Zhang Chaoyang, Penn Physicist Explore Physics of Sand and Smart Materials

Liu, a leading scholar in non-equilibrium statistical physics, won the 2025 American Physical Society Leo P. Kadanoff Prize for her contributions to jamming and disordered solids. This year she also received the Marie Curie Medal of the International Congress of Basic Science.

During the talk, Liu explained jamming transition using shaving foam as an example. Foam consists of about 95% gas and 5% liquid, yet it holds its shape like a solid. In the simple model she described, particles repel only when overlapping, which captures the essence of why disordered solids have rigidity. At a critical volume fraction of about 64% for random close packing, a system of spheres becomes solid, with shear modulus rising as a power law after the transition. This behavior, with an exponent around 0.328 in three dimensions, is universal across many systems, similar to critical phenomena described by the renormalization group.

Liu also contrasted jamming with crystallization. Perfect crystals are studied extensively in physics courses, but real materials are often disordered. Jamming provides a complementary picture of how solids can form without long-range order, and it is robust to added order in a way comparable to how crystals tolerate defects.

Zhang and Liu then discussed how mechanical networks of springs can be trained like neural networks. By adjusting spring stiffnesses using gradient descent, a physical network can be taught to produce desired input-output relationships, such as a deformation at one point causing a specified deformation elsewhere. Liu emphasized that unlike standard neural networks, a real physical network must also satisfy mechanical equilibrium, adding an extra constraint. More importantly, the researchers aim to avoid global gradient calculations and use local rules that only depend on nearby information. This approach, Liu said, is closer to how the brain learns: a neuron does not need to know the state of every other neuron to adjust its synapses.

The conversation also touched on the potential for low-power computing. Zhang noted that current AI consumes enormous energy, and learning without global computation could offer a path to more efficient materials. Liu stressed that this line of work emerged naturally from earlier research on jamming, rather than being a direct extension, and it provides physicists a simple, controlled model to study how systems learn.

According to the live discussion, Liu’s work on trainable mechanical networks may become a useful model for understanding learning in physical systems and could inspire low-power intelligent materials.