Ooh, this is so cool, part of my PhD was on the topology of liquid crystal textures like these! The LC's in this movie are in the "cholesteric nematic" phase: the molecules are rod-shaped and like to line up with each other with a "twist", wiki: https://en.wikipedia.org/wiki/Cholesteric_liquid_crystal … 1/nhttps://twitter.com/vancew/status/1087870532911955968 …
-
-
The pinwheels arise from structures called "torons", which look like this! The blue dots correspond to "hyperbolic hedgehog" defects, where the orientation of the rods is undefined. Here's a challenge – try to visualize the lines changing from the last picture to this one! 6/npic.twitter.com/hbJ7gv3BoC
Prikaži ovu nit -
It's quite hard (for me at least) because there's a different direction living at each point in 3D. That's a lot of data to keep in your head at once, and seeing how they all flow is harder still. But what if I told you there's another way?
7/nPrikaži ovu nit -
Way back in 2013, I published a paper with Paul Ackerman, Gareth Alexander, Randy Kamien (my PhD advisor!) and Ivan Smalyukh that uses the "Pontryagin-Thom construction" to visualize 3D line fields like this as colored surfaces. The Hopf fibration becomes a rainbow donut
: 8/npic.twitter.com/vH1pJpFg9Q
Prikaži ovu nit -
Very rough idea: draw a surface element at each point in the sample where the lines lie in the xy-plane. The color hue corresponds to the angle in the xy-plane (e.g. red is E/W, blue is N/S). The pattern of colors can be interpreted in terms of the topology of the texture, 9/n
Prikaži ovu nit -
which makes it less sensitive to noise and thus applicable to the messy real world! Here's a donut computed from data from a double-twist loop, and also two views of a toron. The toron's surface is a rainbow-striped beach ball, and the points at the top and bottom where the 10/npic.twitter.com/mYjEdiGfTj
Prikaži ovu nit -
rainbow colors collide correspond to the hedgehog defects. Now, to turn a toron into the double-twist loop, open up the defects into holes, and then pull the holes together through the middle and glue into a donut! Much easier to visualize and it's topologically the same. 11/npic.twitter.com/9VhDed3jzs
Prikaži ovu nit -
To read more on this, see this nice summary of our work by Miha Ravnik: https://physics.aps.org/articles/v6/65 (a link to our paper is there too) and this more recent article on some wild new textures that Paul and Ivan found called "twistions": https://phys.org/news/2017-02-never-before-seen-topological-solitons-experimentally-liquid.html … 12/13
Prikaži ovu nit -
To summarize, (1) liquid crystals are awesome, (2) topology is awesome, and (3) you should follow
@vancew to see more beautiful pictures and movies! Thanks for reading my first thread! 13/13 oh god it's been years, i'm just a theorist, i hope i haven't misinterpreted the movie...Prikaži ovu nit
Kraj razgovora
Novi razgovor -
Čini se da učitavanje traje već neko vrijeme.
Twitter je možda preopterećen ili ima kratkotrajnih poteškoća u radu. Pokušajte ponovno ili potražite dodatne informacije u odjeljku Status Twittera.
(image from