We have studied the contact network properties of two and three dimensionalpolydisperse, frictionless sphere packings at the random closed packing densitythrough simulations. We observe universal correlations between particle sizeand contact number that are independent of the polydispersity of the packing.This allows us to formulate a mean field version of the granocentric model topredict the contact number distribution P(z). We find the predictions to be ingood agreement with a wide range of discrete and continuous size distributions.The values of the two parameters that appear in the model are also independentof the polydispersity of the packing. Finally we look at the nearest neighbourspatial correlations to investigate the validity of the granocentric approach.We find that both particle size and contact number are anti-correlated whichcontrasts with the assumptions of the granocentric model. Despite thisshortcoming, the correlations are sufficiently weak which explains the goodapproximation of P(z) obtained from the model.
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