Have you ever wondered how pedestrians “know” how to fall into lanes when moving through a crowd, without the issue being discussed or even consciously thought about?
A new theory developed by mathematicians at the University of Bath in the UK led by Professor Tim Rogers explains this phenomenon and is able to predict when tracks will be both curved and straight. The theory can even describe the inclination of a wobbly road when people are used to passing to one side rather than the other (for example, in a situation where they are often reminded to “pass to the right” ).
This mathematical analysis unifies conflicting views on the origin of pathway formation and reveals a new class of structures that in everyday life may go unnoticed. The discovery, reported this week (Friday March 3) in the newspaper Scienceconstitutes 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.
Arena tested
To test their theory, the researchers had a group of volunteers walk through an experimental arena that mimicked different layouts, with changes to the entrance and exit gates.
An arena was set up in the style of King’s Cross station in London. When the researchers watched the video footage of the experiment, they observed mathematical patterns taking shape in real life.
Professor Rogers said: “At a glance, a crowd of pedestrians trying to get through two gates might look messy, but when you look closer you see the hidden structure. Depending on the layout of the space, you can observe either the classic straight line tracts or more complex curved patterns such as ellipses, parabolas and hyperbolas. »
Lane formation
Single-file processions formed at busy pedestrian crossings are just one example of lane formation, and this study is likely to have implications for a range of scientific disciplines, particularly in the fields of physics and biology. Similar structures can also be formed by inanimate molecules, such as charged particles or organelles in a cell.
So far, scientists have given several different explanations for why human crowds and other active systems naturally self-organize into corridors, 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, which makes predictions that can be tested.
Encouraged by how their theory agreed with numerical simulations of particle collisions, they then teamed up with Professor Bogdan Bacik – an experimentalist from the Academy of Physical Education in Katowice, Poland – and conducted a series of experiments. experiments (like the one modeled after King’s Cross) using human crowds.
Lead author Dr Karol Bacik said: “Lane formation does not require conscious thought – the participants in the experiment were unaware that they had organized themselves into well-defined mathematical curves.
“Order emerges spontaneously when two groups with different goals pass each other in a crowded space and try to avoid colliding. The cumulative effect of many individual decisions inadvertently leads to the formation of pathways.”
The researchers also tested the effects of traffic rules imposed from outside, namely, they asked participants to pass others on the right. In agreement with the theoretical prediction, the addition of this rule has modified the lane structure.
“When pedestrians have a preference for right turns, the lanes end up tilting and that introduces frustration that slows people down,” Dr. Bacik said.
“What we have developed is a neat mathematical theory that predicts the propensity for pathway formation in a given system,” Prof Rogers said, adding: “We now know that there is a lot more structure than meets the eye. thought so before.”