NDNS+ WORKSHOP June 22-23, 2020 ONLINE MEETING
Date:
22-23 June 2020
Speaker: dr. Ivan Kryven - University of Utrecht
Title: Modelling networks and modelling with networks
Abstract:
Recently, much attention was directed towards understanding effects of extensive networks and interconnections on dynamical systems that range from very small scales, as in materials science, to very large ones, as in the studies of the Internet. In many cases, the structure of networks in question is not fully known, and one thus seeks an appropriate mathematical framework for formalising and modelling such objects. In this talk, I will discuss several concepts allowing us to model dynamic networks of large size and irregular structure. Interesting implications will be presented for materials science where these models explain kinetics-driven phase transitions and other emergent phenomena. In the second part of the talk, I will view irregular networks as models in themselves and draw an analogy between non-linear PDEs and random graphs. I will then hint on how such connection may be exploited to construct a new class of numerical methods for solving non-linear PDEs in multiple spatial dimensions.