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Discrete and continuum modelling of biological network formation. Speaker: Jan Haskovec (KAUST: King Abdullah University of Science an Technology)

17 July 2018 10:30am11:30am
Motivated by recent papers describing rules for natural network formation in discrete settings, we propose an elliptic-parabolic system of partial differential equations. The model describes the pressure field due to Darcy’s type equation and the dynamics of the conductance network under pressure force effects with a diffusion rate representing randomness in the material structure. After a short overview of the principles of discrete network modelling, we show how to derive the corresponding macroscopic (continuum) description. The highly unusual structure of the resulting PDE system induces several interesting challenges for its mathematical analysis. We give a short overview of the tools and tricks that can be used to overcome them. In particular, we present results regarding the existence of weak solutions of the system, based on recent results on elliptic regularity theory. Moreover, we study the structure and stability properties of steady states that play a central role to understand the pattern capacity of the system. We present results of systematic numerical simulations of the system that provide further insights into the properties of the network-type solutions.

SCIE1000 - Theory and Practice in Science

21 June 2018 11:00am
Associate Professor Tim McIntyre and Dr Sara Herke (The University of Queensland)

A group-theoretic viewpoint on Falconer type theorems

19 June 2018 3:00pm4:00pm
Eyvindur Ari Palsson (Virgina tech)

The dynamics of malaria infection: A modelling perspective

18 June 2018 2:00pm3:00pm
Dr Lauren Childs (Virginia Tech)

Optimization formulations of data analysis problems

13 June 2018 10:00am11:00am
Stephen Wright (University of Wisconsin-Madison)

Dynamics of illegal harvest: how to protect natural resources from criminal behaviour

12 June 2018 11:00am12:00pm
Dr Matthew Holden (School of Mathematics and Physics, The University of Queensland)

Hitchin Systems in Mathematics and Beyond

11 June 2018 2:00pm3:00pm
Steven Rayan (University of Saskatchewan)

An entropy-based measure for comparing distributions

11 June 2018 11:00am12:00pm
Rajeev Rajaram (Kent State University, Ohio)

Mathematics for Data Science 1

5 June 2018 11:00am12:00pm
Dr Yoni Nazarathy (The University of Queensland)

Revamping ACCT1001

9 May 2018 1:00pm2:00pm
Speakers: Associate Professor Julie Walker and Ms Robyn Parry (BEL Faculty, The University of Queensland)

Modelling environmental factors in a population in the example of Lates calcarifer (Barramundi)

1 May 2018 11:00am12:00pm
Dr Sabrina Streipert (School of Mathematics and Physics, The University of Queensland)

From homotopy theory to representation theory

30 April 2018 2:00pm3:00pm
Dr Yaping Yang (University of Canterbury)