2015/09/30 by Alessio Brancolini, Benedikt Wirth · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #Applied mathematics #Biochemical engineering #Combinatorics #Computer science #Diffusion and Search Dynamics #Engineering #Eulerian path #Flux (metallurgy) #Geometric Analysis and Curvature Flows #Lagrangian #Mass transport #Materials science #Mathematical optimization #Mathematics #Point processes and geometric inequalities #Preference #Ramification #Statistics #math.AP #math.CA #math.OC #msc:49Q10 #msc:49Q20 #msc:90B10
paper · pdf · doi:10.1016/j.matpur.2016.03.008
published as J. Math. Pures Appl. (9) 106 (2016), no. 4, 695-724 · Few typographical errors corrected; in press on Journal de Mathématiques Pures et Appliquées
openalex publication_date 2016/03/19 · arxiv created 2016/06/01 · arxiv updated 2017/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider two variational models for transport networks, an urban planning and a branched transport model, in both of which there is a preference for networks that collect and transport lots of mass together rather than transporting all mass particles independently. The strength of this preference determines the ramification patterns and the degree of complexity of optimal networks. Traditionally, the models are formulated in very different ways, via cost functionals of the network in case of urban planning or via cost functionals of irrigation patterns or of mass fluxes in case of branched transport. We show here that actually both models can be described by all three types of formulations; in particular, the urban planning can be cast into a Eulerian (flux-based) or a Lagrangian (pattern-based) framework.