187 research outputs found
Pattern formation and nonlocal logistic growth
Logistic growth process with nonlocal interactions is considered in one
dimension. Spontaneous breakdown of translational invariance is shown to take
place at some parameter region, and the bifurcation regime is identified for
short and long range interactions. Domain walls between regions of different
order parameter are expressed as soliton solutions of the reduced dynamics for
nearest neighbor interactions. The analytic results are confirmed by numerical
simulations
New results on twinlike models
In this work we study the presence of kinks in models described by a single
real scalar field in bidimensional spacetime. We work within the first-order
framework, and we show how to write first-order differential equations that
solve the equations of motion. The first-order equations strongly simplify the
study of linear stability, which is implemented on general grounds. They also
lead to a direct investigation of twinlike theories, which is used to introduce
a family of models that support the same defect structure, with the very same
energy density and linear stability.Comment: 6 pages, 1 figur
Wave-unlocking transition in resonantly coupled complex Ginzburg-Landau equations
We study the effect of spatial frequency-forcing on standing-wave solutions
of coupled complex Ginzburg-Landau equations. The model considered describes
several situations of nonlinear counterpropagating waves and also of the
dynamics of polarized light waves. We show that forcing introduces spatial
modulations on standing waves which remain frequency locked with a
forcing-independent frequency. For forcing above a threshold the modulated
standing waves unlock, bifurcating into a temporally periodic state. Below the
threshold the system presents a kind of excitability.Comment: 4 pages, including 4 postscript figures. To appear in Physical Review
Letters (1996). This paper and related material can be found at
http://formentor.uib.es/Nonlinear
Equilibrium topology of the intermediate state in type-I superconductors of different shapes
High-resolution magneto-optical technique was used to analyze flux patterns
in the intermediate state of bulk Pb samples of various shapes - cones,
hemispheres and discs. Combined with the measurements of macroscopic
magnetization these results allowed studying the effect of bulk pinning and
geometric barrier on the equilibrium structure of the intermediate state.
Zero-bulk pinning discs and slabs show hysteretic behavior due to geometric
barrier that results in a topological hysteresis -- flux tubes on penetration
and lamellae on flux exit. (Hemi)spheres and cones do not have geometric
barrier and show no hysteresis with flux tubes dominating the intermediate
field region. It is concluded that flux tubes represent the equilibrium
topology of the intermediate state in reversible samples, whereas laminar
structure appears in samples with magnetic hysteresis (either bulk or
geometric). Real-time video is available in
http://www.cmpgroup.ameslab.gov/supermaglab/video/Pb.html
NOTE: the submitted images were severely downsampled due to Arxiv's
limitations of 1 Mb total size
A Non-Equilibrium Defect-Unbinding Transition: Defect Trajectories and Loop Statistics
In a Ginzburg-Landau model for parametrically driven waves a transition
between a state of ordered and one of disordered spatio-temporal defect chaos
is found. To characterize the two different chaotic states and to get insight
into the break-down of the order, the trajectories of the defects are tracked
in detail. Since the defects are always created and annihilated in pairs the
trajectories form loops in space time. The probability distribution functions
for the size of the loops and the number of defects involved in them undergo a
transition from exponential decay in the ordered regime to a power-law decay in
the disordered regime. These power laws are also found in a simple lattice
model of randomly created defect pairs that diffuse and annihilate upon
collision.Comment: 4 pages 5 figure
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
Coupled-mode theory for photonic band-gap inhibition of spatial instabilities
We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean-field models for singly and doubly degenerate optical parametric oscillators. Analytical expressions for the new (higher) modulational thresholds and the size of the "band gap" as a function of the system and photonic crystal parameters are obtained via a coupled-mode theory. Then, by means of a nonlinear analysis, we derive amplitude equations for the unstable modes and find the stationary solutions above threshold. The form of the unstable mode is different in the lower and upper parts of the band gap. In each part there is bistability between two spatially shifted patterns. In large systems stable wall defects between the two solutions are formed and we provide analytical expressions for their shape. The analytical results are favorably compared with results obtained from the full system equations. Inhibition of pattern formation can be used to spatially control signal generation in the transverse plane
From ballistic to Brownian vortex motion in complex oscillatory media
We show that the breaking of the rotation symmetry of spiral waves in
two-dimensional complex (period-doubled or chaotic) oscillatory media by
synchronization defect lines (SDL) is accompanied by an intrinsic drift of the
pattern. Single vortex motion changes from ballistic flights at a well-defined
angle from the SDL to Brownian-like diffusion when the turbulent character of
the medium increases. It gives rise, in non-turbulent multi-spiral regimes, to
a novel ``vortex liquid''.Comment: 5 pages, 4 figure
Ordered and Disordered Defect Chaos
Defect-chaos is studied numerically in coupled Ginzburg-Landau equations for
parametrically driven waves. The motion of the defects is traced in detail
yielding their life-times, annihilation partners, and distances traveled. In a
regime in which in the one-dimensional case the chaotic dynamics is due to
double phase slips, the two-dimensional system exhibits a strongly ordered
stripe pattern. When the parity-breaking instability to traveling waves is
approached this order vanishes and the correlation function decays rapidly. In
the ordered regime the defects have a typical life-time, whereas in the
disordered regime the life-time distribution is exponential. The probability of
large defect loops is substantially larger in the disordered regime.Comment: 8 pages revtex, 8 figure
Tensor gauge field localization in branes
In this work we study localization of a Kalb-Ramond tensorial gauge field on
a membrane described by real scalar fields. The membrane is embedded in an
AdS-type five dimensional bulk space, which mimic a Randall-Sundrum scenario.
First, we consider a membrane described by only a single real scalar field. In
that scenarios we find that there is no localized tensorial zero mode. When we
take into account branes described by two real scalar fields with internal
structures, we obtain again a non-localized zero mode for a Kalb-Ramond
tensorial gauge field. After modifying our model of one single scalar field by
coupling the dilaton to the Kalb-Ramond field, we find that this result is
changed. Furthermore, we analyze Kaluza-Klein massive modes and resonance
structures.Comment: 12 pages, 8 figures. Abstract improved. Revised and enlarged version.
To appear in Physical Review
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