Aggregation and deaggregation of interacting micro swimmers
Jan Wehr (University of Arizona)
Abstract: A swarm of light-sensitive robots is moving in a planar region, changing the direction of motion randomly. Each robot emits light; in turn, it adapts the speed of its motion to the total intensity of the light shed on it by the other robots. The adaptation takes time---the sensorial delay. Using a natural approximation of the equations of motion, the robots may be programmed to make the sensorial delay negative. In this case they are, in some sense, predicting the future. In a series of experiments by the Giovanni Volpe group and the University of Gothenburg (Sweden) it was shown that at a certain negative value of the delay, the collective behavior of the robots changes qualitatively from aggregation to deaggregation. I am going to explain this phenomenon by an asymptotic analysis of the system of stochastic differential equations, describing the motion of a single robot in an inhomogeneous landscape.
The results were obtained in a joint work with Giovanni Volpe, Mite Mijalkov and Austin McDaniel. They display an interesting feature: while the original system is driven by a single noise source, the limiting one contains two independent ones. I will explain this by showing how one can generate two independent Wiener processes from a single one. Using this fact to rigorously justify the asymptotic results is a work in progress with Jeremiah Birrell.
mathematical physics
Audience: researchers in the discipline
( video )
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