Inanimate particles, such as gas molecules, reach thermal equilibrium, a stable state in which they are distributed evenly within a container, regardless of its shape or the material it is made of.

Objects that move autonomously, such as microorganisms or robots, are very sensitive to what happens on the walls of the environment that contains them. Understanding the relationship between edge effects and spatial distributions could allow the design of containers with shapes optimised for the geometric control of so-called active matter.

In a study published in PNAS, Roberto Di Leonardo from the Department of Physics at Sapienza University, together with researchers from the Biological Research Centre in Hungary, introduced a new method that allows the movement of active particles to be guided according to the rules by which they bounce off the edges of the environment in which they move.

The method was tested with the single-celled microalgae Euglena gracilis, which, like a ball on a billiard table, moves in a straight line, bouncing between the light and shadow boundaries of an illuminated area. Unlike gas molecules, which are distributed evenly within a container, microalgae can cover a “spot” of light with distributions that are highly sensitive to the surrounding conditions. In particular, by designing a sort of multi-stage “micro-billiard table”, it was possible to guide the microalgae into accumulation regions defined solely by the shape of this “light billiard table”.

In general, this method makes it possible to design the shape of containers so that the active objects inside them accumulate spontaneously or avoid certain regions.

The applications could be numerous: from spatial control and isolation of microorganisms to the design of navigation algorithms for microscopic and macroscopic robots capable of exploring complex and unknown environments more efficiently.

“It is always exciting to see, says Roberto Di Leonardo, how concepts of classical physics, originally developed for inanimate matter, can be generalised to objects that move autonomously, what we now call active matter. Every time this happens, new ideas emerge that not only deepen our understanding of what we thought we already knew, but also pave the way for new applications for living or robotic systems."
 

References:“Active billiards: Engineering boundaries for the spatial control of confined active particles” - Roberto Di Leonardo et al. PNAS, 122, e2426715122, (2025) - https://doi.org/10.1073/pnas.2426715122