title: Stochastic cycle selection in active flow networks.
abstract: Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such nonequilibrium networks. Here we connect concepts from lattice field theory, graph theory, and transition rate theory to understand how topology controls dynamics in a generic model for actively driven flow on a network. Our combined theoretical and numerical analysis identifies symmetry-based rules that make it possible to classify and predict the selection statistics of complex flow cycles from the network topology. The conceptual framework developed here is applicable to a broad class of biological and nonbiological far-from-equilibrium networks, including actively controlled information flows, and establishes a correspondence between active flow networks and generalized ice-type models.
authors.affiliation: Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom; F.G.Woodhouse@damtp.cam.ac.uk.
authors.forename: Francis G
authors.initials: FG
authors.lastname: Woodhouse
authors.affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge MA 02139-4307;
authors.forename: Aden
authors.initials: A
authors.lastname: Forrow
authors.affiliation: Centre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia.
authors.forename: Joanna B
authors.initials: JB
authors.lastname: Fawcett
authors.affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge MA 02139-4307;
authors.forename: Jörn
authors.initials: J
authors.lastname: Dunkel
mesh_terms: D008962:Models, Theoretical; D055585:Physical Phenomena; D013269:Stochastic Processes
keywords: active transport; networks; stochastic dynamics; topology