Numerically Computed Double and Triple Bubbles in $R^3$ for Density $r^p$

TL;DR

This paper uses numerical methods to verify and propose conjectures about the optimal shapes of double and triple bubbles in three-dimensional space with density functions of the form r^p.

Contribution

It numerically verifies existing conjectures for double bubbles and introduces new conjectures for triple bubbles in R^3 with density r^p.

Findings

Confirmed previous conjectures for double bubbles

Proposed new conjectures for triple bubbles

Demonstrated effectiveness of Brakke's Evolver in this context

Abstract

Using Brakke's Evolver, we numerically verify previous conjectures for optimal double bubbles for density $r^p$ in $R^3$ and our own new conjectures for triple bubbles.