A surprising discovery about self-loops
The researchers found that networks of simple two-state units, called hysterons, can spontaneously start cycling between states. These cycles, known as self-loops, were long thought to be unphysical because they suggest motion that should not appear in passive materials like crumpled paper or magnetic systems. Instead of dismissing these loops as simulation errors, the team discovered that they point to something deeper and more interesting. The loops arise because energy is effectively injected into the network. This means hysteron models can describe both passive and active materials, including systems that move or oscillate because they consume energy.
Why hysterons matter
Hysteron models are used to simulate many kinds of disordered materials. They help scientists understand how such materials store memories of past events. However, the appearance of self-loops makes it hard to use these models to study materials that do not display active behavior. First author Paul Baconnier set out to understand why the loops are so common and how to control them. He discovered that as the number of hysterons in the network increases the number of possible loop structures grows extremely fast. This makes the loops almost unavoidable, unless their structure is fully understood.
Developing new tools to overcome the challenge
To tackle this, fellow researcher Margot Teunisse developed a full classification of all possible self-loop structures. This provided the insight needed to design new ensembles of hysterons that are completely free of such loops. With these new ensembles, researchers can now reliably simulate purely passive disordered materials without unwanted oscillations. At the same time, they can deliberately include active behavior when they want to study systems that inject or consume energy.
Broader importance and future possibilities
The results open new ways to model materials that show memory effects and could influence fields ranging from soft robotics to biophysics. Because the findings link hysteron networks to active and living systems, they may also offer clues to how complex oscillations arise in nature. The team is now exploring experimental platforms capable of reproducing the active oscillations predicted in this work – an effort that could ultimately guide the design of autonomous materials or mechanical information-processing devices.
Learn more
If you have questions about this research, please contact Martin van Hecke (email: m.v.hecke@amolf.nl).
This paper was published in Physical Review Letters: Dynamic Self-loops in Networks of Passive and Active Binary Elements by Paul Baconnier, Margot H. Teunisse and Martin van Hecke.
