Category: Nonlinear Dyn.

Summary: Testing whether quenched threshold disorder suppresses the small-world avalanche crossover most strongly at intermediate shortcut density.

Small-world shortcuts can spread avalanches more efficiently in sandpile models, but quenched disorder in local toppling thresholds may counteract that effect. This experiment asks whether threshold heterogeneity has its strongest suppressive impact in the intermediate regime where the system is crossing over between lattice-like and shortcut-dominated behavior.

The simulation runs large GPU-batched dissipative sandpiles while varying shortcut density and quenched threshold disorder. It measures spanning-avalanche rates and toppling-footprint entropy to detect whether disorder most strongly blocks delocalization in the crossover window rather than in either extreme network limit.

That makes the project a competition study between shortcut-driven mixing and local heterogeneity. The value lies in locating where disorder matters most structurally, not just whether it reduces avalanche sizes on average.

Method: GPU-batched small-world sandpile simulations sweeping shortcut density and quenched threshold heterogeneity.

What is measured: Spanning-avalanche rate, toppling-footprint entropy, crossover location, and disorder-induced suppression across shortcut densities.