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| We study the Landau-de Gennes free energy to describe the undulatory instability in smectic A liquid crystals subjected to
magnetic elds. We prove this phenomena by the bifurcation theory to the nonlinear system of Landau-de Gennes model
for smectic liquid crystals. We nd the critical eld and oscillatory description of the undulations which are consistent
with experimental results. When the applied eld is suciently large, the smectic states are maintained, with the director
parallel to the eld. We perform numerical simulations to illustrate the results of our analysis and demonstrate the tilted
layers and directors near the boundary at the equilibrium state. The three dimensional study for smectic liquid crystals
under the magnetic eld will be also discussed. |
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