Phase-Field Allen-Cahn Dynamics L1-327

Materials ScienceNon-conserved order parameter dynamicsδ=5 · challengingL_DAG = 3.5📋 Stub — not mineable

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Forward model E

d p hi / d t = - M_{p} hi \cdot (d F / d p hi) = M_{p} hi \cdot (k a pp a \cdot L a pl a c ian (p hi) - W \cdot f^{'} (p hi))

Allen-Cahn evolution for non-conserved order parameter phi; gradient flow of Landau free energy F = integral [W*f(phi) + (kappa/2)*|grad phi|^2] dV.

L-DAG

E.free_energy -> E.gradient_flow -> D.time -> O.domain_map

E.free_energyE.gradient_flowD.timeO.domain_map

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 300

Well-posed parabolic PDE; inversion for (kappa, M, W) is ill-conditioned due to kinematic degeneracy between mobility and barrier.

Solvability C

Solver class:: Semi-implicit Fourier spectral; Adam/adjoint parameter inversion
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.