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dc.contributor.authorHaskovec, Jan
dc.contributor.authorMarkowich, Peter A.
dc.contributor.authorPilli, Giulia
dc.date.accessioned2019-10-22T13:27:52Z
dc.date.available2019-10-22T13:27:52Z
dc.date.issued2019-09-09
dc.identifier.citationHaskovec, J., Markowich, P., & Pilli, G. (2019). Murray’s law for discrete and continuum models of biological networks. Mathematical Models and Methods in Applied Sciences, 1–18. doi:10.1142/s0218202519500489
dc.identifier.doi10.1142/S0218202519500489
dc.identifier.urihttp://hdl.handle.net/10754/659074
dc.description.abstractWe demonstrate the validity of Murray's law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biological networks. We first consider discrete networks with general metabolic coefficient and multiple branching nodes and derive a generalization of the classical 3/4-law. Next we prove an analogue of the discrete Murray's law for the continuum system obtained in the continuum limit of the discrete model on a rectangular mesh. Finally, we consider a continuum model derived from phenomenological considerations and show the validity of the Murray's law for its linearly stable steady states.
dc.description.sponsorshipGiulia Pilli acknowledges support from the Austrian Science Fund (FWF) through the grants F 65 and W 1245.
dc.publisherWorld Scientific Pub Co Pte Lt
dc.relation.urlhttps://www.worldscientific.com/doi/abs/10.1142/S0218202519500489
dc.rightsElectronic version of an article published as [Mathematical Models and Methods in Applied Sciences, [Volume], [Issue], 2019] DOI:10.1142/S0218202519500489 © [copyright World Scientific Publishing Company]
dc.subjectBiological transportation networks
dc.subjectMurray’s law; Continuum limit.
dc.titleMurray's law for discrete and continuum models of biological networks
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalMathematical Models and Methods in Applied Sciences
dc.rights.embargodate2020-01-01
dc.eprint.versionPost-print
dc.contributor.institutionFaculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna
kaust.personHaskovec, Jan
kaust.personMarkowich, Peter A.
refterms.dateFOA2019-10-31T07:10:41Z


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