Porosity and conductivity in ballistic deposition with power-law distributed noise

The The ballistic deposition (PD) model of rod-like particles with power-law distributed noise is studied by the Monte Carlo simulation. In this modified model instead of particles with fixed unit sizes, vertical rods whose length follows the power-law distribution P(l)similar to l(-(mu+1)) are deposited, where mu denotes the power-law strength exponent. This deposition leads to porous rock structures with varying porosity and conductivity. The time evolution of the surface roughness and the porosity of the resulting structures are studied. The conductivity of the structures is calculated using the parallel resistors in the percolation model using a random walk algorithm. Finally, we discuss the relation between porosity, conductivity and the strength exponent of the power-law noise. The results show that the surface roughness increases as a pseudo-step function versus deposition time for mu=1, which leads to an observable reduction in porosity and conductivity. By increasing the mu exponent, the growth exponent of beta=0.33 +/- 0.02 for the Gaussian model appears. The conductivity increases as s=sigma(0)exp(Phi/phi) versus porosity, f, and remains constant for mu >= mu(c)= 5 which the value of mu(c)= 5 has been identified for PD.