Aromas from a kitchen fill a house. A drop of dye colors an entire bucket of water. It’s all because molecules diffuse; they roam around in all directions.
But what would happen if the molecules–instead of moving completely randomly–were influenced by peer pressure? If molecules or particles or people tended to follow the paths of their trendiest neighbors, they might aggregate, even in locations far from their origins.
This type of peer-influenced behavior might explain many puzzling patterns that show up in everything from financial data to fluctuations in animal populations, says a team of physicists that has modeled the behavior mathematically.
“The equations are complex, but they have a rather simple physical meaning,” says Jayanth R. Banavar of Pennsylvania State University in State College. He and his colleagues describe their model in the Aug. 19 Physical Review Letters.
The researchers used simple diffusion as the starting point for their model. Simple diffusion is like a random walk, Banavar explains. In such a walk, the direction of each successive step is governed by chance. If a crowd of random walkers starts from the same point, the pattern of dispersal of the crowd is predictable. At first, the walkers cluster relatively near the starting point, with only a few farther away. As time goes on, this bell-curve distribution becomes flatter and flatter until the crowd of walkers is evenly dispersed from the starting point, like the dye in the water bucket.
To bring in peer pressure, Banavar and his colleagues added a so-called drift term to the classic equation for diffusion. When applied to walkers, the term dictates that walkers are more likely to move in whichever direction they spot more people.
In the long run, if the peer pressure is small–which happens if walkers can’t see very far or aren’t influenced much by their peers–normal diffusion takes over, Banavar says. But if peer pressure is strong enough, at a certain point, diffusion is overcome by an increasingly powerful tendency to aggregate. Statisticians refer to the resulting distribution as fat-tailed, which means the aggregates of people or particles often end up quite far away from the origin.
Banavar’s group “came up with the same tailed distributions that we found empirically,” says H. Eugene Stanley of Boston University. Stanley says that there are numerous examples of data that form fat-tailed distributions, including bird populations, nations’ economic productivity, and stock prices (SN: 11/27/99, p. 344: http://www.sciencenews.org/sn_arc99/11_27_99/bob1.htm). No one had a broad explanation for these data before, Stanley says.
The new model may form a foundation for studying diverse systems that operate under a kind of peer pressure: from ants and bacteria that lay down kin-attracting chemical gradients to people that sell stocks or donate money based on what their peers do, Banavar says.