Diffusive transport through a double-cone channel under stochastic resetting.

We study three-dimensional diffusive transport of particles through a double-cone channel under stochastic resetting by means of the modified Fick-Jacobs equation. Exact analytical expressions for the unconditional first-passage density and the mean first-passage times in the channel are obtained, and their behavior as a function of the resetting rate is highlighted. Our results show a difference in the mean first-passage times between a narrow-wide-narrow and wide-narrow-wide double-cone geometry. We find in the narrow-wide-narrow double-cone channel with absorbing boundaries a discontinuous transition for the optimal resetting rates, which is not present for the wide-narrow-wide double-cone channel. Furthermore, it is shown how resetting can expedite or slow down the escape of the particle through the double-cone channel. Our results extend the solutions obtained by Jain et al. [J. Chem. Phys. 158, 054113 (2023)].