267 research outputs found
The Eckhaus and the Benjamin-Feir instability near a weakly inverted bifurcation
We investigate how the criteria for two prototype instabilities in one dimensional pattern forming systems, namely for the Eckhaus instability and for the Benjamin-Feir instability, change as one goes from a continuous bifurcation, to a spatially periodic or spatially and/or time periodic state, to the corresponding weakly inverted, i.e., hysteretic, cases. We also give the generalization to two dimensional patterns in systems with anisotropy as they arise from hydrodynamic instabilities in nematic liquid crystals
Confinement effects in a guided-wave interferometer with millimeter-scale arm separation
Guided-wave atom interferometers measure interference effects using atoms
held in a confining potential. In one common implementation, the confinement is
primarily two-dimensional, and the atoms move along the nearly free dimension
under the influence of an off-resonant standing wave laser beam. In this
configuration, residual confinement along the nominally free axis can introduce
a phase gradient to the atoms that limits the arm separation of the
interferometer. We experimentally investigate this effect in detail, and show
that it can be alleviated by having the atoms undergo a more symmetric motion
in the guide. This can be achieved by either using additional laser pulses or
by allowing the atoms to freely oscillate in the potential. Using these
techniques, we demonstrate interferometer measurement times up to 72 ms and arm
separations up to 0.42 mm with a well controlled phase, or times of 0.91 s and
separations of 1.7 mm with an uncontrolled phase.Comment: 14 pages, 6 figure
N-tree approximation for the largest Lyapunov exponent of a coupled-map lattice
The N-tree approximation scheme, introduced in the context of random directed
polymers, is here applied to the computation of the maximum Lyapunov exponent
in a coupled map lattice. We discuss both an exact implementation for small
tree-depth and a numerical implementation for larger s. We find that the
phase-transition predicted by the mean field approach shifts towards larger
values of the coupling parameter when the depth is increased. We conjecture
that the transition eventually disappears.Comment: RevTeX, 15 pages,5 figure
Mutually Penetrating Motion of Self-Organized 2D Patterns of Soliton-Like Structures
Results of numerical simulations of a recently derived most general
dissipative-dispersive PDE describing evolution of a film flowing down an
inclined plane are presented. They indicate that a novel complex type of
spatiotemporal patterns can exist for strange attractors of nonequilibrium
systems. It is suggested that real-life experiments satisfying the validity
conditions of the theory are possible: the required sufficiently viscous
liquids are readily available.Comment: minor corrections, 4 pages, LaTeX, 6 figures, mpeg simulations
available upon or reques
Measurement of the ac Stark shift with a guided matter-wave interferometer
We demonstrate the effectiveness of a guided-wave Bose-Einstein condensate
interferometer for practical measurements. Taking advantage of the large arm
separations obtainable in our interferometer, the energy levels of the 87Rb
atoms in one arm of the interferometer are shifted by a calibrated laser beam.
The resulting phase shifts are used to determine the ac polarizability at a
range of frequencies near and at the atomic resonance. The measured values are
in good agreement with theoretical expectations. However, we observe a
broadening of the transition near the resonance, an indication of collective
light scattering effects. This nonlinearity may prove useful for the production
and control of squeezed quantum states.Comment: 5 pages, three figure
Macroscopic quantum fluctuations in noise-sustained optical patterns
We investigate quantum effects in pattern formation for a degenerate optical parametric oscillator with walk-off. This device has a convective regime in which macroscopic patterns are both initiated and sustained by quantum noise. Familiar methods based on linearization about a pseudoclassical field fail in this regime and new approaches are required. We employ a method in which the pump field is treated as a c-number variable but is driven by the c-number representation of the quantum subharmonic signal field. This allows us to include the effects of the fluctuations in the signal on the pump, which in turn act back on the signal. We find that the nonclassical effects, in the form of squeezing, survive just above the threshold of the convective regime. Further, above threshold, the macroscopic quantum noise suppresses these effects
Worm Structure in Modified Swift-Hohenberg Equation for Electroconvection
A theoretical model for studying pattern formation in electroconvection is
proposed in the form of a modified Swift-Hohenberg equation. A localized state
is found in two dimension, in agreement with the experimentally observed
``worm" state. The corresponding one dimensional model is also studied, and a
novel stationary localized state due to nonadiabatic effect is found. The
existence of the 1D localized state is shown to be responsible for the
formation of the two dimensional ``worm" state in our model
Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow
A unique pattern selection in the absolutely unstable regime of a driven,
nonlinear, open-flow system is analyzed: The spatiotemporal structures of
rotationally symmetric vortices that propagate downstream in the annulus of the
rotating Taylor-Couette system due to an externally imposed axial through-flow
are investigated for two different axial boundary conditions at the in- and
outlet. Unlike the stationary patterns in systems without through-flow the
spatiotemporal structures of propagating vortices are independent of parameter
history, initial conditions, and system's length. They do, however, depend on
the axial boundary conditions, the driving rate of the inner cylinder and the
through-flow rate. Our analysis of the amplitude equation shows that the
pattern selection can be described by a nonlinear eigenvalue problem with the
frequency being the eigenvalue. Approaching the border between absolute and
convective instability the eigenvalue problem becomes effectively linear and
the selection mechanism approaches that one of linear front propagation.
PACS:47.54.+r,47.20.Ky,47.32.-y,47.20.FtComment: 15 pages (LateX-file), 8 figures (Postscript
Fractalization of Torus Revisited as a Strange Nonchaotic Attractor
Fractalization of torus and its transition to chaos in a quasi-periodically
forced logistic map is re-investigated in relation with a strange nonchaotic
attractor, with the aid of functional equation for the invariant curve.
Existence of fractal torus in an interval in parameter space is confirmed by
the length and the number of extrema of the torus attractor, as well as the
Fourier mode analysis. Mechanisms of the onset of fractal torus and the
transition to chaos are studied in connection with the intermittency.Comment: Latex file ( figures will be sent electronically upon
request):submitted to Phys.Rev. E (1996
Effect of noise on coupled chaotic systems
Effect of noise in inducing order on various chaotically evolving systems is
reviewed, with special emphasis on systems consisting of coupled chaotic
elements. In many situations it is observed that the uncoupled elements when
driven by identical noise, show synchronization phenomena where chaotic
trajectories exponentially converge towards a single noisy trajectory,
independent of the initial conditions. In a random neural network, with
infinite range coupling, chaos is suppressed due to noise and the system
evolves towards a fixed point. Spatiotemporal stochastic resonance phenomenon
has been observed in a square array of coupled threshold devices where a
temporal characteristic of the system resonates at a given noise strength. In a
chaotically evolving coupled map lattice with logistic map as local dynamics
and driven by identical noise at each site, we report that the number of
structures (a structure is a group of neighbouring lattice sites for whom
values of the variable follow certain predefined pattern) follow a power-law
decay with the length of the structure. An interesting phenomenon, which we
call stochastic coherence, is also reported in which the abundance and
lifetimes of these structures show characteristic peaks at some intermediate
noise strength.Comment: 21 page LaTeX file for text, 5 Postscript files for figure
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