204 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
Diffusion-induced spontaneous pattern formation on gelation surfaces
Although the pattern formation on polymer gels has been considered as a
result of the mechanical instability due to the volume phase transition, we
found a macroscopic surface pattern formation not caused by the mechanical
instability. It develops on gelation surfaces, and we consider the
reaction-diffusion dynamics mainly induces a surface instability during
polymerization. Random and straight stripe patterns were observed, depending on
gelation conditions. We found the scaling relation between the characteristic
wavelength and the gelation time. This scaling is consistent with the
reaction-diffusion dynamics and would be a first step to reveal the gelation
pattern formation dynamics.Comment: 7 pages, 4 figure
Weakly nonlinear theory of grain boundary motion in patterns with crystalline symmetry
We study the motion of a grain boundary separating two otherwise stationary
domains of hexagonal symmetry. Starting from an order parameter equation
appropriate for hexagonal patterns, a multiple scale analysis leads to an
analytical equation of motion for the boundary that shares many properties with
that of a crystalline solid. We find that defect motion is generically opposed
by a pinning force that arises from non-adiabatic corrections to the standard
amplitude equation. The magnitude of this force depends sharply on the
mis-orientation angle between adjacent domains so that the most easily pinned
grain boundaries are those with an angle between four and eight degrees.
Although pinning effects may be small, they do not vanish asymptotically near
the onset of this subcritical bifurcation, and can be orders of magnitude
larger than those present in smectic phases that bifurcate supercritically
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
Two field BPS solutions for generalized Lorentz breaking models
In this work we present nonlinear models in two-dimensional space-time of two
interacting scalar fields in the Lorentz and CPT violating scenarios. We
discuss the soliton solutions for these models as well as the question of
stability for them. This is done by generalizing a model recently published by
Barreto and collaborators and also by getting new solutions for the model
introduced by them.Comment: 12 pages, 2 figure
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
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