Many materials have a way of remembering past events, similar to how wrinkles can reveal the history of a crumpled piece of paper. Recently, a group of physicists from Penn State has discovered that, under certain conditions, specific materials can seem to go against established mathematical principles to retain memories of prior deformations.
Many materials possess a form of material memory that captures information about their past states, much like how wrinkles on crumpled paper tell its story. A team of physicists from Penn State has revealed that, under certain circumstances, some materials can violate foundational mathematical concepts to remember the order of prior distortions. The findings, highlighted in a paper published today (Jan. 29) in the journal Science Advances, might pave the way for innovative methods to retain information in mechanical systems, including combination locks and computer technology.
One way materials can remember is through a mechanism known as return-point memory, which functions in a manner similar to a single-dial combination lock, explains Nathan Keim, a Penn State physics associate professor who leads the research team. In a lock, turning the dial in a specific sequence—both clockwise and counterclockwise—results in a specific outcome, like the lock opening, which is dependent on how the dial was moved. Similarly, materials exhibiting return-point memory can retain a record of sequences when they undergo alternating positive and negative deformations, allowing researchers to read or erase these memories.
“This same foundational mechanism or mathematical framework of memory formation can be applied to various systems, from the magnetization of computer hard drives to damages in solid rocks,” Keim noted. His team recently demonstrated that the same mathematics applies to memories in disordered solids, where particle arrangement appears random but actually encodes details of prior deformations.
Return-point memory relies on alternating the external force or “driving” exerted on the material. This could be achieved, for example, by alternating a magnetic field or by pulling on the material from alternating sides. However, it’s generally believed that materials cannot form return-point memory with forces applied unidirectionally. For instance, Keim mentioned that a bridge may sag due to the weight of passing vehicles, but it does not recover its shape once the cars have left.
“The mathematical principles governing return-point memory suggest that if the driving force is one-sided or ‘asymmetrical,’ we shouldn’t be able to encode a sequence,” Keim explained. “Just like if a combination lock dial cannot turn counterclockwise past zero, it can only retain a single number. However, we discovered a unique scenario where such asymmetrical driving can indeed encode a sequence.”
The researchers conducted various computer simulations to determine the conditions that allow for sequence encoding in materials. They adjusted numerous factors, including the amount and direction of the external force, as well as how it was applied, to observe their effects on memory formation and the length of the stored sequence. To do this, they reduced the system’s components—like the particles in a solid or the small domains in magnets—into conceptual elements termed hysterons.
“Hysterons are components of a system that might not respond right away to external conditions and can maintain a previous state,” stated Travis Jalowiec, an undergraduate at the time of the research who now holds a physics bachelor’s degree from Penn State and is a co-author of the paper. “Similar to how parts of a combination lock indicate the dial’s prior positions rather than its current state. In our model, hysterons can exist in two potential states, working together or against one another, and this generalized model allows it to apply to many systems.”
In the model, hysterons interact in either a cooperative manner—where a change in one promotes change in another—or a non-cooperative or “frustrated” manner, where changes in one hinder others. Jalowiec explained that frustrated hysterons are essential for forming and recovering sequences in systems with asymmetric driving.
“A good analogy for frustration is a bendy straw, which features small bellows that can either collapse or expand,” Keim said. “If you gently pull on both ends of the straw and release, one segment will expand, indicating that the others do not. This change alleviates the system’s stress.”
The team discovered that systems with cooperative interactions could only encode sequences when the driving force was symmetric, involving alternating directions. However, even a single pair of frustrated hysterons could encode a sequence when exposed to asymmetric driving, provided other conditions are satisfied.
“Identifying a pair of frustrated hysterons in real materials has proven challenging,” Keim admitted. “It’s difficult to detect because the hallmark of frustration is often the absence of an expected occurrence. The phenomena we observed are rare, yet they could be quite conspicuous in a real material, giving us a novel method to search for and examine materials with frustration. Moreover, we believe this insight can guide the design of artificial systems with this unique type of memory, starting with simple mechanical constructs, like a bendy straw, and eventually advancing to something akin to an asymmetric combination lock.”
The researchers believe these findings could lead to new methods for storing, retrieving, and erasing information in materials and mechanical systems.
“One significant aspect of this memory is that it ensures the storage of both the greatest deformation and the latest deformation,” Keim noted. “If we can develop a system that retains a sequence of memories, it could function similarly to a combination lock, verifying a specific history or retrieving diagnostic or forensic data about past events. There’s a growing interest in mechanical systems that can sense environments, perform computations, and react or adapt without using electricity. A deeper understanding of memory enhances these possibilities.”
In addition to Keim and Jalowiec, the research team includes Chloe Lindeman, a graduate student at the University of Chicago during the research and now a Miller Postdoctoral Fellow at Johns Hopkins University. This work was supported by funding from the U.S. Department of Energy, Penn State Schreyer Honors College, and the Penn State Student Engagement Network.
