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The development of massively parallel supercomputers provides a unique opportunity to advance the state of the art in $N$-body galaxy simulations. For systems with long range forces it is important to increase the number of particles to $N \ge 10^7$ particles. Increasing the number of particles reduces the sensitivity to random fluctuations, which increases the effective relaxation time of the system (decreases the rate of increase of random thermal velocities in a cold galactic disk). Significantly improved modeling of collisionless $N$-body systems can be expected by increasing $N$, arising from a more realistic representation of physical transport processes involving particle diffusion and energy and momentum transport. In addition, it will be possible to guarantee that physically significant portions of complex physical systems, such as Lindblad resonances of galaxies, will have an adequate population of particles for realistic simulation. We have developed a two-dimensional, particle-mesh (PM) galaxy simulation running on the massively parallel Connection Machine-2 which can accommodate more than 1M $(i.e. 2^{20})$ stars. These simulations exhibit well-defined spiral structure for tens of rotation periods without the introduction of artificial cooling mechanisms. The results are consistent with the slower rate of thermalization observed in these large $N$ simulations.
