Foukzon, J. (2005) Advanced Numerical-Analytical Methods for Path Integral Calculation and Its Application to Some Famous Problems of 3-D Turbulence Theory. New Scenario for Transition to Slow Turbulence. Preliminary Report. Meeting: 1011, Lincoln, Nebraska, AMS CP1, Session for Contributed Papers.
http://www.ams.org/meetings/sectional/1011-76-5.pdf

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.