Continuum percolation threshold for interpenetrating squares and cubes.
Monte Carlo simulations are performed to determine the critical percolation threshold for interpenetrating square objects in two dimensions and cubic objects in three dimensions. Simulations are performed for two cases: (i) objects whose edges are aligned parallel to one another and (ii) randomly oriented objects. For squares whose edges are aligned, the critical area fraction at the percolation threshold phi(c)=0.6666+/-0.0004, while for randomly oriented squares phi(c)=0.6254+/-0.0002, 6% smaller. For cubes whose edges are aligned, the critical volume fraction at the percolation threshold phi(c)=0.2773+/-0.0002, while for randomly oriented cubes phi(c)=0.2168+/-0.0002, 22% smaller.
Baker
Don R
DR
Center for Polymer Studies and Department of Physics, Boston University, Massachussetts 02215, USA.
Paul
Gerald
G
Sreenivasan
Sameet
S
Stanley
H Eugene
HE