The neighbor network in a two-dimensional polydisperse hard-disk fluid with diameter distribution p(sigma)similar to sigma(-4) is examined using constant-pressure Monte Carlo simulations. Graphs are constructed from vertices (disks) with edges (links) connecting each vertex to k neighboring vertices defined by a radical tessellation. At packing fractions in the range 0.24 <=eta <= 0.36, the decay of the network degree distribution is observed to be consistent with the power law k(-gamma) where the exponent lies in the range 5.6 <=gamma <= 6.0. Comparisons with the predictions of a maximum-entropy theory suggest that this apparent power-law behavior is not the asymptotic one and that p(k)similar to k(-4) in the limit k ->infinity. This is consistent with the simple idea that for large disks, the number of neighbors is proportional to the disk diameter. A power-law decay of the network degree distribution is one of the characteristics of a scale-free network. The assortativity of the network is measured and is found to be positive, meaning that vertices of equal degree are connected more often than in a random network. Finally, the equation of state is determined and compared with the prediction from a scaled-particle theory. Very good agreement between simulation and theory is demonstrated.
|Number of pages||8|
|Journal||Physical Review E - Statistical, Nonlinear and Soft Matter Physics|
|Publication status||Published - Nov 2007|
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