Non-singular structures s 1 escape in the third dimension

Let us consider the nematic in a capillary of radius with the director homeotropically aligned at the wall (i.e., with the director normal to the 

the first two terms in the square brackets represent volume integrations, which together give 2nk s, while the third term is a surface integration whose value is nks. Thus the total energy 

Interestingly, the energy is independent of r . On the other hand, the planar structure gives 

The escaped configurations for s=l,c = 7t/2 (involving bend and twist), and for = — 1 (involving twist, bend and splay) are shown in fig. 3.5.7. Structures with the nails pointing in the reverse direction (i.e., with being replaced by — nj are equally probable. 

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