New mathematical formula promises advances in health, energy and industry


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

The new equation, developed by scientists at the University of Bristol, indicates for the first time that the diffusion movement through the permeable material can be modeled exactly.

It comes a century after the world’s leading physicists Albert Einstein and Marian von Smoluchowski derived the first diffusion equation, and marks important progress in representing the movement for a wide range of entitiesfrom microscopic particles and natural organisms to human-made devices.

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

The findings, published in the journal Physical Review Researchprovide a novel technique that presents interesting opportunities in a wide range of environments including healthcare, energy, and the food industry.

Lead author Toby Kay, a PhD candidate in Mathematical Engineering, said it’s a statement: “This marks a fundamental step forward from Einstein and Smoluchowski’s studies on diffusion. It revolutionizes the modeling of diffusion features through complex media at all scales, from cellular components and geological compounds to environmental habitats.”

“Previously, mathematical attempts to represent movement across sparse environments with objects that impede movement, known as permeable barriers, have been limited. By solving this problem, we are paving the way for exciting advances in many different sectors.” because permeable barriers are routinely 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 the random motion microscopically and then zooming out to describe the process macroscopically, it was possible to find the new equation.

More 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 tissue will improve the interpretation of diffusion-weighted MRI (magnetic resonance imaging) readings.

It could also offer a more accurate representation of the spread of air through food packaging materials, helping to determine shelf life and risk of contamination. Furthermore, quantifying the foraging behavior of animals that interact with macroscopic barriers, such as fences and roads, could provide better predictions about 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 in increasing quantity and quality over the last 20 years. This has highlighted the need for more sophisticated modeling tools to represent the motion of powerful entities in their environment, from natural organisms to human-made devices.

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

“It builds on another long-awaited 2020 resolution of a mathematical puzzle to describe random motion in a confined space. This latest discovery is a further significant step toward improving our understanding of motion in all its shapes and forms, collectively referred to as the mathematics of movement, which has many interesting potential applications“.

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