Sunday, November 10, 2013

Attraction based models of collective motion

Daniel Strömbom will present his Phd thesis on this Thursday at 15:15 in Polhemsalen, Ångström, Uppsala. The defense is open to the public, so please come along and watch.  The opponent Andreas Deutsch will first present background to Daniel's research and then Daniel will present his work, before the floor is opened to questions. 

Daniel’s thesis revolves around one very simple yet far-reaching idea. Daniel had the idea during the first year of his PhD. It started during a course I gave on self-propelled particle models. These (I thought at the time) the simplest set of models for how bird flocks and fish schools can move together collectively. They define a set of rules for how the ‘particles’ interact with their local neighbours. Usually, these interactions include rules for repulsion (so that particles don’t crash in to each other) , attraction (so that particles form a group) and alignment (so that the group moves in the same direction). Daniel’s idea was to take away alignment and repulsion, and see what happens with attraction alone.

At first I was sceptical. After all, we are interested in collective motion, and this means groups should move together in the same direction. But Daniel showed that if the particles have a blind angle then collective motion can be generated by attraction alone. Instead of always forming a ring or a clump, as they would without a blind angle, the particles could form a figure of eight. Remarkably, the 8 then moves collectively, sucking up all particles in its way.

You can watch the 8 form in one of the videos on Daniel's webpage, along with a lot of other examples of exotic attraction-only structures. One particular favourite of mine is his synchronised particle dancing simulation. Without noise, with carefully selected initial conditions and a very narrow blind angle, these particles make beautiful kaleidoscope patterns. This is shown in the video.

Daniel took this simple idea (published in 2011) and in the rest of his thesis he thoroughly investigates its consequences. In chapter 2, he shows that putting attraction back in to the model produces patterns that look like real bird flocks and fish schools. In chapter 3, he establishes mathematical properties of the model, such as why the eight moves. Then in chapters 4 and 5, working together with biologists, Andy King and Audrey Dussutour,  he applies his models to understanding sheep herding and ant traffic. 

Daniel's weaving of a simple idea through mathematics and applications is both beautiful and powerful. His model doesn't explain all aspects of animal flocking, but it has forced us to rethink some of the ground assumptions about how animals interact. There is always room for things to be simpler than we first believe. 

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