Ordered packing of elastic wires in a sphere

In this paper we study the ordered packing of wires in a sphere. We propose an analytical model and compare the model predictions with the results of our experiments and simulations for the maximum packing fraction, the number of formed coils, the fractal dimension, and bending energy. We show that the relative system size [i.e., the ratio of the wire radius to the sphere radius (a/R)] is the most important control parameter for the maximum packing fraction. We find that the number of coils obeys a power-law relation of the form N∼(R/a){1.5} and the fractal dimension of the structures is 2.5, independent of the system size. Our theoretical results are in good agreement with the experimental data and the predictions of the numerical simulations.