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Silicon and Astronomy II© Wesley Colley
Computers and Theoretical Cosmology
The field of astrophysics that has benefitted most directly, perhaps, is theoretical cosmology, which relies heavily upon simulations of the entire Universe. A simulation computes the gravitational force at each point in space, and moves mass about just as gravity would. Since Newton's law of gravity has a very simple form, simulating a large number of particles is possible. Not until very recently, however, have computers become sufficiently powerful to evolve the millions of particles necessary to understand the Universe from the scale of galaxies, all the way up to the horizon scale. A simulation that dynamic requires a three-dimensional grid of mass elements, 512x512x512 in size; that's 132 million mass elements that have to be kept track of. If each element requires only two bytes of memory, one has to have 262 megabytes of RAM on board the computer. In practice, several gigabytes are necessary to keep track of individual particles within the grid, and their physical properties, such as temperature and viscosity. Speed is also a grave concern in these simulations. Gravity, although simple has a complicating circumstance: at each time-step in a simulation, the gravitational force of every particle on every other has to be computed. Such a problem is called an N^2 problem, because the number of calculations increases as the number of particles squared. That's 18 quadrillion calculations per time-step. Fortunately, one can invoke a mathematical trick, called a Fourier transform to reduce the problem to an "N log N" problem, which, in this case, reduced the number of calculations from 18 quadrillion to several billion. Several billion operations is still a LOT of processing, and requires the fastest possible chips. These days, supercomputers have many chips onboard, and simulation programs are written to use many of the chips at once. A very powerful machine resides at Princeton University. It has 64 300-MHz chips and several gigabytes of memory. Such a computer can do billions of operations per second, which allows cosmological simulations to execute within non-cosmological times. Cosmological simulations have shed much needed light on our understanding of the Universe. Observations allow us to determine which simulations match best with the present Universe, and hence which are most realistic. The parameters of that simulation become favored over those of other simulations. The currently favored models indicate that we are living an a Universe that will never stop expanding, one in which gravity dominantly creates structures, and collects gas into galaxies and stars . . . facts that were in great dispute only Go To Page: 1 2 |
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