Discrete models of elastic growth and vascular solute transport

Alexander Erlich (University of Manchester)

Thursday 4th October, 2018 14:00-15:00 Maths 311B


When evaluated over a network, there is an elegant equivalence between electric circuits governed by Ohm’s Law, elastic networks governed by Hooke’s Law, and flow networks governed by Poiseuille’s Law. For each application, the network topology can be clearly encoded in an edge-node incidence matrix. Then, a physical law (Ohm, Hooke, Poiseuille) can be stated in terms of the incidence matrix. In this framework it is easy to couple further fields that arise in application. 

We present two applications: 
1) The blood flow and solute transfer in feto-placental capillary networks (in which a diffusing and advecting solute is coupled to a Poiseuille network) and
2) the growth dynamics of a cell model comprised of a an elastic network (in which an evolving growth field is coupled to a Hooke network). 

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