Landau-de Gennes corrections to the Oseen-Frank limit: Anchoring-induced tilt modes

@misc{rajamanickam2026landaude,
  title = {{Landau-de Gennes corrections to the Oseen-Frank limit: Anchoring-induced tilt modes}},
  author = {Prabakaran Rajamanickam},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35127},
  eprint = {2609.35127},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35127},
}

TY  - UNPB
TI  - Landau-de Gennes corrections to the Oseen-Frank limit: Anchoring-induced tilt modes
AU  - Prabakaran Rajamanickam
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.35127
UR  - https://arxiv.org/abs/2609.35127
AB  - An asymptotic analysis of the Landau--de Gennes framework is performed to compute higher-order corrections to the Oseen--Frank limit in a bounded three-dimensional domain under appropriately scaled surface anchoring energy. A systematic decomposition of the Q-tensor into three mutually orthogonal subspaces-the uniaxial scalar, geometric tilt vector, and transverse anisotropy tensor-reveals that the leading 𝒪(ε) correction to the Oseen--Frank director field n_0(x) is dominated by a non-vanishing tilt field p_1(x), where ε represents the ratio of the nematic coherence length to the characteristic domain size. This macroscopic variation constitutes a soft mode released from the boundary once the surface anchoring energy is retained at its physical scaling rather than driven to an infinite strength. We show that this tilt field is governed by the linear Jacobi equation, 𝒥_n_0(p_1)=0, subject to a non-trivial, anchoring-driven Dirichlet boundary condition, where 𝒥_n_0 is the on-shell Jacobi operator of the harmonic map n_0 on 𝕊^2. The two fields are accompanied at 𝒪(ε^2) by an off-shell correction to both the uniaxial scalar and the transverse anisotropy tensor, passively induced by the elastic non-uniformity (∇n_0≠0) and the boundary-driven tilt (p_1≠0). Through 𝒪(ε^2), the tilt enters the energy only through surface terms, not the bulk, providing a pathway for the system to lower its energy . Under the conventional benchmark of rigid Dirichlet conditions, this response is annihilated outright, demonstrating that corrections built upon infinite energy barriers obscure the underlying physics of anchoring-driven tilt modes.
ER  -