Category: Physics

Summary: Finding the prestress gradient where the softest vibrational mode in a disordered cross-braced material relocalizes onto the boundary.

Mechanical metamaterials can host unusually soft vibrational modes, and where those modes live matters for both function and failure. This experiment asks when a smooth prestress gradient pushes the lowest soft mode away from the bulk of a disordered cross-braced structure and onto its boundary.

The script constructs dense symmetric elastic operators, adds disorder, and then bisects the prestress-gradient parameter while iteratively increasing system size. The threshold is defined by a relocalization event in the softest eigenmode rather than by a simple frequency shift alone.

That makes the experiment useful for understanding how controlled prestress can steer mechanical response spatially. It connects disorder, boundary sensitivity, and soft-mode engineering in one finite-size spectral map.

Method: Dense symmetric eigensolve with iterative deepening and bisection on a prestress-gradient parameter.

What is measured: Critical prestress-gradient threshold, boundary localization of the soft mode, minimum eigenvalue behavior, and bracket width.