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dc.contributor.authorBurger, Martin
dc.contributor.authorHaskovec, Jan
dc.contributor.authorMarkowich, Peter A.
dc.contributor.authorRanetbauer, Helene
dc.date.accessioned2019-12-08T10:39:52Z
dc.date.available2019-04-28T13:14:51Z
dc.date.available2019-11-17T09:41:29Z
dc.date.available2019-12-08T10:39:52Z
dc.date.issued2019-12-06
dc.identifier.citationBurger, M., Haskovec, J., Markowich, P., & Ranetbauer, H. (2019). A mesoscopic model of biological transportation networks. Communications in Mathematical Sciences, 17(5), 1213–1234. doi:10.4310/cms.2019.v17.n5.a3
dc.identifier.doi10.4310/cms.2019.v17.n5.a3
dc.identifier.urihttp://hdl.handle.net/10754/632535
dc.description.abstractWe introduce a mesoscopic model for natural network formation processes, acting as a bridge between the discrete and continuous network approach proposed in [D. Hu and D. Cai, Phys. Rev. Lett., 111(13):138701, 2013]. The models are based on a common approach where the dynamics of the conductance network is subject to pressure force effects. We first study topological properties of the discrete model and we prove that if the metabolic energy consumption term is concave with respect to the conductivities, the optimal network structure is a tree (i.e., no loops are present). We then analyze various aspects of the mesoscopic modeling approach, in particular its relation to the discrete model and its stationary solutions, including discrete network solutions. Moreover, we present an alternative formulation of the mesoscopic model that avoids the explicit presence of the pressure in the energy functional.
dc.description.sponsorshipH.R. acknowledges support by the Austrian Science Fund (FWF) project F 65. M.B. acknowledges support by ERC via Grant EU FP 7 - ERC Consolidator Grant 615216 LifeInverse. M.B. would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Variational Methods for Imaging and Vision, where work on this paper was undertaken, supported by EPSRC grant no EP/K032208/1 and the Simons foundation.
dc.publisherInternational Press of Boston
dc.relation.urlhttps://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0017/0005/a003/
dc.rightsArchived with thanks to Communications in Mathematical Sciences
dc.titleA mesoscopic model of biological transportation networks
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalCommunications in Mathematical Sciences
dc.eprint.versionPost-print
dc.contributor.institutionDepartment Mathematik, Friedrich-Alexander Universität Erlangen-Nürnberg, Erlangen, Germany
dc.contributor.institutionFaculty of Mathematics, University of Vienna, Austria
pubs.publication-statusPublisheden_US
dc.identifier.arxivid1806.00120
kaust.personHaskovec, Jan
kaust.personMarkowich, Peter A.
refterms.dateFOA2019-04-29T06:21:49Z
dc.date.posted2018-05-31


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