{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/branching-structures-emerging-from-a","title":"Branching structures emerging from a continuous optimal transport model","arxiv_id":"1811.12691","date":"2018-11-30","proceeding":null,"authors":["Enrico Facca","Franco Cardin","Mario Putti"],"abstract":"Recently a Dynamic-Monge-Kantorovich formulation of the PDE-based $L^1$-optimal transport problem was presented. The model considers a diffusion equation enforcing the balance of the transported masses with a time-varying conductivity that volves proportionally to the transported flux. In this paper we present an extension of this model that considers a time derivative of the conductivity that grows as a power law of the transport flux with exponent $\\beta>0$. A sub-linear growth ($0<\\beta<1$) penalizes the flux intensity and promotes distributed transport, with equilibrium solutions that are reminiscent of Congested Transport Problems. On the contrary, a super-linear growth ($\\beta>1$) favors flux intensity and promotes concentrated transport, leading to the emergence of steady-state \"singular\" and \"fractal-like\" configurations that resemble those of Branched Transport Problems. We derive a numerical discretization of the proposed model that is accurate, efficient, and robust for a wide range of scenarios. For $\\beta>1$ the numerical model is able to reproduce highly irregular and fractal-like formations without any a-priory structural assumption.","url_abs":"https://arxiv.org/abs/1811.12691v2","url_pdf":"https://arxiv.org/pdf/1811.12691v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"branching-structures-emerging-from-a","repo_url":"https://github.com/enricofacca/dmk_l1otp","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"branching-structures-emerging-from-a","repo_url":"https://gitlab.com/enrico_facca/dmk_solver","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}