Research of James Meiss


Much of the research listed below has received support from the National Science Foundation, most recently under grants DMS-0707659, DMS-1211350 and CMMI-1447440.

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The mixing of a passive scalar in a fluid is a familiar process---you see it in action whenever you stir milk into tea, for example. Mixing requires two things: effective stirring and diffusive spreading. Diffusion is only effective when the scales are very small, thus to design an effective mixer, one must first create a stirring process that stretches and folds the fluids. This process has applications to the remediation of contaminated groundwater, as discussed in a paper with R. Neupauer and D. Mays. When the two fluids being mixed can react, the resulting striations can cause localized enhancement of the reaction rates, as discussed in a paper with K. Pratt and J. Crimaldi.

Recently, PhD Student Rebecca Mitchell and I studied the problem of how to design an effective mixer taking into account that the device acts over a finite time (so infinite time considerations of Lyapunov exponents and entropy are not really appropriate) and that there are constraints on its design---for example the energy of the mixer is limited and the shape of the stirring elements is constrained. For a simple model consisting of sequential shears (essentially Harper maps), we find that one can use a step-by-step method to choose the next stirring action and obtain a near optimal result. The sequence of images at the right shows an optimal protocol for a Gaussian density profile.

Bibliographic Information

  1. My Vita (pdf file)
  2. My Erdös number is at most 4
  3. ORCID
  4. Researcher ID
  5. Google Scholar
  6. zbMath

Books, Pedagogy and Reviews


Pedagogical Articles

Fields of Research

Computational Topology

Fluid Dynamics

Hamiltonian Dynamics

Plasma Physics

Classes of Dynamical Systems

Area-Preserving Maps

Symplectic Maps

Volume Preserving Maps

Phemomena and Methods


Invariant Tori

Piecewise Smooth Bifurcations

Polynomial Maps


Transitory Dynamics


Twistless Bifurcations

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revised Sept 24, 2017

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