Time profile (intensity profile) in arbitrary linear units for particles with variable energies (see subplot titles). The distance between the particle origin and the virtual detector is L = 10ℓ₀. The various curves are as follows: The black lines show the profile as obtained from the simulations using the methods described in Sect. 3. The red lines show the three-dimensional diffusion solution (with the normalization factor as an open parameter) from Eq. (7)using the diffusion coefficients as obtained from the simulations via the mean-square displacements. In addition, the result from Eq. (8)is shown for constant diffusion coefficients taken from the simulations (blue lines), i.e., κ_i(t = t_max).