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A nice excuse to tweet something pretty like this photo by Ken Ishikawa: https://www.nikonsmallworld.com/galleries/2012-photomicrography-competition/emergence-of-cholesteric-liquid-crystal-from-isotropic-liquid …pic.twitter.com/79dKaxzuCG
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from Vincenzo Vitelli's group on "edge currents" and "odd viscosity" in active chiral systems like these! (movie from tweet above: https://www.pnas.org/content/113/46/12919.short …) (movie in this tweet: https://www.nature.com/articles/s41467-017-01378-7 …) Conclusion: from toys to active fluids, soft matter physics rules the world!pic.twitter.com/61TU2luxS2
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A difficult and eye-opening paper: you can model the "hydrodynamics" of just about anything if you list the degrees of freedom and symmetries (or at least Tom can!). Fast-forward to a few years ago and I was fortunate to be around to witness some of the exciting developments...pic.twitter.com/ghhJoDzUyd
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After seeing the absolute delight on his face, I looked up his paper with Tsai, Rodriguez, Ye and Gollub on a "chiral granular gas" that was inspired by these toys: https://ww3.haverford.edu/physics-astro/Gollub/publications/A%20Chiral%20Granular%20Gas%20of%20Rattlebacks.pdf … (more movies here https://ww3.haverford.edu/physics-astro/Gollub/chiral/index.html …)pic.twitter.com/qpPVKlvta9
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A final picture: parametric_plot( (2*(27 - 18*t^2 - 8*t^3 - t^4)/(45 - 12*t + 22*t^2 + 4*t^3 + 5*t^4), -(63 + 84*t + 26*t^2 + 20*t^3 - t^4)/(45 - 12*t + 22*t^2 + 4*t^3 + 5*t^4) ), (t,-1e5,1e5), plot_points=1e6)pic.twitter.com/2Wt2w12BBE
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The other component arises if you "flip" the smallest rhombus, collapsing the blue point to one of the other joints.pic.twitter.com/Jaew3aF7Vo
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... and I forgot to point out that there are actually 2 of these gadgets.
pic.twitter.com/L844x6BppE
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I suspect the equation you're missing is the one that constrains these 3 points to be collinear.pic.twitter.com/t8Gowm5bv6
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Long ago, I learned about range expansions from a talk about this paper: Hallatschek, Hersen, Ramanathan, and Nelson, PNAS 104, 19926-19930 (2007), https://www.pnas.org/content/104/50/19926 …. This paper showed that segregation can occur just from genetic drift (small population effects).pic.twitter.com/QkWERKoZ3i
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Indeed, see http://oeis.org/A000081 . The first comment, in particular, makes reference to this delightful image, "Six Circles" by Roger Vogeler.pic.twitter.com/cqy0daSocF
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As an aside, figuring out that "higher Ling soil" = kaolin clay was tricky: the patent reads 高砱土 but it should be 高岭土, after 高岭村 (Gaoling village, see https://en.wikipedia.org/wiki/Kaolinite ). A related oddity: in this screenshot from the scan, you can see 砱 written in by hand! 7/6pic.twitter.com/AkEcooWaL1
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I then found a Baidu article https://baike.baidu.com/item/%E6%B0%B4%E5%86%99%E7%BA%B8/5932571 … (google translation shown) explaining that there are indeed two types: those based on a "physical change" (fitting the Reddit description) and those based on "chemical reactions" (the ones I have seem to be of that type). 4/6pic.twitter.com/FLMjhzxnnx
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Here are photos of our sheets (sorry for the poor lighting). The texture of the gray side reminds me of a blackboard, but it still feels like paper. When the gray side is wet, it turns black. It fades to gray again as it dries. Wetting the back side doesn't have any effect. 3/6pic.twitter.com/FZi5tzZe0t
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In a similar vein, Bragg and Nye used "bubble rafts" to visualize grain boundaries and dislocations in metals back in 1952 (!). They made an amazing film, too: https://www.youtube.com/watch?v=UEB39-jlmdw … (paper: http://web.mit.edu/mikejd/previously_online/aices_mit_2009/Bragg-bubble_raft.pdf …)
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Just for fun, a juxtaposition: images from letters of Johnson's to Lamonte Young and Joan Birman (the former from the interview linked above and the latter from here: https://celebratio.org/Birman_JS/article/640/ …)pic.twitter.com/9cXOwq8BKR
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The above notebook (and the other members of its family https://observablehq.com/@bryangingechen/convex-hull-peeling … & https://observablehq.com/@bryangingechen/convex-hull-peeling-ii …) were inspired by the paper "The Limit Shape of Convex Hull Peeling" by Jeff Calder and Charles K Smart: https://arxiv.org/abs/1805.08278 pic.twitter.com/Ml4BwhdhzE
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Suppose you place a bunch of random points in a region and then repeatedly remove the points on the boundary of the convex hull. Over time, the boundary of the region will shrink to a point. But where will that point be?pic.twitter.com/2rgMP6HPWv
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i.e. pairs of 5- and 7-coordinated vertices, as in this figure. Images from a classic paper by Bowick, Nelson, and Travesset https://arxiv.org/abs/cond-mat/9911379 … that popularized the idea of "grain boundary scars" on curved crystals.pic.twitter.com/93N12l8VKH
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Presumably they're the only vertices with only 5 triangles around them rather than 6? If so, what you're seeing is the concentration of Gaussian curvature at those 12 points - for a more round-looking result you'll need to spread out the curvature by adding "dislocation pairs"...pic.twitter.com/GhKMKoaHKU
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