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The role of dynamics in shaping fluvial and vascular topology

Program in Applied Mathematics Colloquium

The role of dynamics in shaping fluvial and vascular topology
Series: Program in Applied Mathematics Colloquium
Location: Zoom Meeting
Presenter: Eleni Katifori, Department of Physics and Astronomy, University of Pennsylvania

Flow networks are ubiquitous in nature, spanning a broad range of length scales, from microns in the human microcirculation to kilometers in river networks. The structure of these networks, as quantified by the topology and the edge diameters, is not immutable, but subject to gradual change, at timescales that can be days, as in the case of human circulation, to decades, in fluvial systems. These changes are frequently brought about by flow that runs through the channels, providing an active feedback that leads to self-organization. In this talk we will explore how short timescale dynamics in the flow alters the topology of the network in longer timescales, and shapes its morphology. We first will present the system of phenomenological flow equations that govern the structural evolution of flow networks. We will then demonstrate how implicit of explicit dynamics in the boundary conditions can drastically alter the network topology, and discuss the implications for the development and function of human circulation. Moving to a larger system, will provide evidence that the same dynamics developmental rules that are thought to control vascular remodeling in humans also shape tidal delta geomorphology.


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