Live CEOing Ep 788: Design Review of PDE modeling, Solving & Analysis Features

Hello, everyone. Welcome to another Wolfram Language design review, part of our series for version 14.1. And we are looking. We have three design reviews coming up this afternoon. First one here is about PDEs. Okay, where do I start?

You can start with the solid mechanics one. So there we have a new function, von Mises stress.

How many other stress functions do we have?

So there's the main stress function that computes the stress tensor from the strain. And this new function, the von Mises stress, takes the result from this, from that stress tensor and simplifies it to a single.

Obviously, this is kind of illiterate here. I mean, there's no period. This is the wrong tense. Et cetera, et cetera, et cetera. Right. Has this not been looked at by anybody?

Not yet. It's still futurized.

I understand that. But be great if you guys could get these things edited before I look at them. So I just feed you trivial edits.

Good.

I mean, yields the V stress from stress. Okay. Okay. That doesn't make a lot of sense to me. Obviously. That's not. Shouldn't be there. That. Yeah.

I think that this whole, you know, the notes needs to be gone over.

A little bit and the example isn't right. So. So. Okay, so let me. Let me understand.

So the thing is that when we do well in solid mechanics, in particular, we compute displacements from that, we compute strain, from which we compute stress. But generally speaking, there are these quotes, analysis functions. Okay, so this is one of those.

What other ones are there?

There are things we making a catalog and some of them are, you know, brought up in these monographs and their living context, in private contexts. But we would like them to be the things that you need to be system functions.

Okay, so hold on. I mean, we've had different approaches to this. You know, like with image measurements, we have a zoo of functions that are for all possible kinds of image measurements and they're just all in one function. With strings. Yeah.

Yeah.

That's one approach which I'm not that keen on because. One reason I'm not so keen on that approach. Well, it's complicated because, you know, in statistics, for example, we have a bunch of functions which are just exposed. And it's like, you know its name. Well, like spatial statistics has a bunch of these where, you know, you know its name. You care about that one. You just use that one. It's kind of convenient. But also. Or like in, you know, image processing, we have an awful lot of, you know, beyond image measurements, we also have an Awful lot of functions that are definitely minority use. You know, like Chan Vasi binaries or something. Yes, it's kind of like a, you know, really, I mean is that, you know, you either use it and that's what you should always use, or it has a, you know. You see what I'm saying? I mean, in other words.

Yeah. Von Mises stress is the most important stress measure that's in use. So I think that kind of warrants for its own function. If we then later have something more exotic, we could package that up in a different way.

I mean, in other words, what is the von Mises stress really?

So basically, it gives you an indication of whether a material will yield or not. So if you deform an object and you get the stress tensor, then you usually have like six numbers, but you can't really say anything from that. So the von Mises stress takes those six numbers from the stress tensor and combines them in a sensible way into a single number. And if that number is lower than the yield stress of a material, then you, then you are in good shape. Then you know that the material won't yield at that.

So how does this relate to like principal components or some other such way of packaging up. I mean, you've got. The stress tensor is what. It's a rank 2 symmetric tensor. Is that right?

Yeah, yeah, yeah. In most cases, yes. Yeah.

Okay, so what, what mathematically is this thing for a rank 2 symmetric tensor? Or is it nothing that anybody cares about elsewhere?

No, I mean, this. So this is based on, on the year on von Mises failure criterion. And that's kind of. I mean, the theory behind is quite complicated. So it takes the invariance of stresses and computes something sensible from them.

Well, I'm looking at the, the general formula, aren't I right there?

Yes, you are.

Yeah.

Yeah, that's correct.

So, so for example, for electromagnetic, for the F, new electromagnetic tensor, what is this thing for that? I mean, that might be a physics question, but, but you understand, I mean, that's an.

I. I can't say that. I don't know. I, I need to think about that. I can't say anything about that.

So this is a thing mathematically defined on a tensor. Yeah, except the way you're presenting it here with the U, V, W, et cetera, et cetera, et cetera. I mean, ignoring those things.

So the way it works is you give it the variables and the parameters in exactly the same way, like you'd specify a solid mechanics PD component, and you give it the Stress tensor. That's the last argument you have.

Even though it doesn't actually depend on the function.

Correct. Because it, because it's just the same workflow for all functions.

Well, but if, if there was a, if this was a well known, you know, the, the tensor hub or something, you know.

Yes.

If that was a well known function of tensors, you would just apply that function of tensors and, and von Mises would not be in the story, in the picture. Am I right?

I mean, in other words, I don't understand that.

Well, okay, let me give you an example. Okay, so in, let's say in finance, okay, you know, there's the concept of volatility, but actually it's just variance, I guess. Right. So given a time series there, we don't have to have a special function. Maybe we do because of, of crazy dates, calendar stuff and so on. But, but the first instance is just a mathematical operation on the time series, a well known mathematical operation. So I'm asking, can this be thought of as a well known mathematical operation on this tensor as opposed to something which has sort of physics content? That's, you know, because look, there are plenty of.

Probably, yes, but the theory is going to be complicated for it.

Why? I mean, there's a formula right there. That's what you're evaluating. It's that formula. Right, right.

But if you're arguing from that perspective, you might want to know, I mean, there might be even an even more general approach to that.

Well, but there's this approach. I mean, in other words, if this was called the, the hub of a tensor or something, if this quantity was called the hub of a tensor, let's.

Say I. Yeah, yeah, that's fine thing. Got it.

Then you would be happy to just say in your, you know, in your PDE setup, you would say, okay, let's compute the hub of the stress tensor. And I'm, I'm a little bit concerned here that this, you know, that really this is an operation on a, you know, on the symmetric tensor and that.

It'S like a secondary step, you have to compute that tensor before.

I get it, I get it, I get it. But I mean, and I mean, is it the case that there are PDEs in which you would have this function? I mean, you know, in the PDE itself, does it have something that says that represents the stress tensor and then wraps this function around it?

You have that if you do plastic deformation, because then you need to know what the Fermisa stresses is at certain points in the object to decide Whether it has plastically deformed or not.

No, but I understand, but that's post processing. I'm asking, in the presentation of the PDEs, does this quantity appeal? No. So this is pure post processing?

Yes. The only thing that appears is the name is right?

Yeah, I don't think the name is right because I think this is. You're making it look like. And the fact that you have completely redundant arguments here is not a good sign.

Okay, but you get a scalar field instead of a matrix field out, right? So.

Exactly. Yes. And does it matter what the Young's modulus and the Poisson ratio are? No. So this is just full of irrelevant information. I mean really, this is a pure mathematical operation on a tensor.

Yes.

Tensor field.

Right, yeah. Tensor field. Yeah. I mean the question is whether we rather like to have a consistency in the arguments of all functions. PD modeling or whether we.

But that's for the real time. That's for the equation components. All the stuff that you have there is necessary if this was appearing as something in the equation. But this is post processing.

Okay. Yeah.

Which is different from what you had elsewhere. You haven't had very many post processing functions elsewhere, Right?

Correct. Yeah.

What happens with planar. Planar?

No, so. So if you. I mean, so plane strain and plane stress are different formulations of the PDE model and you then use strain and the strain and the stress function to get the strain and stress out of them. There is no. That's not a post processing thing.

Sorry, sorry, sorry. I got distracted by something. Could you say that again?

So what Roger referred to plane strain and plane stress are different ways to formulate solid mechanics PDEs, and they are not post processing. So when you set up a PDE model, you can say you want this in a plane strain or a plane stress form, but you then still do compute the strain and the stress as secondary quantities and you're done with it.

Then.

There'S no function, plane strain or plane stress or something like that.

Right. But the thing I'm trying to understand is, is there any scenario in which inside the setup of the PDEs there will be a thing that says, you know, when event, you know, this thing of something or other greater than whatever.

Yeah, for next. For next.

For plasticity. Yeah. You can have.

But is that something where this thing, you know, would happily sit there in the PDE operating on a symbolic object it wouldn't evaluate? And it only actually evaluates if it's given a specific and explicit tensor, You know, to me. Okay, this, you know, the right name will be something like, you know, von Mises stress, I don't know, measure criterion, I don't know, something like that.

Yeah.

So it isn't the stress itself. It's merely, you give me a stress tensor and I'll tell you this measurement on it.

Correct. And that measurement typically is called the Von Mises stress. So, But I understand, I see what you're saying.

Yeah, yeah, right. But then the argument to that would just be a stress tensor as a symmetrized array, as a list of lists, whatever it is. Right. I just don't know this field, so I don't know what else.

I mean, so for some, I mean, we need a little more information than that. For example, if, for example, if the model form is axisymmetric, then the von Mises stress is computed a little differently. So we have to have these parameters available in some way.

Where are those? So, oh my gosh, I don't know this field. So this is difficult.

Scroll down. I mean, the first, let's see, let's see it in. The first is not a real example. You see there, when it computes for meson stress, it's for, for a field.

Where the hell did it get the XYZ from? From the vars here.

Yeah.

Oh, gosh. I don't think this is the right design, but I'm, I just don't know enough to be able to.

Okay, let, then what, what is, what is your concern? Basically.

That this is a post processing thing. That it isn't a.

It is.

Okay. What other things are there towards stress?

So this is the solid mechanic stress that computes the stress from the computer strain. You see that function in the example you just looked at there? You see the usage of it. So the first thing we compute is the displacement. Then we compute from the displacement, we compute the strains from the strains, we compute the stresses. And from the stresses we can compute the Von Mises stress. So all of those are post processing steps, if you will.

All right. I mean, I, I, it at least has consistency. I'm not wild about it. I think it's, I think there's probably.

Tell me what makes you worried. I'd like to know. I mean.

Well, because I.

My simple argument, Stephen, is that if these are standard things that you want to know, we shouldn't have them in a secret context.

Oh, God, no, no, no. Absolutely not.

Or you shouldn't have to program them yourself.

That's not a no, obviously. But I mean, the thing is these things are things that appear in pde, Right? No, this is the thing. What's that?

Yeah.

Nd sol value of this equals. Well, that's solid. Oh, gosh.

The strain and stress.

The solid mechanics strain and stress are encoded in solid mechanics pde. So there are inside of that. Basically you need that to set that up, but you don't need the von Misest stress to set it up.

This is. But that's only implicit. Whereas here you're explicitly using it with this displacement as input to compute that. All right. Okay. Okay, I'm sold. It's fine. Let's move on.

Okay. So for fluid mechanics, we don't have a new function. We've just generalized one new one material model and we're making an application example. It's not quite ready yet, unfortunately, to show you. So.

But where is this?

If you look at. If you look at fluid flow PD component.

Arg.

You'll find there should be a version 14/ tag on the coro non Newtonian fluid model.

Right there. But there's no 14 plus.

It's a little further. Further down there. Yeah. So it's just a generalization of the model that we've done.

What is mu?

I don't see the mu. So that's the apparent viscosity that's defined a little bit above. Like 2 items or 3 items above.

I thought ATO was the usual symbol for viscosity.

Yeah. In this case it's because it's apparent viscosity. For some reason they've chosen.

But you've given the renovation.

There's a difference between dynamic viscosity and kinematic viscosity.

Yeah. For a non Newtonian fluid. For sure.

Yeah.

I am not wild about using this curly thing for the Reynolds number. I mean, 99 of the time. I see Reynolds number just written as re, you know, in ordinary letters.

But re is a function, so it's a bit.

I know.

So I mean, if, if you. I'll change it.

I don't know. I'm not. I'm not. I'm not well about it. I mean, I. I'm not.

Tell me what you'd be wired about.

No, I. It's not. It's. It's. Okay. That's the kinematic viscosity. Is that right? The mu there.

That's the dynamic viscosity.

What's the thing that's usually called ata? I mean, I usually see this formula, kinematic viscosity. Okay. And that's. But something is divided by density. One of them. Yeah, but there's a density Right there.

Right, that's for the Reynolds number.

Yeah, no, I understand, but why.

Right, so then you'd have the kinematic viscosity is then divided by. Is the one that's divided by density.

Okay, check. You know, I mean, all of these endless names of people referring to things. I mean, it's kind of like, like I don't know how it works in these fields, but you know, one of the things that has happened in physics is, you know, there used to be a thing, the Friedman universe model. Okay. And then it became the Friedman Robertson Walker and then the Freedman Robertson Walker lemetra model. And you know, names got longer and longer. Yes. And you know, because, well, that person really had figured it out and they had some lobbying, you know, organization, so to speak, that said you should, you know, mention them, blah, blah, blah. I don't know whether that's a risk in these cases as well.

Yeah. Okay, so kinematic viscosity is dynamic viscosity divided by density.

Indeed.

Yeah.

Right, but, but usually in the formula there's a. I mean, sometimes I've seen nu as being the eta divided by rho. Right. Look, there's probably a different notation for engineering and for physics. And the question is which one should we be using and how should we deal with that? Because like, like I'm reasonably aware of fluid mechanics and I've never heard of this caro, you know, model. Okay. I haven't done stuff with non returning fluids particularly, but it's definitely not something I'm immediately familiar with and it's presumably in a.

So it's used to, to model blood flow and. Yes, plastic materials, as far as I know. Yeah. And the model that we're working on is actually modeling blood flow.

Ketchup.

Yeah, well, those are different. I mean, you know, blood flow is specific. It has little, you know, things that align with the flow and they distort and so on. By the way, any word, like, I assume you're reporting that as a spelling word and so on.

Yes, yes, yes, yes. Yeah, absolutely.

Ali on our live stream comments. Specialists in Solomon Cancer. We're more familiar with terms like misestress. I didn't know there's some name that general stress. Yeah, yeah, I think so. Okay, what the heck is this? That is not something we do in documentation. What the hell is this? What is that?

So you can specify your own function for an apparent.

Okay, but that's not how we write it in documentation.

How do we write it?

Oh, you know perfectly well. We do it with italics and we just say, you know, function fun, and then you write fun there.

Okay, good.

What the hell is this? Blank. Vars. Blank. Is that really what you write? I don't think that's really what you write. What do you actually write?

No, that's basically the signature of the function.

Okay. But that's not what you write. It's. This is in. This is in a Roman font. That everything in a Roman font is what you actually type. You see what I'm saying?

I. I'll fix it.

Plain font is what you actually type anything. I mean, this is just wrong. I. I assume this should just be fun here. Right?

Yeah.

Viscosity arrow. Fun.

Yeah.

Right. Roger, how are we making sure that mistakes like this don't happen?

I. Look, I, I should have reviewed this. You know, we should. We should do a more careful review. So I'll make sure.

Okay. Okay. All right. Electric current PD model.

Yeah. So that's a new function. There's a new monograph accompanying that set of functions.

I actually, I want you to see. Do you have the decision diagram there?

Yeah, it's. It's in the function page at the bottom.

Which function page?

So in the electric current PD component. So there at the bottom. It's not, It's. It's a draft. It's not, It's.

That's fine. But I, I, For Stephen's understanding, I think it's useful.

Yeah.

For, you know, people on the live stream, too.

So if you scroll down to the, to the function discussion. To the discussion part, you'll see a. Oh, scroll up a bit. Yeah, there, that's it.

Okay.

So this is the sort of modern world of electromagnetics.

Yep. Different from electrostatics to pure circuits to things, but magnetostatics to.

Yeah, yeah, exactly. So the thing that we look at now is basically electric currents when the magnetic influence can be ignored when it.

But let the electric current is in the body of a material with skin depths and all that kind of thing, rather than just, oh, there's this total current eye going through this wire. Is that correct?

Yes.

Yeah.

I have to say it would take me a little bit of thought to understand which aspects of. I mean, you know, for skin depth, for example, in a. In a alternating current and so on. Don't you need.

Yeah. So basically. So this function we're reviewing now is basically usable. If the skin depth doesn't matter.

Okay.

Then you can use that function. And that's the tricky part about electromagnetics, to dispatch on what function to use in what scenario, because.

Yeah, right. But. So I Don't understand. I mean, in a conductor, why isn't the current just uniform across the conductor? If you ignore magnetic effects in a dielectric, I don't know what happens. But on a conductor, why isn't it just uniform?

Yeah. Then. Then you don't have a. So if there's no magnetic field, then. Then there is no, no skin effect.

No, I understand.

The skin depth is larger than the object size and it doesn't matter then.

Yeah, but I, I'm. I'm trying to understand why is there a non trivial function involved if it's just. There's a total electric current and you divide it by the area of the thing and that gives you the, the, you know, current density. I understand why this is different from.

I mean, I mean this is the PDE model. It's not the, not, not the, like the ode.

I know, I know, I know. Isn't it uniform across the. Maybe, I just don't know. I mean. Okay, so for this conductor, presumably we're giving here.

So what we're looking at is basically.

What'S that angle bracket doing?

That's the standard way how we describe that this is a PD component and it can set it equal to boundary conditions.

What are the angle brackets doing in terms of our style for documentation? Is that something. What's that?

Yeah, we haven't really used that elsewhere.

And we really can't. And you know, we either have to introduce something as a big trumpet, you know, thing. We can't just sort of start introducing it in random places. Not least because, you know, we end up with automated systems that pick up things that we have in documentation and they just fail if it isn't consistent. That makes sense.

Yep.

I mean, and similarly with this, which looks quite nice. Is that something we've been using elsewhere? This kind of over.

We're starting to. Because we haven't really explained much historically. We didn't. Our documentation really didn't explain that much. Right. You assumed that you studied it elsewhere and we were just giving you the interface.

I understand. I think it's good to explain stuff.

Right. And so we are doing that. So this, in, in. In some ways this documentation is sort of leading.

Yeah. Okay.

Well, I realized something else, by the way, in our name, if you scroll up. So, you know, we call this electric current PDE component. But PDE stands for partial differential equation component, which is correct. But we should have coined a new term pdc Partial differential components. We should have. You know, it would have been a much shorter. It's too late now, but we should have.

Yeah, it's okay.

So autocomplete basically does. It takes the current continuity equation, inserts Ohm's law, and we use the fact that E is the negative gradient of the potential. And that's what we compute.

Okay. And we do that Currents monograph. Let me just look at this for a second.

Sure.

Oh, Christ. You can't do this kind of nonsense. No, don't do this. No, don't do it. It's a hack history.

We've discussed this, Stephen. Everybody told you that the correct way to do it. I don't know what else I should do.

I mean, if we should fix the system so you don't have to do this.

Yes, go ahead. Absolutely. But until then, I'll.

Okay, so then you need to get. Okay, then get this particular thing. Do I need to do it? Get it into the user assistance meeting, get this discussed.

I'll do it again, no problem. But it's been there. And people told you. No, they told you. It's. That's the way to do it. Mark told you. ITAI told you. I know.

I don't think it's right. I. You know, if we have to do this, we might as well just give up. You know, this is just silly.

I'll bring it up again. Yep, no problem.

Okay. And the reason you're doing it is because you're building up. If you actually run all of this stuff, you're building up a lot of. A lot of state. All these pictures and so on. Okay. Yeah, just like, like. This is so ugly. It's like, like, okay, we're trying to explain something that's sort of a computational description of the world, and then we're thrust. I mean, by the way, I don't know why we need that either. Why do we need that?

Because we make use of low level functions that are okay, but they should.

Be in the function repository. They shouldn't be in some random context.

Stephen, I've been working on this for more than 10 years. It's not an easy thing to just put everything simply in the function repository. We're Talking about like 50,000 lines of code and more.

No, but that's. But that's not the point. The point is you have them in an internal context, but their exposure should be in the function repository if you don't want them in the system. Do you understand what I'm saying?

No, he means that API call. You just call the same function, but you give another interface.

Same thing. Right? It's the exact same thing. But There is documentation in the function repository.

I have documentation. Everything is documented. It's all there.

Where?

Click on, I don't know, two element mesh.

And look, I'm clicking on this and it's not doing anything.

Well, yeah, okay. You just picked that single one that isn't there yet because it's a specific one for this example. Okay.

No, but wait a second. Look, we have a way of doing this now. We didn't have it 10 years ago. We do now. And the way is you put it in the function repository. It's a special purpose thing. It's used only in particular cases. Put it in the function repository, okay? So that it has uniform documentation. So I, for example, know how to find the documentation, which I won't be.

Able to do if you just dump. You just click on it like two element mesh. There it is selected.

Press the right way to do it. Where, where is that?

There, in the middle of the page. There was somewhere. I don't know. Scroll up a bit again, please. We'll find one for you.

This thing here.

No, clicking on that one further up. One further up.

Wait, wait, wait. Is that a built in function to our.

One thing at a time. One thing at a time.

Is that a built in function?

No, it's not, but click on it and press F1.

I'm not finding anything. It's not doing a damn thing.

So it's going to the. To the.

There's no. There's no raft here. There's no. Where. Where's the I raft here that gives information on this function?

On Windows it's F1. On Mac it's.

I don't. Maybe it's something. I mean, just.

Command. What is a command? How do you get.

How do you look up functions in. In the, in the. In the documentations? Even this command.

Something on Mac.

Oh, I'm using what this did. I pressed Command F1 and my screen went black. It's still black. It's not that. What the heck just happened? Oh my gosh.

Does anyone have a Mac here? And know what. How to select a function and look it up in the. In the. In the documentation. Command shift F. If I'm not wrong.

I did that.

There. So that. That's the reference page that goes.

It should be in the function repository. Should not be here. This is what we did years ago and it's not what we should be doing now. We have a good mechanism for it now and that's how we should do.

Okay.

I mean, and. And this particular thing. So then we don't have a needs. We don't have any of that nonsense. I mean that, that was the old world. We have, you know, gone beyond that. What was I looking here was that. Oh, it was in the monograph, which I've.

I mean.

No, no, no. You know, we've gone through a lot of trouble. Nice. And you know.

Yep.

No, put it in the function repository.

Okay.

I mean, yes, this was the right way to do it a decade ago or the only way to do it a decade ago. Okay. Oh, God, sorry. I just annoys me to see all this stuff here. Although the, you know what this is doing is impressive.

Exactly. That's good.

Why is that equation not magnified properly?

I filed a bug about that today. The equation setup is not. It's not looking good in 14.1 currently. Something is wrong there. Someone needs to look at it.

Okay, so all this response, by the way, is wrong. I've reported this about five times. That font is wrong. Look at how big it is. It's just not right.

But generally the page doesn't look right. I mean, there's very little space on the left hand side. So something's wrong with the page generally.

All right. Okay. Yeah, these figures look kind of, you know, like they were drawn in Mac draw.

Actually, this is a typical example. I was going to say that working on these modeling and applications, where we use them really stresses and drives the framework forward. So in particular that picture you have there, where you have like a cake of materials, you have discontinuities.

Yes.

And then you need discontinuities in your interpolating function, which in higher dimensions, which was something that needed to do that.

A built in function line element.

It's a finite element context function. And this would be in the function repository then?

Yeah. How many functions are we talking about there?

I don't know, 50, 100, I don't know how many there are. 50, maybe more. 50? Yeah. And tons of documentation. So I'm not even sure that the function repository is capable of representing all the documentation that I have, but I'll check that. I still there. Hello?

Yeah, yeah, I'm sorry, I'm distracted by something. Sorry. Well, it's lovely. I mean, the thing about something like this is. I mean, I'll really know if it's lovely or not the day I actually try to use it. And that will determine, you know, I really can't tell. I mean, other than these pictures really look ugly. I mean really ugly.

Yep. Come on. As I said, I find a bug. I did find a bug about this.

Is that a problem with the rendering or is that a problem with the picture?

I think in this case the picture.

I mean is this all production or is this.

Pictures you see are programmed in Mathematica. So everything is done in Mathematica in. In the language.

Okay, but I mean that's good. But it's just like. Like somebody picked that blue which is not. Which is rather ugly.

So normally we have Tim go over these things in which case they come out.

Tim, if I say yes, that that's what I would hope for. Okay. But that's not happening. That hasn't.

Not yet.

Yeah. Okay, so that's just a yet not a. Okay. Yeah, fine. How far does the electromagnetics. I mean like if I want to design a weird fractal antenna, can I do it? Would that give me.

Probably not because that's a high frequency thing and we need full electromagnetic wave stuff which we haven't done yet. So the next thing we're going to do is magnetostatics. Yeah, we're almost done with that but it's not going to make it for 14 1. Okay, but then, then after that we'll do electromagnetic wave stuff.

Okay, cool. How many more domains are there that are kind of like common? I mean that's a common one obviously.

I think we, we've. We've touched base with about all of them now. Now there's like cross coupling. Like for example, if you chemistry would be one that.

That's uses a chemical engineering. Well, yes.

I mean if you're designing.

We have mass transport, heat transfer. That's long.

Yeah, but you don't have phase change, you know like.

Yeah, we do. Absolutely. Absolutely.

Can you model a rocket engine?

I'm sorry?

Can you model a rocket engine that's full of phase change and so on?

That's probably. That's. I mean I. I can't say off. I haven't looked at that thing specifically so I can't promise that it's going to work. But we can do model ph change like melting of ice and stuff like that.

But like in system model we have multi phase flows and stuff. Do we have that here?

So what we can do is free surface flow, if that's what you mean. That's. That we can't do that yet. But that's still. I mean Stephen asked about the, the fields that we've touched. So we've touched a lot. I mean we've done something fluid dynamics, but we. I mean all of these fields can be fleshed out.

Right.

Indefinitely. I haven't Done.

General activity, which I think is probably physics.

Stephen, I need help with that.

You know that well, but I think we need. We need to do it.

Yeah.

I mean, that's, that's one that's important.

Yeah.

Yeah.

Oh, for.

For what?

For rocket engines?

No, no, for our users, who are physicists, of which there are many.

I'm teasing. Yes.

So for the Schrodinger PD component, there's only a small change. The mass can now be completely anisotropic.

Why is that sensible? What. What does that even mean? When would. When do you use that?

Yeah, that, that, that's. That's beyond me, but.

Well, I don't think that makes any sense.

Michael discussed this and they came to the conclusion it's useful, so we've done it. So there it is.

I don't know what the heck it's useful for. I have no idea. So maybe something.

Once they've done this, they've used this in quantum dot computations of some. Some sort.

So it's an effective mass, that is.

Yeah. Correct. Okay, all right, but I must. I'm. I'm a bit out of the depth here, so I can't really say much about that. So there's nothing, nothing else besides that single node.

Okay.

That we've added. And there is the accompanying example, the axisymatic quantum dot example is the example that goes with it.

These pictures are too big. I mean, they're actually not bad looking pictures, but they're obviously the wrong size here. Right.

Okay.

Did you agree?

Yeah.

And also, look, we don't do figure two. This is like a, you know, this makes, you know, this is like we're going back to. Oh, we have to print it on pages and we have to refer to figures because the figure might be seven pages away type thing. This is very ponderously textbook written.

Okay, we'll remove those.

Well, I just don't think, you know. No, I mean, this is not the style that we normally write these things.

In, you know, Stephen, I mean, that's absolutely fine. The problem I have is no one tells me stuff like this until I'm in a meeting with you. Why. Why doesn't anybody tell me before?

Well, because you guys are not interacting properly with. Okay, never mind. But to be discussed elsewhere. Fair point. But, you know, you know, Roger can perhaps comment on this, but maybe not here. Yeah. Right.

Okay, so the last item on the agenda.

No, I want to see your quantum dot.

Okay. Yeah, yeah, go ahead.

No dot has been seen yet.

It's just a dot.

I don't Understand why these headings have lowercase letters here? That seems very odd. I didn't know that was a style.

Yeah, I've been instructed to only use lowercase letters in headings.

Width has a typo there. Come on, guys, look at it. Widht. No. Where would that be caught?

Usually DQA gets stuff like this, but. Yeah, yeah.

Where's. Where's the bottom line here? What. What. Whatever happened here. So I don't understand. What. What. What are we computing about this quantum dot?

So if you. If you go down to the conclusion.

I did the conclusion. It didn't have O. It has a. What is this? I mean, this reads like an academic paper. That's not what this. I mean, what are we trying to do here? It's not the style we should be writing these in.

Okay.

It's just not the right thing.

Okay.

You know, if it was an academic paper, fine, but, you know, is it an academic paper? I don't think we should be doing academic papers. Not our business.

Yeah.

Oh, universities and places like that, they get paid to make academic papers. We do not. So what is this? What. What. What is the. I mean, you know, I just don't understand. We. The.

So we use the athen quantum number to compute these quantum dots.

Well, what do you mean by computer quantum dot? What aspect of it? I mean, quantum dots are being used in quantum computers. For example. There's like, hello, it's a qubit type thing. And I don't know how much of that, you know, is not pure one particle Schrodinger equation. But.

So we set up the. The Schrodinger equation for it and then compute the eigenvalues from that thing.

Okay, but, but, but look, the way people care about this is you have an array of these quantum dots and you're trying to make it into a quantum computer, for example. Right. So given that we can compute all this stuff about this quantum dot, what happens if we make an array of these things? You should be able to make a picture that shows. I don't know exactly what the right visualization is, but I mean, I just don't know what the conclusion is here. It just seems like it just sort of flaps around and doesn't. It looks lovely, but, you know, it's kind of like. It kind of needs a beginning, middle, end.

Yeah. Okay.

Whereas what actually seems to happen here is the end is just like. Oh, well, you could look at a different thing here. I, I just don't. I. I don't understand that. This is not, you know, like what's the point here?

So the main point of this is to introduce the computation of quantum dots. And I'm. I admit I'm not an expert in this. I can't really answer your question now. So I don't.

Okay.

This is what Michael and Ricardo discussed and what they came up with. And I.

Nobody involved in that is in this meeting. Is that right? That's not part of the rules for these meetings is, you know, when you come here and you're like, well, I've got this thing and I don't know anything about it. It's not a very helpful meeting. Yeah, but, but I mean, look, I agree, I think with these examples, it's like normally in examples you've shown for engineering type things, it's kind of like. And then the answer is the velocity field looks like this in a stirred, you know, pot of this kind. Right. So here I just want to see the answer is.

Yep, we'll add that in.

I mean, I don't know what in place, but just sort of going and saying academic things about it isn't really the point. Yeah, because. Because what people are looking for is, I've got a problem. I'm going to use Wolfram language to get an answer. Not, this is a model for how I write a paper, which is their business. Not, you know, it's not really. That's not relevant. I mean, it's kind of like.

So we will. We'll not have like this paper style.

No, I mean, I think what you need to do is say we are computing, you know, the wave function for a quantum dot in this situation.

Yeah.

And the answer is boom.

Okay.

Right.

Yeah.

And, you know, maybe there's some extra pieces that say, and we could add this effect and that effect, and then when we add this effect, the answer is boom.

Yeah. Okay.

Right. Whereas what we're seeing here in sort of. I mean, presumably some of these things are answers.

Yeah, absolutely.

I mean, it's not. I mean, is this the answer? We don't have a clue. I mean, this says boundary conditions in the eigenvalue problem solution. Okay. I mean, it. Yeah, it's just not very clear on what the answer is. Whereas, you know, the examples you've shown me before for PDEs really are very clear. This is the answer.

Yeah.

Okay.

Okay.

Rather than. I'm clever and I can say a few things about what's going on in the system, it's like, okay, I got.

It, I got it.

I'm sorry, I'm just reemphasizing Because I'm.

Yeah, it's okay. We'll change the style for those. Yeah.

Okay.

The next group here is primarily a set of examples, but the question is when do you use ODE or lumped models versus when do you use a PDE and distributed models.

Yes.

And how can one use them together? Can you use. Well, you can see the use cases there from an ODE where you model typically a complex system, but then you want full details on something like I think a room heating was here, where.

You got the whole. So then you're looking at the volumetric temperature in the room, even though you started off by just saying it's overall heated in this way. Is that right?

Yeah. So that's, I mean, part of the how to say challenge in this approach. So you have an ode, a system model, but now you want to make a PDE model from it or use the ODE model to drive the PDE model. But you need to make additional assumptions that are not present in the ODE model because this model just doesn't care. So that, that's what, what's happening here.

So how, how are you actually doing that?

So, and for this. So I mean, there is no, there is no final solution for that in this case. What we've done is we've made it such that the temperature we assume with the radiator in the, in the, in the room is average. So on average you have that temperature that the ODE model has. That's one approach to.

I see. But then you could. And then that's some kind of driving term.

Correct? Correct. Yeah. So you use the ode, the system model result to drive the PDE model.

Correct.

But you need for this to work and that, that's not a limitation in any way. But for this to work, you need to make additional assumptions for the PDE model.

For sure.

Yeah. So that needs to be done. Right.

Okay. I mean, seems interesting.

Yeah. And the other example is the other way around. If we can just briefly look at that. There we have a PDE model and derive stuff for a system model. So what we have here is you're.

Trying to get the aggregate spring even though inside you're looking at the individual stresses and so on.

Correct. But now stuff starts to get interesting because we can do hyper elastic material models that are non linear, so the spring constant is not a constant any longer, but we still can do it. So. And I mean while it's. It may be trivial to do for a constant spring, it's non trivial for a. I get it.

So it's no longer Yeah, a spring on a weight. Where the. Sorry, A weight on a spring. If the spring isn't. Is hyper elastic, then it probably isn't a sine wave anymore. Which is what you're showing here.

Yeah, correct. Correct.

Correct. That's interesting.

This, this is the more I find the more interesting approach where you have like a detailed drill down PDE model. Did you do something that you can.

What was the indicator that you used? How did you derive. So you've got the stress as a function of position? Well, in the end it's the average strain or something that you want, which is the extension of the thing or somehow it's the average stress, average strain or something. Well, how does that work? Or is it some integral of those things?

So let me quickly look. So we have the displacement. So we have the displacement compared to the force basically. So we know the input force to the deformation.

Okay.

So it's, it's fairly, it's really straightforward. It's not, not as complicated.

Okay. Okay.

Yeah.

Very nice.

Good.

That's impressive. That's, that's. So how many more, you know, if you were. I mean there should be one on quantum mechanics, presumably.

We haven't actually made these into books yet.

There's still to do that then. We're working on those. Yeah.

Cool.

But we're getting there. We're getting there.

All right. So look, some things about overall style that need to be aligned. Otherwise very impressive stuff. It's some. I, I mean it would be interesting to see at some point a multi year roadmap for what, you know, these different areas. I mean we really should cover the physics areas. We have a lot of physics users. We really should.

True, true, true. But I need help with that. Yeah, well, fine.

I mean I, I would talk to Michael about it.

I mean.

And there are other people, I mean Michael has some people who are definitely, you know, physics enabled. I think it's just a question of switching around, you know, who's doing what. But I would think, I mean, you know, we need, I mean, I think in physics we need optics type things. We need and that.

That you mean not electromagnetic optics or. What do you mean?

Well, I guess it is electromagnetics, yes. I mean it's not.

Well, there are two ways. I mean there's this sort of geometric.

Ray tracing that's completely separate thing. That's not what we're talking about. I mean for the physics stuff, it's mostly, you know, diffraction type optics.

Yeah.

And then general relativity and quantum mechanics. I think those are the main Main things, I mean, and. Yeah, all right, well, sounds good. I mean. Okay. And I mean, I suppose in. In. In solid mechanics, so it's not really physics. There's all the stuff with crack propagation and all these kinds of things.

Not quite yet, but we'll get there. We'll get there.

So the next thing is plastic.

Plastic deformation is what we're working on now. So if you. If you deform something beyond the yield limit, it stays deformed because it's basically. Yeah, deformed.

So that's kind of actually sort of interesting that if you had a regular PDE up until you reached a yield point and you effectively change the pde.

Right.

You know, when it's in. It's kind of like a fluid at that point, I guess.

Yeah. There's rheological models to do that. The problem is we have a working kind of a code, a prototype type of code that does what it's supposed to do. But the question is how to get that into nd solve. So we're thinking about that. It's a bit tricky, but we'll figure something out that's hopefully reasonable and usable.

All right, good stuff. Okay, thank you. I could see I really messed up my computer screens by that command. F1. I have no idea what it actually did, but they're all misconfigured now. Oh, well, I have to untangle that. All right, thanks. Good stuff. Thanks. Bye now.