5 problems

Let $n\geq 2$, let $\rho^n$ denote the function associated with equilibria whose largest eigenspace has dimension $d=1$, and let $\rho^*>0$ be the threshold density. For…

Let $c$ be the Landau–de Gennes tensor order parameter at a point on a disclination line, and let $s$ denote its scalar order parameter and $c{n}$ its director. Disclination-line c…

Consider disclination lines in the Landau–de Gennes theory, including $7k/2$-disclination lines and the $71/2$-disclination line. Half-integer disclination-line stability conjectur…

Consider defects in the Landau–de Gennes model, including $k$-disclination lines whose profiles are obtained from the corresponding profile equations. Profile conjecture. The local…

In the Landau–de Gennes model, let point defects and disclination lines be the two defect forms, with excessive energy concentrated near the defects. Energy-concentration genericit…