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Mathematics
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groundbreaking mathematical equation has been discovered which could transform medical procedures, natural gas extraction and plastic packaging production in the future. The new equation, developed by scientists at the Univer- sity of Bristol, indicates that diffusive movement through permeable material can be modelled exactly for the very irst time. It comes a century after world-leading physicists Albert Einstein and Marian von Smoluchowski derived the first diffusion equation and marks important progress in repre- senting motion for a wide range of entities, from microscopic particles and natural organisms to man-made devices. Until now, scientists looking at particle motion through po- rous materials such as biological issues, polymers, various rocks and sponges have had to rely on approximations or incomplete perspectives. The findings, published in the journal Physical Review Research , provide a novel technique presenting exciting opportunities in a diverse range of se@ings, including health, energy and the food industry. Lead author Toby Kay, who is completing a PhD in Engineering Mathematics, said, This marks a fundamental step forward since Einstein and Smoluchows- ki's studies on diffusion. It revolutionizes the modelling of diffusing entities through complex media of all scales, from cellular components and geological compounds to envi- ronmental habitats. Previously, mathematical at- tempts to represent movement through environments scattered
The Mathematical Formula Set to Change the World
with objects that hinder motion, 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 rou- inely encountered by animals, cellular organisms and humans. Creativity in mathematics takes different forms and one of these is the connection between different levels of description of a phenomenon. In this instance, by representing random motion in a microscopic fashion and then subsequently 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 model accurately the diffusion of water molecules through biological tissue will ad- vance the interpretation of dif- fusion-weighted MRI (Magnetic Resonance Imaging) readings. It could also offer more accurate representation of air spread- ing through food packaging materials, helping to determine
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