Landau-de Gennes Liquid Crystal Theory L1-479

Polymer PhysicsNematic liquid crystal field theoryδ=5 · challengingL_DAG = 3.8📋 Stub — not mineable

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Unclaimed Principle — open for contribution

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Forward model E

F [Q] = in t e g r a l [A (T - T \cdot) \cdot T r (Q^{2}) /2 - B \cdot T r (Q^{3}) /3 + C \cdot (T r (Q^{2}))^{2} /4 + (L 1/2) \cdot ∣ g r a d Q ∣^{2}] d V; E u l er - L a g r an g e : - L 1 \cdot L a pl a c ian (Q) + d F_{b} u l k / d Q = 0

Landau-de Gennes free energy in symmetric traceless Q-tensor: bulk term (A*Q^2 + B*Q^3 + C*Q^4) + elastic gradient term (L_1*|gradQ|^2 + ...); minimizers are nematic textures with disclinations.

L-DAG

E.free_energy_LdG -> O.regularize -> O.Q_tensor_field -> O.optical_image

E.free_energy_LdGO.regularizeO.Q_tensor_fieldO.optical_image

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 900

Non-unique globally due to topological sector; locally unique in each sector. Defect cores are singular in one-constant approximation.

Solvability C

Solver class:: Gradient flow with finite elements; nudged elastic band for topological transitions
Convergence rate q:: 2
Complexity:: O(N_mesh^{1.3}) per iteration

Specs (0)

No L2 specs registered yet for this principle.