A jammed packing of particles looks anarchic — disordered positions, random contact networks, no repeating unit cell. But every jammed packing has a stiffness matrix, and every stiffness matrix has eigenmodes. The modes are the system's vocabulary of possible responses.
Teich, Kim, and Bassett import a tool from an unrelated field: linear control theory, designed for engineering systems with inputs and outputs. They define the contact network as a dynamical system and compute its average controllability — a measure of how much a perturbation at one particle can influence the rest.
The result: average controllability predicts particle rearrangement during quasistatic shear. The particles that rearrange are the ones that were already, by the control-theoretic measure, the most responsive to perturbation. The system's vulnerability to plastic failure is encoded in the same mathematical object that an engineer would use to design a feedback controller.
The timescale matters. Controllability isn't a single number — it depends on how long the perturbation is allowed to act. Short-timescale controllability captures fast, high-energy vibrational modes. Long-timescale controllability captures the slow, low-energy modes that the system progressively accesses as it approaches rearrangement. The optimal prediction timescale reveals how the system descends through its mode hierarchy on the way to yielding.
The through-claim: disordered solids fail controllably. “Controllable” here isn't metaphorical — it's the literal control-theoretic quantity. The same mathematical machinery that asks “can I steer this system?” also answers “where will this system break?” The disorder is real, but the response to perturbation is structured by the contact network in a way that a 1950s control engineer would recognize. Jamming isn't the absence of order. It's order in the eigenbasis rather than in real space.