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Gnomonious projections for bend-free textures: thoughts on the splay-twist phase

Proc. Roy. Soc. A 476 (2020) 20190824, by Nandita Chaturvedi and Randall D. Kamien

The Hopf fibration has inspired any number of geometric structures in physical systems, in particular, in chiral liquid crystalline materials. Because the Hopf fibration lives on the three sphere, 𝕊3, some method of projection or distortion must be employed to realize textures in flat space. Here, we explore the geodesic preserving gnomonic projection of the Hopf fibration, and show that this could be the basis for a new liquid crystalline texture with only splay and twist. We outline the structure and show that it is defined by the tangent vectors along the straight line rulings on a series of hyperboloids. The phase is defined by a lack of bend deformations in the texture, and is reminiscent of the splay-bend and twist-bend nematic phases. We show that domains of this phase may be stabilized through anchoring and saddle-splay.

General News (News Archive)

  • Lisa Tran wins 2020 Glenn Brown Dissertation Prize of the International Liquid Crystal Society For her outstanding work on the geometric confinement introducing complex defect structures and revealing new insight into liquid crystal self-organization. Her work exploits an elegant interplay of topological constraints and geometric frustration to guide the formation of unexpected self-assembled complex structures. (May 2020)

  • Lisa Tran accepts faculty position at Utrecht University. (May 2019)

  • Eric Horsley successfully defends thesis! (January 2019)

  • Hillel Aharoni accepts faculty position at the Weizmann Institute! (November 2018)

  • Helen Ansell awarded Department of Physics and Astronomy's 2018 Werner B. Teutsch Prize, Awarded annually to the graduate student who, by his or her performance in the first year courses, shows the most promise for outstanding achievement in research. (June 2018)

  • Hillel Aharoni wins 2018 Michi Nakata Prize for Early Career Achievements of the International Liquid Crystal Society For his impressive evolution of research on topological and geometric applications in soft matter physics from the pattern formation in smectic liquid crystals, demonstrating how nature uses simple geometric principles for achieving complex functionality. His unusual broad view on the soft matter physics including liquid crystal physics, based on strong mathematical and geometrical skills, will make him grow as a prominent scientist. (June 2018)

  • Ex-postdoc Tom Machon wins 2018 Glenn Brown Dissertation Prize of the International Liquid Crystal Society For his theoretical work on the topology and field states in soft matters, especially in complex liquid crystalline environments, with the goal to predict and determine topological properties of the objects such as field knots and topological defects. Another aspect of his contribution to soft matter, the stability of minimal surfaces, opens up a fascinating new field at the intersection of physics and mathematics. (June 2018)

  • Ex-student Dan Beller accepts faculty position at UC Merced! (June 2018)

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Last Modified 5 May 2020