Groundbreaking mathematical formula paves the way for exciting advancements in health, energy and food industries

Groundbreaking mathematical formula paves the way for exciting advancements in health, energy and food industries

A groundbreaking new equation has been developed to accurately simulate the movement of diffusion through a permeable material for the first time.Credit: University of Bristol

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


New equations developed by scientists at the University of Bristol show that the movement of diffusion through a permeable material can be accurately modelled for the first time. It comes a century after world-leading physicists Albert Einstein and Marian von Smoluchowski derived the first diffusion equation, marking the transition from microscopic particles and natural organisms to man-made Important progress has been made in the motion representation of a wide range of entities in devices.

Until now, scientists have had to rely on approximate or incomplete perspectives to observe particle motion through porous materials such as biological tissue, polymers, various rocks and sponges.

The findings are published today in the journal Physical Review ResearchOffers a new technology that offers exciting opportunities in a variety of settings including the health, energy and food industries.

Lead author Toby Kay, who is completing his Ph.D. The PhD in Engineering Mathematics said: “This marks a fundamental step forward since Einstein and Smoluchowski’s work on diffusion. It passes all scales from cellular components and geological compounds to environmental habitats. The complex media has revolutionized the modeling of diffusing solids.

“Previously, mathematical attempts to represent motion by means of an environment interspersed with objects that impede it, known as osmotic barriers, have been limited. By solving this problem, we are paving the way for exciting advances in many different fields because osmotic barriers Animals, cellular organisms and humans are often encountered.”

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

Further research is needed to apply this mathematical tool to experimental applications to improve products and services. For example, being able to accurately model the diffusion of water molecules through biological tissue will facilitate the interpretation of diffusion-weighted MRI (magnetic resonance imaging) readings. It can also provide a more accurate representation of airborne transmission in food packaging materials, helping to determine shelf life and contamination risk. In addition, quantifying the behavior of foragers interacting with macroscopic barriers such as fences and roads can better predict the consequences of climate change for conservation purposes.

Over the past 20 years, the use of geolocators, mobile phones, and other sensors has seen the tracking revolution generate an ever-increasing quantity and quality of motion data. This highlights the need for more sophisticated modeling tools to represent the movement of a wide range of entities, from natural creatures to man-made devices, in their environments.

Senior 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 diffusion when building tools and techniques to represent spatial heterogeneity; that is, when the underlying environment varies by location different.

“It builds on the solution to another long-awaited mathematical puzzle in 2020 to describe random motion in confined spaces. This latest discovery is another step forward in improving our understanding of motion in all shapes and forms An important step forward – collectively known as the mathematical movement – and it has many exciting potential applications.”


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More information:
Toby Kay and Luca Giuggioli, Diffusion through percolating interfaces: fundamental equations and their application to first-pass and local time statistics, Physical Review Research (2022). journals.aps.org/prresearch/ac…9165d2cc3a57a416bdf4

Provided by University of Bristol

Citation: Groundbreaking mathematical formula paves the way for exciting advancements in health, energy and food industries (September 6, 2022) Retrieved September 7, 2022 from https://phys.org/news/2022 -09-mathematical-formula-paves-advances-health.html

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