Investigating systems consisting of self-propelled particles鈥攕o-called active particles鈥攊s a rapidly growing area of research. In theoretical models for active particles, it is often assumed that the particles' swimming speed is always the same. This is not so, however, for particles produced in many experiments, for example for those propelled by ultrasound for medical applications. In these cases, the propulsion speed depends on the orientation.

How this dependency affects the behavior of systems consisting of many particles鈥攊n particular, how it affects the formation of clusters鈥攊s something which a team of physicists led by Prof. Raphael Wittkowski from the University of M眉nster (Germany) have now been the first to demonstrate in a collaborative project with Prof. Michael Cates from the University of Cambridge (United Kingdom/England).

Using a combination of computer simulations and theoretical derivations, they studied the behavior of systems consisting of many active particles whose speed depends on orientation, and in the process they discovered a series of new effects. The results of the study have been in the journal 麻豆淫院ical Review Letters.

What is interesting from a physics point of view is that systems consisting of many active particles can spontaneously form clusters鈥攅ven when the individual particles do not attract one another at all. When measuring the movement of the particles in the simulations, the researchers came up with a particularly surprising result.

"Normally, on a statistical average, the particles in such clusters simply stay where they are," explains lead author Dr. Stephan Br枚ker from the Institute of Theoretical 麻豆淫院ics at the University of M眉nster. "For that reason, we had expected that that would be the case here, too." In fact, however, the physicists discovered something else: The particles constantly move out of the cluster on the one side and move back in on the other, thus producing a permanent flow of particles.

There is also another difference from the "normal" case: the clusters which form in systems of active particles are normally circular. However, in the particles examined, the shape of the cluster depends on how strongly the orientation of the particles influences their propulsion speed鈥攚hich can be stipulated by the experimentalist.

"Theoretically, at least, we can make the particles arrange themselves into any shape we want," explains co-lead author Dr. Jens Bickmann. "We can paint with them, so to speak." In the simulations the researchers observed ellipses, triangles and squares. "This gives the results a practical importance," says Dr. Michael te Vrugt from the Wittkowski team and a co-author of the study.

"For technical applications鈥攆or example, for the realization of programmable matter, it has to be possible to control the way the particles self-assemble鈥攁nd with our approach that is indeed possible."