510 research outputs found
Ramped-induced states in a parametrically driven Ginzburg-Landau equation
We introduce a parametrically driven Ginzburg-Landau (GL) model, which admits
a gradient representation, and is subcritical in the absence of the parametric
drive (PD). In the case when PD acts uniformly in space, this model has a
stable kink solution. A nontrivial situation takes places when PD is itself
subject to a kink-like spatial modulation, so that it selects real and
imaginary constant solutions at +infinity and -infinity. In this situation, we
find stationary solutions numerically, and also analytically for a particular
case. They seem to be of two different types, viz., a pair of kinks in the real
and imaginary components, or the same with an extra kink inserted into each
component, but we show that both belong to a single continuous family of
solutions. The family is parametrized by the coordinate of a point at which the
extra kinks are inserted. Solutions with more than one kink inserted into each
component do not exist. Simulations show that the former solution is always
stable, and the latter one is, in a certain sense, neutrally stable, as there
is a special type of small perturbations that remain virtually constant in
time, rather than decaying or growing (they eventually decay, but extremely
slowly).Comment: A latex text file and 8 ps files with figures. Physics Letters A, in
pres
Harmonic forcing of an extended oscillatory system: Homogeneous and periodic solutions
In this paper we study the effect of external harmonic forcing on a
one-dimensional oscillatory system described by the complex Ginzburg-Landau
equation (CGLE). For a sufficiently large forcing amplitude, a homogeneous
state with no spatial structure is observed. The state becomes unstable to a
spatially periodic ``stripe'' state via a supercritical bifurcation as the
forcing amplitude decreases. An approximate phase equation is derived, and an
analytic solution for the stripe state is obtained, through which the
asymmetric behavior of the stability border of the state is explained. The
phase equation, in particular the analytic solution, is found to be very useful
in understanding the stability borders of the homogeneous and stripe states of
the forced CGLE.Comment: 6 pages, 4 figures, 2 column revtex format, to be published in Phys.
Rev.
Hydro-dynamical models for the chaotic dripping faucet
We give a hydrodynamical explanation for the chaotic behaviour of a dripping
faucet using the results of the stability analysis of a static pendant drop and
a proper orthogonal decomposition (POD) of the complete dynamics. We find that
the only relevant modes are the two classical normal forms associated with a
Saddle-Node-Andronov bifurcation and a Shilnikov homoclinic bifurcation. This
allows us to construct a hierarchy of reduced order models including maps and
ordinary differential equations which are able to qualitatively explain prior
experiments and numerical simulations of the governing partial differential
equations and provide an explanation for the complexity in dripping. We also
provide a new mechanical analogue for the dripping faucet and a simple
rationale for the transition from dripping to jetting modes in the flow from a
faucet.Comment: 16 pages, 14 figures. Under review for Journal of Fluid Mechanic
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
On the Origin of Traveling Pulses in Bistable Systems
The interaction between a pair of Bloch fronts forming a traveling domain in
a bistable medium is studied. A parameter range beyond the nonequilibrium
Ising-Bloch bifurcation is found where traveling domains collapse. Only beyond
a second threshold the repulsive front interactions become strong enough to
balance attractive interactions and asymmetries in front speeds, and form
stable traveling pulses. The analysis is carried out for the forced complex
Ginzburg-Landau equation. Similar qualitative behavior is found in the bistable
FitzHugh-Nagumo model.Comment: 5 pages, RevTeX. Aric Hagberg: http://t7.lanl.gov/People/Aric/; Ehud
Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.htm
Exact Solutions of the One-Dimensional Quintic Complex Ginzburg-Landau Equation
Exact solitary wave solutions of the one-dimensional quintic complex
Ginzburg-Landau equation are obtained using a method derived from the
Painlev\'e test for integrability. These solutions are expressed in terms of
hyperbolic functions, and include the pulses and fronts found by van Saarloos
and Hohenberg. We also find previously unknown sources and sinks. The emphasis
is put on the systematic character of the method which breaks away from
approaches involving somewhat ad hoc Ans\"atze.Comment: 24 pages, regular LaTeX, no figure
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
Frequency Locking in Spatially Extended Systems
A variant of the complex Ginzburg-Landau equation is used to investigate the
frequency locking phenomena in spatially extended systems. With appropriate
parameter values, a variety of frequency-locked patterns including flats,
fronts, labyrinths and fronts emerge. We show that in spatially
extended systems, frequency locking can be enhanced or suppressed by diffusive
coupling. Novel patterns such as chaotically bursting domains and target
patterns are also observed during the transition to locking
Nonequilibrium-induced metal-superconductor quantum phase transition in graphene
We study the effects of dissipation and time-independent nonequilibrium drive
on an open superconducting graphene. In particular, we investigate how
dissipation and nonequilibrium effects modify the semi-metal-BCS quantum phase
transition that occurs at half-filling in equilibrium graphene with attractive
interactions. Our system consists of a graphene sheet sandwiched by two
semi-infinite three-dimensional Fermi liquid reservoirs, which act both as a
particle pump/sink and a source of decoherence. A steady-state charge current
is established in the system by equilibrating the two reservoirs at different,
but constant, chemical potentials. The nonequilibrium BCS superconductivity in
graphene is formulated using the Keldysh path integral formalism, and we obtain
generalized gap and number density equations valid for both zero and finite
voltages. The behaviour of the gap is discussed as a function of both
attractive interaction strength and electron densities for various
graphene-reservoir couplings and voltages. We discuss how tracing out the
dissipative environment (with or without voltage) leads to decoherence of
Cooper pairs in the graphene sheet, hence to a general suppression of the gap
order parameter at all densities. For weak enough attractive interactions we
show that the gap vanishes even for electron densities away from half-filling,
and illustrate the possibility of a dissipation-induced metal-superconductor
quantum phase transition. We find that the application of small voltages does
not alter the essential features of the gap as compared to the case when the
system is subject to dissipation alone (i.e. zero voltage).Comment: 13 pages, 8 figure
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