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Because one run of the computer simulation is extremely sensitive to initial conditions, the only way to understand the planetary system in general is to run thousands of simulations with different initial conditions and then examine the statistical probabilities of each outcome. "You can't do just a few numerical simulations and have the answer to everything," Rasio says.
All those simulations -- each spanning 1 million to 100 million virtual years in the lives of the planets -- consume a lot of computer time. Therefore Rasio is taking advantage of the Condor computing system developed by Alliance member Miron Livny at the University of Wisconsin. Condor distributes simulations across an existing network of university workstations, taking advantage of otherwise idle time on the computers.
On a single workstation, the calculations would "take forever," Rasio says. "Here we can do thousands of integrations on the order of weeks. It's a very nice system." Rasio is also running some of the simulations on the SGI CRAY Origin2000 machine at Boston University, an Alliance member site.
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For Frederic Rasio and his collaborators, tapping into the distributed power of Condor was relatively simple.
"Condor is probably best suited to 'embarrassingly parallel' codes; that is, programs in which each processor works independently," says Eric Ford, one of Rasio's students. "For example, we're doing Monte Carlo integrations in which we give each processor one test run at a time. Each processor does the same thing over and over again, but on slightly different initial conditions. Since there's no need for interprocessor communications while running any individual simulation, Condor works well."
Rasio and Ford originally wrote the two-planets-orbiting-a-star simulation on run-of-the-mill computer workstations in late 1995. In 1996, they ported the code to a parallel-processing IBM SP2 at the Cornell Theory Center at Cornell University.
Because the computer programs were originally written on workstations, the shift to Condor -- a network of workstations -- was straightforward. Similarly, Ford says, moving the code from the SP2 to Boston University's SGI Cray Origin2000, "was easy since both have Fortran compilers and support MPI (the Message Passing Interface, a set of computer libraries to handle parallel processing)."
Condor does not support MPI, but because the original code was written to work on workstations without MPI, those sections with MPI references were easily commented out.
"The only other difference is in one line of code which opens files," Ford says. The Fortran compilers on Condor and the Origin2000, he says, "seem to disagree on the proper call for opening a file."
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According to Ford, the area that required the most work wasn't the actual computations, but rather the scripts that submit jobs to the computer and copy datafiles between magnetic tapes and disks.
"While both the Origin2000 and Condor have advantages and disadvantages, I've found the most significant differences to be in the human interaction rather than the computations or coding," Ford says. "For example, I find the Condor scheduling and transparent file handling preferable to the Origin2000's scheduler and multiple disks. On the down side, Condor requires installing software -- and upgrades -- on your own computer. This can take some time, especially if your system has a nonstandard configuration."
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Rasio published his initial results in Science in 1996 based on simulations run at the Cornell Theory Center. That paper was based on fewer than 1,000 simulations. When completed, the current round of simulations will number in the tens of thousands and will cover many variations on the configuration of planetary systems.
What he expects the simulations to confirm are current observations that planets in circular orbits are rare. That may not bode well for the possibility of extraterrestrials. With the large planets meandering about, any other planets that may have formed around a star -- the equivalent of Earth, for instance -- "are almost certainly going to be destroyed one way or another," Rasio says. "That's not particularly interesting from the point of view of developing life."
In the meantime, we may want to be thankful we have only one Jupiter.
This research was funded by the National Science Foundation, NASA, and the Alfred P. Sloan Foundation.
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