The table below has links to the movies. The movies differ slightly from the figures in the text so a description of what is shown in them is also provided. 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.
Because these movies are smaller than the F ring movies below, only full sized versions are supplied. 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. Axis labels are not present in these movies so one should refer to the paper to see the details of the geometry of the simulation cell. The number in the top left corner shows the location of the leading azimuthal edge in synodic radians.
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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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||||
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High
|
Mid
|
Low
|
MPEG-4
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|||||
|
A
|
62500
|
10.64
|
0.7
|
124.6
|
||||
|
B
|
62500
|
10.64
|
0.5 |
89.0
|
||||
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C
|
250000
|
5.32
|
0.7
|
62.3
|
||||
|
D
|
250000
|
5.32
|
0.5
|
44.5
|
||||
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E
|
1000000
|
2.66
|
0.5
|
22.3
|
||||
|
F
|
250000
|
5.32
|
0.0
|
0.0
|
||||
These movies all have three colored panels. With one exception, they also have a fourth panel to show detail from one of the others. The top panel, which is colored blue, shows the magnitude of the forced eccentricity of the particles. The Cartesian particle positions are used for calculating the colors and it saturates at 5e-5. This figure is most helpful for seeing when the ring passes the moon, and what part of the ring passes the moon at apoapse. The second panel, which is in green, shows the density of particle guiding centers in units like optical depth and saturates at 0.02. This shows where particles are by they semimajor axis and their mean anomoly instead of their actual position. This panel is the most useful in seeing how the system is evolving because the epicyclic motion of the ring particles around their guiding centers happens on a rather short timescale and this averages it out. The third panel, which is white, shows the particles by position as optical depth and also saturates at 0.02. This is basically what the ring would look like at any given time and it is where one would look for features that resemble those seem in F ring observations. In some of the movies this will look somewhat jumpy because there are not many frames per orbital period. If there is a fourth frame, it is a section of the third that is closer to a 1:1 aspect ratio. The geometry of the panels is discussed below.
Each panel, except the fourth, 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. Axis labels are not present in these movies so one should refer to the paper to see the details of the geometry of the simulation cell. Each frame has a number printed in the top left corner showing the location of the leading edge of the cell. Unlike the figures in the paper, this is the left edge in the movies and particles move from right to left relative to the moon. For those familiar with guiding center coodinates, in these plots X increases upward and Y increases to the right. The azimuthal extent of the cell is always the distance a particle would move relative to the moon in one oribtal period. The radial extent is given in the table below units such that 1 in the semimajor axis of Prometheus (roughly 140,000km) and it is measured as a distance outside the orbit of Prometheus.
The versions with high temporal resolution (a frame every 100 timesteps) look much better when viewing the actual particle positions, but are significantly longer. If one has the capabilities, we strongly recommend viewing the last movie as it has the most impressive display of how these systems evolve and the types of structures that can be formed.
For those trying to get the bigger picture, remember that this simulation cell is roughly 3 degrees long, but the boundaries are not pure periodic. As such, the same image would not be repeated before and after this one. The boundaries are instead what one might called "sheared periodic" so to the left of the image one can imagine a similar image, but one which has been sheared so that the straight vertical edge on the leftt is tipped over to match the edge on the right. The version on the other side would be sheared the other way. Of course, the real system wouldn't be even that periodic and the versions on the left and right might resemble the particle distribution at those locations during other synodic periods or it is possible that slight differences in particle histories will cause particles to accumulate in ways that we can't model with our semi-periodic boundary conditions.
The full size version of the movies are 1600 pixels across and between 700 and 750 pixels tall. If your screen can handle 1600 pixels across, this is the ideal format to view the movies in, as that is the resolution the data was binned at. If that is too big for your screen, the small versions are half the size in both directions. As one would guess, the small versions also are shorter in total bytes if your connection to this server is not that fast. In all cases though you should watch to the end of the movie because that is where many of the most interesting features occur.
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Radial Extent
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Timesteps per Frame
|
Corresponding Figures
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QuickTime Movies
|
|||
|
High
|
Mid
|
Low
|
MPEG-4
|
|||
|
0.0063-0.0069
|
100
|
3, 4, 5, 6
|
||||
|
0.0065-0.0067
|
1000
|
7, 8, 9
|
||||
|
0.0066-0.0068
|
1000
|
10, 11, 12
|
||||
|
0.0065-0.0068
|
100
|
13, 14, 15, 16, 17, 18
|
||||