- Helical Phase:

**n**(z)=**x**cos(q z)+**y**sin(q z) - Twists in Only One Radial Direction

- Double Twist Tube:

**n**(r) =**z**cos(q r) -**theta**sin(q r) - Twists in Both Radial Directions
- Double Twist in Center,

Single Twist at r = pi/2 q

- 45 degree Tubes Pack at Right Angles
- Defect Lines Thread Right-Handed Corners
- Cubic Blue Phases

- 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

This research was paid for by

- Sethna's Research 90-94
- Entertaining Science done at
- LASSP.

Last modified: November 2, 1995

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

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