2016 SUMMER UNDERGRADUATE REU PROGRAM
New Jersey Institute of Technology
Mathematical Modeling of Construction Dynamics of Army Ants - Simon Garnier
One of the most spectacular examples of construction by social insects are the self-assembling structures formed by New World army ants. In order to conquer the rough and complex terrain of the tropical forests of Central and South America, these nomadic ants create temporary bridges with their own bodies. These bridges can self-assemble across a wide variety of environments, and have been shown to recover from damage, adapt their size according to traffic, and even spontaneously disassemble when under-used. For this project, the student will work with NJIT Assistant Professor Simon Garnier toward developing and implementing a general mathematical model of self-assembly that can reproduce the construction dynamics of army ants. The model will be used to generate predictions about the stable state of the self-assembling structure under different configurations of the local environment. These predictions will be compared to data and observations collected over the last 3 years on ant colonies in Panama. The model will also serve as a general guide for the design of ant-inspired robot swarms as part of a collaboration with roboticists at Harvard University and Northwestern University.
Mathematical Modeling of Foraging Behavior - Simon Garnier, with Jason Graham (Department of Mathematics, University of Scranton)
When foraging, ants take in a variety of input signals that play a role in determining both the individual and the collective motion of the foraging group. Among the most prominent signals are the local population density, chemotactic signals in the form of pheromone gradients, and the local topography of the terrain of the foraging environment. The goal of this project - which will be located at NJIT - is for students to work with University of Scranton Assistant Professor Jason Graham and NJIT Assistant Professor Simon Garnier in order to construct and critically analyze a mathematical model that incorporates how these salient features of foraging act together to produce the optimal emergent collective motion patterns observed in recent experiments. Furthermore, the model will be used to make predictions about foraging behavior that is beyond the scope of current experiments. The results of this work will help to clarify some open questions in the collective decision making mechanisms that underlie ant foraging behavior.