FIG. 2.

The time dependences of the fraction of time spent by the particle in the main tube, f_m(t), panel (a), the mean square displacement, ⟨x²(t)⟩, panel (b), and function α(t), panel (c), defined in Eqs. (2.7), (2.9), and (3.13), respectively. Solid curves show the dependences for the tube with infinitely long dead ends, L = ∞, while the dashed lines show these dependences for tubes with dead ends of a finite length L. The values of L are given near the curves. The dependences are obtained by numerically inverting the Laplace transforms $⟨{\widehat{t}}_m\left(s\right)⟩$ and $s⟨{\widehat{t}}_m\left(s\right)⟩$, where $⟨{\widehat{t}}_m\left(s\right)⟩$ is given by Eq. (3.5) for L = ∞, and by Eq. (3.15) for L ≠ ∞, assuming that the other parameters are R = l = 1, a = 0.1, and D₀ = D_de = 1.