| Abstract: |
| We study the polar director structure in thin planar cells filled with bent-core liquid crystals in the ferroelectric smectic-A phase ($\text{SmAP}_F$). We analyze a continuum phenomenological model proposed by Gornik et al., present rigorous proof of existence and uniqueness of the equilibrium solutions, and discuss qualitative properties of nontrivial solutions. The effects of bias electric field, surface anchoring and cell thickness on the structure of polar director are also discussed. Our results agree with previous experimental and numerical simulations in the physics literature. |
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