The table below has links to the movies. We provide several bandwidth versions of every movie. The low bandwidth versions will be sufficient to give you some feel for what happens in the simulation, but they lack significantly in quality. If at all possible, you want to view the high bandwidth versions. We provide movies in QuckTime .mov and MPEG-4 .mp4 formats and we have been able to view them in QuickTime and RealPlayer under Windows and Totem and xanim under Linux (QT Movies only). If you think that you might be watching a movie more than once, please feel free to right click on it and save it for your personal viewing. This will make performance better for you and network bandwidth happier for us. Be warned that the largest movie is over 1GB though so you will need some free disk space to do this. The MPEG-4 version retains much of the quality of the high bandwidth QuickTime and has a much smaller file size if you are able to view it. The MPEG-4 movie is only at the full resolution. When you first start viewing the movies we suggest trying a low bandwidth version first simply to see if it works, then you can try the higher bandwidth version.
These movies show the evolution of the self-gravitating systems. Each one shows four panels that display different values in the simulation to help the viewer better understand the dynamics of the system. The first panel shows the particles by their positions. That is to say that they basically show what one might expect to see if one were tracking a group of particles moving down away from Pan near the edge of the Encke gap. The white in these images has been stretched so that it saturates at an optical depth of 0.5. The green image shows the density of guiding centers as discussed in the paper and has been stretched to saturate at 0.4. The blue shows the magnitude of the forced eccentricity. It saturates at 2.5e-5. Lastly, the red image shows the epicyclic phases of the particles. The color is black at -PI radians and saturates at PI radians. The way this angle is measured in guiding center coordinates, 0.0 is periapse and both PI and -PI are apoapse.
If your connection can support it, it is strongly recommended that you use the high or mid bandwidth versions as the low bandwidth version loses much of the details.
One comment should be made on the guiding center display. Unlike the other panels, this one is binned in guiding center X and Y. In all the panels, the azimuthal bounds are set so that they will include all particles while the radial bounds are fixed at 0.00119 and 0.00131 (in units of Pan semimajor axes, roughly 133,000km as measured outward from Pan's orbit). Because of this, the guiding center panel seems a bit compressed and the guiding center coordinates "undulate" as the particles move about their orbits. This undulation is caused by the fact that the particle positions and guiding center positions are not the same, and the boundary conditions have to be applied to one. Since the collisions happen in physical space it was decided that the boundary conditions would be applied in this space to keep the physical distribution square. In these simulations that has a very visible impact because the forced eccentricities are a large fraction of the cell size.
One feature of these movies that might confuse many viewers is the way the moon wakes move only outward, but never back in. The particles, of course, do move outward and inward repeatedly. This phenomenon is analogous to waves at a beach. A small collection of water makes excursions toward the shore and away, but on average doesn't go anywhere. Our eyes focus on the waves though which, because of the organized motion of the water, appear to move inward. The moon wake peaks occur at particular epicyclic phase angles. Because of shear, particles on the inner edge are futher ahead in their orbits than the particles directly outside of them. The result is that the compressed regions propogate outward constantly. This collective behaviors though does not require any net motion of the individual particle.
Also, all of these movies have one frame every 100 timesteps of the simulation. Each panel shows the entire simulation region. The vertical axis is the radial direction increasing in distance from both Saturn and the moon as one goes up a panel. The number in the top left corner shows the location downstream from the moon in radians. The simulation cell is square.
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Particle Count
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Particle Radius (m)
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Internal Density (g/cm^3)
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Surface Density (g/cm^2)
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Movies
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||||
|
High
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Mid
|
Low
|
MPEG-4
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|||||
|
A
|
62500
|
10.64
|
0.7
|
124.6
|
||||
|
B
|
62500
|
10.64
|
0.5 |
89.0
|
||||
|
C
|
250000
|
5.32
|
0.7
|
62.3
|
||||
|
D
|
250000
|
5.32
|
0.5
|
44.5
|
||||
|
E
|
1000000
|
2.66
|
0.5
|
22.3
|
||||
|
F
|
250000
|
5.32
|
0.0
|
0.0
|
||||
Poster from conference in different formats. (PowerPoint, OpenOffice, PDF) Note that the PDF version is lacking in quality.