7,724 research outputs found
Generalized dimensions of Feigenbaum's attractor from renormalization-group functional equations
A method is suggested for the computation of the generalized dimensions of
fractal attractors at the period-doubling transition to chaos. The approach is
based on an eigenvalue problem formulated in terms of functional equations,
with a coefficient expressed in terms of Feigenbaum's universal fixed-point
function. The accuracy of the results is determined only by precision of the
representation of the universal function.Comment: 6 pages, 2 table
Hyperbolic Chaos of Turing Patterns
We consider time evolution of Turing patterns in an extended system governed
by an equation of the Swift-Hohenberg type, where due to an external periodic
parameter modulation long-wave and short-wave patterns with length scales
related as 1:3 emerge in succession. We show theoretically and demonstrate
numerically that the spatial phases of the patterns, being observed
stroboscopically, are governed by an expanding circle map, so that the
corresponding chaos of Turing patterns is hyperbolic, associated with a strange
attractor of the Smale-Williams solenoid type. This chaos is shown to be robust
with respect to variations of parameters and boundary conditions.Comment: 4 pages, 4 figure
Features of pulsed synchronization of a systems with a tree-dimensional phase space
Features of synchronization picture in the system with the limit cycle
embedded in a three-dimensional phase space are considered. By the example of
Ressler system and Dmitriev - Kislov generator under the action of a periodic
sequence of delta - function it is shown, that synchronization picture
significantly depends on the direction of pulse action. Features of
synchronization tons appeared in these models are observed.Comment: 16 pages, 11 figure
LOFAR observations of fine spectral structure dynamics in type IIIb radio bursts
Solar radio emission features a large number of fine structures demonstrating
great variability in frequency and time. We present spatially resolved spectral
radio observations of type IIIb bursts in the MHz range made by the Low
Frequency Array (LOFAR). The bursts show well-defined fine frequency
structuring called "stria" bursts. The spatial characteristics of the stria
sources are determined by the propagation effects of radio waves; their
movement and expansion speeds are in the range of 0.1-0.6c. Analysis of the
dynamic spectra reveals that both the spectral bandwidth and the frequency
drift rate of the striae increase with an increase of their central frequency;
the striae bandwidths are in the range of ~20-100 kHz and the striae drift
rates vary from zero to ~0.3 MHz s^-1. The observed spectral characteristics of
the stria bursts are consistent with the model involving modulation of the type
III burst emission mechanism by small-amplitude fluctuations of the plasma
density along the electron beam path. We estimate that the relative amplitude
of the density fluctuations is of dn/n~10^-3, their characteristic length scale
is less than 1000 km, and the characteristic propagation speed is in the range
of 400-800 km/s. These parameters indicate that the observed fine spectral
structures could be produced by propagating magnetohydrodynamic waves
Nonlinear mirror modes in the presence of hot electrons
A non-perturbative calculation of the gyrotropic pressures associated with
large-scale mirror modes is performed, taking into account a finite, possibly
anisotropic electron temperature. In the small-amplitude limit, this leads to
an extension of an asymptotic model previously derived for cold electrons. A
model equation for the profile of subcritical finite-amplitude large-scale
structures is also presented
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