This work is devoted to the study of unbiased diffusion of point-like Brownian particles through channels with radial symmetry of varying cross-section and elliptic shape. The effective one-dimensional reduction is used with distinct forms of a position-dependent diffusion coefficient, D(x), found in literature, to obtain expressions for (I) narrow escape times from a single open-ended tube, (II) its correspondent effective diffusion coefficient, both as functions of the eccentricity of the tube, ε, where ε = 0 returns the system to a spherical vesicle with two open opposite sides, and (III) finally, Lifson-Jackson formula that is used to compute expressions to assess the mean effective diffusion coefficient for a periodic elliptic channel formed by contacting ellipses, also as a function of the eccentricity. Mathematical expressions are presented and contrasted against computational simulations to validate them.
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