Radu Ignat

Stability of the Melting Hedgehog in the Landau–de Gennes Theory of Nematic Liquid Crystals

We investigate stability properties of the radially symmetric solution corresponding to the vortex defect (the so called “melting hedgehog”) in the framework of the Landau–de Gennes model of nematic liquid crystals. We prove local stability of the melting hedgehog under arbitrary Q-tensor valued perturbations in the temperature regime near the critical supercooling temperature. As a consequence of our method, we also rediscover the loss of stability of the vortex defect in the deep nematic regime.

Instability of point defects in a two-dimensional nematic liquid crystal model

We study a class of symmetric critical points in a variational

A compactness result for Landau state in thin-film micromagnetics

2D

A Regularizing Property of the 2D-Eikonal Equation

Landau - de Gennes model where the state of nematic liquid crystals is described by symmetric traceless

A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types.

3\times 3

SINGULARITIES OF DIVERGENCE-FREE VECTOR FIELDS WITH VALUES INTO S1 OR S2: APPLICATIONS TO MICROMAGNETICS

matrices. These critical points play the role of topological point defects carrying a degree

Interaction energy of domain walls in a nonlocal Ginzburg-Landau type model from micromagnetics

\frac k 2

Kinetic formulation of vortex vector fields

for a nonzero integer

Asymmetric Domain Walls of Small Angle in Soft Ferromagnetic Films

k

Stability of the vortex defect in the Landau-de Gennes theory for nematic liquid crystals

. We prove existence and study the qualitative behavior of these symmetric solutions. Our main result is the instability of critical points when