Category: Physics

Summary: Finding the weakening level where the softest mode in a braced modular spring network collapses onto the weakest module.

Modular spring networks can distribute soft motion across several coupled parts, especially when bracing prevents any single region from dominating. This experiment asks how much one module must be weakened before the lowest soft mode stops being shared and becomes trapped on that weakest module.

The model builds dense symmetric stiffness matrices for disordered modular spring networks with fixed inter-module bracing. It bisects a module-specific weakening parameter while increasing system size and records when the softest eigenmode becomes strongly concentrated on one module.

That turns a qualitative localization idea into a threshold problem. The output shows when structural heterogeneity overwhelms the stabilizing effect of the braces and causes a clean weakest-module capture transition.

Method: Dense symmetric eigensolve with iterative deepening and bisection on module weakening in a braced modular spring network.

What is measured: Critical weakening threshold, weak-module mass, softest-mode localization, system size reached, and bracket width.