Lesson 08
Phase Defects and Boundaries
A system can be locally ordered while preserving a global mismatch.
Neighbouring phases can align smoothly while the system as a whole still contains a twist, discontinuity or defect. Boundaries strongly influence whether that mismatch remains or disappears.
Live explanation
What is happening?
Most neighbouring phases are aligned. No net winding around the ring.
Controls
Shape the field
Periodic wraps around, fixed pins the edges to 0°, free lets edges evolve freely.
Controls how quickly the phase field adjusts. (This model has no velocity, so this is not physical damping.)
What to notice
- Local alignment does not guarantee global uniformity.
- A complete phase winding cannot always be removed by a small local adjustment.
- Boundaries can trap or release defects.
- Opposite defects may cancel.
Show the maths
Optional — the intuition already covers the important ideas.
W counts the net number of phase turns around a closed path. On the ring, W is the integer number of complete twists visible around the circle.
Finished this lesson?
Mark it complete to track your progress across the series.