David -- Thanks for checking this out.  To me the pictures look pretty 
differrent.  I see some reconnections involving thick lines.  A good 
fraction of the forces seem to change noticeably.  Wow.  But I don't see how 
your explanation can work.  In Alexei's program the beads CAN'T 
move.  The only nonlinear thing that happens is that bonds move.  Roux's 
argument says there should be a unique state even with these bond moves 
taken into account.  Meanwhile, we have to put together an answer to Roux's 
Comment; see separate note.  

This is exciting... Best, TW

On Mon, 26 Nov 2001, David Head wrote:

> Guys -
> 
>    I also don't see where anything might be going wrong with
> Roux's convexity approach, but I can at least confirm that we
> are still getting non-unique states, even with the null bonds
> accounted for.
> 
> Example: Here a system was first stabilised under a vertical load:
> 
> http://www.ph.ed.ac.uk/~dhead/strut/Not_Unique_1.pdf
> 
> restabilised under an angle of 0.2 rads, then restabilised again
> under the same vertical load as before:
> 
> http://www.ph.ed.ac.uk/~dhead/strut/Not_Unique_2.pdf
> 
> As you can see, while the networks are at first glance similar,
> there are small differences. Both networks were checked to ensure
> that all the forces on a bead balanced, so they are both physically
> correct.
> 
> It strikes me that this apparent non-uniqueness may actually correspond
> to slightly different bead geometries. If you look closely at the above 
> examples,
> you can see that some bonds have moved, which (within the approximations
> of the adaptive network algorithm) should correspond to a slight 
> alteration
> in the positions of the beads. Thus we may not be in contradiction with
> Roux's results after all, it may just be that we cannot `see' the small 
> changes
> in bead positions that we know must be taking place.
> 
> David.