Search

We study transport of tracer particles in a two-dimensional incompressible inviscid flow produced by three point vortices of equal strength. Time dependence of the flow caused by vortex motion gives rise to chaotic tracer trajectories, which fill parts of the flow plane referred to as mixing regions. For general vortex positions, a large connected mixing region (chaotic sea) is formed around vortices. It comprises a number of coherent fluid patches (islands), which do not mix with the rest of the chaotic sea, inside them particle motion is predominantly regular; three near-circular islands surrounding vortices are distinguished by their robust nature. Tracers in the chaotic sea rotate around the center of vorticity in an irregular way. Their trajectories are intermittent, long flights of almost regular motion are caused by trappings in the boundary regions of regular islands. The statistics of tracer rotation exhibits anomalous features, such as faster than linear growth of tracer ensemble variance and asymmetric probability distribution with long power tails. Exponent of the variance growth power law is different for different time ranges. Central part of the tracer distribution and its low (noninteger) moments evolve in a self-similar way, characterized by an exponent, which is different from that of the variance, and contrary to the latter is constant in time. Algebraic tails of the tracer distribution, controlling the behavior of the variance, are responsible for this effect. Long correlations in tracer motion lead to non-Poissonian distribution of Poincare recurrences in the mixing region. Analysis of long recurrences proves, that they are caused by tracer trappings inside boundary layers of islands of regular motion, which always exist inside the mixing region. Statistics of Poincare recurrences and trapping times exhibit power-law decay, indicating absence of a characteristic relaxation time. Values of the decay exponent for recurrences and for escape from the analyzed traps are very close to each other; long correlations are not dominated by a single trap, but are a cumulative effect of all of them, relative importance of a trap is determined by its size, and by its rotation frequency with respect to the background.

We observe immense delocalization of the order of 10(9) for a kicked Harper model when a control parameter K is taken to be K*=6.349 972. This "magic" value corresponds to special phase space topology in the classical limit, when a hierarchical self-similar set of sticky islands emerges. The origin of the effect is of the general nature and similar immense delocalization can be found in other systems.

To explore the character of underlying transport in a sandpile, we have followed the motion of tracer particles. Moments of the distribution function of the particle positions, =D(0)t(nnu(n)), are determined as a function of the elapsed time. The numerical results show that the transport mechanism for distances less than the sandpile length is superdiffusive with an exponent nu(n) close to 0.75, for n<1.

Compressible helical flow with div v not equal to 0 drastically increases the area of chaotic dynamics and mixing properties when the helicity parameter is spatially dependent. We show that the density dependence on the z coordinate can be incorporated in new variables in a way that leads to a Hamiltonian formulation of the system. This permits the application of various important results like the Kolmogorov-Arnold-Moser theory and, particularly, an understanding of why and in which sense the compressible helical flow is "more chaotic" than the incompressible one. Simulation demonstrates this property for an analog of the ABC flow. An interesting type of the dynamical system with "dense" island chains is described.

We present evidence that anomalous transport in the classical standard map results in strong enhancement of fluctuations in the localization length of quasienergy states in the corresponding quantum dynamics. This generic effect occurs even far from the semiclassical limit and reflects the interplay of local and global quantum suppression mechanisms of classically chaotic dynamics. Possible experimental scenarios are also discussed.