We have developed numerical codes to simulate the transport and noise properties of devices based on a two-dimensional electron gas, also in the presence of an orthogonal magnetic field, and we have applied them to the investigation of several structures. In particular, we have carried out an analysis of shot noise suppression in mesoscopic cavities as a function of the details of the potential and of the orthogonal magnetic field. Moreover, we have simulated the results achievable with electron flow imaging based on a scanning probe method. Furthermore we have numerically studied several properties of carbon nanotubes: we have determined their energy bands and density of states, using both global and local methods. We have computed the wave functions of the free electrons in the nanotube and the dispersion relations for the phonons.