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Article citations


Walsh, J.B. Finite Element Methods for Parabolic Stochastic PDE’s. Potential Analysis, 23, 1-43.

has been cited by the following article:

  • 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.