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Pioneering mathematical formula paves method for exciting advances in health, energy, and food industry

Pioneering mathematical formula paves way for exciting advances in health, energy, and food industry
A groundbreaking new equation has been developed to model diffusive movement through permeable material exactly for the first time. Credit: University of Bristol

A groundbreaking mathematical equation which could transform surgical procedure, gas extraction, and plastic packaging production later on has been discovered.

The brand new equation, produced by scientists at the University of Bristol, indicates that diffusive movement through permeable material could be modeled exactly for the first time. It comes a hundred years after world-leading physicists Albert Einstein and Marian von Smoluchowski derived the initial diffusion equation, and marks important progress in representing motion for an array of entities from microscopic particles and natural organisms to man-made devices.

As yet, scientists considering particle motion through porous materials, such as for example biological tissues, polymers, various rocks and sponges experienced to depend on approximations or incomplete perspectives.

The findings, published today in the journal Physical Review Research, give a novel technique that displays exciting opportunities in a diverse selection of settings including health, energy, and the meals industry.

Lead author Toby Kay, who’s completing a Ph.D. in Engineering Mathematics, said, “This marks a simple step of progress since Einstein and Smoluchowski’s studies on diffusion. It revolutionizes the modeling of diffusing entities through complex media of most scales, from cellular components and geological compounds to environmental habitats.

“Previously, mathematical attempts to represent movement through environments scattered with objects that hinder motion, referred to as permeable barriers, have already been limited. By solving this issue, we have been paving just how for exciting advances in lots of different sectors because permeable barriers are routinely encountered by animals, cellular organisms and humans.”

Creativity in mathematics takes different forms and something of these may be the connection between different degrees of description of a phenomenon. In this situation, by representing random motion in a microscopic fashion and subsequently zooming out to spell it out the procedure macroscopically, it had been possible to get the new equation.

Further research is required to apply this mathematical tool to experimental applications, that could improve services and products. For example, having the ability to model accurately the diffusion of water molecules through biological tissue will advance the interpretation of diffusion-weighted MRI (Magnetic Resonance Imaging) readings. It might also offer more accurate representation of air spreading through food packaging materials, assisting to determine shelf life and contamination risk. Furthermore, quantifying the behavior of foraging animals getting together with macroscopic barriers, such as for example fences and roads, could provide better predictions on the result of climate change for conservation purposes.

The usage of geolocators, cell phones, along with other sensors has seen the tracking revolution generate movement data of ever-increasing quantity and quality in the last 20 years. It has highlighted the necessity for more sophisticated modeling tools to represent the movement of wide-ranging entities within their environment, from natural organisms to man-made devices.

Senior author Dr. Luca Giuggioli, Associate Professor in Complexity Sciences at the University of Bristol, said, “This new fundamental is another exemplory case of the significance of constructing tools and ways to represent diffusion when space is heterogeneous; that’s, once the underlying environment changes from location to location.

“It builds on another long-awaited resolution in 2020 of a mathematical conundrum to spell it out random movement in confined space. This latest discovery is really a further significant step of progress in improving our knowledge of motion in every its shapes and formscollectively termed the mathematics of movementwhich has many exciting potential applications.”

More info: Toby Kay and Luca Giuggioli, Diffusion through permeable interfaces: Fundamental equations and their application to first-passage and local time statistics, Physical Review Research (2022). 9165d2cc3a57a416bdf4

Citation: Pioneering mathematical formula paves method for exciting advances in health, energy, and food industry (2022, September 6) retrieved 7 September 2022 from

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