Core hysteresis in nematic defects.

We study field-induced transformations in the biaxial core of a nematic disclination with strength m=1, employing the Landau-de Gennes order tensor parameter Q. We first consider the transition from the defectless escaped radial structure into the structure hosting a line defect with a negative uniaxial order parameter along the axis of a cylinder of radius R. The critical field of the transition monotonically increases with R and asymptotically approaches a value corresponding to xi(b)/xi(f) approximately 0.3, where the correlation lengths xi(b) and xi(f) are related to the biaxial order and the external field, respectively. Then, in the same geometry, we focus on the line defect structure with a positive uniaxial ordering along the axis, surrounded by the uniaxial sheath, the uniaxial cylinder of radius xi(u) with negative order parameter and director in the transverse direction. We study the hysteresis in the position of the uniaxial sheath upon increasing and decreasing the field strength. In general, two qualitatively different solutions exist, corresponding to the uniaxial sheath located close to the defect symmetry axis or close to the cylinder wall. This latter solution exists only for strong enough anchorings. The uniaxial sheath is for a line defect what the uniaxial ring is for a point defect: by resorting to an approximate analytic estimate, we show that essentially the same hysteresis exhibited by the uniaxial sheath is expected to occur at the uniaxial ring in the core structure of a point defect.