Engineers have developed tools that mathematically describe the kinetics in a system right before it dissolves into randomness. Led by Rajan K. Chakrabarty, assistant professor of energy, environmental and chemical engineering, the researchers have provided 11 equations that they applied to directional statistics. The resulting tools mathematically describe the kinetics in a system right before it dissolves into randomness as well as the walker’s turning angle distribution. The tools have the potential to be useful in predicting the onset of chaos in everything from nanoparticles to checking accounts.

Picture a herd of sheep or cattle emerging from a shed or barn to graze a field. They head straight out of their digs to the pleasure of the pasture pretty much as one entity, but as the land opens up and the “grass gets greener” they disperse randomly in a motion that has neither rhyme nor reason. Individual animals depart at different angles from the herd and then at different angles from their original departure and so on until “the cows come home.” In physics, this movement that starts off on the straight-and-narrow (ballistic) and is correlated and then dissolves into randomness (diffusive), uncorrelated, is called a ballistic-to-diffusive transition. Researchers in a number of fields call this motion a “random walk,” also known as diffusive motion, a universal phenomenon that occurs in both physical (atomic-cluster diffusion, nanoparticle scattering and bacterial migration) and nonphysical (animal foraging, stock price fluctuations and “viral” internet postings) systems.

Source (Washington University in St. Louis. “New tools reveal prelude to chaos.” ScienceDaily. ScienceDaily, 6 June 2018.)

Original paper: Liu, P., Heinson, W.R., Sumlin, B.J., Shen, K.Y. and Chakrabarty, R.K., 2018. Establishing the kinetics of ballistic-to-diffusive transition using directional statistics. Physical Review E, 97(4), p.042102.