Day 1 (Tuesday 11 April) @ 13:45–15:15

Marcello Seri (University of Groningen)

Geometric integration via the contact lenses

Geometric integrators are numerical schemes that, by construction, approximately preserve certain geometric invariants of the integrated flows.

In the talk we will present of a new family of geometric integrators for non-conservative systems defined in terms of contact geometry.

We will then show some of their properties and motivate their relevance on some examples from celestial mechanics and non-linear oscillators.

Robbin Bastiaansen (Utrecht University)

Fragmented tipping in a spatially heterogeneous world

Many climate subsystems are thought to be susceptible to tipping—and some might be close to a tipping point. The general belief and intuition, based on simple conceptual models of tipping elements, is that tipping leads to reorganization of the full (sub)system. Here, we explore tipping in conceptual, but spatially extended and spatially heterogenous models. These are extensions of conceptual models taken from all sorts of climate system components on multiple spatial scales. By analysis of the bifurcation structure of such systems, special stable equilibrium states are revealed: coexistence states with part of the spatial domain in one state, and part in another, with a spatial interface between these regions. These coexistence states critically depend on the size and the spatial heterogeneity of the (sub)system. In particular, in these systems the crossing of a tipping point not necessarily leads to a full reorganization of the system. Instead, it might lead to a reorganization of only part of the spatial domain, limiting the impact of these events on the system’s functioning.

Alethea Barbaro (TU Delft)

A contagion model for fearful crowds

What would you do if you were at a crowded event, and all of a sudden, you hear people screaming?  Would you start pushing?  Would you run for the exits? We all hear about the tragic sequelae of such situations in the news, yet most mathematical models for pedestrian dynamics fail to account for the emotional component of these situations. The models generally consider this to be a problem with purely physical components and constraints.  In this talk, we will introduce an agent-based flocking model for crowd dynamics where every agent has an evolving emotional variable in addition to a position and velocity.  The emotion levels vary based on the emotions of nearby agents, and this, in turn, affects the agent’s velocity.  We will detail the agent-based model, show simulations, and then derive a corresponding kinetic equation.