title: Diffusional screening in treelike spaces: an exactly solvable diffusion-reaction model.
abstract: A renormalization approach is used to derive an analytic formula for the total current crossing the reactive surface of a Cayley tree of cylindrical tubes under a Helmholtz-type approximation to the full diffusion-reaction problem. We provide analytic conditions for the emergence of a plateau in the current-a region of maximum insensitivity of the current to variations in either the reaction rate (membrane permeability) or the diffusivity. The occurrence of such a plateau is associated with a partial screening regime wherein most of the active surface is screened to incoming diffusing particles. Large trees trade efficiency for fault tolerance, a valuable feature which may provide robustness to mammalian respiratory systems and tolerance to catalytic poisoning in chemical reactors.
authors.affiliation: Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65201, USA. michael.l.mayo@usace.army.mil
authors.forename: Michael
authors.initials: M
authors.lastname: Mayo
authors.forename: Stefan
authors.initials: S
authors.lastname: Gheorghiu
authors.forename: Peter
authors.initials: P
authors.lastname: Pfeifer
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D008956:Models, Chemical; D008958:Models, Molecular; D049329:Nanostructures / Q000737:chemistry* / Q000648:ultrastructure*