Formation and Growth of Transport Networks in Nature: From Rivers to Vascular Systems

Speaker: Prof. Piotr Szymczak
Affiliation: Faculty of Physics, University of Warsaw, Poland
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Meeting ID: 384 074 694 009
Passcode: 7fzzgY

Abstract:

Many physical processes involving moving boundaries produce branched patterns. Well-known examples include viscous fingering, electrochemical deposition, but also the formation of river networks or even vascular systems. They all involve a field (pressure, concentration, or height of the water table, depending on the problem) that drives growth, with the growth velocity dependent on the field gradient. The growing interface is often unstable to perturbations that evolve into fingers. The fingers split as they grow, with the daughter branches competing with each other for the available flux, resulting in a ramified, network-like pattern.
In this seminar, we will closely examine the dynamics of growth of such networks. In which directions and at what speeds do the branches grow? Does the growth of one branch affect the direction of another? Can we deduce the governing laws of growth by analyzing the network structure? These are the questions we will seek to answer. In particular, we will try to explain why the tributaries of Apalachicola river in Florida meet at an angle of 72 degrees.

Chairman: Prof. Ireneusz Weymann

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