2014/12/03 by Giuseppe Forte, Fabio Cecconi, Angelo Vulpiani
Mathematics · Physics and Astronomy · #Computer science #Diffusion #Dissipation #Mathematical analysis #Mathematics #NMR spectroscopy and applications #Physics #Section (typography) #Spectroscopy and Quantum Chemical Studies #Thermodynamics #Variable (mathematics) #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.90.062110
published as Phys. Rev. E vol. 90, 062110 (2014) · RevTeX 4-1, 11 Pages, 11 pdf figures
openalex publication_date 2014/12/03 · arxiv created 2014/12/10 · arxiv updated 2014/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the asymptotic and preasymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient D(eff) is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries, considering even cases of steep variations of the channel boundaries. Moreover, we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known Fick-Jacobs approximation. Building an effective one-dimensional equation for the longitudinal diffusion, we obtain an approximation for the effective diffusion coefficient. Such a result goes beyond a perturbation approach, and it is in good agreement with the actual values obtained by the numerical simulations. We discuss also the preasymptotic diffusion which is observed up to a crossover time whose value, in the presence of strong spatial variation of the channel cross section, can be very large. In addition, we show how the Einstein's relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and preasymptotic regimes.