Murray's law for discrete and continuum models of biological networks
Analysis of PDEs
2019-08-06 v1
Abstract
We 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.
Cite
@article{arxiv.1908.01197,
title = {Murray's law for discrete and continuum models of biological networks},
author = {Jan Haskovec and Peter Markowich and Giulia Pilli},
journal= {arXiv preprint arXiv:1908.01197},
year = {2019}
}