Predicting fiber contact in a three-dimensional model of paper

We present a new methodology for the mathematical analysis of 3D paper stru cture and apply it to a model that can be simulated on a computer. We rigor ously derive upper and lower bounds for fiber contact areas, and derive an approximation that is very close to values calculated from the simulations. The method involves the stochastic geometry and combinatorics of large num bers of randomly located sets, which quantify the interactions between fibe rs. The main calculation involves a sum resembling a partition function wit h many-body interactions of all orders.