126 research outputs found
Traveling Wave Fronts and Localized Traveling Wave Convection in Binary Fluid Mixtures
Nonlinear fronts between spatially extended traveling wave convection (TW)
and quiescent fluid and spatially localized traveling waves (LTWs) are
investigated in quantitative detail in the bistable regime of binary fluid
mixtures heated from below. A finite-difference method is used to solve the
full hydrodynamic field equations in a vertical cross section of the layer
perpendicular to the convection roll axes. Results are presented for
ethanol-water parameters with several strongly negative separation ratios where
TW solutions bifurcate subcritically. Fronts and LTWs are compared with each
other and similarities and differences are elucidated. Phase propagation out of
the quiescent fluid into the convective structure entails a unique selection of
the latter while fronts and interfaces where the phase moves into the quiescent
state behave differently. Interpretations of various experimental observations
are suggested.Comment: 46 pages, 11 figures. Accepted for publication in Phys. Rev.
Asymmetric Squares as Standing Waves in Rayleigh-Benard Convection
Possibility of asymmetric square convection is investigated numerically using
a few mode Lorenz-like model for thermal convection in Boussinesq fluids
confined between two stress free and conducting flat boundaries. For relatively
large value of Rayleigh number, the stationary rolls become unstable and
asymmetric squares appear as standing waves at the onset of secondary
instability. Asymmetric squares, two dimensional rolls and again asymmetric
squares with their corners shifted by half a wavelength form a stable limit
cycle.Comment: 8 pages, 7 figure
Domain-size control by global feedback in bistable systems
We study domain structures in bistable systems such as the Ginzburg-Landau
equation. The size of domains can be controlled by a global negative feedback.
The domain-size control is applied for a localized spiral pattern
Worm Structure in Modified Swift-Hohenberg Equation for Electroconvection
A theoretical model for studying pattern formation in electroconvection is
proposed in the form of a modified Swift-Hohenberg equation. A localized state
is found in two dimension, in agreement with the experimentally observed
``worm" state. The corresponding one dimensional model is also studied, and a
novel stationary localized state due to nonadiabatic effect is found. The
existence of the 1D localized state is shown to be responsible for the
formation of the two dimensional ``worm" state in our model
The Sivashinsky equation for corrugated flames in the large-wrinkle limit
Sivashinsky's (1977) nonlinear integro-differential equation for the shape of
corrugated 1-dimensional flames is ultimately reducible to a 2N-body problem,
involving the 2N complex poles of the flame slope. Thual, Frisch & Henon (1985)
derived singular linear integral equations for the pole density in the limit of
large steady wrinkles , which they solved exactly for monocoalesced
periodic fronts of highest amplitude of wrinkling and approximately otherwise.
Here we solve those analytically for isolated crests, next for monocoalesced
then bicoalesced periodic flame patterns, whatever the (large-) amplitudes
involved. We compare the analytically predicted pole densities and flame shapes
to numerical results deduced from the pole-decomposition approach. Good
agreement is obtained, even for moderately large Ns. The results are extended
to give hints as to the dynamics of supplementary poles. Open problems are
evoked
Phase-space structure of two-dimensional excitable localized structures
In this work we characterize in detail the bifurcation leading to an
excitable regime mediated by localized structures in a dissipative nonlinear
Kerr cavity with a homogeneous pump. Here we show how the route can be
understood through a planar dynamical system in which a limit cycle becomes the
homoclinic orbit of a saddle point (saddle-loop bifurcation). The whole picture
is unveiled, and the mechanism by which this reduction occurs from the full
infinite-dimensional dynamical system is studied. Finally, it is shown that the
bifurcation leads to an excitability regime, under the application of suitable
perturbations. Excitability is an emergent property for this system, as it
emerges from the spatial dependence since the system does not exhibit any
excitable behavior locally.Comment: 10 pages, 9 figure
Real-Time DSP-Free 100Gbit/s/λ PAM-4 Fiber Access Link using EML and Direct Detection
A 100 Gbit/s/ λ PAM-4 fiber link with an optical budget of 30 dB and 20 km fiber reach is achieved in real time experiments. This is compliant with class A (20 dB) point to point (PtP) applications as mobile fronthaul for example, and with class N1 (29 dB) point to multipoint (PtMP) for residential market. We used an integrated externally modulated laser, an analog pre-equalizer, an optical booster amplifier and/or non-filtered preamplifier and direct detection without any digital signal processing (whether real-time or offline)
A note on the extension of the polar decomposition for the multidimensional Burgers equation
It is shown that the generalizations to more than one space dimension of the
pole decomposition for the Burgers equation with finite viscosity and no force
are of the form u = -2 viscosity grad log P, where the P's are explicitly known
algebraic (or trigonometric) polynomials in the space variables with polynomial
(or exponential) dependence on time. Such solutions have polar singularities on
complex algebraic varieties.Comment: 3 pages; minor formatting and typos corrected. Submitted to Phys.
Rev. E (Rapid Comm.
Coexisting Pulses in a Model for Binary-Mixture Convection
We address the striking coexistence of localized waves (`pulses') of
different lengths which was observed in recent experiments and full numerical
simulations of binary-mixture convection. Using a set of extended
Ginzburg-Landau equations, we show that this multiplicity finds a natural
explanation in terms of the competition of two distinct, physical localization
mechanisms; one arises from dispersion and the other from a concentration mode.
This competition is absent in the standard Ginzburg-Landau equation. It may
also be relevant in other waves coupled to a large-scale field.Comment: 5 pages revtex with 4 postscript figures (everything uuencoded
Flame front propagation IV: Random Noise and Pole-Dynamics in Unstable Front Propagation II
The current paper is a corrected version of our previous paper
arXiv:adap-org/9608001. Similarly to previous version we investigate the
problem of flame propagation. This problem is studied as an example of unstable
fronts that wrinkle on many scales. The analytic tool of pole expansion in the
complex plane is employed to address the interaction of the unstable growth
process with random initial conditions and perturbations. We argue that the
effect of random noise is immense and that it can never be neglected in
sufficiently large systems. We present simulations that lead to scaling laws
for the velocity and acceleration of the front as a function of the system size
and the level of noise, and analytic arguments that explain these results in
terms of the noisy pole dynamics.This version corrects some very critical
errors made in arXiv:adap-org/9608001 and makes more detailed description of
excess number of poles in system, number of poles that appear in the system in
unit of time, life time of pole. It allows us to understand more correctly
dependence of the system parameters on noise than in arXiv:adap-org/9608001Comment: 23 pages, 4 figures,revised, version accepted for publication in
journal "Combustion, Explosion and Shock Waves". arXiv admin note:
substantial text overlap with arXiv:nlin/0302021, arXiv:adap-org/9608001,
arXiv:nlin/030201
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