Abstract:In a one-dimensional molecular timing channel with a perfectly absorbing receiver, constant positive drift yields an inverse-Gaussian (IG) first-hitting-time distribution, whereas pulsatile drift makes the arrival statistics depend on the molecular release phase. We propose a phase-normalized corrected inverse-Gaussian (C-IG) approximation for pulsatile drift with positive mean. The model combines an exponential term determined by cumulative drift with a Gaussian positive-part prefactor. A phase-dependent normalization factor ensures unit probability mass. For a known periodic environment, these factors can be tabulated offline, enabling subsequent pointwise density evaluation without solving a time-recursive integral equation. The model also recovers the classical IG law exactly under constant positive drift. Comparisons with a numerical Volterra solution and independent particle simulations assess both density and cumulative-distribution accuracy. In a representative pulsatile case, C-IG better captures the oscillatory density structure than constant-drift IG models, while an oracle IG fit achieves a smaller cumulative-distribution error. An amplitude-frequency sweep over release phases at a fixed Peclet number identifies the operating regimes in which C-IG meets prescribed accuracy criteria. Most tested settings below the flow-reversal threshold meet these criteria, whereas transient flow reversal substantially reduces accuracy and can lead to discrepancies in density peak counts. These results support C-IG as a computationally convenient model for phase-dependent arrival statistics within its numerically assessed range of validity.
From: Yen-Chi Lee [view email]
[v1]
Tue, 17 Feb 2026 03:47:40 UTC (168 KB)
[v2]
Fri, 27 Mar 2026 04:19:54 UTC (168 KB)
[v3]
Sun, 28 Jun 2026 06:24:01 UTC (85 KB)
[v4]
Sun, 6 Sep 2026 09:36:37 UTC (184 KB)
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