Research Interests

Many organisms display self-organized collective motion, such as flocks of birds, swarms of locusts, and schools of fish. Such groups can be composed of hundreds to millions of members, with all individuals responding rapidly to their neighbors to maintain the collective motion.  Animal aggregates can display a wide range of behaviors and can quickly and efficiently transition between them without loss of group coherence. These transitions could be due to changing behavioral rules, environmental factors including introduction of predators, or stochastic effects.  It is of fundamental importance to understand how and why animal groups change between different collective states, as well as how individual decisions effect the group dynamics. Questions of this nature arise in the control and prediction of locust swarm outbreaks, management of over fishing, crowd and traffic control in human populations, as well as the design and control of unmanned vehicles and sensor networks.  New computational techniques and mathematical theory must be developed to model and analyze the dynamics of both natural and engineered self-organizing aggregates.  Currently my research is focused on:

  1. understanding the relationship between spatial position and collective response in fish schools
  2. quantifying information propagation in schools
  3. the development of coarse-grained multi-scale computational algorithms to characterize population-level processes from individual-based models
  4. the design and optimization of interaction rules

Major Fields of Interest:

        

 

Publications

 

  1. A. Kolpas, J. Moehlis, and I.G. Kevrekidis, Coarse-grained analysis of stochasticity-induced switching between collective motion states, Proceedings of the National Academy of Sciences, 104, 5931-5935, 2007.       

         Supplementary Information:  Figure 7, Appendix.          

  1. H. Li, A. M. Kolpas, L. Petzold, and J. Moehlis, Parallel Simulation for a Fish Schooling Model on a General Purpose Graphics Processing Unit, to appear Concurrency and Computation: Practice and Experience
  1. A. Kolpas, J. Moehlis, T. A. Frewen, and I. G. Kevrekidis, Coarse Analysis of Collective Motion with Different Communication Mechanisms, to appear Math. Biosciences
  1. A. Kolpas and J. Moehlis, Optimal Switching Between Coexisting Stable Collective Motion States, to appear Applied Mathematics Letters
      

              

 

 

 

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