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Geodesic Fibrations for Packing Diabolic Domains


PNAS 117 (2020) 24102, by Randall D. Kamien and Thomas Machon

We describe a theory of packing hyperboloid "diabolic" domains in bend-free textures of liquid crystals. The domains sew together continuously, providing a menagerie of bend-free textures akin to the packing of focal conic domains in smectic liquid crystals. We show how distinct domains may be related to each other by Lorentz transformations and that this process may lower the elastic energy of the system. We discuss a number of phases that may be formed as a result, including splay–twist analogues of blue phases. We also discuss how these diabolic domains may be subject to “superluminal boosts,” yielding defects analogous to shock waves. We explore the geometry of these textures, demonstrating their relation to Milnor fibrations of the Hopf link. Finally, we show how the theory of these domains is unified in four-dimensional space.

General News (News Archive)

  • Helen Ansell successfully defends her thesis! Congratulations Dr. Ansell! (April 2021)

  • Helen Ansell accepts postdoctoral position at Northwestern University! (March 2021)

  • Nandita Chaturvedi accepts postdoctoral position at the National Centre for Biological Sciences in Bangalore! (November 2020)

  • Daria Atkinson arrives from UMass Amherst! Welcome! (September 2020)

  • Nandita Chaturvedi successfully defends her thesis! Congratulations Dr. Chaturvedi! (August 2020)

  • 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 12 April 2021