Nematic Liquid Crystals Used in Wrist Watches (twists light along director) No (long-range) Translational, Head-Tail Order Described by Headless Vector n(x)

• Order Parameter Field is Mapping from Physical Space into Order Parameter Space
• Nematic Order Parameter Space is RP² (Real Projective Plane: Hemisphere with Opposing Equatorial Points Identified)
• (Also Cross Section of a Fiber Bundle)

• The Blue Phases: Introduction
• What Are Liquid Crystals?
• Order Parameter Fields
• Defects in Nematic Liquids
• Homotopy Theory and Defects
• Parallel Transport and Energy
• Twisted Parallelism: Chiral Nematics
• Chiral Nematic Phases: Helical and Blue
• Blue Phases: Networks of Defect Lines
• Defect Lines and Frustration: Curved Space

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Sethna's Research 90-94

Entertaining Science done at

LASSP.

James P. Sethna, sethna@lassp.cornell.edu

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).