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Discontinuous order parameters in liquid crystal theories
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ball, John. M. |
| Copyright Year | 2014 |
| Abstract | Continuum theories of liquid crystals describe defe cts in different ways. For example, in the Oseen-Frank theory the mean molecular orientation o f a nematic liquid crystal is described by a director field n. In the case of equal elastic constants it is know n that the only possible discontinuities of n in energy-minimizing configurations are isolated p oint defects. While this is not known to be the case for unequal elastic constants, natural candidates f or line defects have infinite energy. One possible way out of this problem is to modify the growth of the fr e-energy density for very large ∇n, so that it grows subquadratically, but this introduces a new difficu lty, that, for example, an index 1⁄2 singularity is nonorientable, so that a description in terms of a vector field n is questionable. As regards two-dimensional defects, in which n jumps across a surface, the calculation of the ene rgy of such configurations depends on how the gradient ∇ of n is interpreted, but in the usual interpretation of this gradient (mathematically, as a weak derivative) suc h configurations are not allowed. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://programme.exordo.com/ilcc2014/programme/ilcc2014.exordo.com/data/paper_attachments/1034/initial_draft/ballilcc.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
