137 research outputs found
Instability and Chaos in Non-Linear Wave Interaction: a simple model
We analyze stability of a system which contains an harmonic oscillator
non-linearly coupled to its second harmonic, in the presence of a driving
force. It is found that there always exists a critical amplitude of the driving
force above which a loss of stability appears. The dependence of the critical
input power on the physical parameters is analyzed. For a driving force with
higher amplitude chaotic behavior is observed. Generalization to interactions
which include higher modes is discussed.
Keywords: Non-Linear Waves, Stability, Chaos.Comment: 16 pages, 4 figure
Internal Temperature Decline Rate in Beef Primals is Reduced in Heavier Carcasses
The objective of this study was to determine the influence of increasing beef hot carcass weights on internal temperature decline during chilling
Winding number instability in the phase-turbulence regime of the Complex Ginzburg-Landau Equation
We give a statistical characterization of states with nonzero winding number
in the Phase Turbulence (PT) regime of the one-dimensional Complex
Ginzburg-Landau equation. We find that states with winding number larger than a
critical one are unstable, in the sense that they decay to states with smaller
winding number. The transition from Phase to Defect Turbulence is interpreted
as an ergodicity breaking transition which occurs when the range of stable
winding numbers vanishes. Asymptotically stable states which are not
spatio-temporally chaotic are described within the PT regime of nonzero winding
number.Comment: 4 pages,REVTeX, including 4 Figures. Latex (or postscript) version
with figures available at http://formentor.uib.es/~montagne/textos/nupt
Dynamics and Selection of Giant Spirals in Rayleigh-Benard Convection
For Rayleigh-Benard convection of a fluid with Prandtl number \sigma \approx
1, we report experimental and theoretical results on a pattern selection
mechanism for cell-filling, giant, rotating spirals. We show that the pattern
selection in a certain limit can be explained quantitatively by a
phase-diffusion mechanism. This mechanism for pattern selection is very
different from that for spirals in excitable media
Lyapunov spectral analysis of a nonequilibrium Ising-like transition
By simulating a nonequilibrium coupled map lattice that undergoes an
Ising-like phase transition, we show that the Lyapunov spectrum and related
dynamical quantities such as the dimension correlation length~ are
insensitive to the onset of long-range ferromagnetic order. As a function of
lattice coupling constant~ and for certain lattice maps, the Lyapunov
dimension density and other dynamical order parameters go through a minimum.
The occurrence of this minimum as a function of~ depends on the number of
nearest neighbors of a lattice point but not on the lattice symmetry, on the
lattice dimensionality or on the position of the Ising-like transition. In
one-space dimension, the spatial correlation length associated with magnitude
fluctuations and the length~ are approximately equal, with both
varying linearly with the radius of the lattice coupling.Comment: 29 pages of text plus 15 figures, uses REVTeX macros. Submitted to
Phys. Rev. E
Microextensive Chaos of a Spatially Extended System
By analyzing chaotic states of the one-dimensional Kuramoto-Sivashinsky
equation for system sizes L in the range 79 <= L <= 93, we show that the
Lyapunov fractal dimension D scales microextensively, increasing linearly with
L even for increments Delta{L} that are small compared to the average cell size
of 9 and to various correlation lengths. This suggests that a spatially
homogeneous chaotic system does not have to increase its size by some
characteristic amount to increase its dynamical complexity, nor is the increase
in dimension related to the increase in the number of linearly unstable modes.Comment: 5 pages including 4 figures. Submitted to PR
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
Synchronization in coupled map lattices as an interface depinning
We study an SOS model whose dynamics is inspired by recent studies of the
synchronization transition in coupled map lattices (CML). The synchronization
of CML is thus related with a depinning of interface from a binding wall.
Critical behaviour of our SOS model depends on a specific form of binding
(i.e., transition rates of the dynamics). For an exponentially decaying binding
the depinning belongs to the directed percolation universality class. Other
types of depinning, including the one with a line of critical points, are
observed for a power-law binding.Comment: 4 pages, Phys.Rev.E (in press
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
The dynamics of thin vibrated granular layers
We describe a series of experiments and computer simulations on vibrated
granular media in a geometry chosen to eliminate gravitationally induced
settling. The system consists of a collection of identical spherical particles
on a horizontal plate vibrating vertically, with or without a confining lid.
Previously reported results are reviewed, including the observation of
homogeneous, disordered liquid-like states, an instability to a `collapse' of
motionless spheres on a perfect hexagonal lattice, and a fluctuating,
hexagonally ordered state. In the presence of a confining lid we see a variety
of solid phases at high densities and relatively high vibration amplitudes,
several of which are reported for the first time in this article. The phase
behavior of the system is closely related to that observed in confined
hard-sphere colloidal suspensions in equilibrium, but with modifications due to
the effects of the forcing and dissipation. We also review measurements of
velocity distributions, which range from Maxwellian to strongly non-Maxwellian
depending on the experimental parameter values. We describe measurements of
spatial velocity correlations that show a clear dependence on the mechanism of
energy injection. We also report new measurements of the velocity
autocorrelation function in the granular layer and show that increased
inelasticity leads to enhanced particle self-diffusion.Comment: 11 pages, 7 figure
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