180 research outputs found
Harmonic forcing of an extended oscillatory system: Homogeneous and periodic solutions
In this paper we study the effect of external harmonic forcing on a
one-dimensional oscillatory system described by the complex Ginzburg-Landau
equation (CGLE). For a sufficiently large forcing amplitude, a homogeneous
state with no spatial structure is observed. The state becomes unstable to a
spatially periodic ``stripe'' state via a supercritical bifurcation as the
forcing amplitude decreases. An approximate phase equation is derived, and an
analytic solution for the stripe state is obtained, through which the
asymmetric behavior of the stability border of the state is explained. The
phase equation, in particular the analytic solution, is found to be very useful
in understanding the stability borders of the homogeneous and stripe states of
the forced CGLE.Comment: 6 pages, 4 figures, 2 column revtex format, to be published in Phys.
Rev.
Frequency Locking in Spatially Extended Systems
A variant of the complex Ginzburg-Landau equation is used to investigate the
frequency locking phenomena in spatially extended systems. With appropriate
parameter values, a variety of frequency-locked patterns including flats,
fronts, labyrinths and fronts emerge. We show that in spatially
extended systems, frequency locking can be enhanced or suppressed by diffusive
coupling. Novel patterns such as chaotically bursting domains and target
patterns are also observed during the transition to locking
A Phase Front Instability in Periodically Forced Oscillatory Systems
Multiplicity of phase states within frequency locked bands in periodically
forced oscillatory systems may give rise to front structures separating states
with different phases. A new front instability is found within bands where
(). Stationary fronts shifting the
oscillation phase by lose stability below a critical forcing strength and
decompose into traveling fronts each shifting the phase by . The
instability designates a transition from stationary two-phase patterns to
traveling -phase patterns
Bouncing localized structures in a liquid-crystal light-valve experiment
Experimental evidence of bouncing localized structures in a nonlinear optical
system is reported.Comment: 4 page
Points, Walls and Loops in Resonant Oscillatory Media
In an experiment of oscillatory media, domains and walls are formed under the
parametric resonance with a frequency double the natural one. In this bi-stable
system, %phase jumps by crossing walls. a nonequilibrium transition from
Ising wall to Bloch wall consistent with prediction is confirmed
experimentally. The Bloch wall moves in the direction determined by its
chirality with a constant speed. As a new type of moving structure in
two-dimension, a traveling loop consisting of two walls and Neel points is
observed.Comment: 9 pages (revtex format) and 6 figures (PostScript
A simple derivation of Kepler's laws without solving differential equations
Proceeding like Newton with a discrete time approach of motion and a
geometrical representation of velocity and acceleration, we obtain Kepler's
laws without solving differential equations. The difficult part of Newton's
work, when it calls for non trivial properties of ellipses, is avoided by the
introduction of polar coordinates. Then a simple reconsideration of Newton's
figure naturally leads to en explicit expression of the velocity and to the
equation of the trajectory. This derivation, which can be fully apprehended by
beginners at university (or even before) can be considered as a first
application of mechanical concepts to a physical problem of great historical
and pedagogical interest
Expanding direction of the period doubling operator
We prove that the period doubling operator has an expanding direction at the
fixed point. We use the induced operator, a ``Perron-Frobenius type operator'',
to study the linearization of the period doubling operator at its fixed point.
We then use a sequence of linear operators with finite ranks to study this
induced operator. The proof is constructive. One can calculate the expanding
direction and the rate of expansion of the period doubling operator at the
fixed point
From Labyrinthine Patterns to Spiral Turbulence
A new mechanism for spiral vortex nucleation in nongradient reaction
diffusion systems is proposed. It involves two key ingredients: An Ising-Bloch
type front bifurcation and an instability of a planar front to transverse
perturbations. Vortex nucleation by this mechanism plays an important role in
inducing a transition from labyrinthine patterns to spiral turbulence. PACS
numbers: 05.45.+b, 82.20.MjComment: 4 pages uuencoded compressed postscrip
Log-periodic corrections to scaling: exact results for aperiodic Ising quantum chains
Log-periodic amplitudes of the surface magnetization are calculated
analytically for two Ising quantum chains with aperiodic modulations of the
couplings. The oscillating behaviour is linked to the discrete scale invariance
of the perturbations. For the Fredholm sequence, the aperiodic modulation is
marginal and the amplitudes are obtained as functions of the deviation from the
critical point. For the other sequence, the perturbation is relevant and the
critical surface magnetization is studied.Comment: 12 pages, TeX file, epsf, iopppt.tex, xref.tex which are joined. 4
postcript figure
Dynamic Front Transitions and Spiral-Vortex Nucleation
This is a study of front dynamics in reaction diffusion systems near
Nonequilibrium Ising-Bloch bifurcations. We find that the relation between
front velocity and perturbative factors, such as external fields and curvature,
is typically multivalued. This unusual form allows small perturbations to
induce dynamic transitions between counter-propagating fronts and nucleate
spiral vortices. We use these findings to propose explanations for a few
numerical and experimental observations including spiral breakup driven by
advective fields, and spot splitting
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