Fig. 1. Three types of deformation to the director^［10］

Fig. 2. Core of an s=1/2 disclination^［39］. The center is uniaxial with negative order parameter. It transforms via a biaxial ring into a uniaxial form with a positive s.

Fig. 3. Types of topological defects in schlieren textures on a thin planar cell of NLCs^［45］

Fig. 4. (a) Schematic diagram of a spherical structure; (b) Concentric configuration in 3D representation; (c) Cross section diagram of the equatorial plane； (d) Cross section diagram of the position 1/4 away from the two poles； (e)Eigenvalues at the center axis^［46］.

Fig. 5. Profiles of the scalar order parameter in the bulk and on the outer surface of nematic liquid crystal shells. (a，b)Configurations with Boojum defects; (c，d)Configurations containing tetrahedral defects^［47］.

Fig. 6. Cholesteric shell configurations. (a) LC spiral mode around the shell at low chiral strength; (b，c，d)Three finite quasicrystals configurations： (b) OHS(octagonal/hexagon/square），(c) PH(pentagonal/hexagon)and (d) OHP (octagonal/hexagon/pentagonal）； (e)Director field pattern of two half-skyrmions and nine -1/2 defects defining a pentagon and a hexagon in (c）； (f)Amorphous configuration^［52］.

Fig. 7. Defect configurations in a nematic liquid crystal surrounding a spherical particle. (a~c)Quadrupolar (Saturn-ring)state; (d~f)Dipolar state； (g)Corresponding regimes in the phase diagram where these states have the lowest free energies^［61］.

Fig. 8. (a) Reversible formation and in situ crosslinking of molecular assemblies; (b) Self-assembly of amphiphiles in LC defects^［64］.

Fig. 9. (a~l)Nematic colloidal system made of peanut-shaped hematite particles ^［65］

Fig. 10. (a~k)Nematic colloidal system consisting of mesostructures of gold capable of inducing elastic multipoles of different order ^［66］

Fig. 11. (a) Schematic diagram of the nematic liquid crystal device; (b) Two stable equilibrium solutions^［21］.

Fig. 12. Coordinate systems in the Oseen model^［79］

Fig. 13. Energy per unit area of different director configurations along the minimum energy paths at different voltages

Fig. 14. Numerical simulations of the cholesteric finger pattern (a) and translationally invariant cholesteric configuration (b）^［90］

Fig. 15. Circular domains in smectic (a，b)and cholesteric (c，d)liquid crystals^［93］

Fig. 16. (a) Schematic view of a liquid crystal beam control device; (b) Control of the output beam is carried out in three steps： the incident beam is shifted，deflected and expanded^［96］.