1,628 research outputs found
Front Structures in a Real Ginzburg-Landau Equation Coupled to a Mean Field
Localized traveling wave trains or pulses have been observed in various
experiments in binary mixture convection. For strongly negative separation
ratio, these pulse structures can be described as two interacting fronts of
opposite orientation. An analytical study of the front solutions in a real
Ginzburg-Landau equation coupled to a mean field is presented here as a first
approach to the pulse solution. The additional mean field becomes important
when the mass diffusion in the mixture is small as is the case in liquids.
Within this framework it can lead to a hysteretic transition between slow and
fast fronts when the Rayleigh number is changed.Comment: to appear in J. Bif. and Chaos, 7 pages (LaTeX) 1 figur
Reentrant and Whirling Hexagons in Non-Boussinesq convection
We review recent computational results for hexagon patterns in non-Boussinesq
convection. For sufficiently strong dependence of the fluid parameters on the
temperature we find reentrance of steady hexagons, i.e. while near onset the
hexagon patterns become unstable to rolls as usually, they become again stable
in the strongly nonlinear regime. If the convection apparatus is rotated about
a vertical axis the transition from hexagons to rolls is replaced by a Hopf
bifurcation to whirling hexagons. For weak non-Boussinesq effects they display
defect chaos of the type described by the two-dimensional complex
Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf
bifurcation becomes subcritical and localized bursting of the whirling
amplitude is found. In this regime the coupling of the whirling amplitude to
(small) deformations of the hexagon lattice becomes important. For yet stronger
non-Boussinesq effects this coupling breaks up the hexagon lattice and strongly
disordered states characterized by whirling and lattice defects are obtained.Comment: Accepted in European Physical Journal Special Topic
Ordered and Disordered Defect Chaos
Defect-chaos is studied numerically in coupled Ginzburg-Landau equations for
parametrically driven waves. The motion of the defects is traced in detail
yielding their life-times, annihilation partners, and distances traveled. In a
regime in which in the one-dimensional case the chaotic dynamics is due to
double phase slips, the two-dimensional system exhibits a strongly ordered
stripe pattern. When the parity-breaking instability to traveling waves is
approached this order vanishes and the correlation function decays rapidly. In
the ordered regime the defects have a typical life-time, whereas in the
disordered regime the life-time distribution is exponential. The probability of
large defect loops is substantially larger in the disordered regime.Comment: 8 pages revtex, 8 figure
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