415 research outputs found
Elasticity effects on the stability of growing films
It is shown how the combination of atomic deposition and nonlinear diffusion
may lead, below a critical temperature, to the growth of nonuniform layers on a
substrate. The dynamics of such a system is of the Cahn-Hilliard type,
supplemented by reaction terms representing adsorption-desorption processes.
The instability of uniform layers leads to the formation of nanostructures
which correspond to regular spatial variations of substrate coverage. Since
coverage inhomogeneities generate internal stresses, the coupling between
coverage evolution and film elasticity fields is also considered, for film
thickness below the critical thickness for misfit dislocation nucleation. It is
shown that this coupling is destabilizing and favors nanostructure formation.
It also favors square planforms which could compete, and even dominate over the
haxagonal or stripe nanostructures induced by coverage dynamics alon
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
Convective and Absolute Instabilities in the Subcritical Ginzburg-Landau Equation
We study the nature of the instability of the homogeneous steady states of
the subcritical Ginzburg-Landau equation in the presence of group velocity. The
shift of the absolute instability threshold of the trivial steady state,
induced by the destabilizing cubic nonlinearities, is confirmed by the
numerical analysis of the evolution of its perturbations. It is also shown that
the dynamics of these perturbations is such that finite size effects may
suppress the transition from convective to absolute instability. Finally, we
analyze the instability of the subcritical middle branch of steady states, and
show, analytically and numerically, that this branch may be convectively
unstable for sufficiently high values of the group velocity.Comment: 13 pages, 10 figures (fig1.ps, fig2.eps, fig3.ps, fog4a.ps, fig
4b.ps, fig5.ps, fig6.eps, fig7a.ps, fig7b.ps, fig8.p
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
Patterns arising from the interaction between scalar and vectorial instabilities in two-photon resonant Kerr cavities
We study pattern formation associated with the polarization degree of freedom
of the electric field amplitude in a mean field model describing a nonlinear
Kerr medium close to a two-photon resonance, placed inside a ring cavity with
flat mirrors and driven by a coherent -polarized plane-wave field. In
the self-focusing case, for negative detunings the pattern arises naturally
from a codimension two bifurcation. For a critical value of the field intensity
there are two wave numbers that become unstable simultaneously, corresponding
to two Turing-like instabilities. Considered alone, one of the instabilities
would originate a linearly polarized hexagonal pattern whereas the other
instability is of pure vectorial origin and would give rise to an elliptically
polarized stripe pattern. We show that the competition between the two
wavenumbers can originate different structures, being the detuning a natural
selection parameter.Comment: 21 pages, 6 figures. http://www.imedea.uib.es/PhysDep
Fluctuations impact on a pattern-forming model of population dynamics with non-local interactions
A model of interacting random walkers is presented and shown to give rise to
patterns consisting in periodic arrangements of fluctuating particle clusters.
The model represents biological individuals that die or reproduce at rates
depending on the number of neighbors within a given distance. We evaluate the
importance of the discrete and fluctuating character of this particle model on
the pattern forming process. To this end, a deterministic mean-field
description, including a linear stability and a weakly nonlinear analysis, is
given and compared with the particle model. The deterministic approach is shown
to reproduce some of the features of the discrete description, in particular,
the existence of a finite-wavelength instability. Stochasticity in the particle
dynamics, however, has strong effects in other important aspects such as the
parameter values at which pattern formation occurs, or the nature of the
homogeneous phase.Comment: 17 pages, 8 figures, elsart style; To appear in Physica
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
Theory for the spatiotemporal dynamics of domain walls close to a nonequilibrium Ising-Bloch transition
© 2015 American Physical Society. We derive a generic model for the interaction of domain walls close to a nonequilibrium-Bloch transition. The universal scenario predicted by the model includes stationary Ising and Bloch localized structures (dissipative solitons), as well as drifting and oscillating Bloch structures. Our theory also explains the behavior of Bloch walls during a collision. The results are confirmed by numerical simulations of the Ginzburg-Landau equation forced at twice its natural frequency and are in agreement with previous observations in several physical systems.Peer Reviewe
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