8 Sept 2022
Mathematicians at the University of Bristol say a new study indicating diffusive movement can now be modelled exactly in permeable materials is a “fundamental” step forward.
Allister Webb
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Image © University of Bristol
Scientists believe a newly published mathematical equation, building on the work of Albert Einstein, could lead to better future treatment options for vets.
The study, by academics from the University of Bristol, indicates that diffusive movement through permeable materials, which allow the passage of liquids or gases, can now be modelled exactly for the first time.
Although the first diffusion equation was devised by Einstein and Marian von Smoluchowski a century ago, researchers have had to rely on approximate perspectives until now.
Toby Kay – lead author of the study, which has been published in the journal Physical Review Research, said the discovery was a “fundamental step” forward.
He said: “Examples of permeable barriers are found throughout biological and physical systems of various sizes and arrangements, meaning the accurate modelling of diffusion in the presence of these objects has far-reaching applications.
“The most exciting aspect of this discovery is that now one is able to account exactly for the presence of these barriers in the system of interest, and is thus a huge improvement on previous methods relying on approximate descriptions or time-consuming computer simulations.”
The researchers have identified health care, energy, the food industry and even predicting the impact of climate change on conservation among the areas where the new equation could be applied, and have called for further research to be undertaken.
Asked specifically about the implications for animal health, Mr Kay, who is reading for a PhD in engineering mathematics, said: “The practice of diffusion-weighted MRI is a key technique for detecting cerebral diseases in animals.
“Due to the exact nature of our model, it could provide better interpretation of the readings from the MRI results, thus meaning easier and more accurate diagnosis leading to improved treatment of the animal.”
Senior author Luca Giuggioli, associate professor in complexity sciences at the University of Bristol, added: “This new fundamental equation is another example of the importance of constructing tools and techniques to represent diffusion when space is heterogeneous – that is, when the underlying environment changes from location to location.”
