The University of Arizona

Statistical mechanics of phototactic robots

Statistical mechanics of phototactic robots

Series: Mathematical Physics and Probability Seminar
Location: Math 402
Presenter: Janek Wehr, University of Arizona

I will describe experiments performed by Giovanni Volpe and his groups at Bilkent University (Turkey) and at the University of Gothenburg (Sweden).  In these experiments, small light-sensitive robots were moving in a plane, changing the direction of motion randomly at a high change frequency. The speed of the motion was a function of the local light intensity, and was adjusted to it with a delay. 

I will introduce a mathematical model of this experiment and study its properties in a certain limit, in which the dynamics simplifies to allow an explicit calculation of the stationary state.  It turns out that the properties of the model depend in a sensitive way on the amount of the delay with which robots react to the light intensity.  I will show that this delay can be meaningfully made negative, which means that the robots can be programmed to try to predict the future.  For a certain negative value of the delay, the model undergoes a dynamical phase transition and its properties change qualitatively.  This is in excellent agreement with the experimental results.  I will discuss possible applications of this effect and, if time permits, I will mention several related models and projected experiments.  The work I will describe was done jointly with Giovanni Volpe, Austin McDaniel and Mite Mijalkov. 

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