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Author Berezhkovskii, Alexander M. ♦ Shvartsman, Stanislav Y.
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY ♦ BOUNDARY CONDITIONS ♦ DIFFUSION ♦ INSECTS ♦ OXYGEN ♦ SIMULATION
Abstract Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.
ISSN 00219606
Educational Use Research
Learning Resource Type Article
Publisher Date 2016-05-28
Publisher Place United States
Journal Journal of Chemical Physics
Volume Number 144
Issue Number 20


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