08:02:41 All right, Welcome everybody to the second week of our program. So this week will be the father to extreme mechanics and chair of the today's discussion will be Chris Santangelo from Syracuse, and I hope you already watched the pre recorded talks from 08:03:01 And you know if you missed our first week of the program I just want to remind you that, you know, please mute yourself when you're not speaking so that we minimize the background noise. 08:03:03 Samantha Matsumoto from Georgia Tech and Marcel ideas from anywhere. 08:03:11 And whenever you would like to you know get a word to you know ask questions or participate in discussion, please raise your hand on zoom by going through reactions, and then raise your hand. 08:03:22 Right. And, and then just maybe you saw that you know though these discussions are recorded and they will then be posted on the KTP website, and will also say the zoom chats, where often you find useful information and we're going to share this with the 08:03:38 participants. 08:03:39 Alright So will this our end the intro remarks, you know, you know, give the floor to Chris. 08:03:46 Hi everybody. I think we should just jump right into it, and I am going to favor live questions over the written questions, so when there are live questions i think that's that's what we'll do, but I've got some I've gone through and sort of curated all 08:04:03 the written questions too especially the ones that haven't been answered yet, so don't feel pressure so with that said, the first question is going to come from 10 meanie rainy, rainy Monday. 08:04:17 So, I'm fairly I was very excited. 08:04:21 This morning. So, for this question is actually for somebody so I'm somebody who nets and crushes a lot, as evidenced by Mike, I don't know if you can see that the background but I always like one of the nice things about zoom meetings is nobody needs 08:04:36 to know what you're doing, like when you're listening so I've noticed so much in the past year. So one question for you, when you talk about the mechanics of the fabric is that the stretch of the fabric the net fabric really depends on both the arm and 08:04:51 the needle, that's used the needle size this used, so I can use the same your arm and use the same stage. 08:05:00 But then if I use a different needle or, you know, two different people are reading it, you get a different tension of course you can kind of control for that with an industrial knitting machine. 08:05:09 But I was wondering if you could comment on that, because the deal with the seed stage for example, if you have somebody who has a tight tension, you're not going to get the same elasticity. 08:05:23 So just curious how that plays into. 08:05:28 Yeah, that's a fantastic question. Um, so I guess my all of my intuition is like you from Hans knitting, I, you know, Euston it all the time and now it's my job I don't knit quite as much anymore. 08:05:47 But also we did some experiments about hand knitting versus the machine knit, so we didn't do the full like the last SV for hand minutes, because there were just too many things we couldn't control for, but the one thing we did look out was, was like 08:06:04 the stitch size between like the four different types of fabric we did. So we did stock in a guard or ribbon seed. 08:06:17 And so we did experiments on like making the hand that swatches and versus making a machine knit ones and the machine that ones that have like all, even if you set the tension the same they have like really radically different stitch sizes through like 08:06:31 for the four different fabrics but hand it's have a really consistent stitch size. So all of them are approximately the same, it's the same person that's. 08:06:41 So that's something that we can control on, you know, by changing needle size and so we also have that in our simulations where there's like a fixed yarn length. 08:06:55 We haven't yet very that because we haven't had experiments where we can, like corroborate that we have a new industrial knitting machine where you can actually set a stitch link. 08:07:09 Um, so, we're going to see how both number one will see if that's actually consistent because they have no units. 08:07:19 Like, no matter what the machine is 12 is the like normal stitch size, whatever that means. 08:07:26 And it's unclear if its scale or if they're fixed or if they're in kilometers like it just doesn't it there's, we'll have to figure out what that setting means first. 08:07:39 I think you're probably what we'll see is that it has an effect on like shifting the overall like slopes, like the overall rigidities of the fabrics, by making them softer if you have bigger stitches on like tighter or more rigid if you have tighter stitches. 08:08:07 I guess that's sort of my experience of I tend to be a, not necessarily a titan enter but I like knitting on smaller needles for like compared with what the patterns live says so. 08:08:23 I suspect, just from my experience with I will end up with stuff that's a bit more rigid if it's smaller, but that's just an intuition I don't have any physics to back that up. 08:08:36 Actually no, I do have physics, because you still have to do the same. 08:08:41 Like, assuming that the yarn is still has the same radius the deformations in and out of the plane, are going to be like in those affirmations are going to be the same regardless of if you have a small stature, or big stitch, but if you have a small stitch, 08:08:56 you're going to have to bend it more tightly around different things so it's going to take up a larger fraction of the arc length to try to straighten it out so you'll have places where you get less straight portions and the more curved portions. 08:09:17 So I think that would be my back of the envelope physics argument for it. 08:09:23 Can I ask a quick follow up. I promise I won't keep going. 08:09:31 One is if you actually block the fabrics though, because depending on how you block the fabric so for those who are not familiar with you. I'm not something you saw the I just roll in the video of the swatch that. 08:09:39 So, I just, I'm gonna cheat on two questions. 08:09:43 So you actually have a technique of blocking it before you put it together in a sweater or something so you're straightening out the edges you. It can be using steam or starch and so what do you think would happen if you blocked the swatch, and then a 08:09:58 sort of follow up on that as if you crocheted so my experience if your crochet, rather than net, the stitches, the nod is completely different and then the same yarn. 08:10:14 Same effective gauge, you get a very stiff fabric compared knitting so have you thought about that as well. So the blocking. 08:10:19 Yeah, like, yes I'll answer crochet is definitely differ and you can kind of understand why because knitting is sort of this process of taking basically a single piece of yarn and then kind of pulling loops through so it's really easily kind of connected 08:10:38 laterally but when you crochet, you have sort of loops within loops and then they get kind of pulled through so they're almost locally anchored down so you don't have the, you don't have kind of this collect the ability to sort of collectively stretch 08:10:52 in the same way as nuts about blocking. 08:10:57 That's another fantastic question, and from the physics point of view I guess I'm like, I'm sort of always on the fence like do we want to block things do we want to not block things when we do experiments on them because I don't. 08:11:13 There's so much physics in what goes on in the yarn relaxation process when you get it what or when you steam it, and I'm a little bit, like, I don't know how much of that I need to know before I can accurately us I mean I think we're definitely going 08:11:32 to try both just to see what happens like does it change the overall stitch length does it, you know what, elastic properties does that change, but without access to I think a lot more high powered imaging techniques when we have. 08:11:52 I think I'm a little hesitant to make any claims about it other than. It's a finishing technique that's used in it does make for sort of certainly nicer appearance to pieces but I don't know what the plastic that formations are, but they're going to, 08:12:11 like, how that's going to affect it. 08:12:15 So that's a little bit of a, you know, I mean I'm really curious, but I'm also like I I worry a little bit that I'm not going to have the techniques to understand that the way I want to. 08:12:28 I just want to start to finish. 08:12:39 Finish and close it and then I'll stop because Indonesian crochet, you go along the road like unit, and then you anchor like your crochet so then you get a very nice fabric that's in between those. 08:12:58 Carlos, who actually had a question that's related to the compressor ability of the yarn that I think is not, and it's somewhat related to this, so maybe it would be maybe this is a time to if he wants to ask this question live, maybe this would be the 08:13:18 time to ask it will thank you for bringing me in your description you're modeling golf, the process relies on the curvature of the strengths. 08:13:33 I wonder if this choice was an obvious choice because the army is quite sick. 08:13:40 The thickness of the strength is actually almost comparable with the cell size. So, these things can be compressed a lot. Is there a gym in the stretching curves were to compress ability of the arm itself could dominate the could dominated the response. 08:13:58 Oh, that's a great question. Um, so, I think this is something that is related to spine yarn versus sort of our normal Alaska, are like sort of kickoff rod, understanding. 08:14:16 So spun yarn. You definitely have a lot more decoupling between like bending and radius, then you do, if it was a solid elastic piece. 08:14:30 So, in that, in that sense, we're kind of able to treat it just as a compress ability and bending almost separately. 08:14:45 Um, if we were knitting with like model filament or some other elastic medium, I think, then we really do get into the regimes that you're interested in, and there's places where you could have compression that dominates like I think there's a in math, 08:15:09 there's a 08:15:12 branch of sort of geometry to call it, or I guess it would be geometry primarily that looks at basically unintended global loops so if you have like two loops like this and put one around the other like this, you know, talk logically, you can just pull 08:15:30 them apart. But, if they're thick and sort of rigid rigid as far as like they don't have any compression to them. 08:15:42 You can get these race track configurations where those are unintelligible so you do get stuck in these sort of states that are almost meta stable based on the, like, where the curvature gets concentrated and that's something that we definitely saw in 08:15:58 this simulations when you made this ditch was too small, they get stuck in these weird configurations and you end up having like a stiffer slope before a softer one where it kind of like pops through different sort of different configurations. 08:16:15 I'm not sure how physical that is I'm not sure if it's actually possible to make those things like it would certainly break an industrial machine and it would probably break most needles you tried to do it on by hand, but we did see something like that 08:16:30 in. 08:16:33 In the simulations before we kind of got the yarn diameter to yarn length pin down. 08:16:43 Okay, so we've got a backlog of hand raised hands so let's the next person to raise their hand was scotch in their own car, you want to go ahead and ask a question. 08:16:58 So this is a continuation of the last two questions from the mini and Carlos, and you almost, almost tackled it right now. I just want to preface this by saying that I'm an experimental is for the background and plastics processing. 08:17:14 And one of the things about the urns is that they are, they are 08:17:19 the individual fibers that comprise the yarn are heavily crimped usually there is this fascinating process in plastics processing called false twist texture in that is used to develop that cream. 08:17:33 So that acrylic fibers will will behave a little bit more like well I guess. 08:17:45 The consequence obviously is that the yarns can slim down enormously as they stretch, and then the crimp also affects their friction and, and as somebody just pointed out, it allows the fibers to bend in. 08:17:55 Well, I don't know. So you mentioned right now that ideally, sort of ideal comparison might be with one of filament fiber, modify the filament fibers, something like, I would recommend fishing lines like this. 08:18:10 Have you done experiments with that, and second question as a technical is you cannot knitting machine actually handle mono filaments. 08:18:20 So we haven't done mono filaments. Other people have I don't feel like they behave the way, textiles that we're familiar with behave. So, I think you get a lot of artifact in them, like, I think there was a there was a cool paper. 08:18:43 By signing off on Khloe, and they were looking at like this with avalanche behaviors in them and I think that's something that you get, because it's mana filament like you get these really interesting dynamics of like, Monica element on mana filament, 08:18:58 but I don't think that's the same thing that we would see in like a spun fiber. 08:19:04 I don't think that's the same thing that we would see in like a spun fiber. So the spun fiber, as you say like these little like crimping gives it like extra almost, it's almost like a fake of volume like it takes up more area then it would just because 08:19:19 of these sort of static interactions of the little fuzzy fibers. 08:19:26 So that does mean that are are sort of compatibility like the core, the core of this sort of core shell is really small compared with how fluffy, the yarn is and that definitely as you say, affects the friction So far everything we've done as quasi static 08:19:43 so we're not we're not yet dealing with that friction I think if we go to dynamics we probably will do friction, that's based on that kind of idea where you have to like pieces of yarn near each other and then within some, Some sort of radius, you have 08:20:06 basically sort of artificial springs that get added once they're close enough, and then they sort of stretch, and then reform, depending on where you are. 08:20:17 So that's probably how we would implement that. That type of friction. I think it's really, really important thing to deal with especially because a lot of these do have up quite over and damage dynamics and the friction comes in a very different way 08:20:43 So, I think I think you're absolutely right. And that sort of analysis of those. 08:20:45 friction in a sort of damp spring behaves or a spring in like of its guess liquid. 08:20:51 I didn't remember what you called the processing of it but that those extra sort of kinky fibers to kind of add the texture, the processes. This is probably getting off topic here, the process is called funds, twist, texture thing. 08:21:16 as interesting. In this context, but for people who like mechanics, it's a fascinating process. Thank you. Thank you. 08:21:18 Okay, so I'd like to still kind of cover the backlog a little bit. Next question asked her what the next question is from Sherry Leon. 08:21:37 Hi. I was just wondering, in your video or in the top, it showed like a relatively small fabric. And we saw at the edges of your squat fabric curls and I was wondering who the size of your swatch with matter for your experiments. 08:21:48 That's a good question. Um, so, the sides of the fabric crows in stock and here I've got a little sample here. 08:21:57 The fabric curls and I was wondering what the size of your swatch would matter for your experiment. 08:22:03 They, it's just a property of this particular type of stitches that they do curl up the boundaries. 08:22:13 And unless you process it by blocking it and even if you do block it it's going to want to curl back up again. 08:22:22 That's something that just that sort of the relaxed state of this fabric is to curl. 08:22:28 So you do have some sort of, I guess, you do have a small boundary effect of the curling on this. 08:22:37 But since we were looking at the, the stress and strain and not the force extension. 08:22:49 Presumably, that's a smaller effect. I think we also need to. 08:22:55 I think the boundary doesn't actually play that big of a role in the actual plasticity it doesn't it doesn't, there's nothing about the boundary that sort of confining in any way. 08:23:10 Um, so I think if that was the case then we'd really have to worry, but here it's a pretty smooth, I mean, depending on how you finish it. 08:23:19 You choose to make the boundaries and you can have extra boundary effects in it but I think we did them so that that we kind of mitigated. The, the, that's sort of an extra boundary layer that we could have. 08:23:36 I don't know if that answers your question. 08:23:38 So I guess you're saying, like, even though you have a boundary doesn't matter. 08:23:43 But you know how much of a boundary like how small of us walk you would have to make in order for the boundary mattering your measurements. 08:23:55 I mean it would be like two stitches. 08:23:58 As far as like possible places where the technology is different. 08:24:03 As far as the curling is concerned, that is a thats related to aspect ratio more than it is related to mechanics, it's basically if I have a long skinny piece it's all going to roll up in one direction and if I've got short, fat piece it's all going to 08:24:21 roll in the other direction but it's, it's still the same mechanics throughout. 08:24:27 So, I don't think that we would have a. 08:24:32 I mean the boundary layer that could exist would be from how we choose to, like, change the change the direction of the row. 08:24:40 And so that's, you know, one stitch of change and then maybe an extra like stitch to, like, mitigate so i don't i think it would be pretty small like you have to have something that's like four stitches across for it to be dominated by three. 08:25:00 So, I want to bring Marcello into the conversation a little bit with the next question. 08:25:05 And there was a question on maybe one of the live people have one for him but there was a question on the, on the slack. That Benny asks, and there was a little bit of an exchange they're having to do with the interaction between earphones in an actual 08:25:22 curiosity structure and maybe this is a good time for Benny to jump in and ask his question. 08:25:32 Sure show things with. 08:25:34 You have to think for myself it was really nice to kind of use any good. 08:25:39 the politics of the single econ and we discuss the relevance of searching at on properties of the single Econ, Econ solving of the cons. 08:26:01 But But what what what they have helping to understand and that that's a thing that changes Calista refill to, it is, how do you envision the symbol timeless action or interaction if you wish between many cones, which, find the same quality that you would 08:26:20 like to think of you will keep the gummy. And in such case I think you you find a food Co Op yo yo comment, or that's what they do not fully understand. 08:26:30 So the whole response if I understand correctly of killing gummy is supposed to be a symmetric. 08:26:36 Right. So, generally, there is no stranger. 08:26:38 If you modify your kilogram if you just have a nice killing me structure unit for me, generally those should be no thing. 08:26:48 Right. 08:26:48 But the coding, if I understood correctly you point. 08:26:52 So, okay, let us give the details the case so if there is no strain, then we know that to Econ, even the boundary between them should have no strength. 08:27:02 But this kind of constraint if you start from a picture of pecans as the building blocks to the gummy seems to be extremely complicated because I don't see how you simply how it simple to eliminate this plane which naturally would exist, because the boundaries 08:27:17 of each econ is quite complicated so generally the boundaries of the individual consumer going to match, and it will generate lots of strain, naturally, but because we know that the overall constraint is that it should be no stain in the whole structure 08:27:32 and then it's all a mess. I mean that's what i i don't see a path forward. So that was my question. 08:27:39 Okay no yeah so I think I'm happy to say a few things about this with the caveat that I, I haven't yet fully understood that, that question and this is the thing that I'm also trying to dig into to try to know, give a bit of a perspective on how strains 08:27:59 are playing a role in building up the curriculum structure because I don't believe that strength can completely be neglected. In the case of the Econ, Econ interaction. 08:28:14 So perhaps I could share a little bit of a few slides here to just point that out to some people who may be wanting to visualize this because there is a lot of hand waving at the moment because, again, I don't understand that completely yet, but I will 08:28:34 try to answer this question by making this analogy with the, the D calm. 08:28:49 So, most should be familiar with this idea that if you have to the cons on the team sheet, they are going to interact with one another via stretching rich. 08:28:56 And what's going on here along this rages that there is a buildup of dancers stresses that pull the rich apart. 08:29:05 And there is an emergence of negative Dawson curvature in this bridge. 08:29:10 So what Ben is bringing up to the table here is on the Karaganda structure. 08:29:17 The types of localization that appear that at least the main motif of localization, which on this side here would be the deacon. 08:29:29 The way I see the motifs on the right hand side is that you have equals along the edges of this Karaganda structure. 08:29:40 And there is a whole massive interaction and you're right so most of what's going on here, and I like this picture because it shows exactly the point I'm trying to make and and the point is that you touched upon. 08:29:54 Most of what's happening on the right on the left, try to ignore this grain boundary, type, the formation here for the time being the center. 08:30:14 But there are center regimes of the formations of the trigger me, and which will fall into this sort of what I call symmetric configuration and opposite to this anti symmetric configuration of the econ. 08:30:21 What most what was what's going on here is that stresses are completely released and and and then that sense I would agree with you. 08:30:30 And whenever we have this type of situation here and then I think the buildup of stresses may need to a situation in which we have to care about strains and that's what I was referring to 08:30:46 what that exactly is a yet don't know but I, I'm happy to continue this with one more slide to perhaps make a point here than than that I think I've been trying to make for some time. 08:31:01 calculations on this still need to be made, I have some preliminary financial results on this that confirm what I'm about to say, but once again just to recap, to put this into context Ican Ican Ican Ican interaction gives you 10 size dresses. 08:31:22 Here on Michael Martin feel oh yeah this is, this is my convention so some right so temptation here and I'm putting it to be negative, rent. 08:31:34 So, and there is an emergence of zero, negative Gaussian curvature, as I already mentioned. 08:31:48 There is something interesting here. What is this configuration is quite stable right so you can actually book, the deep Hong Kong, around, and the, the configuration is going to be completely stable things won't move about very much. 08:31:51 What's happened to in this situation here in the Econ, Econ interaction. 08:32:05 The Econ, Econ is quite distinct because, actually there is 08:32:12 an instability that arises due to a build up of contrast of stresses between the two Econ, Econ interactions. 08:32:23 So my claim to this incident. There is actually a region here in between that is going to be compressed stresses. Therefore, there is going to be the material points are going to move closer together. 08:32:40 And in fact, there is indication for my preliminary results that this is what, but I mean take this with a huge grain of salt right but that this is going to be a region of positive doesn't curvature. 08:32:56 And, and it's, it's sort of clear from from this interaction that the, the key GM is going to release the stress by this boss bifurcation behavior here which we have like a, an instability, after the fact, that does exactly what you already pointed out, 08:33:17 basically when you, when you flip this query gummy in this asymmetric configuration that releases all the stresses. 08:33:26 Right, so, but once again this is, this is very preliminary and and and i think that the discussion will continue in fact from the last question you asked me Benny from my PhD dissertation, I think I'm still answering that to you. 08:33:49 And it's been almost 10 years so I think we'll continue this this talk. 08:33:55 Okay, so let's go to a live question, I think, if I have not confused the order of hand raising that Joshua Zimmer Berg is next. 08:34:08 Okay. Okay, thanks. Um, I was just writing. 08:34:11 I was saying, I kind of just totally captivated so it's a quick comment for the, for knitting. And I was just captivated by the talk, and it reminded me. 08:34:30 And what I was missing was kind of. 08:34:34 I know, not very little about what's going on but spontaneous curvature seemed to be absent from most, a lot of the equations on on how prick given us Helfferich bending. 08:34:48 And I remember my sisters in the early, early 60s used to set their. If it's like wall if it's wall base. It's keratin, and my sisters used to iron their hair, which was naturally wavy to get it flat, or they would heat it in that would want while winded 08:35:09 on cylinders. I was younger than them but the thoughts I did, they would wind it on different cylinders and they had all these cylinders of different radio I have curvature. 08:35:19 And so I wonder if this blocking the committee was talking about, which seemed to involve heating could be used to set an analog of spontaneous curvature in your systems. 08:35:33 Oh, I haven't seen blocking used in that what i mean i guess it, it is some, to some extent used in the opposite of that way so if you knit lace, for instance, when it comes out, it's, I have to run into the other room to grab a sample but it's all kind 08:35:50 kind of like puckery. And if you want like the pattern itself to show you what you do is you block it usually this one doesn't involve key, but you get it. 08:35:59 What like very thoroughly. What, and then sort of blot out the extra water and then you basically pin it like pulling it as hard as you possibly can in a rectangle then when it dries it stays on a rectangle. 08:36:14 So I'm not sure if that has to do with like, I mean that has definitely has to do with capillary forces I don't know what it's doing to the fiber it seems to do the same thing to the fiber, whether it's made out of acrylic or silica or wall or. 08:36:31 So I think it's well, pretty well understood how it would be nature as you give a pulse of high temperature, like you could wrap your, your fabric around different shapes, give a pulse of high temperature, that would be nature, and then allow. 08:36:51 I think it's 16 bonds that reform or something like there's a reforming of some linkage isn't keratin that's reversible. 08:37:01 After a pulse of I temperature. 08:37:05 That's interesting. 08:37:07 And I do know that there's other ways using strip topological defects to give spontaneous curvature to some of these, so far we've only looked at like in plan, different nations I think the next wave of grad students coming in will start looking at some 08:37:23 out of playing different nations to thank you tonight Can I jump in on that, if you don't mind, please share. 08:37:31 Yeah. Yeah, go ahead. 08:37:35 I say so one one. So I think what to get that spontaneous curvature that you're talking about. And Joshua I think the rabbit image that Sarah had in the end where she was trying to get a not a black piece but so a lot of it has to do with increasing and 08:37:53 decreasing stitches so the little discriminations on the defects that she talked about, to, to get a curvature of a certain scale and that's usually used a lot in the shaping of sweaters for men versus women. 08:38:09 So, I'm again speaking with somebody who knits garments more than, you know, from the mechanics person it does a whole like knitting us letter for my son versus something for my daughter that it does a whole shaping that goes in by increasing and decreasing 08:38:22 teachers. And one way that we kind of deal with spontaneous curvature socks is a good example unit in the round, and you essentially have to come up with a meeting technique so you're meeting with three or four needles that are time so you're moving them 08:38:39 around to form cylinders, that for socks. 08:38:44 But other interesting techniques like cable knitting that give you that sort of rise, new sort of add on sweaters and things like that they're sort of like braiding almost but then they give you some local spontaneous curvature but it's essentially some 08:39:00 hierarchical organization of the same net and procedures. 08:39:06 I think the socks example is great because, so the difference between like a tube sock and have like a sock with a heel comes precisely from from that so like I mean they both start out like these cylinder so those would be flat so they would have no. 08:39:21 Well, I guess they they'd have no spontaneous galaxy and curvature. 08:39:26 But what you do is you add basically some destinations around, whereas a heel is and that basically sort of gives this almost, I mean you basically have like to almost deacons like one on either side and that kind of gives you the shaping of your he'll 08:39:44 just to maybe throw it back to my cello. 08:39:51 Um, okay so let's go to the patient David Nelson, who is the next person. 08:39:59 So, always patient. 08:40:00 I use a try. 08:40:02 So this is a question for Mark Hello So thanks for the lovely talk. 08:40:11 Abby plumber, when in her thesis didn't look at, he comes, but she looked at by stable objects as I discussed, and then indeed their interactions and when you have three of them, you have what physicists called geometrical frustration. 08:40:15 First, a comment. 08:40:30 And you can easily get into us I can spin glass region if you have some sort of sloppy triangular lattice. And I think the mechanics of such a thing are extremely interesting. 08:40:44 And also I would, I would urge you, if you haven't already talked to the general relativist at your university because they often use the Reggie calculus, which is a tetrahedral on location. 08:41:00 And I think some of your tracks and some of your results could be very helpful to them generativity came along, a 10 years after the fall one common equations to committees have a lot to say to each other. 08:41:16 So I'll end with, with a very question which I think is a short answer. 08:41:21 You talked about how the error to continuous continuum theory goes away as the number of fast 08:41:33 econ goes to infinity, which I thought was really quite nice. How does it go Where does it go exponentially in the number of facets. 08:41:44 Sorry it's goes away in. In what sense Can you can you show in one of your slides, I forget which one you gradually increased the number of units. 08:41:59 Number of econ segments, if you like where you had hinges, you had boundary conditions across the hinges. And as the hinge number went to infinity, you would approximate a continuum. 08:42:12 And you saw that limit, being approached rather rapidly and rather nicely. And I want, but how the error went away with a number of hinges. Right. 08:42:25 Yeah, so the the slider, maybe that you were referring to socially, if I can share once again. Would this be the case. Yes. Yeah, so, so what we are tracking here as. 08:42:45 So when we looked at this lip moment reaction as a function of the rotating lips. Yes, we wanted to be able to, to ensure that we could also capture this positive application behavior here by computing the point in which you have this mapping transition. 08:43:05 Right. 08:43:08 So, and this is what we are tracking down over here so this is that that critical 08:43:15 rotation. 08:43:17 And we are plotting this as a function of the number of facets, in there. yes. And that's what we are getting this convergence. 08:43:25 Right. And my question is how does the blue dots approach the red line for large em. Aha, yeah the explicit function then which Ok, I see. Yeah, no yeah I actually we haven't looked at into this. 08:43:39 My, my postdoc generated this this data right before my talk. 08:43:44 Yeah so and we just saw this is quite preliminary but yeah so this is a good question maybe we should actually explicitly stated that. 08:43:55 I mean it could be exponential and it would be worth money to these ticket descriptor stations in Reggie calculus or at any of the problems, it's good to know how your air goes away. 08:44:08 Yeah, no, I see your point completion Yeah, sure. Yeah, but I cannot provide the answer right now yeah, we don't know. Thank you. 08:44:16 Thank you, David Benny put a question into the chat if you have, he wants to know if you have a prediction for how it should. 08:44:28 Oh well I don't, I'm embarrassed to be put on the spot, I would guess exponential but I don't know. 08:44:36 Okay. 08:44:36 All right. So, next question I guess is, Let's, let's do another live question Eduardo v trolls next. 08:44:46 Hi. 08:44:48 Thank you, Bruce. So my question is for stability. 08:44:52 So I was very interested in the nonlinear analysis the state of the problem, especially in your request for obtaining continuum theory, and 08:45:04 what would it be a proper is stress for your different stitch patterns. 08:45:10 So I actually have two questions about it. 08:45:13 One is just to check if I understood it well. 08:45:21 So you start with this Keshav model, where you are, first interested in, minimizing the energy for checking the flow of dangerous different configurations of minimum energy, like the stock net gather reap and seed stage. 08:45:39 And then from there when you apply the load in your energy, you. 08:45:53 So the nonlinear. 08:45:55 It accounts for this energy as a function of the, of the separation. Right. 08:46:03 And then my question about is, is how to actually do this bloods because you mentioned something about a feeling. 08:46:12 So this this feeling of place for the simulations to I mean how how real pertaining the parameters you need for for generating the Bloods and it My second question is, I think about what you you and Michael doing or. 08:46:25 Now where did recently. 08:46:34 Because I think some of you mentioned about course grainy. 08:46:39 So I was curious about what you fought in terms of multi scale techniques. 08:46:47 I mean if something like homogenization or computational commercialization would apply to a problem. And, like, what exactly are you talking about, as coarse grain, you know, I mean, are thinking in terms of some kind of order Pyro material or what exactly 08:47:09 is this course green. Thank you. 08:47:11 I guess the first question. 08:47:15 I guess the first question. Um, so basically the linear versus nonlinear does have a lot to do with the sort of amount, like the load that's applied to the fabric so it for small deformations it does be hateful in the early, and then at some point, what 08:47:35 happens is that like when you pull it really taught I'm not sure if my camera will focus if you pull it really taught basically you have these areas where you have all of the stitches aligned with each other and they're like kind of looped around each 08:47:48 other so basically they're you're just you're probing these Yarn Yarn interactions so it's going to be highly dependent on the, like the specific mechanics of the yarn. 08:48:01 And it seems like the behavior of those is pretty similar for all, all of the different stitch types, they all seem to kind of elongate and have that like interaction with each other. 08:48:14 And so that also came, we did a do a another sort of carve a sort of model for for that which is like basically if you sort of fix the tangent factors at the end points, and then sort of keep pulling, really hard on the, on the fabric, like a fabric on 08:48:40 on a strand of yarn, like what the sort of energy of scale is so we find that that goes like one over one minus r so the distance between the start and end and then divided by L so the total length of the yarn so that kind of gives us the shape of the 08:48:58 nonlinear stress strain so we have. 08:49:01 If you sort of make that into a tensor then you have, like, like a linear piece and then you have. 08:49:12 I guess you could say you've gone it. 08:49:16 I think you've got like 08:49:19 four different nonlinear terms because we're doing, we're doing the fit for both the both data sets at the same time so there's the the fitting parameters are the elastic Constance basically. 08:49:37 And so what we want to fit the data set where we're pulling like this with the data and the data site we're pulling like this simultaneously so they're all subject to the constraint but there's stress free boundaries. 08:49:53 And so, basically, that's what the fit is, since it has so many parameters we tend to get quite good fits so we fit the experimental data and the simulation data independently. 08:50:13 And then we can compare the elastic modularized for those. 08:50:19 It's not horribly insightful because it is they're just fitting parameters so I have, I guess a project that my students are working on now is trying to go from first principles to what those constants should be so how do those depend on like bending 08:50:36 modulus and compress it compress it and yarn length and things like that so trying to remove potential parameters from there. 08:50:48 So it's, I mean there there fits to a constitutive model and the finite element. Looks like the fabric when you do that with the fit. 08:51:01 But it's, it's not really insightful. 08:51:06 And then other question was about sort of the the multi physics and of course greening. 08:51:13 So I think there is something, to some extent, you can think of some of these fabrics, as having an order parameter, particularly the particularly ones where you have defects in them so dislocations and declination, you basically have places where you've 08:51:37 got like almost like a field of stitches like the stitches all go on one direction and then you're sort of looking at how they bend around so I think that's the place where the constitutive model, really does have power because that has a set of stuff 08:51:57 fixed axes so you can look at how that field changes around the singularities. 08:52:05 And so I think, I think that's probably the most concrete direction between them. 08:52:14 But I really like the kind of idea of multi scale modeling since I think not all come up a lot more one we have to do dynamics. 08:52:25 Right now everything's quasi static so an energy minimum is an energy minimum. 08:52:31 But I think once we get to doing things where there are lots of forces interacting with it then the multi scale is going to be super important. 08:52:45 So, speaking of all this, there was, there actually two questions on the slack that I think might be somewhat related and I'm going to do them a little out of order, I think, Eric. 08:52:54 Eric do frame had two questions posted about this, the, the stress strain curves that you see in your experiments and maybe this is a good time for to ask those questions here. 08:53:12 Don't care. I don't think he's online. 08:53:15 All right, well, I'm sure I say ask them anyway, or on his behalf. 08:53:22 Maybe he wants to hear the answer, I don't know. 08:53:26 I don't know I feel like he's not here he kind of misses out. Let's go to Marcus Why don't you ask your question. Instead, which is about the seat stitch dresses. 08:53:39 Yeah, yeah. So, yeah, you pointed out that you had all these experiments on the stress strain relations for the fabric and you don't replicate them in numerical simulations of that particular stitch and. 08:53:52 And in one particular example I think it was the seed, it didn't go very well and you argue that's if I understood correctly, you argued that happened because in the, the numerical calculations you get some stocking local minima, because of the way that 08:54:06 things are stuck together. First of all is, did I understand that correctly was that sort of the reason why things. Okay. Yeah, so it turns out that simulation box is that when has the largest set of, like, largest fundamental domain. 08:54:26 So, basically, we just had so many Yarn Yarn interactions with one another, that, and the Yarn Yarn interactions are the thing that kind of screws up a lot of our time, our gradient descent algorithm, like that, it gets caught in those. 08:54:45 Okay, so then I understood that correctly but then I was confused about which way the arrow actually went, because if I imagine that the numerical calculation get sort of stuck in a local minimum and doesn't find all its way down, then I would imagine, 08:54:59 at best case scenario, it would actually fall into a deeper energy minimum and relax the fabric better and then I would imagine that in the truly relaxed state the stresses are lower. 08:55:09 But you seem to be predicting the opposite. 08:55:16 So we're a yes. 08:55:20 The, the thing that is that we're trying to get the transverse response to so you can kind of play with where those curves, sit. So I think we were having so I'm one of those cases I think the transverse response was, like, kind of nonsense when it matches 08:55:43 what it should be for the, for the nonlinear response the like lunch for today no response. 08:55:55 Um, so there's, there is a free parameter that you're playing, or there's two three parameters one is sort of the core size and the other is like how kind of how, like the functional form of how it goes from like zero to core. 08:56:13 And so those, those you have a lot of freedom and pushing the curves around in different ways. 08:56:19 So, if you get it to match on one side it's so far off on the other side that it doesn't seem like it's a, it makes physical sense. So that was kind, I mean that's. 08:56:34 But to be honest, that's a little bit of a choice. 08:56:38 As that's the one that kinda balanced them both better. 08:56:45 I think that's the same way in both cases, but I because I was just surprised how you would, in case of not being able to relax, how you would under predictive stress. 08:56:57 Yeah, I think, when one gets different the other get softer. Okay, okay, that would be. 08:57:05 So, so I think this is the one that, you know, didn't have something that had an extension that was like, you know, you pull on it a little bit and you get like five x extension for like no force and the other direction which makes no sense. 08:57:21 So I think this is the one that kind of kept everything in the like the right orders of magnitude so I think the, I think what happened was when you make us have a wider action gets really soft when the extraction gets stiffer in the particular simulation, 08:57:39 but I think we need to do a better job of 08:57:46 basically finding an algorithm that doesn't get us stock in some of the local minima. And we also get stuck in local minima when the best da curve control points are co linear, that's another place where we get some, some degeneracy in the code that you 08:58:08 don't see in the, in the configuration of the fabric like those are those are degeneracy is in the geometry. 08:58:20 Thank you. 08:58:22 Okay, so, um, I do want to circle back to Eric's question eventually but I let's do, let's do another live question first. Andre cousin morons is the next question asked her how did I do. 08:58:37 Very good. 08:58:37 So, customer is actually cost model but so cautious but otherwise the rest was fun. 08:58:43 Okay, so I have a question for Marcella. 08:58:51 You know, like you briefly mentioned programming shapes and motion right and you know you you you know show the examples of how you designed like leave your role and peach and your comment that. 08:58:57 Oh, in principle, one could do some sort of look at linear combinations right but I was just wondering like more generally like you know like if I want to press, you know design like gimme gimme cuts to you know get like a particular motion. 08:59:10 Are there like in the field some, you know, guiding principles or is so complicated that always have to just solving this problem on a computer. 08:59:19 Yeah, so, yeah. So this is, this is a good question how we started doing this business. This by the way this work was in collaboration with doc homes and we've, we've been talking for for a while about this and basically trial and error, at least in the 08:59:38 mode that we that you saw that I showed in the, in the slides. 08:59:43 However, we did, dig a little deeper into this, and I can perhaps. 08:59:50 shed a little bit more light in it so as with an example, in particular. 08:59:58 So, let me see here. 09:00:01 You guys see this. Yeah. 09:00:05 So, here we were trying to find the guiding principles as you as you mentioned, to regulate, for example this role motion that we that we showed so in this, in this example here, what do we have this cut pattern, and you apply tension on the sheet, along 09:00:24 the horizontal direction. 09:00:29 And now that I'm changing here is the depth of the cut here, and the central cut. 09:00:35 Right. 09:00:36 So the interesting thing that we observe here is that for this basically two different types within a continuum of shapes that you can get is that you can classify this network of cracks, connect into crack tips as contracts or concave polygons. 09:00:57 So what do you observe in this case is that within. 09:01:02 Having this measure of convexity as another quarter parameter of the system is that the game is going to be activated in a different way. And in fact, we see a transition from no rotation whatsoever to rotation right when you lose complexity in the system. 09:01:22 So this gave us some hope that we could start building this, this, the designing correct area, rather than just guessing from cutting things randomly. 09:01:39 So, and this has to do in this particular case, that lines of tension within the sheet, are going to be broken. Right. So when you lose convexity this lines of patients are broken and you give this other degree of freedom to the system. 09:01:55 Whereas before the transition. The system is too stiff to rotate because there are lines of tension connecting the two different boundaries. 09:02:07 And this principle appear to us to be quite generous in fact, all the other patterns that we that we propose that were initially guessed. 09:02:19 They fell within this category. 09:02:22 Right. 09:02:23 So another interesting point of this, which is also how we think about this as a design principle is that the, the switch that this convexity brings to the system in terms of the measure of bending and stretching energies. 09:02:41 So pretty much before the transition you have a system that is entirely dominated by stretch and this is this the same thing for all the patterns that we we proposed. 09:02:57 But that is also consistent with what I mentioned regarding the lines of station across the system. 09:03:04 So when you are able to break those lines of tension, the stretch energy, the case. And then when the energy dominates, therefore you get this mode this motion that you program or the plane, which is being taken up by the end. 09:03:18 Right. So, yeah, so I think this is this is more or less what I what I have to say I guess. Thanks, just one more question so you know, so you know since, you know, hear your program like everything interesting is happening and the hinges that are, you 09:03:36 know, bending and what in right. Is there a way to also do some select like hierarchical structures so that you know the panel that's getting rotated would then something else interesting would happen you know inside that panel, because it seems to me 09:03:55 that the panel is getting rotated is basically almost strained free, so it's been hard to, you know, transfer things to do the job. Now, no I see what you're saying. 09:04:00 Yeah. 09:04:00 Well this interesting to think about, I think, because you kind of need this source of tension in the system. So I'm trying to wonder where this is going to come from within. 09:04:15 For example, like here in this, in this particular situation here where you have the, the mix mode so let me just here in this mix mode over here, right. 09:04:25 So, all that I could have done here, in this case is that I mixed the, the pitch and the lift. 09:04:32 But within this platform there is not much else I can do here. I can use perhaps the bendy energy in order to, sort of, regulate, if I have extra cuts on top of this platform. 09:04:52 But, but yeah so this would be an interesting question to investigate for sure. Yeah. 09:04:52 Oh actually Joey, I think had his question was about the lift pitch your role. And so maybe this is a good time for him to ask it, and then we'll come back to Laney next, sorry. 09:05:05 Thanks, Chris. 09:05:07 So yeah, so I was also fascinated by these. These cut patterns and sort of the design problem of mapping it cut pattern to a 3d motion. 09:05:16 But, you know, by far the weirdest one is yeah right like Lyft is straight cuts role is straight cuts pinches a few straight cuts. Yeah has a huge amount of material removed, and it's got kind of zigzags, and it's like, totally weird. 09:05:32 So one question is, do you think there's a simpler way to make er, or is this the simplest. 09:05:37 Can you do it without removing like half the sheets. 09:05:41 Yeah. And can you walk us through like what's going on, what you know do different parts of the thing, are they doing distinct really distinct roles. So those are kind of my questions about Yeah. 09:05:52 So I think what we, we went for here is that we basically wanted the platform to just rotate in that manner. 09:06:01 In order to do this we needed to basically pull this arms here, equally on each side. Right. 09:06:12 So you you actually need really deep cuts in order for this to happen, otherwise you fall into this symmetric mode that I had shown before. 09:06:21 And that will not pull the arms in that manner. So the thing you will do is, it's quite difficult to get right because it's quite unstable out of the plane there. 09:06:34 So, so yeah, but I guess we needed to remove a lot of material because we need really deep cuts in order to have this, this motion here that flips right so it breaks the symmetry in this way and then it's pulling the are equally. 09:06:57 But I guess we could have removed, less, less material we just actually wanted to highlight the motion of the platform over there. 09:07:11 Okay, thanks. 09:07:15 Thank you, Martha for the mother nice talk so my question has kind of been answered already consensually, but maybe I would like to discuss it a little bit with you explicitly. 09:07:32 And that is when you prescribe the leap in your, in your talk, you fix it to a straight line if I understand correctly, right. 09:07:41 When you prescribe the land when you prescribe the boundary condition around with you do the rotation right. And in a lot of the experiments that you became a GM experiments that your show. 09:07:55 That's not true at least away from the singularity. So, can you comment a little bit about that, and especially it ties to vanish question about the boundary conditions and the strain. 09:08:13 And it also ties to the discussion with with David on how you can piece them together what would be effective interactions and all that. 09:08:21 Yeah. 09:08:22 Yeah. 09:08:25 I think yeah thanks I think that there is a lot to say in this of course we, we basically, open the lip in line, and we control the lips like so. Right, rotating. 09:08:38 Obviously this to simplify our lives as well. 09:08:42 Right, so we needed to be able to compute something and and and and thankfully, these boundary conditions are interesting enough already because what we meant to capture there was this instability. 09:08:59 Right pause bifurcation of the initial opening. 09:09:04 So I think that 09:09:08 with the answers that we took, as long as we keep that in terms of being constrained to give us only clinical solutions. 09:09:20 I don't see why not we couldn't have other types of boundary conditions, right. So, this could also be explored. 09:09:29 So, so I think this is what I say about that. So it was really a matter of convenience there and then that the conditions that we apply already captured the phenomena that we wanted to capture right which is this napping transition, which is already rich 09:09:50 as it is, but one other way that I've been trying to understand these things is, as you said, You apply, so now imagine you have your full Krieger me. 09:10:04 And, and you apply the boundary conditions, and lots of things are happening in between right you can really control so a lot of the solutions that we have proposed in the continuum case would not be exactly the same, right. 09:10:18 So I maybe I can show the next 09:10:23 simple model here, which we're still working on. 09:10:28 So let's see if I can find something here that maybe and millennia, please. 09:10:35 Just jump in if I'm kind of digressing for you from your question, or, or if, if this is in line that's all right. 09:10:42 But, for example, in, in this case here, which is just one cut in the middle and here I'm also looking at the organized version of this just for sake of simplicity, you see that the lips are not necessarily aligned right so they are the lips themselves 09:11:00 are going out of the plane. 09:11:03 So, I think we could still look this by know mapping this tool and elastic on a fear but just as a simple example. 09:11:17 We could also apply the Gulf map technique to this. 09:11:21 So, and, and, and basically we can track the solutions and you can say things about the deflection and so on and so forth for example here, we can predict the amount of deflection of this central part here this generator. 09:11:39 By simply computing the girls map all around and keeping track of all the singularity so that appear in the system. So, but maybe I should, is this more or less in line I'm not sure if I'm answering your question oh this is exactly yeah that's. 09:11:56 Thanks. Okay, yeah, you're welcome. Thank you, 09:12:03 David. David Nelson has the next question. 09:12:06 Thank you. So this is a question for us, the better. I had to step away from the zoom meeting briefly so if I've already been answered, I apologize. This is sort of stepping back and just. 09:12:19 Can you tell us what you know about how you manufacture yarn was a given gauge I think of it as some kind of bunch of strands they're all a finite length they are offset. 09:12:34 And they sort of hang together and then that's what goes into these beautiful crushes on stuff. But how do they figure out how to take sheep's wool, or whatever, maybe synthetic material and make it into this rather robust uniform material. 09:12:52 And as part of that. 09:12:54 What are the different ways of rolling up and compact defying yarn Of course you could do it around a cylinder but I have also seen balls of yarn where you see wraparound multiple different the Quakers. 09:13:07 Can you tell us what you know about that, please. 09:13:12 Absolutely. So, the idea of taking fibers and turning them into rope or yarn, definitely predates knitting and weaving technologies that's one of the, one of those very prehistoric early technologies but people have although it didn't get to the level 09:13:32 of sheep I think people would use other like plant based fibers. 09:13:38 But what you do for for shape I guess I've done some spinning before. So most of the fibers have what's called a staple length, which is the. I don't know the length of the sheep wall after it's been shared, or for silk it's, you know, however, many kilometers 09:14:02 go into the, the cocoon, but. 09:14:10 So the staple length is really important. 09:14:13 And so what you do when you spin, is you start off a little piece on your, your spindle user, basically, first you first thing you have to do is you card so everything has like mnemonic order. 09:14:31 So the word card, you say card and you just wrap literally wrapped around the car. 09:14:36 No, no it's, they're basically are these are, these, it's 32 brushes that basically have nails sticking out of them. 09:14:45 And you go like this like each other or there's. 09:14:49 It looks a little bit like some of those like cotton gin those wheels that have, like, spokes on them so basically you're taking all of the fiber and you're giving it some sort of mnemonic order. 09:15:00 Okay, and the phone. I restrained. If not, silkworm stuff will be a finite link so how do you, they are there, so they're there, there's a, it's called the staple links. 09:15:15 The fiber point of view. 09:15:17 So it's gonna it's going to be whatever it is, I'll get, I'll get to how this affects it in just a minute I'm just going to kind of walk you through the procedure first and then tell you how the different things interact so the procedure is first you 09:15:32 roughly align the fibers, and then when you start spinning you sort of take a little knob at the end you can kind of tangle it up if you need to to get hooked on to something, but basically you get hooked. 09:15:46 And then you start spinning. Usually this is I'll just tell you how it works for like a sort of a drop spindle, which is basically just a way that has some sort of extent so you basically are storing angular momentum in it so you give it a spin. 09:16:06 And it's going to rotate pretty fast. So, add, and what happens is there's, you get that spinning, and you can kind of pinch it so it's spinning in a small area, so the process. 09:16:18 So the twist is just extending like between where your fingers are and the end of the drop. 09:16:24 And then there's sort of a nomadic up here. And then there's this region called the shed. So it's this little triangular region, where here taking these fibers in a small amount and you're pulling them you're letting them slide past each other so you're 09:16:41 sort of like letting them, rotate, almost. And then basically you feed that into the bit that's twisting so you sort of take that and then you move up so you're spreading that twist that and then once it gets long enough for us to wrap it around the bottom 09:16:57 and you continue this process. 09:17:00 So, what happens it. 09:17:03 Sorry, the number of fibers they get fed, that will ultimately determine the thickness of the product. 09:17:13 Exactly. So the that determines the thickness. 09:17:17 The thing that's important between the staple length and the number of twists is sort of controlled by the size of this shed. 09:17:25 So if you have very small short fibers like Marino, is it is a type of shape but it's a. It has pretty short fibers. So you're going to want something that has a much higher twist So, more, more twists per inch. 09:17:42 And you'll end up having a pretty sort of small shed then so if you have a really long. If you have long staple fibers like, like I Shetland will then you'll have a wider shed where you can, because you want the fibers there to slide past each other smoothly. 09:18:01 And so the number of as you correctly point out the number of fibers that go into this shed is what is going to control the width of your yarn. So this is something that ends up, you end up with this very highly twisted thing you sort of roll it into 09:18:18 the end of your spindle. 09:18:19 And then you do that, multiple times, and then you basically take advantage of that that's reflected name instability where you have like twisty things that rotate to the counter rotate around themselves. 09:18:33 And then you basically take lots of things that are parallel to one another that have say all right handed twist. And then you do the spinning process to them again with what fewer twists, but now in the left handed direction to sort of relax those twists 09:18:52 and turn it into more rope structure. So it's really really hierarchical. 09:19:00 Both. 09:19:00 Both are present in rope and yarn. 09:19:03 Both Kairos nowadays are present, you typically see, I don't know if you'll be able to see this if I hold it up. You can kind of see that there's like a z pattern. 09:19:25 be an S for you. So that is the direction of the counter twist, so each of these, each of the things that go into these twists, those are called plies, and you can change the number of plies to create yarn of different thickness and different behavior. 09:19:43 I see, I see an intern if you don't get the balance between positive and negative twist right becomes like a non Simic. 09:19:52 Call us Derek, and then there'll be some macroscopic see the coil. 09:19:57 Yeah, so in spinning this would be called an unbalanced yarn you have a preference for Kairos it in one hand and this is a balanced when you have exactly the right number of town or twists to counteract the twist the initial twist. 09:20:16 And that's why I can hang my piece by this piece of yarn and it's not going to twist. Yes, so I see, so now there's, there's no story torque in this. 09:20:29 Thank you, that's that's very helpful and then just briefly how to how do you wrote what many ways of rolling it up into a ball or so. 09:20:37 How is that determined. 09:20:39 There are many ways so typically when you die if you're doing small dying you're going to die it and what are called Hanks, so Hanks are basically you take the thing and you sort of do you're basically wrapping it around something it's about the size 09:20:55 of your elbow so it's not too tight, and then you kind of tie little things on it so that lets the die, poor me all portions of it. 09:21:04 And then it's often actually sold that way so you basically sort of twisted up and then sort of pull it through itself, and you get like these. They're the sort of cute little twisted bundles. 09:21:17 You all can often buy them like that. 09:21:20 Industrial yarn is virtually always done on a cone. 09:21:25 So basically you just have a cone and you wind it around that so you do have a little bit of this sort of category on oy link equals plus ride so you can get additional twist in it sometimes that way. 09:21:37 But that's all industrially honors on a cone 09:21:42 It is Autumn is set by industry or it's just people that do different cone angles. 09:21:49 Um, I don't think it's super matters, but probably whoever makes that they're all in just a little cardboard tubes so whoever makes those properties that's the cone angle. 09:22:01 It doesn't super matter it's just that that gives you a stable place for the yarn to get pulled up and through a shoot. 09:22:09 So it doesn't, basically, then the cone stay still and you're just feeding the on off the top of it. 09:22:16 There's different types of yarn balls. Usually people like what are called center pull balls, which are the ones that are basically wrapped in all sorts of different directions. 09:22:26 And what you want, there is you want to be able to pull from the inside and that's where the yarn comes out so that the outside doesn't roll around and create a nuisance for your cat to attack it because it's rolling all over the floor is your unraveling 09:22:39 it. Yep. 09:22:42 it. Yep. Um, so that that you can do basically with this sort of like you rotate it this way then this way then this way and you sort of have these, like, almost planetary systems, there's also some machines that do that by having it rap more times one 09:22:59 way then around the other way. 09:23:03 So I have like a little hand crank thing that does those balls for you. 09:23:09 So that's those are already. Those are pretty much the most common ones that I know of. 09:23:16 You're going to get different yarn type, the yarn roles for handling versus machine knitting basically so cones are everywhere in industry, and those sort of balls that you pull from the center are pretty much the most common that you'll either us or 09:23:33 buy for my yarn shop. 09:23:37 Thank you very much. 09:23:40 Okay, so, um, there are a number of other questions on the slack and, maybe, maybe we should go back to a few of them. One of the questions that I kind of skipped over because he wasn't here but I decided that wasn't totally fair is one from for some 09:24:00 better from Eric to frame, and I'll just summarize this question, which was, he was brilliant he's interested in what portions of the stress strain curves and your experiments. 09:24:11 Can you do you get from for example just looking at the not density, right, or you know whether all those curves that you have fall or predicted from some particular master curve of stress strain. 09:24:31 Um, so I'm not sure we'll ever be able to get a master curve because the topology seems to matter. So, there's always going to be something kind of discrete added into that. 09:24:47 I think they, there's some sort of master behavior that's like linear to nonlinear so if I had lots and lots and lots of different types of yarn, I presumably should be able to do the fit of them on to each different yarn type. 09:25:08 At least that's my hope I don't, I don't know for sure but that's that's the goal of what we're trying to understand. 09:25:16 I think the the density is important, but I think what may be more important is we have a range of a range of length skills so with the VR and length of stitch, like the yarn per stitch distance between stitches, there's all these are, these links scale 09:25:36 so looking at, which link scale is most important in which regime, it seems like is the is more the driving force between where you end up with a crossover. 09:25:54 So I guess the crossover between like linear and nonlinear. So, I guess when you have your sort of bending, like the sort of like the amount of Ben the curvature, and it is on the scale of the stitch size they are kind of in the linear regime but when 09:26:14 it's on the scale of the yarn radius, you're probably in the nonlinear regime. 09:26:20 So, so I think it's it's looking at those. 09:26:25 The dimensional ratios of length that are probably more likely to be the thing that determines the overall behavior. 09:26:37 By the way, did you have a question you have your hand up, so better. Oh, I had a question for Marcello I was really curious about your, I guess, Joey's question, made me curious about. 09:26:54 You have since you have that sort of like, in playing rotation. 09:26:58 It looks like that's the start of a lot of different like exotics So, have you thought about like combining these to make things I have negative plus one ratio or are there. 09:27:09 I mean I think that's the one that has the really interesting in plain motion, but I'd be curious to hear about those. 09:27:15 Ya know for sure. Now this this is a good point actually I forgot about that, because there are many people who actually have looked at exotic structures, inspired by Craig me, right. 09:27:28 So, so yeah so you're right but in that, in that case, the hinges are completely aligned with the that direction like with the art of the difference with the yard that we produced the hinges they actually they twist in space. 09:27:45 Right. 09:27:46 So that's, that's a difference there. But, but yeah, I guess, those would also classify as your, so there are tons of papers on this. 09:27:59 I think the last I can remember like ma just publish something like a week ago on this thing. 09:28:06 But, there, there are many people before him, have pointed out to the toxicity coming from this paradigm is structures that remain Leitner. 09:28:19 Thanks. 09:28:21 Michael Sandler, you have the next question. 09:28:26 Yes. 09:28:29 I have a question for submit Matsumoto. 09:28:34 Actually, I wasn't bit astonished that you managed to extract stress strain curves from the experiment. 09:28:45 And I would like to dig into, into that, at what point you actually use measurements. And at what point you use modeling to target these curves, because I mean, let me let me start from the beginning if you, if you take the stress 10 slot. 09:29:10 And here it's divergences zero because you don't apply any local forces, and you have a gauge freedom. 09:29:18 So you could add any others. So new form of the same equation. 09:29:25 So any, any divergence free nine to 10 so you could add to distress. And this would modify your, your constituent equation. 09:29:40 So, Do you see my problem. 09:29:49 Okay. Um, well, 09:29:57 I if I made that up, I still don't see the problem so maybe if you can expand on your question. 09:30:03 Do you mean that, for no material, supposing just have a simple who key and material. I cannot measure it stressful in relation. 09:30:12 Yes. 09:30:17 You don't have constraints, that is the problem. Yes, we don't know you're here right we don't do is solve an equation with some boundary conditions, the equation to solve is actually I want to stress free, local divergence of that spreadsheet. 09:30:37 but then you have to specify the boundary conditions, and your shots this. 09:31:06 used to this place to the measures. And we should know that stress at the boundary I mean that's just a factory term I mean that's the force divided by the length of the current, I mean that's just the standard way of expressing that. 09:31:19 So, I mean, to be honest, we look at the stress on the boundary and the strain at the midpoint for the, 09:31:29 for, for the experimental results so you're right, we can't get the stress tensor everywhere. I think there's a bit of about the divergence free part. 09:31:43 Also when they're extremely. I mean I think that makes sense for, like I said tropic. I mean, correct me if I'm wrong but I to me that sort of makes sense for isotopic elasticity like when you're doing the there's like a. 09:32:01 What are they like airy stress functions like it sort of makes sense for that but once you have something that's extremely and is a tropic I don't, I mean, I guess I haven't thought about this in depth but it seems like having something that's divergence 09:32:19 free no longer makes sense because you'd be waiting to divergence by whatever your anisotropy is 09:32:32 not as interested in. 09:32:34 is interested in. In the modern English we lose. 09:32:45 As a topic. 09:32:45 So we don't everything of ours is and I subtropics so there's where we're assuming I guess the full like rank for Alaska city tensor, we're allowing for whatever symmetries or for whatever 09:33:02 entries we get from experiment, we're not putting an asymmetry on top of it, It just comes out of whatever the experiment is. 09:33:24 I don't think I'm answering your question. Exactly. Well, 09:33:34 at the moment I'm unable to, let's say, to use the pieces of information okay me about the area functions to answer it for me. 09:33:45 I guess I guess my understanding of that divergence free kind of came from the formulation. 09:33:51 From that formulation of the areas dress, cancer, but also relied on it being isotopic. So it seems like if you have some, you know, a field that's divergence free make sense if it's isotopic but if it's an isotopic it seems like you'd have to wait divergence 09:34:12 based on the topic, the different directions for that to make sense but that's, as I said, I haven't thought deeply about that. So, that would just that, that's what I would just come to mind. 09:34:30 Without without serious thought. 09:34:37 So, let's, um, let's go to another question we can always come back to this, if you know once there's some more time to digest right. 09:34:47 But Paul kicinski has a question. 09:34:49 Yeah, I guess, what it was kind of this same question and maybe I'll phrase it in a different way. 09:34:56 Isn't it a question of, like, so you're doing nonlinear elastic deformations in your experiments, but you're really measuring engineering strain. 09:35:08 And then, and kind of force over area engineering stress, but then you're mapping, your model to this engineering strain engineering stress so I guess maybe from the previous question his comments are how did you map this this nonlinear model to experiment 09:35:28 which is doing engineering strain of engineering stress. 09:35:34 Okay, um, 09:35:38 so I guess. I think Mike is actually here so he's the one who did the fitting so he might have a better answer than I would offer. And, I mean, I guess the. 09:35:56 I think this is maybe a little bit of what you get out of simulation versus what you get out of what you get out of the experiment so the simulation we can obviously probe a little bit more in depth, but also because this is this is a net. 09:36:18 It is hierarchical it's got all these holes in it, like pulling on a unit syllabus that she is always going to be, in some sense, engineering stress and engineering string because you're basically pulling on like you only have like one point of information. 09:36:35 It's not a, it's not actually a continuum. So, but since about next time. It's an integrator. I mean it's, you know, integrating out some of the, but doesn't the deformed stitches look very different from the reference configuration. 09:36:52 I mean the deformed stitches, do. But, I mean, It depends on what you mean, very different. 09:37:03 I mean I guess that this is a thing that there's a little bit of, I think, trends, I mean I think part of the thing is, we're a lot of us are sort of brought up and I continue on the last city model world where this all does make sense, I think all of 09:37:23 this, whether it's a continuum, or our measure of engineering strain, and the experiment, or the simulation it to some extent. 09:37:36 There's a little bit of funkiness going on with, with the stitches themselves because you really can't treat. Once you get below a single stitch level, treating it as a continuum doesn't actually make sense, necessarily. 09:37:53 I mean we're, we're sort of treating it as if it is like kind of an empirical model and doing fits to it, but I think there are some gaps between how we build up 09:38:11 like a really concrete relationship. 09:38:23 I don't know if you wanted to throw in something like 09:38:28 know just waiting for the our understanding of the discussion. 09:38:33 So, it's for Michael and for Paul, if so better had given the talk about say a rubber band. Would you have asked the same question, and if not, why. 09:38:48 I mean this is a good question and I would say that. I mean when you write down a continuum theory, which depends on the defamation gradient then it's somehow clear, kind of, in there is a way of mapping the experiments to the modeling and. 09:39:08 And in this problem it's not clear to me how it's being mapped, I think, um, but actually the, the others, the other. 09:39:19 the other question or probably has a better explanation than I do. So, I'll let him say what he has to say my book, I was reading this form of a very fundamental point if you have a rubber band, you stretch it. 09:39:36 You have strain your commercial all the displacement and expect. 09:39:46 Commercial all the displacements and extract strain cancer from it. That is all the kinematics. 09:39:49 And now for the dynamics for the for the stressed and so you have no local measurement for it. 09:39:57 The only thing you can actually measure is the total force at which you're pulling. 09:40:03 And you can somehow get back to the local stress by solving an equation using whatever finite elements of your phone's off. 09:40:15 But then you, you have to take the boundary condition. 09:40:23 Several other things I'm not absolutely sure what you really need. 09:40:31 But in principle, a local constitutive equation always suffers from this point that you have a gauge freedom, on the stress. 09:40:46 So there is no constitutive equation that is unique. 09:40:55 So if I might jump in to give a detail a little bit more about how we're making these measurements and comparisons. 09:41:05 So, we're making. 09:41:10 So, in the experiments, there is a swatch of fabric that is clamps, so that there's no sort of transfers strain, at the plant boundaries. 09:41:27 And we're making, we're making an approximation that what's happening sort of in the center of the fabric is somehow representative of the bulk mechanics of the material. 09:41:49 And in that process were approximating the boundary conditions on this sort of Central swatch the central sort of unit of fabric that the normal stress, and the free boundaries direction is zero, and that the stress and the longitudinal direction is 09:42:15 is a terms of, I guess, yeah the engineering stress, which is the force applied to the clamps divided by. 09:42:23 The, the width, essentially. 09:42:27 So, so yeah so it's not a local. 09:42:35 It's probably not one that we can rigorously say it's a local constituent of relation, but it's it's an average constituent of relation it's a place to start. 09:42:46 And this is, this is specifically something that we're doing for a uni axial setup. 09:42:51 So there's. 09:42:55 So, there is potentially other terms that can mix some of the elastic constants that were we're pulling out through fitting that we may not be accounting for. 09:43:12 That being said, we, when we fit the data to our constitutive model, we take our supposed boundary conditions into effect. So, assuming, again, 09:43:26 that we have free boundaries on the edge were approximating those as traction with boundary conditions. And we're doing the fits in the longitudinal direction. 09:43:38 And the longitudinal direction. With our model in a way that is consistent with these boundary conditions so we're simultaneous and fit into the transverse direction. So, We're while you know we can't, it's it's true that we can't necessarily get a true 09:43:55 sort of microscopic constitutive model. 09:44:00 What we're doing is trying to get our best guests to what a I guess like a homogenized like outer beauty Expo definitions Does, does that make sense. 09:44:15 Yes it does. 09:44:17 But at the same time that having this small periodic box with the filament inside, and if I remember correctly, you'll relate this to, to actually compare the measurement ones with that, in America as well. 09:44:36 Yes. So, um, so So, in that case, of course you miss the, The overall shape changes distress. 09:44:49 And I could be an explanation for why one of these causes of the other 09:45:00 people last thing you just said I explains why one of the curves is something that one, if I remember remember correctly, you showed theoretical numerical curves and experimental curve so there's some point. 09:45:18 Two of them didn't match. 09:45:21 Yeah. 09:45:22 And I was just awful one of the nation for it. 09:45:30 the nation for it. Okay, I think the. 09:45:34 I think the X for mental versus new numeric curves, and then they match, very well for all but one set of one type of fabric. 09:45:47 So it would be unclear why one specific, it only happened for one fabric, and that was. 09:46:00 And there's there's another parameter that we tweak that actually kind of controls that but it was. 09:46:07 It's coupling the longitudinal on transfer behavior in a weird way that's what Marcus had asked about earlier. So there's another there's something, there's a basic play the compatibility is something in the numeric that controls that behavior and there's 09:46:26 there's. 09:46:28 It's a basically that's more of the art and the science right now because we don't have actually talked to someone recently that has a better way of modeling the compression between two pieces of yarn, like we just kind of chose sort of beads spring like 09:46:47 closest approach measurements which apparently there's some fancy or things that I heard about like about, like, three or four days ago, that can that should be able to help us get that but right now, that's just a, that's a by hand tuning parameter but 09:47:06 we can push it closer or further away but it is coupled so it's it's there, it's not a systematic, everything is often just happened to be that one fabric that has a lot more Yarn Yarn interactions than all of the others like it has twice as many as the 09:47:23 next lowest yarn interaction interactions that's the thing that was that sort of throwing us off his book jaan jaan interactions are like we, we don't have a great model for that right now. 09:47:39 So let me let me jump in here and, and there's, there's two ends up, I suspect there about this but. 09:47:46 So we're not necessarily leaving this subject but constant in energy and I guess has had his hand up for a while. 09:47:57 You're muted. Yeah, unfortunately, you're muted. 09:48:04 Thank you. I have a question for Marcella. 09:48:13 And, as I understand, you can create a lot of different structures on these teeny tiny. 09:48:21 Thank you for interesting talk. 09:48:24 And they all look rather lovely but at the same time, quite complicated and power. 09:48:34 So, if you think about any other any hidden in variance in the structures that can make the picture more structured. 09:48:52 I mean, is there is no stranger the surface area remains the same, but what is about, maybe other ingredients. the number of peace or something like that. 09:49:13 which can make the picture this video this guy anymore. But, 09:49:15 yeah, thanks for listening. I think I think this, this is exactly the reason why I decided to, 09:49:22 you know, look at a simple problem. So I started with all this complicated cases as you pointed out and they seem quite 09:49:32 Okay, because as you mentioned, and, and we ended up trying to look at what is the most fundamental motif of the formation of this trigger me and and and that boils down to look at what's happening at the crock tip of each one of this individual cuts. 09:49:55 So, so far we have only results for what's happening with a single console with us with the edge of a single crack. 09:50:08 And there are inherent symmetry stare that tells us what types of the formations, you can have and what types of instabilities that are inherent to that system alone. 09:50:22 So, so that that's what we attempted to do there to break it down. This, this very simple motif of the formation. 09:50:30 But of course there are other types of questions that we are intending to address. And so, hopefully soon enough, which has to do with Benny's questions related to the interaction amongst this different motives of the formation. 09:50:48 So, so I guess this is a ongoing story right so we are trying to break it down exactly to be able to give us factory answer to what you asked. 09:51:01 So, I think that's what I would say about that if. Yeah, but we can continue the discussion right because I I'm stopping here because I think it's an open question to me. 09:51:13 Thank you. We'll be ready to. 09:51:16 Thank you. 09:51:19 Do you wanna chime in your hand is still up so 09:51:24 Sure, I can but it's going back to the issue that was raised by Michaels and Paul's question so now it's up to you the chair with their chairs and putting it back on you if you want if this is a pressing question and it's you know sounds like it might 09:51:42 be to some people. 09:51:45 If there are no other. 09:51:46 I'll go for it. So I think it will be valuable for me and I probably would get for other people here to explain this. So, let's start with a simple thing so it's basically it's a question for Michael and forward, Paul. 09:52:01 So, so, so let's assume that they have a really who can material for which I can perfectly a few that is so key answer so I have only who can etc. So the next thing deviation, and they do a measurement. 09:52:18 Okay. That is a measure of the false image on the display simply want to extract the result. In this case, it still, you know, you still have the gauging variants, but I would say that by boundary conditions, it's being lifted you don't have any more 09:52:31 discouraging variance, due to the divergence fleet status. 09:52:35 You cannot just add the deep sigma equals zero, because it will not send it will not satisfy the boundary conditions. 09:52:43 So if you have a well defined boundary condition and you measure Stetson relation, and your materials okay and I would say yeah that's perfectly fine you can determine. 09:52:53 Honest to God the stress reduction of this material for me under the assumption is Tolkien. 09:52:57 So if I understand correctly you problem starts when there is some non linearity, like when a certain ratio is not enough, and they would 09:53:09 Pepe if you could guide me through. Where exactly the problem rise, like why this gauge gauging values that was lifted by boundary condition in the linear case. 09:53:22 How does it show up in the, in the other the karma of the key message when when you have when you have no moral when you don't no longer have the cookie identity assumption. 09:53:39 I would like to start at a different point, take consecration class, plus five equals zero. 09:53:48 And you impose some boundary conditions. You know that around. 09:53:56 A simple domain, you can you can impose deletion a boundary conditions on my mind boundary conditions from mixed ones where you have traditionally on one of my mind on the other was. 09:54:13 Now, The, the question for electricity for me is 09:54:27 when you have when you have this cage freedom, you're solving divergence of distress equals zero, in principle, you can have any field that solves the same equation and adage to distress, if you like, but of course you have to care for the boundary conditions. 09:54:50 Now, if you have these mixed boundary conditions, I do not see a way to really take stuff page, you know, in a reasonable way. 09:55:03 If I had to everybody. Good enough. 09:55:08 Yes, everything is we know all the linear 09:55:18 missed that power Did you just say, I believe in, I think, Ian Tabasco is in this, in this audience and he can correct me if I'm wrong, but I believe in the linear case there's uniqueness, but when you go to nonlinear deformations and you have mixed boundary 09:55:32 conditions. I think that's in general and open question. 09:55:38 Um, But I think. 09:55:41 I mean, for uni axial tension test I think you know you can take the. 09:55:48 You can you can take the force over the deformed area. 09:55:51 At the center and, and probably map it to a constitutive law but when you start getting to buy axial loading I think it becomes a. 09:56:01 You really have to address what what is a good representation of the local defamation gradient of a system in order to really kind of, you know, map these things in a reasonable way, that's just my, my feeling in the nonlinear case in the nonlinear axial 09:56:21 ending the nonlinear Okay, yeah, let me, let me jump in for a second because, so some of these questions actually seem important broadly for a lot of these extreme mechanics problems. 09:56:34 And so, to RKTB host is there is there a format for sort of creating a sub discussion that we can have on these things especially because we only have four minutes left, and we're probably not going to get to any kind of resolution here, can we can we 09:56:50 just take this part of the discussion and and you know actually address it very specifically at some you know at some, some formal way. 09:57:06 I would like to. 09:57:06 You have organizing this meeting we had purposefully left the Fridays, open, so that people can spontaneously arrange meetings on their own for instance on a Friday, during the 8am Santa Barbara time slot that would still work across most of us participants, 09:57:23 and then create a meeting you can just use the extreme mechanics Slack channel to announce we're going to discuss the particular following extreme mechanics question on Friday morning but the bar. 09:57:34 I'm not sure. I don't think we can use the Zoom links of KTP because that they that was have to be some key to be present present, but you can just create your own zoom link, put it on slack. 09:57:45 And then just announce it and then have a go. 09:57:48 Okay, so maybe, maybe we should do that or if not, this may we could also there's also like to gather town, the right for this for this program that we could probably also meet a nice because that's open all the time I believe right open all the time. 09:58:04 Okay, so I, I'm going to propose that someone put in a you know suggested time for a discussion about this particular issue that could be had on a Friday, either either on zoom but but I would say gather town then anyone could come and join when they 09:58:25 when they feel like it. 09:58:27 And then, you know, with that that leaves us with about two minutes here. 09:58:33 To finish the discussion. 09:58:36 If that's all right. And I, I did want to actually bring up some there's there's lots of other questions on the slack including a bunch of new questions I see that came up after I've gone through the list of questions. 09:58:51 The first time I do want to say though that there were a number of questions about, I guess what would be called Non, non canonical knitting or non canonical stitches things, you know, things that are you know like chain mail or or in fact like those 09:59:09 those DNA, things that that Alex showed us talked about, what was it last, last week or something with the, with the. I don't remember what they were called. 09:59:23 Right. But those tangles of DNA or, you know, just generally disordered knots or things disorder stitches or things with defects and I wonder if I don't have a cannot like a definite question that I want to pull up but I do wonder so betta, if you have 09:59:42 any way of or any any pathway to doing things that aren't so periodic and maybe are more disordered 09:59:56 yeah so that's a great question. Um, I mean there's multiple ways of looking at non periodic and just ordered in some senses. 10:00:09 The way that I guess the way we've been thinking about things have has always been trying to be consistent with what it means to knit. 10:00:20 So, a different talk which I didn't talk about here because this is the extreme mechanics as we do have a, like a not theory version of like this, that basically says like if it's an editable. 10:00:50 free grammar for how that works. So, everything we've looked at has been from that point of view. So we haven't necessarily looked at things like chain mail so things where you have like actual sort of ass ones that are like contract, would be stripped 10:01:08 intractable loops except that they're caught on other things. 10:01:13 So I don't, I think that's a little harder for the way we've done some of the mechanical modeling just because that sort of introduced this constraints in a way that isn't present in the way we're sort of thinking about things. 10:01:35 I, I would love to hear what other people have. As for disorder, we're thinking about disorder from the point of view of, like, the sort of minutes and pearls so like if I had 10:01:51 like random notes and random pearls, how does that affect the behavior. 10:01:59 And also what does the like the size of the domains. 10:02:04 So if we were to do something like, you know, some sort of like spin out all the composition or something that keeps the statistics the same but allows the domain size to change, sort of let the resolution of that to change. 10:02:19 But, So we're interested in looking at that. 10:02:24 So that's an Krishna who did all of the experiments, I think that's the follow up thing that she's interested to do to kind of finish off for a PhD is to look at that and look at kind of like is there. 10:02:36 I mean, I suspect that what what's going to happen is that the interface between the net regions and the pro regions are going to be what matters so do we get some sort of. 10:02:47 Is there a like percolation transition or something like that, coming from Bob so she is super interested on that so I think that that's that. Stay tuned. 10:02:56 And the next like year and a half and maybe we'll have more to say, but randomness as far as, as a lot of these things are concerned I think crush is probably a much better, medium, but I don't. 10:03:11 I mean I can, I can crochet, and I can make a lot of things with crochet but I don't understand it, but the mathematical level that I do with knitting. 10:03:19 So, there's a huge, open, open sort of questions there. 10:03:25 Well, alright so I think one of the 3pm, East Coast time is when we're supposed to finish right so how did this usually work I guess we should think the everybody for coming and thanks to betta and myself for fielding all of our questions. 10:03:47 And, yeah, right. 10:03:49 And I don't know I'm going to turn it back to my turn it back to my, you know the kid, the workshop hosts. Thanks Chris and thanks also to you for sharing the session. 10:04:04 So you know, now you're welcome to join us tomorrow in gather town for informal meetings, or we can even formally discuss the open questions that were raised today. 10:04:15 And then on Thursday, we're going to continue with the second discussion on the topic of extreme mechanics, where you know you're supposed to watch the talks from Benny Davidovich and Dominique Bella. 10:04:27 Oh and by the way I'm sorry we didn't get to all of the questions that people put into the slack but I would encourage everybody to both subreddit Marcella to go back through and find them and answer anything 10:04:42 that we didn't get to, because there were some really good questions we just, you know, ran out of time so, and on often like there there tends to be more questions after discussions. 10:04:52 So, yeah, sure, that's what they're for right. Yes. 10:04:56 All right. 10:04:58 Thanks everyone. We'll see you tomorrow and Thursday.