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