NLSM 3D AMR Research
The Singularity Threshold of the Nonlinear
Sigma Model Using 3D Adaptive Mesh
LANL preprint: gr-qc/0202093
Movie of near critical evolution: (4/17)
(Doesn't show coarsest grid)
X-Y Plane; Smooth Mesh (1MB MPG)
Y-Z Plane; Smooth Mesh (1MB MPG)
1D Cuts through X and Z axes; (6MB MPG)
Recent Movies: (4/02)
X-Y Plane; Smooth Mesh (4MB MPG)
X-Y Plane; Wire Mesh (4MB MPG)
Y-Z Plane; Smooth Mesh (4MB MPG)
Y-Z Plane; Wire Mesh (4MB MPG)
|Two colliding pulses
X-Y Plane; Smooth Mesh (3MB MPG)
X-Y Plane; Wire Mesh (3MB MPG)
|Spinning Ellipsoidal Pulse (Spinning about z-axis) Singularity Forming
X-Y Plane; Smooth Mesh (0.5MB MPG)
X-Y Plane; Wire Mesh (0.5MB MPG)
More Recent Results: (11/01)
- Near critical evolution (0.5 MB).
- Zooming in at critical time on above solution (0.3 MB).
- Monopole (0.3 MB) pair collapse in a different model (easily adapted from NLSM code).
Preliminary Results: (8/30/01)
Spherically symmetric and time symmetric pulse in chi:
- Movie of near-critical chi (z=0 slice).
Any self-similarity demonstrated by the solution is not clear
in this movie because it's hard to see the dynamics on the various
scales. However, the following demonstrates it more clearly at
the expense of cutting out much of the data.
- Movie of near-critical chi. Here,
an x=0, y=0, z>=0 cut is shown versus log(r). This is analogous
to such plots done with explicitly spherically symmetric adaptive
codes. The solution shows the familiar self-similar behavior chi(r/t).
Movie of chi with
bounding boxes on the various grids (z=0 slice).
Movie of the near-critical energy density (z=0 slice).
The above movies appear not to work on non-SGI systems. I've since
changed the process by which I make them so that future movies won't
have this problem. I've also fixed up the data output from the code,
so that you don't see as much flashing and the video looks better.
Again, let me say these are preliminary results.
One other thing about the above. In this nlsm model, I use a generalized
hedgehog ansatz which requires somewhere that the field goes to zero.
I fix the field to be zero at the origin, and that's why you see the zero
point at the origin in the above.
Last updated April 15, 2002.
Copyright 2000 S.L. Liebling
Research Supported by NSF