Branching structures emerging from a continuous optimal transport model

Recently a Dynamic-Monge-Kantorovich formulation of the PDE-based -optimal transport problem was presented. The model considers diffusion equation enforcing balance transported masses with time-varying conductivity that evolves proportionally to flux. In this paper we present an extension time derivative grows as power-law flux exponent ?>0. A sub-linear growth (01) favors concentrated leading emergence steady-state “singular” “fractal-like” configurations resemble those Branched We derive numerical discretization proposed is accurate, efficient, robust for wide range scenarios. For ?>1 able reproduce highly irregular fractal-like formations without any a-priory structural assumption.