Topological analysis of nuclear pasta phases

TL;DR

This paper applies algebraic topology to analyze nuclear pasta phases from simulations, revealing subphases, relating topology to geometry, and showing boundary conditions affect results.

Contribution

It introduces the use of Betti numbers for detailed phase characterization and suggests refining phase classifications based on topological analysis.

Findings

Some phases can be subdivided into subphases

Betti numbers provide finer phase characterization

Boundary conditions influence topological outcomes

Abstract

In this paper the analysis of the result of numerical simulations of pasta phases using algebraic topology methods is presented. These considerations suggest that some phases can be further split into (sub)phases and therefore should be more refined in numerical simulations. The results presented in the paper can also be used to relate the Euler characteristic from numerical simulations to the geometry of the phases. The Betti numbers are used as they provide finer characterization of the phases. It is also shown that different boundary conditions give different outcomes.