08:09:21 From Markus Deserno : My guess would be that needle diameter somehow sets the size of the loops in the fabric—and hence, the radius of curvature of the interwoven Euler elastica. From my vague memory of their stress strain relation I’d hence imagine that the fabric modulus is going to be inversely proportional to the square of needle diameter? Does that sound reasonable? At any rate, it seems testable. 08:23:37 From Padmini Rangamani : Random tidbit: This curling is also one of the reasons why sewing at home knit fabrics is hard (the edges won’t lay flat like cotton fabric will). 08:24:40 From Markus Deserno : In the image that Sabetta just showed, the curling looked like it wants to create negative Gaussian curvature. Is this a thing? Maybe stitch dependent? 08:24:56 From Padmini Rangamani : And sweaters have ribbing for the sleeve cuffs and ‘base’ to minimize curling. Plus ribbing offers the elasticity that has already been discussed. 08:24:57 From Robin Selinger : Markus I think needle diameter sets the fixed yarn length per stitch. I wonder if the curvature of the knit is related to the net chirality of the stitch combination pattern. 08:25:46 From Sabetta Matsumoto : @Markus Yes, it does want to have negative gaussian curvature 08:26:19 From Markus Deserno : Then you could suppress it by removing a few loops around the edge? 08:26:37 From Andrej Kosmrlj : Can you control the preferred curvature by patterning knits and perls? 08:27:04 From Robin Selinger : You can make curvature in macramé by adding up chiral knots. 08:27:05 From Sabetta Matsumoto : @Markus No, it has to do with an asymmetry between the top and bottom of the fabric. What @Padmini said is how you can remove it 08:27:55 From Padmini Rangamani : @Andrej — the rib stitch or the seed stithc 08:28:13 From Padmini Rangamani : Sorry too fast — the rib stitch and the seed stitch essentially achieve that 08:28:20 From Andrej Kosmrlj : Great, thanks 08:29:38 From Sabetta Matsumoto : @Andrej one thing you can do is to change the aspect ratio and/or boundaries to help control curvature. It’s very similar to the seed pod paper by Efi and Eran 08:30:12 From Markus Deserno : Hm. But a top-vs-bottom difference should give you some positive or negative mean curvature, no? How does it give you Gaussian curvature? 08:30:12 From Sabetta Matsumoto : @Andrej, I think also changing the length of stitches might change this too 08:30:50 From Sabetta Matsumoto : @Markus the top wants to expand in the left-right direction, but the bottom wants to extend in the top-bottom direction 08:31:05 From Sabetta Matsumoto : It’s almost like an anisotropic elastic bilayer 08:31:18 From Markus Deserno : Aaah! Excellent! That’s what I’ve been missing! Thanks! 08:32:05 From Edward Lyman : In case you haven’t seen Theo Jansen’s “Strandbeests.” Evolutionary cousins of kirigami: https://youtu.be/LewVEF2B_pM 08:32:16 From Andrej Kosmrlj : This is indeed very similar to seed pods 08:33:50 From Sabetta Matsumoto : @Andrej You can also get get the same chiral behavior by choosing the boundary to be diagonal. I have a sample, but it’s in our lab 08:40:39 From Markus Deserno : If you Google “crochet gaussian curvature” and look for images, you see a ton of super pretty example as to what happens if you add or remove stitches 😀 08:41:06 From Sabetta Matsumoto : @Robin Selinger wrote a fantastic article about that! 08:41:27 From Markus Deserno : ☺️ 08:41:43 From Markus Deserno : We evidently have all the right people here! 08:42:23 From Sabetta Matsumoto : https://www.researchgate.net/publication/273868544_Toying_with_science 08:44:05 From Benny Davidovitch : David — can I ask if you have a prediction ? 08:44:14 From Markus Deserno : Plot the difference log-log! It smells like a weak power law, 1/m or 1/m^2, doesn’t look particularly fast. 08:44:49 From Markus Deserno : What would set the scale for exponential? 08:45:08 From Carlos Marques : It does not look exponential 08:45:23 From Padmini Rangamani : Anecdotally, when teaching someone how to crochet, it’s how you tell them their crocheting is wrong. The number of stitches aren’t the same so the edges curled. It wasn’t until I was introduced to differential geometry that I appreciated these ‘mistakes’ 08:54:57 From Robin Selinger : I made a picture two crocheted rounds. one where the extra stitches are stacked forming grain boundaries, and one where the extra stitches are randomly spaced. https://www.dropbox.com/s/mnx10bw73bl9cmp/crochet%20grain%20boundaries.pdf?dl=0 09:10:44 From david nelson : Ian Tobasco asked for a reference on the Regge calculus. See the Misner Thorne and Wheeler book on general relativity, which i think has a chapter on polytetrahedral tessellations of space-time. 09:18:07 From Christian Santangelo : I imagine the Regge calculus is done on a 3+1D version of a simplicial complex? 09:18:56 From Markus Deserno : Here’s a short youtube video in what Sabetta just explained (minus the word “nematic”): https://www.youtube.com/watch?v=bKAJTKvl0nE 09:20:48 From Riccardo Capovilla : Originally, Regge calculus was 2+1 . Interesting the role of a defect angle, that probably provoked David’s comment 09:25:13 From Riccardo Capovilla : Ruth Williams http://cds.cern.ch/record/230326/files/th-6236-91.pdf on Regge calculus 09:30:05 From Markus Deserno : How is the non-uniqueness of the stress tensor specific to knitting? 09:37:26 From Markus Deserno : For those not familiar with the lingo: is the question how we can talk about the strain in a system that has seen large macroscopic deformations that are not everywhere the same? 09:38:20 From Christian Santangelo : Marcus, why don’t you chime in and ask 09:38:25 From Benny Davidovitch : I second Markus — can someone explain better the question ?? 09:40:10 From david nelson : Yes, the Regge calculus was originally 2 + 1, with an important role for deficit angles, where, say, 5, 6 & 7 different triangles come together at a common vertex. There is a generalization to polytetrahedral tilings of 3d space. 09:46:25 From Markus Deserno : It would seem, at least empirically, that you get the longitudinal stress of the fabric at the center by dividing the total force by the width of the fabric *at the center*, not at the clamp. That requires implicit knowledge of the solution of the shape, though. 09:48:04 From Paul Plucinsky : Yes that works ok. But if you go to biaxial loading at some point, your going to have to deal with the non-linear elasticity I think 09:49:02 From Markus Deserno : Yes, that seems very plausible! 09:50:55 From Sabetta Matsumoto : @Paul Yes, that’s true. I think there’s also some level of empiricism to any “constitutive” model we use. All of these notions would require that we have a better understanding of what corsegraining knits to continuum materials means. To some extent this model is a design tool for doing inverse problems for the knitting industry. 09:56:51 From Buddhapriya Chakrabarti : Create a channel in slack I guess 10:02:03 From Paul Plucinsky : Thanks Sabetta. Yes, I think it is an interesting and challenging question! I certainly don’t know the answer to it. Look forward to seeing what you come up with.