The diffusion equation is vital for understanding the transport properties at the nanoscale. The general form of the diffusion equation is: \[ \frac{\partial C}{\partial t} = D \nabla^2 C \] where \( C \) is the concentration, \( t \) is time, and \( D \) is the diffusion coefficient. This equation helps in analyzing processes like the diffusion of nanoparticles in a medium or the distribution of dopants in semiconductor nanowires.
