Category: Physics

Summary: Finding when a staggered ladder of shell defects captures the prestress-rescued softest mode more effectively than a contiguous defect chain.

Thin shell buckling is highly sensitive to defects, prestress, and the way soft modes localize. This experiment asks whether arranging defects as a staggered ladder creates a sharper capture threshold for the softest mode than packing comparable defects into a single chain.

The script builds dense symmetric shell operators and increases system size through iterative deepening while bisecting the ladder-strength parameter. By tracking when the prestress-rescued soft mode becomes concentrated on the ladder pattern, it turns a structural localization question into a finite-size threshold estimate.

That matters because shell localization near interacting defects is known qualitatively, but precise threshold maps for ladder-like defect architectures are scarce. The result is meant to isolate whether geometry of the defect arrangement is itself a strong control knob for soft-mode capture.

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

What is measured: Critical ladder threshold, soft-mode capture status, localization of the softest mode, leading eigenvalue behavior, and bracket width.