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Noise-sustained structure,intermittency, and the Ginzburg-Landau equation
Authors:Robert J Deissler
Institution:(1) Los Alamos National Laboratory, Center for Nonlinear Studies, MS B258, 87545 Los Alamos, New Mexico;(2) Present address: Physics Department, University of California at Santa Cruz, 307 Nat Sci II, 95064 Santa Cruz, California
Abstract:The time-dependent generalized Ginzburg-Landau equation is an equation that is related to many physical systems. Solutions of this equation in the presence of low-level external noise are studied. Numerical solutions of this equation in thestationary frame of reference and with anonzero group velocity that is greater than a critical velocity exhibit a selective spatial amplification of noise resulting in spatially growing waves. These waves in turn result in the formation of a dynamic structure. It is found that themicroscopic noise plays an important role in themacroscopic dynamics of the system. For certain parameter values the system exhibits intermittent turbulent behavior in which the random nature of the external noise plays a crucial role. A mechanism which may be responsible for the intermittent turbulence occurring in some fluid systems is suggested.
Keywords:Dynamical systems  nonlinear dynamics  chaos  turbulence  intermittent turbulence  intermittency  noise  external noise  fluctuations  external fluctuations  Ginzburg-Landau equation  amplitude equation  spatially growing waves  convective instability  spatial instability  secondary instability  noise-sustained structure  noise amplification  spatial noise amplification  pattern formation
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