Category: Physics

Summary: Estimating when increasing gouge compliance shifts the dominant elastic soft mode from a wall-pinned pattern to a balanced asperity-gouge-asperity bridge.

Earthquake nucleation depends on how stress is shared between locked fault asperities, damaged gouge, and the surrounding elastic medium. This experiment asks when making the gouge more compliant causes the softest collective deformation mode to stop hugging one boundary and instead span two asperities through the gouge layer.

The script builds dense disordered elastic stiffness operators and uses iterative deepening with repeated eigensolves to bisect the compliance threshold across system sizes from N=64 to 2048. It tracks whether the lowest mode becomes bridge-localized across the asperity-gouge-asperity structure rather than remaining pinned to a wall-like region.

That matters because a bridge-like soft mode would mark a more cooperative failure geometry than a localized boundary weakness. The docstring frames this as a threshold map that has not been systematically charted in dense finite-size form for disordered gouge-asperity systems.

Method: Dense symmetric eigensolves with iterative deepening and bisection on gouge-compliance strength in disordered elastic stiffness matrices.

What is measured: Critical compliance threshold, bridge-localization of the lowest soft mode, wall-pinned versus balanced mode character, and bracket width.