22/3/2011: Seminar Modeling Complex Socio-Economic Systems and Crises 6Tuesday March 22, 2011, 17:15 - 18:45
ETH Zurich, Main Campus, CAB G52
Charlotte Hemelrijk (University of Groningen): Complex Aerial Displays of Thousands of Starlings, a Model
Michel Rascle (University of Nice): Some Mathematical Models of Traffic and/or Pedestrian Flow
Flocks of birds are highly variable in shape in all contexts (while travelling, avoiding predation, wheeling above the roost), more so than fish schools that are usually described as being oblong. A particularly amazing variability is observed during the aerial displays of huge flocks of starlings (Sturnus vulgaris ) above the sleeping site at dawn. About the causes of the variability of the shape of bird flocks, hardly anything is known. Here we hypothesise that variability of shape increases when there are larger local differences in movement behaviour. We investigate this hypothesis with the help of a model of the self-organisation of a travelling group, since such a model has also increased our understanding of what causes the oblong shape of schools of fish. In the present paper, we test this hypothesis with the help of our model, called StarDisplay, whose flocking patterns resemble qualitatively and quantitatively those of real birds, in particular of starlings. We measure the shape of the flock as regards its relative proportions and the orientation of its longest dimension relative to the movement direction. Because local differences in movement may be larger if a) flock size is larger, b) interaction partners are fewer, c) the flock turns more strongly, d) individuals roll into turns, and e) move with a higher variability of speed, we expect in these cases flock shape to be more variable. We confirm this except for the case where speed variability is higher. In contrast, when variability of speed is high, both the shape of the flock and the positions of individuals within it are more static. We indicate the adaptive value of high locality of interaction and low variability of speed and develop testable hypotheses.
The talk will focus on mathematical models of traffic flow and/or pedestrian flows. In the latter case one aspect, namely the notion of geodesics (shortest paths), with (old) applications to mesh generation and some ongoing project with people from geography will be briefly analyzed. As to traffic flow, some of the many mathematical results since 2000, from our Aw-Rascle paper ("Resurrection"), after the celebrated "Requiem" paper of Daganzo, to much more recent discussions with J. Greenberg to revisit (a variant of) the Intelligent Driver Model of Helbing-Treiber, will be presented. As the audience is scientifically multi-cultural the aim is to forget as much as possible to about equations and to focus on the underlying ideas (e.g, do we react to a space or a time variation of the density?), using graphic arguments whenever it's possible, both on the computer and the blackboard.