196 research outputs found
Violation of hyperbolicity via unstable dimension variability in a chain with local hyperbolic chaotic attractors
We consider a chain of oscillators with hyperbolic chaos coupled via
diffusion. When the coupling is strong the chain is synchronized and
demonstrates hyperbolic chaos so that there is one positive Lyapunov exponent.
With the decay of the coupling the second and the third Lyapunov exponents
approach zero simultaneously. The second one becomes positive, while the third
one remains close to zero. Its finite-time numerical approximation fluctuates
changing the sign within a wide range of the coupling parameter. These
fluctuations arise due to the unstable dimension variability which is known to
be the source for non-hyperbolicity. We provide a detailed study of this
transition using the methods of Lyapunov analysis.Comment: 24 pages, 13 figure
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
Novel A-B type oscillations in a 2-D electron gas in inhomogenous magnetic fields
We present results from a quantum and semiclassical theoretical study of the
and resistivities of a high mobility 2-D electron gas
in the presence of a dilute random distribution of tubes with magnetic flux
and radius , for arbitrary values of and . We
report on novel Aharonov-Bohm type oscillations in and ,
related to degenerate quantum flux tube resonances, that satisfy the selection
rule , with an integer. We discuss possible
experimental conditions where these oscillations may be observed.Comment: 11 pages REVTE
Flow distributed oscillation, flow velocity modulation and resonance
We examine the effects of a periodically varying flow velocity on the
standing and travelling wave patterns formed by the flow-distributed
oscillation (FDO) mechanism. In the kinematic (or diffusionless) limit, the
phase fronts undergo a simple, spatiotemporally periodic longitudinal
displacement. On the other hand, when the diffusion is significant, periodic
modulation of the velocity can disrupt the wave pattern, giving rise in the
downstream region to travelling waves whose frequency is a rational multiple of
the velocity perturbation frequency. We observe frequency locking at ratios of
1:1, 2:1 and 3:1, depending on the amplitude and frequency of the velocity
modulation. This phenomenon can be viewed as a novel, rather subtle type of
resonant forcing.Comment: submitted to Phys. Rev.
Manipulation of Microparticles By Bessel Light Beam
We consider perspectives of optical manipulation of microscopic objects in the area of biology, biophysics and medicine. The first part of the work is devoted to a brief review of the microparticles’ manipulation. The second part contains calculations of the focusing of laser radiation parameters and some results on the formation of Bessel light beams. The experimental setup based on the optical manipulation technique of micron-sized particles was developed
Penetration of the magnetic field into the twinning plane in the type I and II superconductors
It is demonstrated that in the type I and II superconductors with
low-transparent twinning planes (TP) the penetration of external parallel
magnetic field into the region of the twinning plane can be energetically
favorable. In the type I superconductors the twinning planes become similar to
Josephson junctions and the magnetic field penetrates into the center of the TP
in the form of soft Josephson-like vortices. This leads to increase in the
critical magnetic field values. The corresponding phase diagram in the
parameter plane "temperature - magnetic field" essentially differs from the one
obtained without taking the finite value of the magnetic field near the TP into
account. Comparison between obtained phase diagrams and experimental data for
different type I superconductors can allow to estimate the value of the TP
transparency, which is the only fitting parameter in our theory.Comment: 5 pages, 2 figure
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