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Moller, M., Lange, W., Mitschke, F., Abraham, N.B. and Hubner, U. (1989) Errors from Digitizing and Noise in Estimating Attractor Dimensions. Physics Letters A, 138, 176-182.
has been cited by the following article:
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TITLE:
New Scenario for Transition to Slow 3-D Turbulence
AUTHORS:
Jaykov Foukzon
KEYWORDS:
3D Turbulence, Chaos, Quantum Chaos, Additive Thermal Noise, Nikolaevskii System
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.3,
March
30,
2015
ABSTRACT: Analytical
non-perturbative study of the three-dimensional
nonlinear stochastic partial differential equation with additive thermal noise, analogous to that proposed by V. N. Nikolaevskii [1]
08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003400310035003200310033003400300034000000
-[5]
08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003400310035003200310033003400300035000000
to describe longitudinal seismic waves, is presented. The equation has a
threshold of short-wave instability and symmetry, providing long wave dynamics.
New mechanism of quantum chaos generating in nonlinear dynamical systems with infinite number of degrees of freedom is
proposed. The hypothesis is said, that physical turbulence could be identified
with quantum chaos of considered type.
It is shown that the additive thermal noise destabilizes dramatically the ground
state of the Nikolaevskii system thus causing it to make a direct transition from
a spatially uniform to a turbulent state.