6 research outputs found
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
A Non-Equilibrium Defect-Unbinding Transition: Defect Trajectories and Loop Statistics
In a Ginzburg-Landau model for parametrically driven waves a transition
between a state of ordered and one of disordered spatio-temporal defect chaos
is found. To characterize the two different chaotic states and to get insight
into the break-down of the order, the trajectories of the defects are tracked
in detail. Since the defects are always created and annihilated in pairs the
trajectories form loops in space time. The probability distribution functions
for the size of the loops and the number of defects involved in them undergo a
transition from exponential decay in the ordered regime to a power-law decay in
the disordered regime. These power laws are also found in a simple lattice
model of randomly created defect pairs that diffuse and annihilate upon
collision.Comment: 4 pages 5 figure
Phase Diffusion in Localized Spatio-Temporal Amplitude Chaos
We present numerical simulations of coupled Ginzburg-Landau equations
describing parametrically excited waves which reveal persistent dynamics due to
the occurrence of phase slips in sequential pairs, with the second phase slip
quickly following and negating the first. Of particular interest are solutions
where these double phase slips occur irregularly in space and time within a
spatially localized region. An effective phase diffusion equation utilizing the
long term phase conservation of the solution explains the localization of this
new form of amplitude chaos.Comment: 4 pages incl. 5 figures uucompresse