Pioneering mathematical formula paves the way for exciting breakthroughs in health, energy and food

Pioneering mathematical formula paves the way for exciting breakthroughs in health, energy and food

Pioneering mathematical formula paves the way for exciting breakthroughs in health, energy and food

A revolutionary new equation has been developed to accurately model diffusive motion through permeable material for the very first time. Credit: University of Bristol

A groundbreaking mathematical equation that could transform medical procedures, natural gas extraction and plastic packaging production in the future has been discovered.

The new equation, developed by scientists at the University of Bristol, indicates that diffusive motion through permeable material can be modeled accurately for the very first time. It comes a century after world-renowned physicists Albert Einstein and Marian von Smoluchowski derived the first diffusion equation and marks a significant advance in representing motion for a wide range of entities, from microscopic particles and natural organisms to artificial devices.

Until now, scientists studying the movement of particles through porous materials, such as biological tissues, polymers, various rocks and sponges, have had to rely on approximations or incomplete insights.

The results, published today in the journal Physical examination researchprovide a new technique that presents exciting opportunities in a wide range of contexts, including health, energy, and the food industry.

Lead author Toby Kay, who is completing a Ph.D. in Engineering Mathematics, said: “This marks a fundamental advance since the studies of Einstein and Smoluchowski on diffusion. It revolutionizes the modeling of diffusing entities through complex media of all scales, cellular components and geological compounds to environmental habitats.

“Previously, mathematical attempts to represent movement through environments strewn with objects that impede movement, called permeable barriers, were limited. By solving this problem, we are paving the way for exciting advances in many different fields, because permeable barriers are regularly encountered by animals, cellular organisms and humans.”

Creativity in mathematics takes different forms and one of them is the connection between different levels of description of a phenomenon. In this case, by representing random motion microscopically and then zooming out to describe the process macroscopically, it was possible to find the new equation.

Further research is needed to apply this mathematical tool to experimental applications, which could improve products and services. For example, being able to accurately model the diffusion of water molecules through biological tissues will advance the interpretation of diffusion-weighted MRI (magnetic resonance imaging) readings. It could also offer a more accurate representation of air propagation through food packaging materials, helping to determine shelf life and risk of contamination. Additionally, quantifying the behavior of foraging animals interacting with macroscopic barriers, such as fences and roads, could provide better predictions of the consequences of climate change for conservation purposes.

The use of geolocators, mobile phones and other sensors has seen the tracking revolution generate movement data of ever-increasing quantity and quality over the past 20 years. This highlighted the need for more sophisticated modeling tools to represent the movement of large-scale entities in their environment, from natural organisms to man-made devices.

Lead author Dr Luca Giuggioli, Associate Professor of Complexity Science at the University of Bristol, said: “This new fundamental equation is another example of the importance of building tools and techniques for represent diffusion when space is heterogeneous; that is, when the underlying environment changes from place to place.

“It builds on another long-awaited 2020 solve of a mathematical puzzle to describe random motion in confined space. This latest discovery is another important step in improving our understanding of motion in all its forms and shapes – collectively referred to as the mathematics of motion – which has many exciting potential applications.”

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More information:
Toby Kay and Luca Giuggioli, Diffusion through permeable interfaces: fundamental equations and their application to first-pass and local-time statistics, Physical examination research (2022). … 9165d2cc3a57a416bdf4

Provided by University of Bristol

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