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Not only is performance model characteristic of one dimensional problem but we also we used a one-dimension parallel decomposition
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Note these one dimensional characteristics are independent of dimension of space that particles move in.
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Normally d is thought of as dimension of physical space in which problem posed.
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But the geometrical interpretation of d is only valid where interaction between particles is itself geometrical i.e. short range
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Rather N body algorithm has no geometric structure and you see d=1 characteristic of algorithm
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See Chapter 3 of Parallel Computing Works for a longer discussion of this from a "Complex Systems" point of view
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Note the simple N-body problem has some interesting features
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Very low communication/compute ratios
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Best parallel methods violate owner computes rule -- also true in recent molecular dynamics problems with shorter range force
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Unexpected dimension
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