A declared candidate, with sensitivity controls
M03-D fixes the writing law and damping convention before a future measured comparison; synthetic results do not select or validate a material model.
One declared research candidate
M03-D: dissipation-written state with fixed viscous coefficient. This is the candidate carried forward for a prospective oscillator comparison. The choice is declared for auditability, not justified as the most physical by these synthetic results. The other five variants are sensitivity alternatives; selecting among them after seeing test outcomes would require a new validation set.
Equations and scope
dq/dt = p dp/dt = u − cp − kq k = L⁻²(1 + βm), c = 2ζ/L dm/dt = α cp²(1 − m) − m/τ
For the synthetic reference: L = 1, α = 0.1, β = 1.5, τ = 15, ζ = 0.12. All quantities are normalized. State writing follows the normalized viscous dissipation rate; α needs a physical energy calibration before a material interpretation. The damping coefficient remains fixed. Ring-down can continue to write state during nominal rest.
Baseline and comparison
| Run at dt = 0.005 | Probe RMS displacement | Meaning |
|---|---|---|
| No-memory baseline, α = 0 | 0.702515407 | Same forcing and initial mechanics; m stays zero. |
| M03-D | 0.962187384 | Different response under an imposed constitutive law; not better performance. |
| M03-D minus baseline | 0.259671977 | Synthetic response contrast; no physical effect size. |
Training 0–30: sin(t); rest 30–50: zero input; probe 50–80: 0.6sin[1.25(t−50)]. Initial q = p = m = 0. The probe can write memory. A prospective comparison must freeze the carrier, observation model, calibration split, parameter constraints and error model before evaluating independent test specimens. No measured held-out comparison is claimed.
Energy accounting
E = ½p² + ½kq² dE/dt = up − cp² + ½q²dk/dt
The oscillator ledger omits the physical mechanism and cost of writing m and changing stiffness. It is a subsystem consistency check, not a proof of thermodynamic completeness.
Sensitivity comparison: candidate and five alternatives
| Writing | Damping held fixed | Fine-step probe RMS | Difference from baseline |
|---|---|---|---|
| drive | ratio | 0.873555389 | 0.171039982 |
| drive | coefficient | 0.934881717 | 0.232366310 |
| strain | ratio | 0.895162756 | 0.192647349 |
| strain | coefficient | 1.029048351 | 0.326532944 |
| dissipation | ratio | 0.879525829 | 0.177010423 |
| dissipation | coefficient | 0.962187384 | 0.259671977 |
The u² and q² writing alternatives and fixed-damping-ratio alternatives remain available for sensitivity analysis. Equal numerical α across different signals is not equal material calibration. These six rows do not select a winner.
Reproduce
Python source · Exact outputs · Solver and energy tables
python model_variants.py
Python standard library. The interactive browser lab remains the explicitly labeled model 0.2.