A breakthrough Math equation discovered, could transform medical processes, natural gas extraction and plastic packaging products in the future.
Scientists have discovered for the first time a new equation for accurately modeling diffusion motion through permeable materials. Image credit: University of Bristol
The new equation, developed by scientists at the University of Bristol, shows that diffusion motion through permeable materials can be accurately modeled for the first time. It comes a century after the world’s leading physicists Albert Einstein and Marian von Smoluchowski formulated the first diffusion equation and marks an important step forward in representing motion for a wide range of entities from microscopic particles, natural organisms to man-made devices.
Until now, scientists looking at the movement of particles through porous materials such as biological tissues, polymers, various rocks and sponges have had to rely on approximate or incomplete perspectives.
The findings, published in the journal Physical assessment studyoffers a new technique that presents exciting opportunities in diverse environments including the health, energy and food industries.
Lead author Toby Kay, who is completing a PhD in Engineering Mathematics, said: “This marks a fundamental step forward since Einstein and Smoluchowski worked on diffusion. It revolutionizes the modeling of entities that diffuse through complex media at all scales, from cellular components and geological compounds to habitats.
“Previously, mathematical attempts to represent motion through environments littered with objects that impede motion, known as permeable barriers, have been limited. By solving this problem, we are paving the way for exciting advances in many different fields because of the permeation barriers frequently encountered by animals, cellular organisms and humans. “
Creativity in mathematics takes many 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 in a microscopic fashion and then scaling it down to describe the process in a macroscopic fashion, a new equation can be found.
Further research is needed to apply this mathematical tool to test applications, which can improve products and services. For example, being able to accurately model the diffusion of water molecules through biological tissue would promote the interpretation of diffusion-weighted MRI (Magnetic Resonance Imaging) readings. It could also provide a more accurate representation of the spread of air through food packaging materials, helping to determine shelf life and risk of contamination. In addition, quantifying the behavior of foraging species that interact with macroscopic barriers, such as fences and roads, may provide better predictions about the consequences of climate change. for conservation purposes.
The use of geolocators, mobile phones, and other sensors has seen a tracking revolution generate motion data in increasing quantity and quality over the past 20 years. This has highlighted the need for more sophisticated modeling tools to represent the movement of vast entities in their environment, from natural organisms to man-made devices.
Lead author Dr Luca Giuggioli, Associate Professor of Complexity Science at the University of Bristol, said: “This new fundamental equation is yet another example of the importance of building tools and techniques. technique to represent diffusion when space is not uniform, i.e. when the underlying medium changes from one location to another.
“It builds on another long-awaited 2020 solution to a conundrum to describe random motion in confined spaces. This latest discovery is a further important step in advancing our understanding of motion in all its shapes and forms – collectively known as the mathematics of motion – which has many applications. interesting potential. “
Source: University of Bristol
