Escape into the third dimension

Fig. 9.9. Possible configurations of a nematic liquid crystal in a capillary tube when molecules are constrained to be normal to the glass surface, (a) Molecules remain in the plane normal to the tube axis and a singularity S = - -l appears at the centre (configuration of Fig. 9.8b). (b) Molecules escape into the third dimension and the singularity disappears, (c) Appearance of a singular point separating two regions in which molecules are infiected in opposite directions...

The alternative solution for — mentioned above also has exactly the same energy as that given by equation (3.370). This means that there are two equivalent directions for escape into the third dimension and this can be interpreted as leading to point defects appearing along the axis of the capillary as observed by Williams, Pieranski and Cladis [279] a schematic diagram of such a director orientation is given in Fig. 3.21(c). This topic is beyond our present discussion and interested readers are referred to the review by Cladis and van Saarloos [43]. 

Right, and if the Flatlanders tried to surround you to keep you in one place, you could escape by moving perpendicularly into the third dimension. In their eyes, you would be a God. ... 

These methods have been refined to give a constant splay/bend ratio in purely planar systems, and they allow one to reproduce the well-known aspects of disclinations in pure bend or pure splay situations. These models have also been extended to three dimensions by taking the twist into account, and one can re-find the geometries of director lines in capillary tubes or other cases of escapes in the third dimension . 

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