混沌动力学
The problem of characterizing the origin of the non-Gaussian properties of transport resulting from Hamiltonian dynamics is addressed. For this purpose the notion of chaotic jet is revisited and leads to the definition of a diagnostic able…
We consider the fractional generalizations of equation that defines the medium mass. We prove that the fractional integrals can be used to describe the media with noninteger mass dimensions. Using fractional integrals, we derive the…
Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often…
The weakly nonlinear regime of a viscoelastic Navier--Stokes fluid is investigated. For the purely hydrodynamic case, it is known that large-scale perturbations tend to the minima of a Ginzburg-Landau free-energy functional with a…
We consider the time required for complete synchronization of two identical one-way coupled vander Pol-Duffing oscillators occurring in the regime of dynamic chaos. The influence of the initial phase differ-ence between oscillators on the…
The mechanism of synchronization of oscillations in two identical coupled flow systems has beenstudied. The time (past the coupling onset) during which a synchronous oscillation regime is establisheddepends on the oscillation phase…
We describe a method for determining the transient process duration in a standard two-dimensionaldynamic system with discrete time (Henon map), occurring in the regime of chaotic oscillations
Transient processes in a third-order radiophysical flow system are studied and a map of the transient process duration versus initial conditions is constructed and analyzed. The results are compared to the arrangement of submanifolds of the…
Dependence of the transient process duration on the initial conditions is considered in one- and two-dimensional systems with discrete time, representing a logistic map and the Eno map, respectively.
The transient chaos regime in a two-dimensional system with discrete time (Eno map) is considered. It is demonstrated that a time series corresponding to this regime differs from a chaotic series constructed for close values of the control…
Results are presented from experimental investigations of oscillatory phenomena in an electron beam with a virtual cathode in a diode gap with a decelerating field. Experiments have revealed a stochastic broadband generation of the…
We examine a strange chaotic attractor and its unstable periodic orbits in case of one degree of freedom nonlinear oscillator with non symmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a…
A general proof that more energy flows upscale than downscale in two-dimensional (2D) turbulence and barotropic quasi-geostrophic (QG) turbulence is given. A proof is also given that in Surface QG turbulence, the reverse is true. Though…
Drag reduction in stationary turbulent flows by bubbles is sensitive to the dynamics of bubble oscillations. Without this dynamical effect the bubbles only renormalize the fluid density and viscosity, an effect that by itself can only lead…
We obtain the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution…
We consider dynamical tunneling between two symmetry-related regular islands that are separated in phase space by a chaotic sea. Such tunneling processes are dominantly governed by nonlinear resonances, which induce a coupling mechanism…
We report a numerical study of turbulence and Bose-Einstein condensation within the two-dimmensional Gross-Pitaevski model with repulsive interaction. In presence of weak forcing localized around some wave number in the Fourier space, we…
Methods of dynamical system's theory are used for numerical study of transport and mixing of passive particles (water masses, temperature, salinity, pollutants, etc.) in simple kinematic ocean models composed with the main Eulerian coherent…
In this paper, we revisit the claim that the Eulerian and quasi-Lagrangian same time correlation tensors are equal. This statement allows us to transform the results of an MSR quasi-Lagrangian statistical theory of hydrodynamic turbulence…
The theory of adiabatic invariants has a long history and important applications in physics but is rarely rigorous. Here we treat exactly the general time-dependent 1-D harmonic oscillator, $\ddot{q} + \omega^2(t) q=0$ which cannot be…