11,700 research outputs found
Pinning control of spatiotemporal chaos
Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a coupled map lattice as an example. The optimal arrangement of the control sites is shown to depend on the symmetry properties of the system, while their minimal density depends on the strength of noise in the system. The method is shown to work in any region of parameter space and requires a significantly smaller number of controllers compared to the method proposed earlier by Hu and Qu [Phys. Rev. Lett. 72, 68 (1994)]. A nonlinear generalization of the method for a 1D lattice is also presented
Domain Coarsening in Systems Far from Equilibrium
The growth of domains of stripes evolving from random initial conditions is
studied in numerical simulations of models of systems far from equilibrium such
as Rayleigh-Benard convection. The scaling of the size of the domains deduced
from the inverse width of the Fourier spectrum is studied for both potential
and nonpotential models. The morphology of the domains and the defect
structures are however quite different in the two cases, and evidence is
presented for a second length scale in the nonpotential case.Comment: 11 pages, RevTeX; 3 uufiles encoded postscript figures appende
Comment on ``The linear instability of magnetic Taylor-Couette flow with Hall effect''
In the paper we comment on (R\"udiger & Shalybkov, Phys. Rev. E. 69, 016303
(2004) (RS)), the instability of the Taylor--Couette flow interacting with a
homogeneous background field subject to Hall effect is studied. We correct a
falsely generalizing interpretation of results presented there which could be
taken to disprove the existence of the Hall--drift induced magnetic instability
described in Rheinhardt and Geppert, Phys. Rev. Lett. 88, 101103. It is shown
that in contrast to what is suggested by RS, no additional shear flow is
necessary to enable such an instability with a non--potential magnetic
background field, whereas for a curl--free one it is. In the latter case, the
instabilities found in RS in situations where neither a hydrodynamic nor a
magneto--rotational instability exists are demonstrated to be most likely
magnetic instead of magnetohydrodynamic. Further, some minor inaccuracies are
clarified.Comment: 3 pages, 1 figure; accepted by Physical Review
Power-Law Behavior of Power Spectra in Low Prandtl Number Rayleigh-Benard Convection
The origin of the power-law decay measured in the power spectra of low
Prandtl number Rayleigh-Benard convection near the onset of chaos is addressed
using long time numerical simulations of the three-dimensional Boussinesq
equations in cylindrical domains. The power-law is found to arise from
quasi-discontinuous changes in the slope of the time series of the heat
transport associated with the nucleation of dislocation pairs and roll
pinch-off events. For larger frequencies, the power spectra decay exponentially
as expected for time continuous deterministic dynamics.Comment: (10 pages, 6 figures
Rayleigh-Benard Convection in Large-Aspect-Ratio Domains
The coarsening and wavenumber selection of striped states growing from random
initial conditions are studied in a non-relaxational, spatially extended, and
far-from-equilibrium system by performing large-scale numerical simulations of
Rayleigh-B\'{e}nard convection in a large-aspect-ratio cylindrical domain with
experimentally realistic boundaries. We find evidence that various measures of
the coarsening dynamics scale in time with different power-law exponents,
indicating that multiple length scales are required in describing the time
dependent pattern evolution. The translational correlation length scales with
time as , the orientational correlation length scales as ,
and the density of defects scale as . The final pattern evolves
toward the wavenumber where isolated dislocations become motionless, suggesting
a possible wavenumber selection mechanism for large-aspect-ratio convection.Comment: 5 pages, 6 figure
A Passive Phase Noise Cancellation Element
We introduce a new method for reducing phase noise in oscillators, thereby
improving their frequency precision. The noise reduction device consists of a
pair of coupled nonlinear resonating elements that are driven parametrically by
the output of a conventional oscillator at a frequency close to the sum of the
linear mode frequencies. Above the threshold for parametric response, the
coupled resonators exhibit self-oscillation at an inherent frequency. We find
operating points of the device for which this periodic signal is immune to
frequency noise in the driving oscillator, providing a way to clean its phase
noise. We present results for the effect of thermal noise to advance a broader
understanding of the overall noise sensitivity and the fundamental operating
limits
Signal Amplification by Sensitive Control of Bifurcation Topology
We describe a novel amplification scheme based on inducing dynamical changes to the topology of a bifurcation diagram of a simple nonlinear dynamical system. We have implemented a first bifurcation-topology amplifier using a coupled pair of parametrically driven high-frequency nanoelectromechanical systems resonators, demonstrating robust small-signal amplification. The principles that underlie bifurcation-topology amplification are simple and generic, suggesting its applicability to a wide variety of physical, chemical, and biological systems
Mean flow and spiral defect chaos in Rayleigh-Benard convection
We describe a numerical procedure to construct a modified velocity field that
does not have any mean flow. Using this procedure, we present two results.
Firstly, we show that, in the absence of mean flow, spiral defect chaos
collapses to a stationary pattern comprising textures of stripes with angular
bends. The quenched patterns are characterized by mean wavenumbers that
approach those uniquely selected by focus-type singularities, which, in the
absence of mean flow, lie at the zig-zag instability boundary. The quenched
patterns also have larger correlation lengths and are comprised of rolls with
less curvature. Secondly, we describe how mean flow can contribute to the
commonly observed phenomenon of rolls terminating perpendicularly into lateral
walls. We show that, in the absence of mean flow, rolls begin to terminate into
lateral walls at an oblique angle. This obliqueness increases with Rayleigh
number.Comment: 14 pages, 19 figure
Noise and dynamical pattern selection
In pattern forming systems such as Rayleigh-Benard convection or directional
solidification, a large number of linearly stable, patterned steady states
exist when the basic, simple steady state is unstable. Which of these steady
states will be realized in a given experiment appears to depend on unobservable
details of the system's initial conditions. We show, however, that weak,
Gaussian white noise drives such a system toward a preferred wave number which
depends only on the system parameters and is independent of initial conditions.
We give a prescription for calculating this wave number, analytically near the
onset of instability and numerically otherwise.Comment: 12 pages, REVTEX, no figures. Submitted to Phys. Rev. Let
Perturbation of magnetostatic modes observed by ferromagnetic resonance force microscopy
Magnetostatic modes of yttrium iron garnet (YIG) films are investigated by ferromagnetic resonance force microscopy. A thin-film "probe" magnet at the tip of a compliant cantilever introduces a local inhomogeneity in the internal field of the YIG sample. This influences the shape of the sample's magnetostatic modes, thereby measurably perturbing the strength of the force coupled to the cantilever. We present a theoretical model that explains these observations; it shows that the tip-induced variation of the internal field creates either a local "potential barrier" or "potential well" for the magnetostatic waves. The data and model together indicate that local magnetic imaging of ferromagnets is possible, even in the presence of long-range spin coupling, through the introduction of localized magnetostatic modes predicted to arise from sufficiently strong tip fields
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