Self-induced motion of line defects
Author:
Jacob Rubinstein
Journal:
Quart. Appl. Math. 49 (1991), 1-9
MSC:
Primary 73B99; Secondary 35Q55, 76A99
DOI:
https://doi.org/10.1090/qam/1096227
MathSciNet review:
MR1096227
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: The evolution of the 2-d Ginzburg-Landau functional under the Schrodinger and the diffusion dynamics is considered. We construct solutions $u\left ( {x, t} \right ), u \in {R^2}, x \in {R^3}$, such that the vector field $u$ vanishes along a singular curve $\gamma$. Equations of motion for $\gamma \left ( t \right )$ are derived by the method of matched asymptotic expansions.
- G. K. Batchelor and H. K. Moffatt (eds.), 25th anniversary issue: editorial reflections on the development of fluid mechanics, Cambridge University Press, Cambridge-New York, 1981. J. Fluid Mech. 106 (1981). MR 622931
S. Chandrasckhar, Liquid Crystals, Cambridge University Press, 1977
- M. C. Cross and Alan C. Newell, Convection patterns in large aspect ratio systems, Phys. D 10 (1984), no. 3, 299–328. MR 763474, DOI https://doi.org/10.1016/0167-2789%2884%2990181-7
R. Feynmann, Statistical Mechanics, Benjamin, New York, 1972
- G. ’t Hooft, Magnetic monopoles in unified gauge theories, Nuclear Phys. B79 (1974), 276–284. MR 0413809, DOI https://doi.org/10.1016/0550-3213%2874%2990486-6
- Y. Kuramoto, Chemical oscillations, waves, and turbulence, Springer Series in Synergetics, vol. 19, Springer-Verlag, Berlin, 1984. MR 762432
- E. M. Lifshitz and L. P. Pitaevskiĭ, Course of theoretical physics [“Landau-Lifshits”]. Vol. 9, Pergamon Press, Oxford-Elmsford, N.Y., 1980. Statistical physics. Part 2. Theory of the condensed state; Translated from the Russian by J. B. Sykes and M. J. Kearsley. MR 586944
- John C. Neu, Vortices in complex scalar fields, Phys. D 43 (1990), no. 2-3, 385–406. MR 1067918, DOI https://doi.org/10.1016/0167-2789%2890%2990143-D
- Jacob Rubinstein, Peter Sternberg, and Joseph B. Keller, Fast reaction, slow diffusion, and curve shortening, SIAM J. Appl. Math. 49 (1989), no. 1, 116–133. MR 978829, DOI https://doi.org/10.1137/0149007
- L. M. Pismen and J. Rubinstein, Motion of vortex lines in the Ginzburg-Landau model, Phys. D 47 (1991), no. 3, 353–360. MR 1098255, DOI https://doi.org/10.1016/0167-2789%2891%2990035-8
- Jacob Rubinstein, Peter Sternberg, and Joseph B. Keller, Reaction-diffusion processes and evolution to harmonic maps, SIAM J. Appl. Math. 49 (1989), no. 6, 1722–1733. MR 1025956, DOI https://doi.org/10.1137/0149104
G. K. Batchelor, An Introduction to Fluid Mechanics, Cambridge University Press, 1967
S. Chandrasckhar, Liquid Crystals, Cambridge University Press, 1977
M. C. Cross and A. C. Newell, Convection patterns in large aspect ratio systems, Physica 10D, 299–328 (1984)
R. Feynmann, Statistical Mechanics, Benjamin, New York, 1972
G. W. ’t Hooft, Magnetic monopoles in unified gauge theories, Nuclear Phys. B79, 276–284 (1974)
Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer-Verlag, 1984
L. D. Landau and E. M. Lifshitz, Statistical Physics, Pergamon Press, 1980
J. Neu, Vortices in complex scalar fields, Physica D (to appear)
J. Rubinstein, P. Sternberg, and J. B. Keller, Fast reaction, slow diffusion and curve shortening, SIAM J. Appl. Math. 49, 116–133 (1989)
L. Pismen and J. Rubinstein, Motion of vortex lines in the Ginzbung-Landau model, Physica D (to appear)
J. Rubinstein, P. Sternberg, and J. B. Keller, Reaction diffusion processes and evolution to harmonic maps, SIAM J. Appl. Math. 49, 1722–1733 (1989)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73B99,
35Q55,
76A99
Retrieve articles in all journals
with MSC:
73B99,
35Q55,
76A99
Additional Information
Article copyright:
© Copyright 1991
American Mathematical Society
