Gradient flow structure for domain relaxation in Langmuir films
Authors:
Mahir Hadžić and Govind Menon
Journal:
Quart. Appl. Math. 70 (2012), 659-664
MSC (2000):
Primary 76D07, 76A20, 35Q35
DOI:
https://doi.org/10.1090/S0033-569X-2012-01263-7
Published electronically:
June 22, 2012
MathSciNet review:
3052083
Full-text PDF Free Access
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Additional Information
Abstract: We describe a gradient flow structure for the inviscid Langmuir layer Stokesian subfluid model introduced recently by Alexander et al. (2007).
References
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- James C. Alexander, Andrew J. Bernoff, Elizabeth K. Mann, J. Adin Mann Jr., and Lu Zou, Hole dynamics in polymer Langmuir films, Phys. Fluids 18 (2006), no. 6, 062103, 10. MR 2243348, DOI https://doi.org/10.1063/1.2212887
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References
- J. Alexander, A. Bernoff, E. Mann, J. Mann, J. Wintersmith, and L. Zou, Domain relaxation in Langmuir films, Journal of Fluid Mechanics, 571 (2007), pp. 191–219. MR 2293238 (2007m:76147)
- J. Alexander, A. Bernoff, E. Mann, J. Mann, and L. Zou, Hole dynamics in polymer Langmuir films, Physics of Fluids, 18 (2006), 10pp. MR 2243348
- R. Almgren, Singularity formation in Hele-Shaw bubbles, Physics of Fluids, 8 (1996), pp. 344–352. MR 1371519 (96j:76055)
- D.G. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Annals of Mathematics (2), 92 (1970), pp. 102–163. MR 0271984 (42:6865)
- D. Lubensky and R. Goldstein, Hydrodynamics of monolayer domains at the air-water interface, Physics of Fluids, 8 (1996), pp. 843–854.
- F. Otto, Dynamics of Labyrinthine Pattern Formation in Magnetic Fluids: A Mean-Field Theory, Archive for Rational Mechanics and Analysis, 141 (1998), pp. 63–103. MR 1613500 (2000j:76145)
- H. Omori, On the group of diffeomorphisms on a compact manifold, Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., (1968) pp. 167–183, American Math. Society MR 0271983 (42:6864)
- L. Simon, Lectures on geometric measure theory, Centre for Mathematical Analysis, Australian National University, 1984. MR 756417 (87a:49001)
- H. Stone and H. McConnell, Hydrodynamics of quantized shape transitions of lipid domains, Proceedings: Mathematical and Physical Sciences, 448 (1995), pp. 97–111.
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Additional Information
Mahir Hadžić
Affiliation:
Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139
Email:
mahir.hadzic@math.uzh.ch
Govind Menon
Affiliation:
Division of Applied Mathematics, Box F, Brown University, Providence, Rhode Island 02912
MR Author ID:
647776
Email:
menon@dam.brown.edu
Received by editor(s):
October 22, 2010
Published electronically:
June 22, 2012
Additional Notes:
The first author was supported by DMS 05-30862
The second author was supported by DMS 07-48482
Article copyright:
© Copyright 2012
Brown University
The copyright for this article reverts to public domain 28 years after publication.
