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What are +1 and -1 topological defects in liquid crystal ?

What are 1/2 and -1/2 topological defects in liquid crystals ?

I put a lot of time to search for it but I could not find an easy explanation.

Could anyone make these concepts clear for me ?

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  • $\begingroup$ Please let me know if the question is not clear. $\endgroup$
    – sara nj
    Apr 6 '17 at 12:16
  • $\begingroup$ I wonder why there is no one that could answer the question. It is not a coplicated question. Is there any problem in the way I explained the question? $\endgroup$
    – sara nj
    Apr 6 '17 at 12:31
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I don't know if this is the easiest explanation.

Such defects are commonly found in the nematic phase. The numbers $\pm1$ and $\pm\frac{1}{2}$ are the topological charge $k=\pm1$ or $k=\pm\frac{1}{2}$ of the defects. They mean how the director $\hat{n}=\cos\phi\ \hat{i}+\sin\phi\ \hat{j}$ behaves around the core of the defect, with $k$ evaluated by the hodograph rule $\oint d\phi=2\pi k$ [1].

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