All runs: ring topology, N=64, stochastic Euler-Maruyama integration, dt=0.001, 5×105 steps (discard first 105). Natural frequencies drawn from N(0, 0.05). Reported r is time-averaged over the last 104 steps.
σ = 0.05, K stepped from 0.5 to 3.0 in increments of 0.5.
| K | ⟨r⟩ | σ(r) | Slip count | Max phase diff |
|---|---|---|---|---|
| 0.5 | 0.187 | 0.062 | 847 | 2.91π |
| 1.0 | 0.293 | 0.074 | 523 | 2.44π |
| 1.5 | 0.458 | 0.058 | 241 | 1.83π |
| 2.0 | 0.721 | 0.031 | 58 | 0.92π |
| 2.5 | 0.904 | 0.014 | 7 | 0.37π |
| 3.0 | 0.971 | 0.006 | 0 | 0.14π |
K = 2.0, σ stepped from 0.01 to 0.15.
| σ | ⟨r⟩ | σ(r) | Slip count |
|---|---|---|---|
| 0.01 | 0.963 | 0.004 | 0 |
| 0.03 | 0.892 | 0.015 | 9 |
| 0.05 | 0.721 | 0.031 | 58 |
| 0.08 | 0.511 | 0.052 | 203 |
| 0.12 | 0.304 | 0.069 | 478 |
| 0.15 | 0.191 | 0.081 | 713 |
K = 1.75, σ = 0.04. Comparing even and odd N. Each run 3×.
| N | ⟨r⟩ (run 1) | ⟨r⟩ (run 2) | ⟨r⟩ (run 3) | Slips (mean) |
|---|---|---|---|---|
| 32 | 0.531 | 0.544 | 0.538 | 119 |
| 33 | 0.487 | 0.476 | 0.491 | 164 |
| 64 | 0.583 | 0.590 | 0.579 | 92 |
| 65 | 0.504 | 0.511 | 0.498 | 148 |
Parity effect is real — odd-N configurations consistently underperform even-N by roughly 12-15% in ⟨r⟩ and 50% more slips.
# coupled-osc run --topology ring --n 64 --K 2.0 --sigma 0.05 \
--dt 0.001 --steps 500000 --burn-in 100000 --seed 20260714 \
--output run_005k_64ring_K2.0_s0.05.h5
Raw HDF5 files available on request. Python analysis scripts in the repo.
Data generated 2026-07-14. Reproducible with the commit tagged v0.3.1.