Category: Physics

Summary: Finding how strong a contiguous defect chain must be before the softest mode in a prestressed shell relocates from the boundary band onto the defect chain.

Thin shells under prestress can buckle or soften in spatially localized ways, and defects can steer where those weak spots appear. This experiment asks for the threshold at which a contiguous chain of defects becomes strong enough to capture the shell's softest mode, pulling it away from the otherwise dominant boundary-localized region.

The model builds dense symmetric operators for random prestressed shells and increases system size through iterative deepening. At each size, it bisects the defect-chain strength and measures whether the softest eigenmode concentrates on the defect chain rather than the shell boundary band.

That makes the project a finite-size threshold map of mode capture, not just a generic shell-buckling calculation. The point is to quantify when clustered defects reorganize where the shell is mechanically weakest, in a form that existing separate studies of buckling, prestress localization, and defect effects do not directly provide.

Method: Dense symmetric eigensolve with iterative deepening and bisection on contiguous defect-chain strength in a random prestressed shell operator.

What is measured: Critical chain-strength estimate, bracket width, capture fraction, minimum eigenvalue, chain-localization score, shell mass, and chain mass.