|WikiProject Systems||(Rated C-class, Mid-importance)|
|WikiProject Mathematics||(Rated C-class, Low-priority)|
I'm a researcher on fluid mixing, and I'm planning to complement this page on chaotic mixing with a team of graduate students next week, on Friday February 3rd. So please don't be surprised if there is a large number of modifications to this page next week and shortly thereafter! EmmanuelleGouillart (talk) 16:30, 23 January 2012 (UTC)
Sounds good. The article could certainly use some work and I'm sure there are many more papers that could warrant inclusion. One very interesting I found recently (though I still haven't finished it) is Wiggins and Ottino (2004), "Foundations of Chaotic Mixing", Phil. Trans. of the R. Soc. London 362: 937-970. There are probably many ideas from Ottino's book that should be included as well, although much of the material is just general fluid mechanics, I believe. There is also work by Nakamura, Thiffault and others that I think are highly relevant although perhaps not directly applicable. Here are three papers that, while they may not warrant inclusion in this article, nonetheless may be relevant to your research:
- N. Nakamura (1995), "Modified Lagrangian-Mean Diagnostics of the Stratospheric Polar Vortices. Part 1..." J. Atmos. Sci. 52(11):2096-2108.
- J.-L. Thiffeault (2003), "Advection-diffusion in Lagrangian Coordinates." Phys. Lett. A 309:415-422.
- A. K. Pattanayak (2001), "Characterizing the metastable balance between chaos and diffusion." Physica D 148:1-19.
- The advection equations listed in Section 1.3 are repeated in Section 2.1 in vector form.
- Actually, the equations in Section 1.2 are also contained in Section 2.1
- I find the definition of the Lyapunov exponent as the time limit of the largest finite-time exponent to be a bit awkward. The entire spectrum can be derived in the asymptotic limit as well. Maybe we need two symbols?
- I wonder if it might be useful to distinquish between the "descriptive" study of chaotic mixing vs. the "prescriptive" study, that is, simply trying to understand chaotic mixing vs. designing the most efficient mixing schemes. By the look of it, most of the work you do falls under the prescriptive heading whereas I was more interested in the descriptive side (the animations were damn cool...)
It might also be worth distinquishing between the Lagrangian coordinates and the Eulerian coordinates. In Ottino, this is done through caps, , versus lower-case, . Peteymills (talk) 17:10, 26 March 2012 (UTC)