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Related Experiment Video

Updated: Jul 14, 2026

Microbubble Fabrication of Concave-porosity PDMS Beads

Microbubble Fabrication of Concave-porosity PDMS Beads

Published on: December 15, 2015

Planar soap bubble clusters with a cavity.

C E Garza-Hume¹, P Padilla

¹IIMAS-FENOMEC, Universidad Nacional Autónoma de México, Circuito Escolar, Ciudad Universitaria, Mexico. clara@mym.iimas.unam.mx

The European Physical Journal. E, Soft Matter

|May 24, 2007

Summary

Researchers constructed energy-minimizing bubble clusters in the plane. These complex bubble clusters are not simply-connected and suggest non-isolated minima in mathematical modeling.

Area of Science:

Geometric measure theory
Differential geometry
Calculus of variations

Background:

Bubble clusters are collections of spherical surfaces that minimize surface area for a given volume.
Local energy minimizers are configurations where any small perturbation increases the energy.
Simply-connected shapes have no holes, unlike shapes with holes.

Purpose of the Study:

To construct and analyze bubble clusters that are not simply-connected.
To investigate the nature of local energy minima in these complex configurations.
To explore whether these minima are isolated or part of a continuous family.

Main Methods:

Utilizing techniques from geometric measure theory to define and construct bubble clusters.
Employing computational methods to numerically approximate and visualize the bubble clusters.

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Analyzing the topological properties and energy landscape of the constructed clusters.

Main Results:

Successfully constructed local energy-minimizing bubble clusters in the Euclidean plane.
Demonstrated that these constructed clusters are not simply-connected, featuring complex topology.
Numerical evidence indicates that these energy minima are not isolated, suggesting a continuous family of solutions.

Conclusions:

Local energy minima for bubble clusters can exhibit complex, non-simply-connected topologies.
The non-isolated nature of these minima has implications for understanding phase transitions and material microstructures.
Further research is needed to fully characterize the space of non-simply-connected energy-minimizing bubble clusters.