Algorithm to compute void statistics for random arrays of disks

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Abstract
In many-particle systems, the void space (the space not occupied by the particles themselves) is of great interest because of its rich topological features and because it is key in determining the macroscopic properties of the system. Unfortunately, the complex shape and connectedness properties of the void space make precise measurements of quantities that characterize it very difficult, and such measurements must often be made by crude sampling techniques. In this paper we present a method by which void characteristics in random systems of disks can be calculated exactly, in principle. This procedure allows us to compute with very high precision ‘‘void’’ nearest-neighbor distribution functions over a wide range of disk densities. A comparison of these nearest-neighbor measurements to recent theoretical predictions reveals that the predictions are highly accurate.