Welsh mathematician helps unlock new model that could transform medical treatments

A team of international scientists, including an Aberystwyth University professor, has developed a new mathematical model that explains how different particles can self-organise into identical geometric patterns.

The breakthrough could pave the way for innovative materials with medical and industrial applications, including smart drug delivery systems, targeted cancer therapies, and tissue engineering for regenerative medicine.

Published in the journal Physical Review E, the study reveals how the self-organisation of particles in confined spaces follows universal rules, regardless of what the particles are made from.

The work was led by Dr Paulo Douglas Lima of the Federal University of Rio Grande do Norte in Brazil, alongside collaborators from Trinity College Dublin, Technological University Dublin, and Aberystwyth University.

Using a simple mathematical framework, the researchers balanced two competing forces: the repulsion between particles and the degree of confinement in which they are placed.

By fine-tuning these variables, they were able to predict and reproduce identical geometric arrangements across completely different materials.

To test their theory, the team conducted experiments with floating magnets, ball bearings, and soap bubbles.

Despite the physical and chemical differences between these objects, each system produced the same organised patterns when placed in carefully designed containers.

Professor Simon Cox, from Aberystwyth’s Department of Mathematics, said the findings demonstrate how universal laws of geometry and physics govern seemingly unrelated systems.

‘Fascinating’

“What’s fascinating is that discrete objects as varied as soap bubbles and magnetic particles can be made to behave in the same way, simply by adjusting how they are confined,” he said.

“It’s a powerful reminder that nature often follows universal rules, even when the ingredients look completely different.”

Professor Cox and his team used computer simulations to model how materials behave under different conditions, confirming that the observed patterns were not unique to any one type of particle but shared across all systems.

The implications of the discovery could be far-reaching. In biomedical engineering, understanding how particles and cells self-assemble could help scientists design smarter therapeutic materials, such as slow-release drug capsules or targeted treatments that deliver medication directly to diseased tissue.

It could also inform tissue engineering, where understanding how biological cells arrange themselves in confined spaces is vital for building effective scaffolds for regenerative therapies.

Packaging

Beyond medicine, the model could benefit industries involved in the packaging and transport of granular materials, such as powders, grains, and pellets, helping to optimise storage and reduce waste.

“Understanding how particles self-assemble in confined spaces is key to designing new materials with tailored properties,” said Professor Cox.

“This research brings us a step closer to harnessing these natural principles to solve real-world challenges.”

Read the full article here: ‘Self-assembled clusters of mutually repelling particles in confinement’, Physical Review E.