Control of mixing in fluid flow: a maximum entropy approach

IEEE Transactions on Automatic Control

Volumn 44, Issue 10, 1999, Pages 1852-1863

  D'Alessandro, Domenico ^b   Dahleh, Mohammed ^a,b   Mezić, Igor ^b  

^a IEEE

^b University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FLOW OF FLUIDS; MATHEMATICAL MODELS; MIXING; SHEAR FLOW; TWO DIMENSIONAL;

EGGBEATER FLOW; ERGODIC THEORETIC TOOLS; OPTIMAL MIXING PROTOCOLS;

PROCESS CONTROL;

EID: 0033337185     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.793724     Document Type: Article

References (22)

1. A. Abed, O. O. Wang, and A. Tesi, "Control of bifurcations and chaos," The Control Handbook, W. S. Levine, Ed. New York: CRC, 1996, pp. 951-966.
2. H. Aref, "Stirring by chaotic advection," J. Fluid Mechanics, vol. 143, pp. 1-21, 1984.
3. V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics. New York: Benjamin, 1968.
4. D. Berend and V. Bergelson, "Ergodic and mixing sequences of transformations," Ergod. Theory Dynam. Syst., vol. 4, pp. 353-366, 1984.
5. N. I. Chernov, "Ergodic and statistical properties of piecewise linear hyperbolic automorphisms of the 2-torus," J. Statistical Phys., vol. 69, pp. 111-133, 1992; see also the Addendum in J. Statistical Phys., vol. 71, pp. 341-347, 1993.
6. D. D'Alessandro, M. Dahleh, and I. Mezić, "An ergodic theoretic analysis of the partitioned-pipe mixer," Internal Rep., Dept. Mechanical and Environmental Eng., Univ. California, Santa Barbara, 1997.
7. D. D'Alessandro, I. Mezić, and M. Dahleh, "Some ergodic theorems for sequences of measure preserving transformations," Internal Rep., Dept. Mechanical and Environmental Eng., Univ. California, Santa Barbara, 1998.
8. J. G. Franjione and J. M. Ottino, "Symmetry concepts for the geometric analysis of mixing flows," Phil. Trans. R. Soc. Lond., pp. 301-323, 1992.
9. P. R. Halmos, Measure Theory. Princeton, NJ: D. Van Nostrand, 1950.
10. _, Lectures on Ergodic Theory. New York: Chelsea, 1958.
11. A. Katok and J.-M. Strelycin, "Invariant manifolds, entropy and billiards - Smooth maps with singularities," Lecture Notes in Mathematica, vol. 1222. New York: Springer-Verlag, 1980.
12. F. H. Ling, "Chaotic mixing in a spatially periodic continuous mixer," Phys. Fluids., vol. A 5, no. 9, 1993.
13. _, "The effect of mixing protocol on mixing in discontinuous cavity flows," Phys. Lett., vol. A 177, pp. 331-337, 1993.
14. M. Liu, F. J. Muzzio, and R. L. Peskin, "Quantification of mixing in aperiodic chaotic flows," Chaos, Solitons Fractals, vol. 4, no. 6, pp. 869-893, 1994.
15. Z. Manna and A. Pnueli, "Verifying hybrid systems," Hybrid Systems (Lecture Notes in Computer Science), vol. 736. New York: Springer-Verlag, 1993, pp. 4-35.
16. J. M. Ottino, "The mixing of fluids," Sci. Amer., pp. 56-67, Jan. 1989.
17. _, The Kinematics of Mixing: Stretching, Chaos, and Transport. New York: Cambridge Univ. Press, 1989.
18. Ya. B. Pesin, "Characteristic Lyapunov exponents and smooth ergodic theory," Russian Math. Surveys, vol. 32, no. 4, pp. 55-114, 1977.
19. K. Petersen, Ergodic Theory (Cambridge Studies in Advanced Mathematics), vol. 2. New York, 1983.
20. T. Shinbrot, L. Bresler, and J. M. Ottino, "Control of transport in a chaotic lattice," Physica, vol. D 93, pp. 191-209, 1996.
21. S. Vaienti, "Ergodic properties of the discontinuous sawtooth map," J. Statistical Phys., vol. 67, pp. 251-269, 1992.
22. S. Wiggins, Chaotic Transport in Dynamical Systems. New York, 1992.