229 research outputs found
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
Dynamics of Turing patterns under spatio-temporal forcing
We study, both theoretically and experimentally, the dynamical response of
Turing patterns to a spatio-temporal forcing in the form of a travelling wave
modulation of a control parameter. We show that from strictly spatial
resonance, it is possible to induce new, generic dynamical behaviors, including
temporally-modulated travelling waves and localized travelling soliton-like
solutions. The latter make contact with the soliton solutions of P. Coullet
Phys. Rev. Lett. {\bf 56}, 724 (1986) and provide a general framework which
includes them. The stability diagram for the different propagating modes in the
Lengyel-Epstein model is determined numerically. Direct observations of the
predicted solutions in experiments carried out with light modulations in the
photosensitive CDIMA reaction are also reported.Comment: 6 pages, 5 figure
Multi-Phase Patterns in Periodically Forced Oscillatory Systems
Periodic forcing of an oscillatory system produces frequency locking bands
within which the system frequency is rationally related to the forcing
frequency. We study extended oscillatory systems that respond to uniform
periodic forcing at one quarter of the forcing frequency (the 4:1 resonance).
These systems possess four coexisting stable states, corresponding to uniform
oscillations with successive phase shifts of . Using an amplitude
equation approach near a Hopf bifurcation to uniform oscillations, we study
front solutions connecting different phase states. These solutions divide into
two groups: -fronts separating states with a phase shift of and
-fronts separating states with a phase shift of . We find a new
type of front instability where a stationary -front ``decomposes'' into a
pair of traveling -fronts as the forcing strength is decreased. The
instability is degenerate for an amplitude equation with cubic nonlinearities.
At the instability point a continuous family of pair solutions exists,
consisting of -fronts separated by distances ranging from zero to
infinity. Quintic nonlinearities lift the degeneracy at the instability point
but do not change the basic nature of the instability. We conjecture the
existence of similar instabilities in higher 2n:1 resonances (n=3,4,..) where
stationary -fronts decompose into n traveling -fronts. The
instabilities designate transitions from stationary two-phase patterns to
traveling 2n-phase patterns. As an example, we demonstrate with a numerical
solution the collapse of a four-phase spiral wave into a stationary two-phase
pattern as the forcing strength within the 4:1 resonance is increased
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
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
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
Topological Hysteresis in the Intermediate State of Type-I Superconductors
Magneto-optical imaging of thick stress-free lead samples reveals two
distinct topologies of the intermediate state. Flux tubes are formed upon
magnetic field penetration (closed topology) and laminar patterns appear upon
flux exit (open topology). Two-dimensional distributions of shielding currents
were obtained by applying an efficient inversion scheme. Quantitative analysis
of the magnetic induction distribution and correlation with magnetization
measurements indicate that observed topological differences between the two
phases are responsible for experimentally observable magnetic hysteresis.Comment: 4 pages, RevTex
Spiral Waves in Chaotic Systems
Spiral waves are investigated in chemical systems whose underlying
spatially-homogeneous dynamics is governed by a deterministic chaotic
attractor. We show how the local periodic behavior in the vicinity of a spiral
defect is transformed to chaotic dynamics far from the defect. The
transformation occurs by a type of period doubling as the distance from the
defect increases. The change in character of the dynamics is described in terms
of the phase space flow on closed curves surrounding the defect.Comment: latex file with three postscript figures to appear in Physical review
Letter
Controlling domain patterns far from equilibrium
A high degree of control over the structure and dynamics of domain patterns
in nonequilibrium systems can be achieved by applying nonuniform external
fields near parity breaking front bifurcations. An external field with a linear
spatial profile stabilizes a propagating front at a fixed position or induces
oscillations with frequency that scales like the square root of the field
gradient. Nonmonotonic profiles produce a variety of patterns with controllable
wavelengths, domain sizes, and frequencies and phases of oscillations.Comment: Published version, 4 pages, RevTeX. More at
http://t7.lanl.gov/People/Aric
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
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