Journal
PHYSICAL REVIEW E
Volume 106, Issue 6, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.106.064137
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- [53,54]
- [14,55]
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The statistical behavior of crossing time of diffusing particles in expanding and narrowing two-dimensional conical channels under an external gravitational field was studied. It was found that the effective diffusivity decreases with increasing amplitude of the external potential, and the mean first-passage time for crossing the channel assumes a minimum at finite values of the potential amplitude.
We study the crossing time statistic of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels under a transverse external gravitational field. The theoretical expression for the mean first-passage time for such a system is derived under the assumption that the axial diffusion in a two-dimensional channel of smoothly varying geometry can be approximately described as a one-dimensional diffusion in an entropic potential with position-dependent effective diffusivity in terms of the modified Fick-Jacobs equation. We analyze the channel crossing dynamics in terms of the mean first-passage time, combining our analytical results with extensive two-dimensional Brownian dynamics simulations, allowing us to find the range of applicability of the one-dimensional approximation. We find that the effective particle diffusivity decreases with increasing amplitude of the external potential. Remarkably, the mean first-passage time for crossing the channel is shown to assume a minimum at finite values of the potential amplitude.
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