Extensive Monte-Carlo simulations were performed to study bond percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic (b.c.c.) lattices, using an epidemic kind of approach. These simulations provide very precise values of the critical thresholds for each of the lattices: pc(s.c.) = 0.248 812 6(5), pc(f.c.c.) = 0.120 163 5(10), and pc(b.c.c.) = 0.180 287 5(10). For p close to pc, the results follow the expected finite-size and scaling behavior, with values for the Fisher exponent $tau$ (2.189(2)), the finite-size correction exponent $omega$ (0.64(2)), and the scaling function exponent $sigma$ (0.445(1)) confirmed to be universal.Comment: 16 pgs, 7 figures, LaTeX, to be published in Phys. Rev.

Precise values for the critical threshold for the three-dimensional “Swiss cheese” continuum percolation model have been calculated using extensive Monte Carlo simulations. These simulations used a growth algorithm and memory blocking scheme similar to what we used previously in three-dimensional lattice percolation. The simulations yield a value for the critical number density $n_c\text{=0.652\hspace{0.05em}960±0.000\hspace{0.05em}005,}$ which confirms recent work but extends the precision by two significant figures.

All-atom molecular dynamics simulations have been used to investigate the adsorption of low molecular weight hyaluronic acid to lipid membranes.