5 problems

Consider the Onsager potential with interaction parameter $\mu>0$. For a positive integer $n$, let $D^{2n\mathrm{h}}$ denote the relevant horizontal dihedral symmetry group, and ca…

Let $\mu$ be the Onsager interaction parameter, and consider the local and global minimizers of the Onsager free-energy functional. A state is axisymmetric if its density is invari…

Fix $\sigma_0$ and suppose that the coupled dipolar/Maier–Saupe potential has a non-axisymmetric critical point at parameter $(\sigma_0,\kappa_0)$. Monotonicity conjecture. If a no…

Let $(\sigma_0,\kappa_0)$ be a parameter pair for the coupled dipolar/Maier–Saupe potential, and identify critical points that differ only by a rotation. A critical point is non-ax…

Consider the coupled dipolar/Maier–Saupe potential with parameters $(\sigma,\kappa)$ and its critical points on the space of admissible orientational densities. A critical point ha…