Discovery of necklace-like links made of dislocations
Résumé
Complex knotted and at the same time linked entanglements of linear topological defects such as vortices in superfluids, disclinations in nematics or dislocations in cholesterics can be generated during symmetry-breaking phase transitions or by mechanical perturbations. In superfluids and in nematics, such dense entanglements are known to untie, by rewiring of their crossings, into independent unknots that finally shrink and collapse. We point out that in cholesterics confined in gaps with variable thickness, the decay of initially dense entanglements of dislocations can be incomplete. Instead of leading to the defect-less state it produces a new category of necklace-like links which consists of many minimal loops tethered on kinks of much larger cargo loops. We show in particular how a necklace with T minimal loops is generated by rewiring of a two components tangle [2T] with numerator closure. This process conserves the linking number T.
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