ENH: Implementing the rheology model

[glyg]

This is a work in progress.

The current state of affairs can be seen in the following notebook:

http://nbviewer.jupyter.org/github/glyg/notebooks/blob/master/tyssue/Rheology/Equations.ipynb

Two questions:

• Why use only half the chord length, $a_{ij}$ in the equations? Although it simplifies some equations, there's a factor of two in most of them, and it is not very instinctive. Plus the library already computes the edge length...
• How to set correct initial conditions? I suspect my actual poor choice is responsible for not finding a solution to the differential equations. If the initial conditions violate the equations, the differential can't be solved, right?

Well, we can discuss that here...
cc @cypriengay (I don't have François github handle yet ;)

[glyg]

From a mail by Cyprien:

Question :
dans le cas que tu traites
où le tissu flotte au milieu de nulle part,
il faut d'une manière ou d'une autre
empêcher le tissu de se translater ou de pivoter.
Autrement dit, si tu ne fais pas ça,
la matrice est singulière et tu ne peux pas l'inverser.

Pour ça, il faut ajouter trois équations.
Je te conseille un truc du genre :

vitesse nulle en x et en y
pour le centre de gravité des trois cellules

Orientation constante (par exemple selon y)
pour le vecteur joignant les deux cellules de droite (A et B).

En contrepartie, il faut virer trois équations quelque part.

So let's do this !

[cypriengay]

Hello Guillaume,
about your questions one week ago.

1. chord or half-chord, I really don't care, use whichever notation you prefer, just make sure to be consistent! :-)
2. Initial conditions is a difficult question. What we have done in simpler geometries is to start from simple, exact situations, like pure disks touching at one single point. Another route is probably to have wrong values for the surface area and letting the program adjust that initially. In other words: instead of having d/dt(volume) = 0 we take d/dt(volume) = (target volume - current volume) / (some time scale) and keep that until the volume is correct, then set d/dt(volume) back to zero.
   By the way, I just tried using the notebook in a fresh ipython3 notebook installation, and failed. Must miss some library or some initial file of yours, I guess.

[glyg]

Hey Cyprien, thanks for the comments!

I'll fix the equations to put on the chord length, it will be simpler later.

As for the install, you need to also install tyssue as we did in Montpellier. If you did so, can you post here the error message you get?

In the latest version, I set up a tri-junction which is supposedly at equilibrium. I tried to set up the center-of-mass and fixed orientation equations, but fell back to a singular matrix. Maybe I didn't choose the wrong equations to take out?

Good news if a trainee can work on that!

Guillaume

PS: I recieve a mail, as you do, when a comment is posted here, so no need to re-send it separately :)

[glyg]

Ok, it looks like the 0.2 milestone was a bit optimistic for this :/
Bumping to 0.3

[glyg]

This is going on in an independent project you can follow here:
https://gitlab.com/EMoisdon/tyssue_rheo