title: Continuum percolation threshold for interpenetrating squares and cubes.
abstract: 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.
authors.affiliation: Center for Polymer Studies and Department of Physics, Boston University, Massachussetts 02215, USA.
authors.forename: Don R
authors.initials: DR
authors.lastname: Baker
authors.forename: Gerald
authors.initials: G
authors.lastname: Paul
authors.forename: Sameet
authors.initials: S
authors.lastname: Sreenivasan
authors.forename: H Eugene
authors.initials: HE
authors.lastname: Stanley