Valeriy Slastikov

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.

Half-Integer Point Defects in the Q-Tensor Theory of Nematic Liquid Crystals

We investigate prototypical profiles of point defects in two-dimensional liquid crystals within the framework of Landau–de Gennes theory. Using boundary conditions characteristic of defects of index k/2, we find a critical point of the Landau–de Gennes energy that is characterised by a system of ordinary differential equations. In the deep nematic regime,

Domain-wall motion in ferromagnetic nanowires driven by arbitrary time-dependent fields: an exact result

b^2

Domain wall motion in magnetic nanowires: an asymptotic approach.

b2 small, we prove that this critical point is the unique global minimiser of the Landau–de Gennes energy. For the case

Fast domain-wall propagation in uniaxial nanowires with transverse fields

b^2=0

Dzyaloshinskii-Moriya domain walls in magnetic nanotubes

b2=0, we investigate in greater detail the regime of vanishing elastic constant