but with different probabilities. In this latter case, $$\label{eq:sII}
  s = \frac{2}{\sqrt{2\pi\sigma^2} } \int_{-\infty}^{\infty}  \exp\left( -\frac{\theta^2}{2\sigma^2} \right) \cos^2 \theta \,d \theta -1.$$ The variance of the normal distribution ($\sigma^2 = \operatorname{Var}(\theta)$) is related to the desired mean order parameter as $$\label{eq:variance}
  \operatorname{Var}(\theta) = -0.5 \ln  s.$$ Figure \[fig:C0O\_OrderParameter\] shows the order parameter, $s$, versus the degree of anisotropy, $A$, for both models.

![Order parameter, $s$, versus the degree of anisotropy, $A$. Model I calculated using , Model II calculated numerically.\[fig:C0O\_OrderParameter\]](svspp){width="0.9\linewidth"}

Obviously, both the models are completely equivalent for the two limiting cases $s=0$ and $s=1$. Nevertheless, they demonstrate slightly different behaviors for intermediate values of $s$.

Computation of the electrical conductivity
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To take account of the electrical properties of both the low conductive substrate and highly conductive fillers, a discretization approach, involving a supporting mesh, viz., a square lattice of size $m\times m$ ($m=64$–2048) was used. When any part of a rod was situated inside a face (cell) of the supporting mesh, this cell was treated as nontransparent and conducting, otherwise the cell was assumed to be transparent and insulating. Such a discretization generated a “zoo of lattice animals”, i.e., a set of polyominoes of different shapes and sizes, 