515 research outputs found
Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities
Two front instabilities in a reaction-diffusion system are shown to lead to
the formation of complex patterns. The first is an instability to transverse
modulations that drives the formation of labyrinthine patterns. The second is a
Nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar
front unstable and gives rise to a pair of counterpropagating fronts. Near the
NIB bifurcation the relation of the front velocity to curvature is highly
nonlinear and transitions between counterpropagating fronts become feasible.
Nonuniformly curved fronts may undergo local front transitions that nucleate
spiral-vortex pairs. These nucleation events provide the ingredient needed to
initiate spot splitting and spiral turbulence. Similar spatio-temporal
processes have been observed recently in the ferrocyanide-iodate-sulfite
reaction.Comment: Text: 14 pages compressed Postscript (90kb) Figures: 9 pages
compressed Postscript (368kb
Propagation Failure in Excitable Media
We study a mechanism of pulse propagation failure in excitable media where
stable traveling pulse solutions appear via a subcritical pitchfork
bifurcation. The bifurcation plays a key role in that mechanism. Small
perturbations, externally applied or from internal instabilities, may cause
pulse propagation failure (wave breakup) provided the system is close enough to
the bifurcation point. We derive relations showing how the pitchfork
bifurcation is unfolded by weak curvature or advective field perturbations and
use them to demonstrate wave breakup. We suggest that the recent observations
of wave breakup in the Belousov-Zhabotinsky reaction induced either by an
electric field or a transverse instability are manifestations of this
mechanism.Comment: 8 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud
Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.htm
Surface Crystallization in a Liquid AuSi Alloy
X-ray measurements reveal a crystalline monolayer at the surface of the
eutectic liquid Au_{82}Si_{18}, at temperatures above the alloy's melting
point. Surface-induced atomic layering, the hallmark of liquid metals, is also
found below the crystalline monolayer. The layering depth, however, is
threefold greater than that of all liquid metals studied to date. The
crystallinity of the surface monolayer is notable, considering that AuSi does
not form stable bulk crystalline phases at any concentration and temperature
and that no crystalline surface phase has been detected thus far in any pure
liquid metal or nondilute alloy. These results are discussed in relation to
recently suggested models of amorphous alloys.Comment: 12 pages, 3 figures, published in Science (2006
Reversible monolayer-to-crystalline phase transition in amphiphilic silsesquioxane at the air-water interface
We report on the counter intuitive reversible crystallisation of two-dimensional monolayer of Trisilanolisobutyl Polyhedral Oligomeric SilSesquioxane (TBPOSS) on water surface using synchrotron x-ray scattering measurements. Amphiphilic TBPOSS form rugged monolayers and Grazing Incidence X-ray Scattering (GIXS) measurements reveal that the in-plane inter-particle correlation peaks, characteristic of two-dimensional system, observed before transition is replaced by intense localized spots after transition. The measured x-ray scattering data of the non-equilibrium crystalline phase on the air-water interface could be explained with a model that assumes periodic stacking of the TBPOSS dimers. These crystalline stacking relaxes upon decompression and the TBPOSS layer retains its initial monolayer state. The existence of these crystals in compressed phase is confirmed by atomic force microscopy measurements by lifting the materials on a solid substrate
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
Monovalent Ion Condensation at the Electrified Liquid/Liquid Interface
X-ray reflectivity studies demonstrate the condensation of a monovalent ion
at the electrified interface between electrolyte solutions of water and
1,2-dichloroethane. Predictions of the ion distributions by standard
Poisson-Boltzmann (Gouy-Chapman) theory are inconsistent with these data at
higher applied interfacial electric potentials. Calculations from a
Poisson-Boltzmann equation that incorporates a non-monotonic ion-specific
potential of mean force are in good agreement with the data.Comment: 4 pages, 4 figure
Quasiperiodic Patterns in Boundary-Modulated Excitable Waves
We investigate the impact of the domain shape on wave propagation in
excitable media. Channelled domains with sinusoidal boundaries are considered.
Trains of fronts generated periodically at an extreme of the channel are found
to adopt a quasiperiodic spatial configuration stroboscopically frozen in time.
The phenomenon is studied in a model for the photo-sensitive
Belousov-Zabotinsky reaction, but we give a theoretical derivation of the
spatial return maps prescribing the height and position of the successive
fronts that is valid for arbitrary excitable reaction-diffusion systems.Comment: 4 pages (figures included
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
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
Initial Conditions for Models of Dynamical Systems
The long-time behaviour of many dynamical systems may be effectively
predicted by a low-dimensional model that describes the evolution of a reduced
set of variables. We consider the question of how to equip such a
low-dimensional model with appropriate initial conditions, so that it
faithfully reproduces the long-term behaviour of the original high-dimensional
dynamical system. Our method involves putting the dynamical system into normal
form, which not only generates the low-dimensional model, but also provides the
correct initial conditions for the model. We illustrate the method with several
examples.
Keywords: normal form, isochrons, initialisation, centre manifoldComment: 24 pages in standard LaTeX, 66K, no figure
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