Solid-State Diffusion (Fick + Onsager) L1-333

Materials ScienceMulti-component diffusionδ=3 · standardL_DAG = 3📋 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.

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Forward model E

d c_{i} / d t = d i v (D_{i} j \cdot g r a d (c_{j}) + D_{t} h er m o \cdot g r a d (T)); t r a cer d i f f u s i v i t y D \cdot_{i} f r o m N er n s t - E in s t e in

Fick's second law in multicomponent form: dc_i/dt = div(sum_j D_ij grad(c_j)); D_ij from Onsager coefficients and Darken activity corrections.

L-DAG

E.onsager_flux -> D.time -> O.concentration_profile

E.onsager_fluxD.timeO.concentration_profile

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 100

Parabolic; well-posed; inversion of off-diagonal D_ij ill-conditioned for small gradients.

Solvability C

Solver class:: Crank-Nicolson FD; FEM for complex geometries; Bayesian inversion for D_ij
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.