A groundbreaking mathematical equation has been discovered that could transform medical procedures, natural gas extraction, and plastic packaging production in the future.
The new equation, developed by scientists at the University of Bristol, suggests that diffuse motion through a permeable material can be completely modeled for the first time. It comes a century after world-leading physicists Albert Einstein and Marian von Smolochovsky devised the first diffusion equation, and records important advances in representing motion for a wide range of entities from microscopic particles and 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 had to rely on approximations or incomplete perspectives.
The results are published today in the journal Physical Review Researchprovides a new technology that presents exciting opportunities in a variety of settings including health, energy and the food industry.
Lead author Toby Kay, who is completing his Ph.D. In engineering mathematics, he said, “This represents a fundamental step forward since Einstein and Smolochovsky’s studies on diffusion. It revolutionizes the modeling of diffuse entities through complex media of all scales, from cellular components and geological compounds to ecological habitats.”
“Previously, mathematical attempts to represent movement through environments littered with objects that impede movement, 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 routinely encountered by animals cellular organisms and humans.”
Creativity in mathematics takes various forms, and one of these forms is the association between the different levels of description of a phenomenon. In this case, by representing the random motion in a microscopic way and then minimizing it to describe the process microscopically, it was possible to find the new equation.
More research is needed to apply this mathematical tool to experimental applications, which can improve products and services. For example, the ability to accurately model the diffusion of water molecules through biological tissues will enhance the interpretation of diffusion-weighted MRI readings. It can also provide a more accurate representation of air diffusion through food packaging materials, helping to determine the shelf life and contamination risks. In addition, quantifying the behavior of foraging animals interacting with macroscopic barriers, such as fences and roads, could provide better predictions about the consequences of climate change for conservation purposes.
The use of GPS devices, mobile phones, and other sensors has seen a tracking revolution generating movement data in ever-increasing quantity and quality over the past 20 years. This has highlighted the need for more sophisticated modeling tools to represent the movement of large-scale entities in their environment, from natural organisms to man-made devices.
Senior author Dr Luca Gigioli, Associate Professor of Complex Sciences at the University of Bristol, said: “This new essential element Equation Another example of the importance of building tools and techniques to represent diffusion when space is heterogeneous; That is, when the underlying environment changes from one location to another.
“It builds on another long-awaited solution in 2020 around a mathematical dilemma to describe random motion in narrow space. This latest discovery is another important step forward in improving our understanding of motion in all its shapes and forms—collectively called the mathematics of motion—which has many applications exciting potential.”
Toby Kay and Luca Giugioli, Propagation through permeable interfaces: basic equations and their application to first-pass statistics and local time, Physical Review Research (2022). Journal.aps.org/prresearch/ac… 9165d2cc3a57a416bdf4
University of Bristol
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