Department of Mathematics

Colloquium

  •  Eric Vanden-Eijnden, NYU
  •  Non-equilibrium transitions between metastable patterns in populations of motile bacteria
  •  02/16/2017
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall

Active materials can self-organize in many more ways than their equilibrium counterparts. For example, self-propelled particles whose velocity decreases with their density can display motility-induced phase separation (MIPS), a phenomenon building on a positive feedback loop in which patterns emerge in locations where the particles slow down. Here, we investigate the effects of intrinsic fluctuations in the system's dynamics on MIPS, using a field theoretic description building on results by Cates and collaborators. We show that these fluctuations can lead to transitions between metastable patterns. The pathway and rate of these transitions is analyzed within the realm of large deviation theory, and they are shown to proceed in a very different way than one would predict from arguments based on detailed-balance and microscopic reversibility. Specifically, we show that these transitions involve fluctuations in diffiusivity of the bacteria followed by fluctuations in their population, in a specific sequence. The methods of analysis proposed here, including their numerical components, can be used to study noise-induced non-equilibrium transitions in a variety of other non-equilibrium set-ups, and lead to predictions that are verifiable experimentally.

 

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Department of Mathematics
Michigan State University
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