By H.-R. Trebin (auth.), Oleg D. Lavrentovich, Paolo Pasini, Claudio Zannoni, Slobodan Žumer (eds.)

Topological defects are the topic of in depth experiences in lots of diversified branches of physics starting from cosmology to liquid crystals and from simple debris to colloids and organic structures. Liquid crystals are attention-grabbing fabrics which current a superb number of those mathematical gadgets and will consequently be regarded as a really important laboratory for topological defects.

This ebook is the 1st try and current jointly complementary ways to the investigations of topological defects in liquid crystals utilizing idea, experiments and machine simulations.

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5 -2 d/~o 5 0 10 20 15 Figure 7. Phase diagram showing the type of solution for a given reduced temperature and reduced capillary size. The depicted solutions are planar-radial, planar-polar, and isotropic. (a) (b) Figure 8. (a) Symmetry breaking alignment tensor solution for a homeotropic droplet. A small disclination loop close to the center has replaced the isotropic core. (b) Sketch of the corresponding director field. only occur very close to the nematic-isotropic transition temperature, or for very small droplets.

The alignment tensor is visualized by a rectangular box which is built from the eigensystem of the tensor. The eigenvalues augmented by ")2/3 IIall to ensure positivity are used as the edge lengths of the box. In this way it is easy to distinguish between uniaxial (two edges have the same length) and biaxial (all three edges are of different length) alignment. , an isotropic tensor would be represented by a very small box. As an example, figure 4 shows the cross section through an s = 1/2 disclination line.

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