Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Monday, November 5, 2018 - 12:00 to 12:45

Location:

STAG 160

Event Link:

Guest Speaker:

Institution:

Department of Mathematics "Tullio Levi-Civita" University of Padova, Italy

Abstract:

Recently we derived a novel formulation called the Dynamic Monge-Kantorovich equations for the simulation of optimal transportation problems, and in particular the Wasserstein-1 OT. An extension of this model considers a time derivative of the transport density that grows as a power law of the transport flux counterbalanced by a linear decay term that maintains the density bounded. A sub-linear growth penalizes the flux intensity (i.e. the transport density) and promotes distributed transport. Corresponding equilibrium solutions are reminiscent of Congested Transport Problems. On the contrary, a super-linear growth favors flux intensity and promotes concentrated transport, leading to the emergence of steady-state ``singular'' and ``fractal-like'' configurations that resemble those of the Branched Transport Problem. We discuss the structure of this formulation, its numerical solution, and applications to natural phenomena, such as the growth of plant roots, formation of river networks, as well as biological applications such as the simulation of the Purkinje network. We will also discuss some connections with compressed sensing and basis pursuit problems.

This work is by Enrico Facca, Franco Cardin, and Mario Putti.