Have you ever wondered how pedestrians “know” how to fall through lanes when moving through a crowd, without discussing or even consciously thinking about the problem?
A new theory developed by mathematicians at the University of Bath in the UK and led by Professor Tim Rogers explains this phenomenon and is able to predict when paths will be curved and straight. The theory could even describe the road’s wobbly slope when people are used to passing to one side rather than the other (eg, in a situation where they are often reminded to “pass to the right”).
This mathematical analysis unites conflicting opinions about the origin of pathway formation and reveals a new class of structures that may go unnoticed in everyday life. The discovery, which was reported this week (Friday, March 3) in the newspaper scienceIt constitutes a major advance in the interdisciplinary science of “active matter” — the study of group behaviors in interacting populations ranging from bacteria to herds of animals.
To test their theory, the researchers had a group of volunteers walk around an experimental yard simulating different designs, with changes to the entry and exit gates.
The plaza is modeled after King’s Cross station in London. When the researchers watched video footage of the experiment, they noticed mathematical patterns forming in real life.
Professor Rogers said: “At a glance, a crowd of pedestrians trying to cross two gates might look chaotic, but when you look closely, you see the hidden structure. Depending on the layout of the space, you can notice classic straight-line paths or more complex curved patterns such as ellipses, parabolas, and ellipses.” excess.”
Single-file processions at busy pedestrian crossings are just one example of lane formation, and this study has potential to have implications for a range of scientific disciplines, particularly in the fields of physics and biology. Similar structures can also be formed by non-living particles, such as charged particles or organelles in a cell.
To date, scientists have offered several different explanations for why humanoids and other energetic systems naturally self-organize into pathways, but none of these theories have been verified. The Bath team used a new analytical approach, inspired by Albert Einstein’s theory of Brownian motion, that makes predictions that can be tested.
Encouraged by the way their theory agreed with numerical simulations of particle collisions, they teamed up with Professor Bogdan Pasek — an experimentalist from the Academy of Physical Education in Katowice, Poland — and ran a series of experiments. via) using human crowds.
Lead author Dr Carol Pasek said: “Path formation does not require conscious thought – the trial participants were unaware that they had organized themselves into well-defined mathematical curves.
“The system arises automatically when two groups with different goals pass through a crowded place and try to avoid collision. The cumulative effect of many individual decisions inadvertently creates the pathways.”
The researchers also tested the effects of externally imposed traffic rules, that is, they asked participants to pass others on the right. In agreement with the theoretical prediction, the addition of this rule modified the corridor structure.
“When pedestrians prefer right turns, they end up in sloping lanes and this creates frustration that slows people down,” said Dr. Pasek.
“What we have developed is an elegant mathematical theory that predicts the tendency for path formation in a given system,” said Professor Rogers, adding: “We now know that there is much more structure than meets the eye. We thought so before.”
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