  We study by means of Monte-Carlo numerical simulations the resistance of
two-dimensional random percolating networks of stick, widthless nanowires. We
use the multi-nodal representation (MNR) to model a nanowire network as a
graph. We derive numerically from this model the expression of the total
resistance as a function of all meaningful parameters, geometrical and
physical, over a wide range of variation for each. We justify our choice of
non-dimensional variables applying Buckingham $\pi-$theorem. The effective
resistance of 2D random percolating networks of nanowires is found to write as
$R^{eq}(\rho,R_c,R_{m,w})=A\left(N,\frac{L}{l^{*}}\right) \rho l^* +
B\left(N,\frac{L}{l^{*}}\right) R_c+C\left(N,\frac{L}{l^*} \right) R_{m,w}$
where $N$, $\frac{L}{l^{*}}$ are the geometrical parameters (number of wires,
aspect ratio of electrode separation over wire length) and $\rho$, $R_c$,
$R_{m,w}$ are the physical parameters (nanowire linear resistance per unit
length, nanowire/nanowire contact resistance, metallic electrode/nanowire
contact resistance). The dependence of the resistance on the geometry of the
network, one the one hand, and on the physical parameters (values of the
resistances), on the other hand, is thus clearly separated thanks to this
expression, much simpler than the previously reported analytical expressions.
