurations.

Findings

One structure closely approaches the best known Kelvin solution.

Quasiperiodic foams can be effective candidates for minimal surface partitioning.

Provides insights into geometrical factors influencing minimal surface arrangements.

Abstract

We present a numerical study of quasiperiodic foams, in which the bubbles are generated as duals of quasiperiodic Frank-Kasper phases. These foams are investigated as potential candidates to the celebrated Kelvin problem for the partition of three-dimensional space with equal volume bubbles and minimal surface area. Interestingly, one of the computed structures falls close (but still slightly above) the best known Weaire-Phelan periodic candidate. This gives additional clues to understanding the main geometrical ingredients driving the Kelvin problem.