Noise-sustained structure, intermittency, and the Ginzburg-Landau equation [electronic resource].
- Los Alamos, N.M. : Los Alamos National Laboratory, 1985. and Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
- Physical Description:
- Pages: 9 : digital, PDF file
- Additional Creators:
- Los Alamos National Laboratory and United States. Department of Energy. Office of Scientific and Technical Information
- Restrictions on Access:
- Free-to-read Unrestricted online access
- The time-dependent generalized Ginzburg-Landau equation is a partial differential equation that is related to many physical systems. In the stationary (i.e., laboratory) frame of reference the equation is: Partial psi/partial t = a psi - ..nu.. (partial psi/partial x) + b (partial squared x/partial x/sup 2/) - c (psi absolute)/sup 2/ psi where the dependent variable psi is in general complex; a, b, and c are constants which are in general complex; and ..nu.. is the group velocity. Consider a small initial localized perturbation about the equilibrium state psi=O. A linear stability analysis reveals that there are three types of behavior which this perturbation can undergo. (1) The perturbation will be damped in any frame of reference. This behavior corresponds to the system being absolutely stable. (2) The perturbation will grow and spread such that the edges of the pertubation move in opposite directions. This behavior corresponds to the system being absolutely unstable. The perturbation will be damped at any given stationary point but a frame of reference may be found in which the perturbation is growing. In other words, even though the perturbation is growing and spreading, it is moving at a sufficiently large velocity such that both edges of the perturbation are moving in the same direction. Thus the system behind the perturbation returns to its undisturbaed state. This behavior corresponds to the system being spatially unstable (i.e., convectively unstable).
- Published through SciTech Connect., 01/01/1985., "la-ur-85-1055", " conf-850165-3", "DE85009626", Conference on solitons and coherent structures, Santa Barbara, CA, USA, 11 Jan 1985., and Deissler, R.J.
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