## Abstract

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.

Original language | English |
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Article number | 056108 |

Pages (from-to) | - |

Number of pages | 8 |

Journal | Physical Review E |

Volume | 76 |

Issue number | 5 |

DOIs | |

Publication status | Published - Nov 2007 |

## Keywords

- WORLD-WIDE-WEB
- STATISTICAL-MECHANICS
- BINARY ASSEMBLIES
- COMPLEX NETWORKS
- SPHERES
- LAW
- ARRANGEMENT
- MIXTURES
- TOPOLOGY
- INTERNET