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Some recent analytical papers have explored limiting behaviors ofLandau-deGennes models for liquid crystals in certain extreme ranges of themodel parameters: limits of "vanishing elasticity" (in the language of some ofthese papers) and "low-temperature limits." We use simple scaling analysis toshow that these limits are properly interpreted as limits in which geometriclength scales (such as the size of the domain containing the liquid crystalmaterial) become large compared to intrinsic length scales (such as correlationlengths or coherence lengths, which determine defect core sizes). Thisrepresents the natural passage from a mesoscopic model to a macroscopic modeland is analogous to a "London limit" in the Ginzburg-Landau theory ofsuperconductivity or a "large-body limit" in the Landau-Lifshitz theory offerromagnetism. Known relevant length scales in these parameter regimes(nematic correlation length, biaxial coherence length) can be seen to emergevia balances in equilibrium Euler-Lagrange equations associated withwell-scaled Landau-deGennes free-energy functionals.

Scalings and Limits of Landau-deGennes Models for Liquid Crystals: A Comment on Some Recent Analytical Papers