  Waves propagate through disordered systems in a variety of regimes. There is
a threshold of disorder beyond which waves become localized and transport
becomes restricted. The intensity I of the wave transmitted through a system
has a dependence on the length L of the sample that is characteristic of the
regime. For example, I decays as 1/L in the diffusive regime. It is of current
interest to characterize the transport regime of a wave from statistical
studies of the transmittance quantities through it. Studies suggest that the
probability distribution of the intensity could be used to characterize the
localized regime. There is an ongoing debate on what deviations from the
classical Rayleigh distribution are to be expected. In this numerical work, we
use scalar waves to obtain the intensity, transmission, and conductance of
waves through a disordered system. We calculate the intensity, by setting an
incoming plane wave towards the sample from a fixed direction. The outgoing
intensity is then calculated at one point in space. This process is repeated
for a collection of samples belonging to the same ensemble that characterizes
the disorder, and we construct the probability distribution of the intensity.
In the case of transmission, we evaluate the field arriving to a series of
points distributed in the far field, and repeat the same statistical analysis.
For the conductance, we calculate the field at the same series of points for
incoming waves in different directions. We analyze the distribution of the
transmittance quantities and their change with the degree of disorder.

Disordered Systems and Neural Networks;Materials Science