Network control of jammed materials

Amorphous and jammed particulate matter constitutes a wide range of natural and synthetic materials. The way in which these systems' disordered and extended chain-like mesoscale structures evolve under stress, leading to particle rearrangements and eventual yield, has profound consequences for phenomena ranging from landscape evolution to cellular unjamming during tumor metastasis. While traditional methods have made progress in relating this mesoscale structure to rearrangement dynamics, the lack of obvious structural order on multiple length scales suggests the need for novel physical theories to better predict yielding behavior. Here, we model disordered solids as spatially-embedded spring networks, and bring linear network control theory to bear on the problem of predicting dynamics from structure. We utilize this network control framework, which has previously proven successful in describing the dynamics and function of various biological, neurological, and mechanical networks, in a manner that is novel in the context of jammed materials. Our work shows that node controllability in this context correlates strongly with particle rearrangement under stress. In general, this work demonstrates that network control theory is a promising mathematical framework for predicting and designing yield behavior in disordered media.