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1) denotes ah ordinary d-dimensional vector, with d the spatial dimensionality.
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33646103379
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note
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l〉 = ρ, in stark contrast to what we observe here (Figure 3) for an inhomogeneous fluid.
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note
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excl were chosen to emphasize this structure; see section III.
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note
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Although we have not proven that the atom-centered local-density distribution must converge to the hard-sphere limit at high temperatures, we have explicitly verified this result for our model system by simulation.
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The reader should recognize that this separation is not necessarily, and, in fact, probably is not, equivalent to the long-range/short-range or direct/indirect breakdown often made on the basis of the Ornstein-Zernike equation (Hansen, J.-P.; McDonald, I. R. Theory of Simple Liquids, 2nd ed.; Academic Press: London, 1986), and discussed in earlier works by one of us (ref 15).
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Or, more rigorously, at the point of maximum compressibility along the (possibly noncritical) isotherm
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Or, more rigorously, at the point of maximum compressibility along the (possibly noncritical) isotherm.
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