random process

Emergence of transportation networks as a self-regulated process

Jan Haskovec, Senior Research Scientist, Applied Mathematics and Computational Sciences

Aug 30, 15:30 - 17:00

B1 L3 R3119

random process transportation networks

In this talk, we shall explain how transportation networks emerge as a self-regulating process, with a particular focus on applications in biology (leaf venation in plants, neuronal networks in animals). We start by introducing a purely diffusive model with tensor-valued diffusivity, derived as a gradient flow of a broad class of entropy dissipations. The introduction of a prescribed electric potential leads to the Fokker-Planck equation. We show that with quadratic entropy density modeling Joule heating, the model is convex with respect to the diffusivity tensor.