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.

Jan Haskovec

Jan Haskovec

Senior Research Scientist, Applied Mathematics and Computational Sciences

random process transportation networks Differential equations Dynamical Systems

Stochastic, partial and functional differential equations applied to study of dynamical processes in physics, biology and social sciences. Optimal transportation networks. Consensus formation with applications to engineering (swarm robotics).