Dendritic Solidification L1-334

Materials SciencePhase-field solidificationδ=5 · challengingL_DAG = 3.8📋 Stub — not mineable

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Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.

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Forward model E

d p hi / d t + d e n d r i t e_{a} n t i_{t} r a pp in g = (1 - p h i^{2}) \cdot (p hi - λ \cdot u \cdot (1 - p h i^{2})); d T / d t = D_{T} \cdot L a pl a c ian (T) + (1/2) \cdot d p hi / d t

Phase-field model of solidification with thermal coupling: dphi/dt from Karma-Rappel anti-trapping; temperature T evolves via diffusion + latent heat release.

L-DAG

E.phi_evolution -> E.thermal_diffusion -> O.iter -> O.dendrite_morphology

E.phi_evolutionE.thermal_diffusionO.iterO.dendrite_morphology

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 600

Stiff reaction-diffusion; well-posed under Karma-Rappel anti-trapping; inversion from morphology is moderate-ill-conditioned.

Solvability C

Solver class:: Adaptive mesh FEM; level-set + thermal; adjoint inversion for anisotropy
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.