Extending Einstein’s description to self-propelled particles

A mathematical description of how self-propelled particles such as swimming microbes interact with passive particles well reproduces observations of such systems.

In 1827, botanist Robert Brown noticed grains of pollen moving randomly in water under the microscope. Brownian motion, as it became known, is caused by the pollen grains being buffeted by water molecules, and it is observed in many physical, chemical and biological systems. It was explained mathematically by Albert Einstein in 1905.

Now, a team led by a Tsukuba University researcher has done the same thing for a system where the particles are not passive but are self-propelled. Examples include swimming microbes and colloids of active particles.

The comprehensive mathematical description explains the quirky loopy motions that have been observed in experiments. It has the potential to shed light on real-world systems such as ecosystems, earthquakes and even financial markets.