1. Murray's law for discrete and continuum models of biological networks.
- Author
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Haskovec, Jan, Markowich, Peter, and Pilli, Giulia
- Subjects
- *
BIOLOGICAL models , *BIOLOGICAL networks , *PHENOMENOLOGICAL biology - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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